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Imaging molecular transport across and nanomaterial interaction with lipid membranes
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Imaging molecular transport across and nanomaterial interaction with lipid membranes
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Content
IMAGING MOLECULAR TRANSPORT ACROSS AND NANOMATERIAL
INTERACTION WITH LIPID MEMBRANES
by
Su Li
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CHEMICAL ENGINEERING)
May 2013
Copyright 2013 Su Li
ii
Acknowledgements
I would like to begin by sincerely thanking my advisor, Prof. Noah Malmstadt for his
constant support, guidance and mentorship over the course of this thesis. He gave me
the freedom to define my thesis statement and always acted as a very helpful sounding
board for my ideas. Whenever I was bereft of ideas, my discussions with him and his
insights always helped me get back on the right track. He has always encouraged me to
explore a wide variety of opportunities. I have truly learnt a lot from him over the past
5 years and for this, I am very grateful.
I would also like to thank my thesis committee members – Prof. Andrea Armani,
Prof. Kwang-Jin Kim, and Prof. Pin Wang for their valuable suggestions and advice.
They were always ready to help me in understanding the function of cell membrane,
concepts with drug delivery, and nanotechnology, and I thank them for their time and
helpful discussions
I am very grateful to the National Science Foundation for the funding they have
provided that has aided me greatly in the completion of this work.
Members of the Malmstadt group have been great sources of cheer and comfort
during the past 5 years and I am grateful to them for their support. I would like to thank
Dr. James Thompson, Peichi Hu, Yasaman Dayani, Gary Newsom, Carson Riche,
Shalene Sankhagowit, Kristina Runas, and Astro Shi-Ju Yang for their friendship over
the years. I would also like to thank Dr. Nazanin Yacobi, Dr. Farnoosh Fazlollahi, Dr.
Kye-il Joo, and Dr. Terry Takahashi for their support over the years and for making my
life at USC so much easier.
iii
On a personal note, I know that this work could not have been completed without the
tremendous support of my friends and family. I would like to thank my friends at USC
for all the good memories they have provided over the past few years. My husband has
been a great source of strength and support for me through each step of the journey and
I thank him for his constant encouragement, optimism and belief in me. Finally, my
gratitude to my parents is beyond measure – all through my life, they have always
sacrificed to ensure that I had the best opportunities possible and they have constantly
believed in me and encouraged me to dream big and to pursue those dreams. I cannot
put into words what their support has meant to me over the years and I dedicate this
thesis to them.
iv
Table of Contents
Acknowledgements ii
List of Tables vii
List of Figures viii
Abbreviations xii
Abstract xiii
Chapter 1: Background and significance 1
1.1 Passive molecular transport across cell membranes and human health 1
1.2 The current theory of passive transport 3
1.3 The current technology for characterizing passive transport 5
1.3.1 Cell and liposome based assays 6
1.3.2 PAMPA and Planar bilayer assays 8
1.4 Unstirred water layer (USL): advantage or disadvantage 10
1.5 Solving these problems with confocal microscopy of giant lipid vesicles13
Chapter 2: Passive membrane transport of a series of hydrophilic molecules (PEG-n-
NBD) 15
2.1 Introduction 15
2.2 Materials and methods 15
2.2.1 Materials 15
2.2.2 Cleaning of glass cover slips 16
2.2.3 GUV preparation and observation 16
2.2.4 Preparation of test molecules 17
2.2.5 Measurement of octonal-water partition coefficients 18
2.2.6 Buffer exchange on a single GUV 18
2.2.7 Image analysis 19
2.2.8 Data processing 20
2.3 Results and discussion 20
2.3.1 Confocal Imaging of Membrane Permeation 20
2.3.2 Concentration Profile 21
2.3.3 Correcting for GUV size-dependence of the fluorescence background
23
2.3.4 Permeability Calculations 24
2.3.5 Comparison to Overton’s rule 27
v
2.3.6 Finite element modeling of diffusion inside the vesicles 28
2.4 Conclusions 31
Chapter 3: Confocal imaging to quantify carboxylic acid passive transport across lipid
membranes 32
3.1 Introduction 32
3.2 Materials and methods 34
3.2.1 Reagents 34
3.2.2 Cleaning of glass cover slips 35
3.2.3 GUV preparation and observation 35
3.2.4 Acid transport experiments 36
3.2.5 Image analysis 37
3.2.6 Correlating fluorescence intensity to acid concentration 38
3.2.7 Finite difference modeling 39
3.2.8 Determining permeability 40
3.3 Results and discussion 41
3.3.1 Acid transport into a single GUV 41
3.3.2 Effect of flow rate 44
3.3.3 Determining permeability 45
3.3.4 Fitting experimental concentration profiles to obtain permeability 48
3.3.5 Statistical behavior of models 51
3.3.6 Modeling the effect of buffer species 54
3.3.7 Model sensitivity to diffusivity 58
3.3.8 Reproducibility across multiple vesicles 59
3.3.9 The effect of liquid ordered-liquid disordered (l
o
-l
d
) phase separation
on the membrane permeability 59
3.3.10 Controlling for membrane lipid composition 61
3.3.11 The effect of GUV binding on membrane tension and permeability62
3.3.12 Simulations to rule out potential convection-related artifacts 63
3.3.13 Comparison to Overton’s rule 67
3.4 Conclusions 68
Chapter 4: Deformation and poration of lipid bilayer membranes by cationic
nanoparticles 70
4.1 Introduction 70
4.2 Materials and methods 73
4.2.1 Materials 73
4.2.2 Nanoparticles 73
4.2.3 GUV preparation and observation 74
4.2.4 PNP attachment experiments 75
4.3 Results and discussion 76
4.3.1 Adhesion of PNP to lipid membrane 76
4.3.2 Time course of PNPs adhesion and membrane deformation 78
vi
4.3.3 Mechanism behind the PNPs/lipid membrane interaction 79
4.3.4 Leakage of high molecular weight dextran from GUV 81
4.3.5 PNPs binding increased membrane steric pressure and surface tension
84
4.3.6 PNPs with different sizes and charges 86
4.4 Conclusions 87
Chapter 5: Permeation of CO
2
through lipid membrane 88
Chapter 6: Conclusions 93
Bibliography 96
vii
List of Tables
Table 1-1 Comparison of the electrical properties of bimolecular lipid
membranes in the presence and absence of hydrocarbon solvent
with those of cell membranes, taken from reference
10
Table 2-1 Permeability of PEG-n-NBD to different size GUVs
28
Table 2-2 Comparison of Overton’s rule to experimental result. Values were
normalized to PEG-12-NBD
31
Table 3-1 Permeabilities (P) from various carboxylic acid permeation
studies (units 10-2 cm/s) Values for this study are expressed in
terms of a maximally likely value and a statistical range as
described in the text.
37
Table 3-2 Calculated permeabilities as diffusion coefficients changes in the
MATLAB program (numbers with asterisks are the literature
diffusion coefficients and corresponding permeabilities)
63
Table 3-3 Best-fit membrane permeability under three different conditions
72
Table 3-4 Comparison of Overton’s rule to experimental results, normalized
to formic acid
74
viii
List of Figures
Figure 1-1 A snapshot of a molecular dynamics simulation of a hydrated
lipid bilayer labeled according to the transport regions
identified by Marrink and Berendsen
5
Figure 1-2 Schematic representation of the basic principles of the
Monolayer assay system
7
Figure 1-3 Schematic of a painted bilayer experiment.
10
Figure 1-4 The traditional model for the steady-state concentration profile
across a permeable membrane with USLs.
11
Figure 1-5 Experimental pH profiles near planar lipid bilayer.
14
Figure 2-1 Preparation of the PEG-4-NBD test molecule. An amine-
terminated 4-unit poly(ethylene oxide) was reacted with an
NHS-ester of the fluorescent dye NBD.
19
Figure 2-2 A time series of SDCM images showing the transport of a
fluorescent molecule PEG-8-NBD (ex 465 nm, em 539 nm) into
a GUV.
22
Figure 2-3 Intensity profiles drawn through the center of the GUV.
24
Figure 2-4 Comparison of the fluorescence profile calculated by out-of-
plane fluorescence theory with experimental data obtained from
a GUV with 40 kDa fluorescein-dextran outside
25
Figure 2-5 Dependence of background intensity at the center of GUVs on
GUV diameter
26
Figure 2-6 Plot of fluorescence intensity inside over intensity outside
GUVs (1:1:1 DPPC:DOPC:cholesterol) as a function of time at
26
o
C.
27
Figure 2-7 Unstirred layer and concentration profile near membrane
29
Figure 2-8 Diffusion profiles of a 40 μm sphere with concentration-
dependant flux boundary conditions.
32
ix
Figure 3-1 GUVs were immobilized on an avidin-functionalized glass
surface
39
Figure 3-2 PDMS channel used for immobilizing and observing acid
permeation into GUVs
40
Figure 3-3 Time series of SDCM images showing the fluorescence
intensity (ex 491 nm, em 525 nm) change when acetic acid is
transported.
45
Figure 3-4 Solution pH change inside and outside the GUV with time for
six carboxylic acids.
47
Figure 3-5 Fluorescence intensity vs. experimental pH. Solution pH vs.
acid concentration
48
Figure 3-6 Fit of hexanoic acid permeation data at a single flow rate to
obtain an apparent rate of change of fluorescence inside the
GUV.
49
Figure 3-7 Modeled concentration profiles of acetic acid and hexanoic
acid.
51
Figure 3-8 Line intensity profiles drawn through the center of the GUV in
different time for hexanoic acid
53
Figure 3-9 Experimental and best-fit model concentration profiles for acid
permeation.
56
Figure 3-10 χ
2
values changes with permeabilities for six carboxylic acids.
58
Figure 3-11 Concentration profiles of hexanoic acid and HEPES as
hexanoic acid permeates through the GUV membrane.
61
Figure 3-12 Concentration profiles of acetic acid and HEPES as acetic acid
permeates through the GUV membrane.
62
Figure 3-13 Calculated best-fit permeabilities at varying diffusivity
64
Figure 3-14 GUVs labeled by Texas-Red-modified DPPE excited at 561 nm
showing the lipid bilayer.
65
x
Figure 3-15 Solution pH change inside and outside the GUV with time for
acetic acid at 27
o
C (left), and 32
o
C (right)
66
Figure 3-16 Solution pH change inside and outside a cholesterol-free GUV
with time for three carboxylic acids.
67
Figure 3-17 3-D image of an immobilized GUV and GUV profile from top,
left and front
68
Figure 3-18 Geometry of the COMSOL simulation
70
Figure 3-19 Concentration profile in the bulk solution and GUV with flow
in the channel.
71
Figure 3-20 The concentration change in the center of GUV under three
different conditions.
72
Figure 3-21 Trends in permeabilities of a homologous series of carboxylic
acids.
74
Figure 4-1 Confocal microscopy images of PNP adhesion to a GUV.
83
Figure 4-2 Fraction of GUVs deformed at various PNP concentrations after
a 3 h incubation.
84
Figure 4-3 The time course of nanoparticle binding as determined by PNP
fluorescence intensity on the membrane and changes to GUV
diameter.
85
Figure 4-4 Nanoparticle fluorescence intensity on a GUV membrane as a
function of PNP concentration for GUVs in varying NaCl
concentration and different lipid compositions.
88
Figure 4-5 Time course of leakage of 2000 kDa, 500 kDa, and 250 kDa fl-
dex from GUVs interacting with PNPs.
90
Figure 4-6 Fluorescent intensity change of GUV-encapsulated fl-dex (250
kDa, 500 kDa, 2000 kDa) monitored in the absence of PNPs
91
Figure 4-7 Confocal microscope image of a phase-separated GUV during
early stages of PNP binding.
92
xi
Figure 4-8 Confocal images of GUVs interacting with various polymeric
nanomaterials.
94
Figure 5-1 Diffusion of CO
2
across a lipid bilayer includes several steps
(from left to right).
98
Figure 5-2 Effect of pH on stability of purified carbonic anhydrase.
99
Figure 5-3 CO
2
concentration and pH shifts adjacent to the membrane at
bulk pH 7.5.
101
xii
Abbreviations
AQP1 : Aquaporin 1
Biotin-DPPE : Biotinylated dipalmitoylphosphoethanolamine
CA : Carbonic anhydrase
D : Diffusion coefficients (cm
2
/s)
DiD : 1,1'-dioctadecyl-3,3,3',3'-tetramethylindodicarbocyanine perchlorate
DOPC : Dioleoylphosphatidylcholine
DOPE : Dioleoylphosphoethanolamine
DOPG : Dioleoylphosphatidylglycerol
DOPS : Dioleoylphosphatidylserine
DPPC : Dipalmitoylphosphatidylcholine
Em : Emmision
Ex : Excitation
Fl-dex : Fluorescein-dextran
GUVs : Giant unilamellar vesicles
I : Intensity
ITO : Indium-tin oxide
K : Oil-water partition coefficient
L
d
: Liquid disordered phase
L
o
: Liquid ordered phase
LDH : Lactate dehydrogenase
LSER : Linear solvation energy relationship
MDCK : Madin-Darby canine kidney
NBD : 4-nitrobenzo-2-oxa-1,3-diazole
P : Permeability (cm/s)
PAMPA : Parallel artificial membrane permeability assay
PDMS : Poly(dimethylsiloxane)
PEG : Poly(ethylene glycol)
PEI : Polyethylenimine
PNPs : Polystyrene nanoparticles
QSAR : Quantitative structure-activity relationship
Rh-dex : Rhodamine-dextran
SDCM : Spinning-disk confocal microscopy
TEER : Transepithelial electrical resistance
TR-DPPE : Texas Red-modified DPPE
USL : Unstirred water layer
WDI : World Drug Index
xiii
Abstract
The ability of a molecule to pass through the plasma membrane without the aid of
any active cellular mechanisms is central to that molecule’s pharmaceutical
characteristics. Passive transport has been understood in the context of Overton’s rule,
which states that more lipophilic molecules cross membrane lipid bilayers more readily.
Standard techniques including planar lipid membrane, liposome, and cell monolayer to
observe passive transport processes are flawed and lack reproducibility.
This research describes assays based on spinning-disk confocal microscopy (SDCM)
of giant unilamellar vesicles (GUVs) that allow for fluorescent molecules to be tracked
as they permeate the lipid membrane. This approach allows for the temporal
development of the concentration field to be directly observed. Precise membrane
permeability can be determined from by fitting the data to a mathematical permeation
model.
A series of molecules of increasing hydrophilicity was constructed by conjugating 4-
nitrobenzo-2-oxa-1,3-diazole (NBD) with poly(ethylene-glycol) (PEG). An analytical
passive transport model was devised, image intensity data was regressed to the model,
and permeability was calculated. The result shows that longer chain PEG molecules
which are more hydrophilic permeate more slowly. This trend is consistent with
Overton’s rule, though it does not seem to fit a simple partition-diffusion model of
membrane transport.
xiv
Low-molecular-weight carboxylic acids have crucial effects on cellular processes.
We studied the transport of carboxylic acids with different carbon chains lengths into
GUVs. Fluorescein-dextran was used to trace the transport of acid. GUVs were
immobilized on the surface of a poly(dimethylsiloxane) (PDMS) microchannel which
allows the changing of buffer solution quickly and uniformly. The results showed that
the permeabilities are consistent with octanol-water partition coefficients and
demonstrate that Overton’s rule applies for this class of molecules.
Synthetic lipid bilayers were used to study potentially harmful interactions between
nanoparticles and biomembranes. Twenty nm polystyrene nanoparticles with cationic
surfaces adhere strongly to lipid membranes. Adhesion is driven by nonspecific
electrostatic interactions between the lipid phosphate groups and the nanoparticles.
Nanoparticle adhesion leads to membrane morphological deformation and the
formation of transient nanoscale pores. These results suggest that nanoparticle adhesion
imposes surface tension on biomembranes via a steric crowding mechanism, leading to
poration.
1
Chapter 1: Background and significance
We have developed new engineering tools to address central shortcomings of
techniques currently used to measure the passive transport of molecules across lipid
bilayer membranes. These passive transport processes have broad implications for drug
development, drug delivery, and environmental toxicology. Existing tools for observing
passive transport can only access bulk concentrations at steady state, leading to highly
limiting measurement artifacts. The tools we have developed allow for the transient
observation of the full concentration profile, which allows for precise measurement of the
parameters that govern passive transport. These tools have potential broad application to
a wide range of problems involving the interaction of small molecules or nanoparticles
with lipid bilayers.
1.1 Passive molecular transport across cell membranes and
human health
There are many ways by which a molecule can cross the cell membrane. Some of these
are protein-associated transport processes that do not expend biochemical energy, like the
passage of potassium ions through an open ion channel (Hodgkin & Huxley 1952). Some
of these are active transport processes, requiring an expenditure of chemical energy, such
as receptor-mediated endocytosis, pinocytosis, and transport against a gradient through
ion pumps, like sodium permeation through human red blood cell membranes
(Cabantch.Zi & Rothstei.A 1974). Here, we are concerned with passive transport
processes that do not depend on any of the cell’s protein machinery. In these processes
2
molecules diffuse with a concentration gradient across the plasma membrane. This mode
of transport is dominated by interactions between the transported molecules and the lipids
constituting the membrane.
Passive transport through the cell membrane represents a major route by which drugs
enter cells. It is the primary route by which orally delivered drugs enter systemic
circulation (Miret et al. 2004). Environmental toxins can also enter the human body by
passively crossing cell membranes. Highly lipid-soluble heavy metal complexes like
dimethylmercury can rapidly and passively cross cell membranes and are extremely
neurotoxic (Foulkes 2000). Also some of the environmental toxins such as lipophilic
hydrocarbons accumulate in the membrane lipid bilayer, affecting the structural and
functional properties of these membranes, leading to a loss of membrane integrity, and an
increase in permeability to protons and ions (Sikkema et al. 1995). Understanding the
mechanistic details of passive transport is essential to understanding how and why certain
molecules make good drugs or dangerous toxins.
In fact, the multifactorial nature of the relationship between molecular structure and
drug activity has long been recognized by the medicinal chemistry community. Structure-
based drug design takes into account several molecular factors, such as molecular weight,
oil/water partition coefficient, hydrogen bonding, dipolarity, and polarizability. In 1997,
Lipinski proposed the “rule of five”—based on studies of over 2500 drugs in the World
Drug Index (WDI)—which states that a molecule that has a molecular weight less than
500, log (partition coefficient) less than 5, and no more than 5 hydrogen bond donors is
more likely to be a good drug (Lipinski et al. 1997). Quantitative structure-activity
3
relationship (QSAR) studies have related drug activity to molecular weight, molecular
refractivity, substructure such as rings and rotatable bonds, lone-pair electrons, and
hydrogen bonding (Patani & LaVoie 1996; Wildman & Crippen 1999; Oprea et al. 2001;
Ajmani et al. 2009). Some work has gone towards understanding specifically how
structural considerations might modulate membrane interactions (Xia et al. 2007), but in
general overall drug activity is the focus of these studies. Clarifying how molecular
structure specifically relates to permeability could be of great value in the rational design
of novel drugs and in the design of drugs targeted to cells with specific membrane
structure and composition. Establishing this relationship, however, requires accurate
measurements of permeability.
1.2 The current theory of passive transport
The simplest model of passive transport treats it as diffusion through a membrane. In
this model (Seader & Henley 2006), the flux of a species through the plasma membrane
is:
()
oi
JPc c 1-1
where c
o
and c
i
are the concentrations of the diffusing species outside and inside of the
membrane, respectively, and P is the permeability of the membrane. According to
Overton’s rule, the permeability is given by:
KD
P
l
1-2
where K is the partition coefficient between the membrane and the surrounding aqueous
environment, D is the diffusivity in the membrane, and l is the length of the membrane
4
(the 4-5 nm length through which diffusing species must pass). For small, drug-like
molecules, K will vary much more than D, so the rate of transport through the membrane
will ultimately be determined by the partition coefficient; that is, the relative affinity that
the transported molecule has for the lipid environment versus the aqueous environment.
Overton’s rule states broadly that the efficacy of a drug is proportional to its lipid
solubility (Kleinzeller 1997). It has been interpreted in the context of partition-limited
diffusion across a lipid bilayer. Measurements of oil-water partition coefficient have
widely been used as proxies for the propensity of molecules to passively cross the cell
membrane (Lipinski et al. 2001).
But treating the plasma membrane as a simple solid diffusive barrier discounts a great
deal of the complexity of the system. The stratification and heterogeneity of the
transverse structure of the lipid membrane is complex. Lipid head groups compose the
outside layer of the lipid membrane which is hydrophilic and may contain charges. Lipid
hydrocarbon tails compose the inner structure of lipid membrane which is hydrophobic
and packed at varying densities.
A typical trans-bilayer profile is given in Figure 1-1, taken from a molecular dynamics
calculation (Tieleman et al. 1997). The bilayer is composed of a perturbed water layer (1),
a hydrophilic/hydrophobic layer including bound water and lipid head groups (Ehrenberg
et al.), a layer consisting of ordered acyl-chain segments similar to soft polymer (3), and
a layer of disordered acyl-chain segments similar to liquid decane (Mouritsen &
Jorgensen 1998).
5
Figure 1-1: A snapshot of a molecular dynamics simulation of a hydrated lipid bilayer labeled
according to the transport regions identified by Bemporad et al (Bemporad et al. 2005).
There are some important implications for the trans-bilayer structure to the transport of
molecules. Layers 1 and 2 play an important role for the discrimination of molecules to
attach and partition into lipid membrane. Layers 3 and 4 present a critical role for the
permeants to diffuse and penetrate into the hydrophobic core of lipid membrane.
1.3 The current technology for characterizing passive transport
Although lipid bilayers play a crucial role in the regulation of membrane passage,
experimental techniques are not sufficiently established to perform systematic studies on
drug-membrane permeation. Membrane permeability is generally estimated according to
Overton’s rule from the oil-water partition coefficient (Faller & Wohnsland 2001), the
affinities to lipophilic phases determined by HPLC (Genty et al. 2001), and parameters
calculated from the molecular size, and hydrogen-bonding capacities (Malkia et al. 2004).
These are non-lipid-membrane related methods.
6
1.3.1 Cell and liposome based assays
There have been a number of cell-based assays developed within the pharmaceutical
industry for examining the ability of putative drug molecules to penetrate the
gastrointestinal epithelium. By far the most widespread of these involves tracking UV-
absorbent compounds as they permeate through a monolayer of Caco-2 cells (an
immortalized human epithelial colorectal adenocarcinoma cell line) (Artursson &
Borchardt 1997; Alsenz & Haenel 2003). A typical Caco-2 based assay proceeds as
follows: The Caco-2 cells are cultivated on snapwell culture inserts with polycarbonate
membrane (diameter of 12mm and pore size of 0.4µm) for 20 days. Transepithelial
electrical resistance (TEER) is used to test the cell growth. After the maturation of the
cells, they are placed between two compartments of diffusion chambers (Figure 1-2). The
bathing solution needs to be maintained at 37
o
C and constant oxygen concentration. The
permeant is put in the donor side of the chamber, and samples are withdrawn from
acceptor side in a regular time step for the concentration analysis. This example protocol
was taken from reference (Berginc et al. 2007). Given the pharmaceutical priority on
finding high-oral-availability drugs, this approach makes functional sense. It is, however,
slow and prone to artifacts (Balimane & Chong 2005). And the systems are too complex
and uncontrolled to deliver data for careful mechanistic studies.
7
Figure 1-2: Schematic representation of the basic principles of the Monolayer assay system, the
image was taken from (Avdeef & Tsinman 2006).
Much membrane permeation research has been conducted on nanoscale liposome
systems. At the size of the liposome (ranges from 50nm to 200nm), the membrane
association and permeation process cannot be directly observed. Techniques used to test
liposome permeation are NMR and luminescence methods. In the NMR technique, the
liposomes are first equilibrated with a peak-shifting metal ion in the exterior space. NMR
spectroscopy can then distinguish between solute inside and outside the liposomes. This
technique is conducted in steady state, and cannot yield dynamic information. Also the
unstirred water layers (to be discussed in Section 1.4) present in steady-state permeation
will cause artifacts in the results. Radioactive chemicals and metals ions are used in NMR,
which makes this method relatively complex to implement. For luminescence methods,
as the size of liposome is around 100nm in diameter, it is hard to observe each liposome’s
structure. Multilamellar liposomes or some other complex structured liposomes may also
be contained in the test batch, which makes it hard to give a correct permeation
coefficient for unilamellar lipid membrane. The size polydispersity in the liposome
sample leads to a varying permeation rate, increasing the uncertainty in the results.
8
1.3.2 PAMPA and Planar bilayer assays
The standard high-throughput cell-free approach to measuring passive membrane
transport is the parallel artificial membrane permeability assay (PAMPA) (Kansy et al.
1998). In PAMPA, a filter membrane is impregnated with a solution of lipids in organic
solvent. The lipid-impregnated filter is then submerged in a well of a microtiter plate, and
transport of drug molecules from one side of the membrane to the other is measured
(typically by UV absorbance spectroscopy).
The assumption underlying PAMPA is that the lipid bilayer membranes formed in the
filter mimic the cell plasma membrane. While there is some electrophysiological
evidence for the formation of bilayer membranes in similar systems (Thompson et al.
1982), the PAMPA configuration is not well controlled. There is no way to assure that
every pore in the filter is occupied by a bilayer: some may be open while others might be
plugged completely by solvent. Even in pores containing bilayers, there is a large amount
of residual solvent. During the formation of a planar lipid membrane, a lipid monolayer
spontaneously forms at the interface between the organic and aqueous phases. The
lipid/solvent solution wets the hydrophobic walls of the aperture, forming a thin film in
the aperture. Once the two sides of the thin film come close enough, the lipid monolayers
fuse, rapidly excluding the remaining solvent, and a bilayer is formed in the center of the
aperture, but a significant annulus of solvent remains at the perimeter (Figure 1-3) (White
1972). Residual solvent is inherent to the structure of the planar artificial bilayers
fabricated from organic solutions of lipids. Montal et al. has tried to modify this method
by replacing the heavy non-volatile solvent with a volatile solvent like chloroform to
9
reduce the residual solvent (Montal & Mueller 1972). But there still existed a lot of
differences in the membrane properties from this kind of membrane to cell membrane
(see Table 1-1). The stability of this membrane is another problem. Typically, planar
lipid membrane can last no more than several hours limiting the long-term permeation
experiments. As a result of the poorly controlled structure and the excess of solvent in the
PAMPA membrane, this system often incorrectly predicts the membrane permeability of
common drugs (Balimane et al. 2005; Chen et al. 2008). Previous PAMPA permeation
studies of drugs like propranolol and testosterone showed that the permeability varied
with solution agitation rate, pH, and other factors (Korjamo et al. 2009). To accurately
recreate passive transport across the plasma membrane, it is necessary to work in a
system with a true, solvent-free, molecular bilayer of lipids.
Figure 1-3: Schematic of a painted bilayer experiment. A sheet of plastic with a small hole in the
center separates the two sides of the chamber. The bilayer is formed across this hole, separating the
two chambers. The electrical properties of the bilayer can be measured by putting an electrode into
each side of the chamber, figure was taken from (Nielsen & Avdeef 2004).
10
Table 1-1: Comparison of the electrical properties of bimolecular lipid membranes in the
presence and absence of hydrocarbon solvent with those of cell membranes, taken from reference
(Montal & Mueller 1972)
1.4 Unstirred water layer (USL): advantage or disadvantage
Current approaches based on artificial membranes face severe limitations. The most
critical of these are related the USL adjacent to the artificial membrane (Barry &
Diamond 1984). The USL represents a significant resistance to permeant transport,
restricting the permeation coefficients that can be measured. Current techniques must
cope with the USL (Grime et al. 2008; Mathai et al. 2009).
The role of the USL in cell membrane transport was reviewed thoroughly by Barry and
Diamond (Barry & Diamond 1984). The unstirred layer can be thought of as a region
adjacent to the membrane in which the fluid is static and diffusive transport dominates
over transport from convective mixing. Here, the concentration cannot be considered
equal to the bulk concentration. The concentration profile in the USL has traditionally
been modeled with Fickian diffusion between a well-stirred bulk concentration c
b
and
concentration-dependent transmembrane flux at the membrane, shown in Figure 1-4.
Note that this is strictly a steady-state configuration.
11
membrane
USL
J
solute
C
b,out
C
b,in
C
m,in
C
m,out
Figure 1-4: The traditional model for the steady-state concentration profile across a permeable
membrane with USLs. At steady state, concentration goes from a constant exterior bulk
concentration to a constant interior bulk concentration.
The essence of the USL problem is that while the bulk concentrations on either side of
the membrane (c
b,in
and c
b,out
in Figure 1-4) are easily measured, it is the concentrations
directly adjacent to the membrane (c
m,in
and c
m,out
in Figure 1-4) that determine the
membrane flux and that therefore must be known in order to determine the membrane
permeability. In fact, the total region surrounding the membrane, including the USL, can
be thought of as a permeable barrier with permeability less than that of the membrane
(since a molecule must diffuse through the USL to reach the membrane). The total
apparent resistance to diffusion across the membrane is equal to the sum of resistances
through the membrane and through the unstirred layer (Wolosin & Ginsburg 1975).
Resistance is equal to the inverse of permeability, so the total apparent permeability, P
app
,
is given by:
11 1
app UL
PPP
1-3
12
where P is the permeability of the membrane itself, and P
UL
is the effective permeability
of the unstirred layer. P
UL
= δ/D
w
, where δ is the length of the unstirred layer and D
w
is the
diffusivity of the solute in water. So for a large enough δ, the transport can be dominated
entirely by diffusion through the unstirred layer, making it difficult to accurately measure
P (Mathai et al. 2009).
Barry and Diamond provide a table relating total USL thickness and the permeability
of the transported species to the expected permeability measurement error (Barry &
Diamond 1984). For permeabilities of 10
-6
cm/s, a 25% measurement error would be
introduced by a USL thickness of 17 μm. The thickness necessary for a 25% error is
inversely proportional to permeability, such that at a permeability of 10
-3
cm/s, 25% error
would be introduced by only a 17 μm USL. In standard membrane permeation
experiments with planar membranes, the unstirred layer has been estimated have a length
in the range of 200 μm to 2 mm (Gutknecht 1990; Missner et al. 2008). The USL length
is dependant on the geometry of the experiment, though some general relations have been
developed. Pedley related USL thickness to fluid parameters as:
1/3 1/ 2
1.6
Dv
va
1-4
where is kinematic viscosity and α is a stirring parameter (Pedley 1980).
By utilizing the properties of USL, some researchers have developed steady-state
measurements of membrane permeability with planar lipid bilayers. These measurements
involve forming a bilayer between two aqueous chambers and allowing a small-molecule
species to diffuse to steady state between these chambers (Antonenko et al. 1993;
Antonenko & Pohl 1995; Grime et al. 2008; Missner et al. 2008; Mathai et al. 2009). The
13
gradient established across the membrane consists of both the immediate concentration
difference across the membrane and a diffusive USL adjacent to the membrane on either
side (Montal & Mueller 1972; Barry & Diamond 1984; Sugano et al. 2004; Balimane et
al. 2005; Chen et al. 2008; Malmstadt et al. 2008). If this USL is well characterized and
properly modeled, steady-state measurements in a planar bilayer format can produce
accurate membrane permeabilities (Figure 1-5) (Antonenko et al. 1993; Antonenko &
Pohl 1995; Missner et al. 2008; Mathai et al. 2009).
Figure 1-5: (a) experimental pH profiles near planar lipid bilayer as acetic acid permeate through.
Copied from reference (Antonenko et al. 1993). (b) Near-membrane pH and H
2
S concentration
distributions for bulk pH7.5 solution as H
2
S permeate through planar lipid bilayer. Copied from
reference (Mathai et al. 2009).
1.5 Solving these problems with confocal microscopy of giant
lipid vesicles
We have developed a straightforward solution to the problem of artifacts in membrane
permeability measurements. We use confocal microscopy to image the transport of
fluorescent molecules into giant unilamellar vesicles (GUVs)—solvent-free spherical
a b
14
lipid bilayer constructs with diameters in the ~10-100 μm range. Confocal microscopy
allows for the interior of GUVs to be trivially distinguished from their exterior.
Fluorescent molecules in the exterior space can therefore be optically tracked as they
permeate the membrane and enter the GUV interior. By using spinning disk confocal
microscopy (SDCM), the entire field is captured in a short (< 100 ms) exposure. This
allows for the temporal development of the concentration field to be tracked with great
precision. Rather than merely observing the bulk concentrations at steady state, as in
traditional permeability measurement techniques, we observe the entire concentration
profile at all times. This rich dataset allows for precise determination of membrane
permeability.
Since this technique is easy to implement, it has great promise as a widely adapted
approach to measuring membrane transport properties. It could have significant impact
on research into passive transport. In the work described here, confocal observations of
GUVs will be used to test Overton’s rule by investigating the transport of series of
molecules with increasing and decreasing lipophilicity. The technique is expanded to the
interaction of nanoparticles with lipid bilayers. Finally, in future work, the passive
transport of carbon dioxide through lipid membrane will be investigated.
15
Chapter 2: Passive membrane transport of a series of
hydrophilic molecules (PEG-n-NBD)
(This work was published in Analytical Chemistry, 82(18):7766-7771, 2010)
2.1 Introduction
In order to investigate how this confocal microscopy based system reports on the
transport of molecules of varying hydrophobicity, we synthesized a series of
fluorescently labeled test molecules. This series consists of poly (ethylene glycol) (PEG)
with short chains of various lengths attached to nitrobenzoxadiazole (NBD) dyes. We
refer to these test molecules as PEG-n-NBD, where n is the number of ethylene oxide
units. As the chain length of PEG-n-NBD increase, the hydrophilicity increases. As the
size of this series of molecules, the permeation process was estimated to be maintained in
a reasonable time, not too fast or too long. This can help give an accurate measurement of
the permeation and determine how the hydrophilicity affects the permeation and whether
Overton’s rule is applicable to this class of molecules.
2.2 Materials and methods
2.2.1 Materials
Dipalmitoylphosphatidylcholine (DPPC), dioleoylphosphatidylcholine (DOPC),
cholesterol, and biotinylated dipalmitoylphosphoethanolamine (biotin-DPPE) were
obtained from Avanti Polar Lipids (Alabaster, AL). Texas Red-modified DPPE (TR-
DPPE), succinimidyl 6-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino) hexanoate (NBD
16
NHS-ester), and avidin were obtained from Invitrogen (Carlsbad, California). Indium-tin
oxide (ITO)-coated glass was obtained from Delta Technologies (Stillwater, MN).
Amine-terminated poly(ethylene glycol) alcohols were obtained from Quanta Biodesign
(Powell, OH). Poly(dimethylsiloxane) (PDMS) was obtained from Dow chemical
corporation (Midland, MI). NoChromix was obtained from Godax Laboratories (Cabin
John, MD). All other chemicals were used as provided by Sigma-Aldrich (St. Louis, MO).
2.2.2 Cleaning of glass cover slips
Glass cover slips were first sonicated in water at 80
º
C for 30 min, and then dipped in
sulfuric acid with NoChromix for 2hr. After rinsing away the acid, the cover slips were
sonicated in water again for 30 min, and stored in methanol for later use.
2.2.3 GUV preparation and observation
GUVs were fabricated according to the electroformation technique of Angelova et al.
(Angelova 1992) from a 1:1:1 (molar ratio) mixture of DPPC, DOPC, and cholesterol. To
visualize GUVs, TR-DPPE was added to this mixture at 1 wt% (relative to total lipid
mass). To immobilize GUVs on the glass surface, 7 wt% biotin-DPPE was added to the
lipid mixture. Lipids were dissolved in chloroform and spread as a thin film on the
surface of a piece of ITO-coated glass. After the solvent had evaporated and the
remaining film was thoroughly dried, it was rehydrated with a buffer containing 2 mM
Hepes at pH 7.0 and 200 mM sucrose. During electroformation, this buffer was heated to
37 ºC in a cell formed from two pieces of ITO-coated glass while an oscillating 100 mV
signal was applied at 1 Hz.
17
After 4 h, the GUV suspension was removed from the cell and transferred to a Sykes-
Moore chamber constructed with #1 cover glass and containing 200 mM glucose
solution. The chamber also contained 0.5-1 μM of the fluorescent test molecule to be
transported into the GUVs. The GUVs immediately sank to the bottom of the chamber
due to the sucrose-glucose density gradient. There, they were observed by SDCM.
SDCM was performed using a Yokogawa (Tokyo, Japan) CSUX confocal head on a
Nikon (Tokyo, Japan) TI-E inverted microscope. Illumination was provided by 50 mW
solid-state lasers at 491, 561, or 640 nm. PEG-n-NBD was excited at 491 nm, and
emission was captured at 525 nm. TR-DPPE was excited at 561 nm, and emission was
captured at 595 nm. An initial image was captured immediately following addition of the
vesicles to the buffer containing the fluorescent species. Subsequent images were taken at
regular intervals thereafter. Constant illumination, exposure, and camera amplification
settings were used across all images in a time series.
2.2.4 Preparation of test molecules
In each synthesis, an amine-terminated poly(ethylene glycol) alcohol containing a
well-defined number of ethylene oxide units was reacted with NBD NHS-ester. Reactions
were run overnight, at room temperature, in 1:1 (vol:vol) chloroform:methanol with
triethylamine added at a 5x molar excess to the amine groups. The reaction products were
separated using thin layer chromatography. The reaction scheme is shown in Figure 2-1,
using PEG-4-NBD as an example.
18
Figure 2-1: Preparation of the PEG-4-NBD test molecule. An amine-terminated 4-unit poly(ethylene
oxide) was reacted with an NHS-ester of the fluorescent dye NBD. To prepare other PEG-n-NBD
molecules, PEG precursors with different numbers of repeating units were used.
2.2.5 Measurement of octonal-water partition coefficients
1.5 mL of octanol and water were added to a test tube to form a two-phase system. 20
μl of 1 mM PEG-n-NBD in water was added to the two phase system and the tube was
vortexed until the solution appeared to become uniform. The two phases were allowed to
settle for 10 min. Then UV-visible absorption spectrum of PEG-n-NBD in each phase
was measured using a Shimadzu (Kyoto, Japan) Biospec-1601 spectrometer at 465 nm.
The extinction coefficients ε of NBD at 465 nm in water and octanol are 24000/M/cm
and 19000/M/cm (Lancet & Pecht 1977) respectively. The concentration of PEG-n-NBD
in each phase was calculated from ε according to the Beer-Lambert law. Partition
coefficients were calculated as K
oct-water
= c
oct
/c
water
.
2.2.6 Buffer exchange on a single GUV
For experiments investigating a single GUV with different chemicals present in the
exterior space, GUVs were immobilized on the #1 cover glass surface of a microfluidic
channel. The channels were made from PDMS patterned via standard polymer
19
micromolding techniques. (Kersten & Crommelin 1995) The patterned PDMS and a #1
cover slip were oxidized by corona treatment (BD-20AC, Elecro-Technic Products,
Chicago, IL) to bond them irreversibly (Gregoria.G et al. 1971). The PDMS channel was
a T-junction (Kamholz et al. 1999) configuration with two inlets and one outlet. The
channel used to observe GUVs had a width of 1 mm, depth of 100 µm, and length of 1
cm. Buffer solutions were injected into either inlet using a Harvard Apparatus (Holliston,
MA) syringe pump. The linear flow velocity in the observation channel was 5 mm/sec.
To immobilize GUVs on the glass surface, the biotin-avidin interaction was used.
GUVs were fabricated with biotin-DPPE in the lipid mixture as described above. To
functionalize the chamber surface with avidin, a 25 μg/mL avidin solution was pumped
into the device and incubated for 10 minutes at room temperature. Afterwards, the
surface was gently flushed with glucose buffer for 1 min to remove unbound avidin.
Then, the functionalized surfaces were incubated with vesicles for 20 min. Unbound
vesicles were removed by gently washing the sample channel with buffer solution for 1
min.
To observe background fluorescence, 0.1 mg/mL of 40 kDa fluorescein-dextran in
glucose buffer (200 mM glucose, 2 mM HEPES, pH 7.0) was first added to the
observation chamber and images were captured. 1 μM PEG-NBD solution was flowed
into the channel to flush away the fluorescein-dextran solution.
2.2.7 Image analysis
Images were analyzed using ImageJ (freely available from the NIH;
rsbweb.nih.gov/ij/) and Matlab (The MathWorks, Inc., Natick, MA). To correct for
20
illumination heterogeneity, the images were flat-fielded in reference to an image of an
empty (no GUVs) field at the same fluorophore concentration. Pixel-by-pixel
multiplicative factors necessary to make the blank field uniform were thereby derived;
this array of multiplicative factors was then applied to the data images.
2.2.8 Data processing
For each vesicle permeation experiment, the solution concentration of PEG-n-NBD
(n=4, 8, and 12) and camera settings were the same. The total fluorescence intensity of a
2-5 μm diameter circle was measured at the center of the GUV. This measurement was
used as the internal intensity. The intensity was also measured in 10 circles with the same
diameter evenly distributed outside of the GUV; deviation from the mean of these
measurements was propagated as a measurement error throughout this analysis. The
mean of the exterior measurements was used as the nominal exterior intensity. To correct
for photobleaching and laser drift, the external fluorophore concentration was assumed to
be constant (the vesicle volume is negligible compared to the total volume). Based on this
assumption, internal and external intensities were adjusted by the same additive factor
necessary to maintain corrected external intensity constant throughout the experiment.
These values were then baseline-subtracted using the initial internal intensity.
2.3 Results and discussion
2.3.1 Confocal Imaging of Membrane Permeation
An initial image was captured immediately following addition of GUVs. Subsequent
images were taken at regular intervals thereafter. A typical time series of images is shown
21
in Figure 2-2. This time series shows the change in internal fluorescent intensity as PEG-
8-NBD permeates the lipid bilayer of a GUV. The PEG-8-NBD concentration can be
seen to gradually increase inside the GUV until the internal and external intensities
match. This indicates that rather than reaching a non-equilibrium steady state, the system
achieves diffusive equilibrium across the membrane.
Figure 2-2: (a) A time series of SDCM images showing the transport of a fluorescent molecule PEG-
8-NBD (ex 465 nm, em 539 nm) into a GUV. (b) GUV labeled by Texas-Red (ex 583 nm, em 603 nm)
modified DPPE excited at 561 nm showing the lipid bilayer. The small orange circles in the center
and attached to the big GUV membrane are small lipid vesicls. Scale bars are 10 μm.
2.3.2 Concentration Profile
To observe the concentration profile adjacent to the vesicle membrane and characterize
any USL, line intensity profiles through vesicles were measured. The trace labeled PEG-
NBD in Figure 2-3(a) is an example of such a profile. These data are from an experiment
with PEG-4-NBD penetrating the vesicle taken at the 1 min time point. The gradual
decrease in fluorescent intensity between the membrane and the vesicle center is an
artifact of SDCM imaging. The spinning disk does not perfectly reject light from outside
of the focal plane. In the regions at the edge of the vesicle, where the distance through the
vesicle along the imaging axis is smaller, more light from fluorophores external to the
vesicle leaks through.
22
To correct for this effect, we used a buffer exchange system with a fluorescent
molecule that cannot penetrate the membrane. The non-penetrating fluorophore we
selected was 40 kDa fluorescein-dextran. The fluorescein-dextran trace in Figure 2-3(a)
(labeled Fl-dextran) is an line profile with fluorescein-dextran exterior to the vesicle.
Notice the resemblance of the curve interior to the membrane to the trace labeled PEG-
NBD. To correct for out-of-plane light leakage, the control fluorescein-dextran trace in
Figure 2-3(a) was subtracted from the PEG-NBD trace in 2-3a. The result, shown in
Figure 2-3(b), is a flat intensity profile throughout the vesicle interior. It is clear that the
concentration rapidly goes to the bulk concentration on either side of the membrane. The
length of the USL interior to the GUV membrane can be no more than 1 µm; it is 5 µm or
less exterior to the vesicle.
Figure 2-3. Intensity profiles drawn through the center of the GUV. (a) A GUV with PEG-4-NBD
permeating (blue trace), and the same GUV with fluorescein-dextran (40kD) outside (red trace), (b)
The PEG-4-NBD line profile through the vesicle corrected to remove background fluorescence.
The curved profiles shown in Figure 2-3(a) are consistent with theoretical expectations
of out-of-plane light leakage in SDCM. According to Sandison and Webb (Sandison &
Webb 1994), the image fluorescence from a single out-of-focus spot is given by:
23
1/ 2
2
21 2
4
16
[, ] 2 cos
22 4
II I
BI
vv v
Iv u u u
uu
2-1
where v
I
is the distance from the optic axis, and u is the distance from the in-focus plane.
The fluorescence leakage into an image plane inside the vesicle can therefore be obtained
by integrating the fluorescence from outside the vesicle. To perform this integration, we
treated the vesicle as a sphere, with the edges of the sphere closer to background
fluorophores than the center of the sphere. Figure 2-4 is a comparison of the fluorescence
leakage along the vesicle axis calculated by theory and intensity data from the
fluorescein-dextran experiment, demonstrating that the intensity profile observed can be
explained by out-of-plane fluorescence in a spherical geometry.
Figure 2-4. Comparison of the fluorescence profile calculated by out-of-plane fluorescence theory
with experimental data obtained from a GUV with 40 kDa fluorescein-dextran outside.
2.3.3 Correcting for GUV size-dependence of the fluorescence
background
As described above, since SDCM does not perfectly exclude out-of-focal-plane light,
there is some fluorescence background present in the vesicle interior in each image. Since
the amount of light leaking into the focal plane is greater for fluorophores closer to the
24
focal plane, the background signal is greater for smaller vesicles (in which the “bulk”
fluorescence region is closer to the image plane). To analyze data from GUVs of various
sizes, we had to correct for this effect. Figure 2-5 shows intensity at the center of vesicles
incubated with 40 kDa fluorescein-dextran as a function of vesicle diameter. This
relationship, captured by the empirical polymeric fit of Equation 2-2, was used to
compare vesicles of various sizes. The center vesicle intensities were adjusted to the
intensity expected for a reference diameter of 40 µm.
2
1.5 200 21000 Id d 2-2
Figure 2-5. Dependence of background intensity at the center of GUVs on GUV diameter.
2.3.4 Permeability Calculations
Permeabilities were calculated from corrected, baseline-subtracted vesicle internal
intensities. As the fluorescent intensity is proportional to concentration, the intensity was
used as a proxy for concentration. To obtain permeability values, we utilized a simple
model of the temporal development of the concentration field. Molecular flux across the
membrane was treated as a simple permeation process: J=P(c
o
-c
i
), with flux J,
permeability P, and concentrations c outside and inside the vesicle. External
25
concentration c
o
was treated as a constant; internal concentrations c
i
were normalized by
this constant. For a single vesicle, J =N /A, where N is the first time derivative of number
of molecules and A is the surface area of the vesicle. The concentration inside the vesicle
is simply c
i
=N/V, where V is the volume of the vesicle. Substituting into the permeation
equation yields a first order ordinary differential equation:
'
o
AP
N N APc
V
2-3
If we apply the boundary condition that at t=0, c
i
=0 and the vesicle is spherical with
diameter d, the solution to this equation is:
6
() 1
P
t
d
io
ct c e
2-4
We obtained temporal fluorescent intensity profiles for PEG-n-NBD molecules with n
= 4, 8, and 12. Representative results are shown in Figure 2-6, along with a single-
parameter (P) fit to Equation 2-4. For each species, the time course of permeation into
three vesicles was observed. The average permeabilities obtained were: PEG-4-NBD:
1.13 ± 0.08 × 10
-5
cm/s; PEG-8-NBD: 2.04 ± 0.17 × 10
-7
cm/s; PEG-12-NBD: 2.27 ±
0.21 × 10
-8
cm/s. Measured permeability is independent of vesicle diameter.
I
i
/I
Time (min) Time Time
26
Figure 2-6. Plot of fluorescence intensity inside over intensity outside GUVs (1:1:1
DPPC:DOPC:cholesterol) as a function of time at 26
o
C. Data points are red circles with black error
bars; regressions of P in Equation 2-4 to the data are blue lines.
Table 2-1: Permeability of PEG-n-NBD to different size GUVs
P (× 10
-6
cm/s)
Diameter of GUV/um PEG-4-NBD PEG-8-NBD PEG-12-NBD
20 0.020 ± 0.003
30 8.9 ± 1.1
35 12.2 ± 0.7 0.19 ± 0.01
40 12.7± 2.1 0.027 ± 0.005
45 0.18 ± 0.03 0.023 ± 0.003
60 0.23 ± 0.04
To compare this method to previous investigations, we used the same procedure to
measure the permeability of fluorescein as 1.94 ± 0.18 × 10
-5
cm/s. This is within the
range measured by other researchers, from 1.6 – 21.2 × 10
-6
cm/s (Ke et al. 1999; Berginc
et al. 2007; Kristl 2009).
The potential effect of the unstirred layer was calculated based on the observations
shown in Figure 2-7 according to the equation described by Barry and Diamond (Barry &
Diamond 1984):
1/ (1/ ) ( '/ ') ( "/ ")
m
PP D D 2-5
Here P is the apparent permeability, P
m
is the actual membrane permeability, δ’ is the
USL thickness inside the vesicle, δ” is the USL thickness outside the vesicle, and D is the
diffusivity inside the unstirred layer. In our experiment, the unstirred layer thicknesses
inside and outside the vesicle were no more than 1 µm and 5 µm respectively (see Figure
2-3(b)). According to Graham’s law, for small molecules, the square root of molecular
weight and diffusivity are inversely proportional (Pickover 2008). Based on the measured
diffusivity of fluorescein-biotin (Kamholz et al. 2001), which has a molecular weight
27
close to that of PED-12-NBD, we can estimate the diffusivities of PEG-4, 8, and 12-NBD
as 5.1, 4.2, and 3.6×10
-6
cm
2
/s respectively. If P is the permeability obtained from the
experiments, P
m
can be derived from Equation 2-5. The percent error introduced by the
USL can be used to estimate the effects of USLs in these experiments. For PEG-4-NBD,
this value is no more than 0.1%. The value for PEG-8-NBD is 2×10
-3
%, and for PEG-12-
NBD it is 2×10
-4
%.
Figure 2-7: Unstirred layer and concentration profile near membrane, figure was copied from
reference (Barry & Diamond 1984).
2.3.5 Comparison to Overton’s rule
The octanol/water partition coefficients K
oct/water
of the three test molecules, listed
according to increasing PEG chain length, were measured as 2.88 ± 0.24, 0.45 ± 0.05,
and 0.20 ± 0.02. The permeation coefficient P is widely described by Overton’s rule in
terms of the oil-water partition coefficient K, as P=KD
mem
/l, where D
mem
is the diffusion
coefficient of the molecule in the membrane and l is the membrane thickness (Orbach &
Finkelstein 1980). Generally D
mem
= D
0
M
-1.22
, where D
0
is the calculated diffusion
coefficient for a solute of unit molecular weight (Bonting 1981). Substituting K and D
mem
into the Overton equation for permeability, the predicted permeabilities of these three
28
molecules have a ratio of 32:3:1 (see Table 2-2). But in the permeation experiments, P
changed nearly an order of magnitude more than this, indicating that there are factors
other than diffusivity and oil-water partition affecting membrane permeability. Examples
of such factors were recently explored by Xia and coworkers, who used Abraham’s linear
solvation energy relationship (LSER) to predict solvent effects on membrane absorption,
taking into account lone-pair electrons, effective dipolarity and polarizability, and
hydrogen bonding (Xia et al. 2007).
Table 2-2: Comparison of Overton’s rule to experimental result. Values were normalized to PEG-12-
NBD
K
oct/water
D = D
0
M
-1.22
P
calc
=KD/l P
exp
PEG-4-NBD 14.4 2.2 32 497
PEG-8-NBD 2.3 1.4 3 9
PEG-12-NBD1 1 1 1
2.3.6 Finite element modeling of diffusion inside the vesicles
Our conclusion is that the USL contribution to the transport process in this GUV
system is negligible. To assure ourselves of the reasonableness of this conclusion, we
built a finite element model of the system. Comsol Multiphysics (Comsol, Inc.,
Burlington, MA) was used to model diffusion into a sphere. Diffusion was governed by
Fick’s Second Law in three dimensions:
()0
c
Dc
t
2-6
Bulk (i.e. external) concentration was fixed (to match the experimental concentration
of 1 μM); the vesicle was modeled with two concentric spheres with a diameter
difference of 0.5 μm. The outer sphere had a diameter of 40 μm. In other words, we
29
created a computational model of a vesicle with a 500 nm-thick bilayer. This thick
bilayer was necessary to successfully mesh the geometry; a realistically sized bilayer
would require a more sophisticated multiscale meshing approach. This geometry would
not be expected to generate an accurate model of concentration profile in the membrane;
however, by tuning the membrane transport properties to match those that we measured
experimentally, we create a simulation in which transport into and out of the regions
adjacent to the membrane is similar to our experimental system.
Membrane transport properties were tuned by modifying the diffusivity in the inter-
sphere region representing the membrane. The diffusivity inside the membrane was set as
D = Pl, where P was experimentally measured permeability and l was the thickness of
model membrane. Flux magnitude in regions adjacent to the membrane was thereby
controlled by the permeability of membrane. Diffusivity in the bulk solution was set to
match that of fluorescein, which is similar in many ways to our test molecules and which
has a diffusivity of 5.4 × 10
-6
cm
2
/s (Kamholz et al. 2001).
Figure 2-8 shows the time evolution of the concentration profile across the sphere.
Two things stand out in these results. First, diffusion at this scale is apparently
sufficiently fast that there is no noticeable concentration gradient across the interior of the
sphere. Second, the calculated concentration values correspond very well to the
experimental results from which the simulated permeability was derived. These results
suggest that for the experimental conditions, the assumption of uniform concentration in
the GUV—required for the development of Equation 2-4 and observed experimentally—
is reasonable.
30
Figure 2-8: Diffusion profiles of a 40 μm sphere with concentration-dependant flux boundary
conditions are shown in a. Time increases moving up from profile to profile; each time step is 20 s.
Comparison of the experimental and simulation PEG-4-NBD results is shown in b.
In summary, we have developed a straightforward solution to the problem of artifacts
in lipid membrane permeability measurements. We use confocal microscopy to image the
transport of fluorescent molecules into GUVs. Confocal microscopy allows for the
interior of GUVs to be trivially distinguished from their exterior. Fluorescent molecules
in the exterior space can therefore be optically tracked as they permeate the membrane
and enter the GUV interior. Experimental results show that, because of the small size of
GUVs relative to the characteristic diffusive lengths of the transported molecules, no
significant USL is established in this system. Since this technique is easy to implement, it
has great promise as an approach to measure membrane transport properties. It can be
generalized to a variety of transported molecules by using fluorescence systems based on,
for example, pH-sensitive fluorophores or fluorogenic molecular reporters. It is optimally
suited to precise quantitative measurements of the dependence of passive transport on
membrane properties, including lipid bilayer composition, charge state, curvature, and
a
b
31
phase. These are central issues in understanding how molecules passively diffuse into
cells.
2.4 Conclusions
We have developed a straightforward solution to the problem of artifacts in lipid
membrane permeability measurements. We use confocal microscopy to image the
transport of fluorescent molecules into GUVs. Fluorescent molecules in the exterior
space can therefore be optically tracked as they permeate the membrane and enter the
GUV interior. Since this technique is easy to implement, it has great promise as an
approach to measure membrane transport properties. It can be generalized to a variety of
transported molecules by using fluorescence systems based on, for example, pH-sensitive
fluorophores or fluorogenic molecular reporters. It is optimally suited to precise
quantitative measurements of the dependence of passive transport on membrane
properties, including lipid bilayer composition, charge state, curvature, and phase. These
are central issues in understanding how molecules passively diffuse into cells.
32
Chapter 3: Confocal imaging to quantify carboxylic acid
passive transport across lipid membranes
(This work was published in Biophysical Journal, 101(3):700-708, 2011)
3.1 Introduction
Overton’s rule broadly states that more lipophilic drug molecules cross cell membranes
more readily, increasing their oral bioavailabilty and pharmaceutical activity (Kleinzeller
1997). Oil/water partition has become an important criterion for determining which
molecules might make good drugs. However, recent studies have suggested that some
carboxylic acids fail to obey Overton’s rule. Grime and co-workers found that
permeability decreased with acyl tail length in a manner contrary to that expected from
the trend of partition coefficients (Grime et al. 2008). Xiang and co-workers found that
the permeability initially decreased as acyl tails got longer (from formic acid to propionic
acid) and then increased with tail length from propionic acid to valeric acid. They
suggested that besides partition coefficient, molecular shape and size must be taken into
consideration and that Overton’s rule needs to be reevaluated (Xiang & Anderson 1998).
Besides their research, the measurement of the permeability of lipid bilayers to small
molecules has been a surprisingly challenging problem, and published results for even
simple systems have been inconsistent. The study of low-molecular-weight carboxylic
acid permeability is an example of these inconsistencies. Studies of carboxylic acid
permeability have produced wildly varying results, spanning orders of magnitude, some
agreeing with (Wolosin & Ginsburg 1975; Walter & Gutknecht 1984; Evtodienko et al.
33
1996) and some contradicting (Xiang & Anderson 1998; Grime et al. 2008) Overton’s
rule. Table 3-1 summarizes these differences. These studies were mainly based on planar
lipid bilayers and liposomes (Thomae et al. 2005; Suhonen et al. 2008).
In an attempt to clarify the discrepancies in reported values of membrane permeability,
we have developed a complementary measurement technique. This technique is based on
directly imaging the evolution of the concentration gradient of a molecule permeating a
cell-sized membrane structure. We first demonstrated the basic principle by using
confocal microscopy to observe the transport of fluorescently labeled molecules into
GUVs (Li et al. 2010). Here, we adapt this technique to transport measurements of
unlabelled, relatively fast-transporting species. Fluorescein-dextran (40 kDa), which is a
pH sensitive dye, is encapsulated in the GUV to visualize the transport of weak
carboxylic acids. The GUV is immobilized on the surface of a microfluidic channel to
allow the rapid exchange of the surrounding solution. The pH gradient on either side of
the membrane is optically tracked as acid molecules in the exterior space permeate the
membrane and enter the GUV interior. The high speed of SDCM allows us to
characterize the rapidly changing acid concentration profile and to obtain a temporal
record of acid permeation.
The use of a single vesicle over all experiments eliminates any artifacts arising from
vesicle polydispersity or variations in preparation. Imaging of the entire concentration
field allows for mixing and diffusion kinetics to be handled explicitly during data
analysis.
34
Here, we apply this technique to analyze the permeation of carboxylic acids containing
between one (formic acid) and six (hexanoic acid) carbon atoms. Our results show that
acid permeability clearly and monotonically increases with chain length and, therefore,
lipophilicity.
Table 3-1 Permeabilities (P) from various carboxylic acid permeation studies (units 10
-2
cm/s) Values
for this study are expressed in terms of a maximally likely value and a statistical range as described
in the text.
Acid Ref.
(Grime
et al.
2008)
Ref.
(Wolosin &
Ginsburg
1975)
Ref.
(Xiang &
Anderson
1998)
Ref.
(Walter &
Gutknecht
1984)
This study
Formic 0.0234 0.0203 0.036 (0.033-0.040)
Acetic 0.22 0.0238 0.0028 0.66 0.060 (0.057-0.063)
Propionic 0.061 0.0025 0.19 (0.16-0.21)
Butyric 0.089 0.115 0.0061 9.5 0.72 (0.69-0.75)
Pentanoic 0.076 0.18 0.111 8.0 (6.6-9.8)
Hexanoic 0.0633 110 23.0 (17.7-33.3)
Temperatur
e,
o
C
20±2 25 30 22±2 22±2
3.2 Materials and methods
3.2.1 Reagents
Dipalmitoylphosphatidylcholine (DPPC), dioleoylphosphatidylcholine (DOPC),
cholesterol, and biotinylated dipalmitoylphosphoethanolamine (biotin-DPPE) were
obtained from Avanti Polar Lipids (Alabaster, AL). Texas Red-modified DPPE (TR-
DPPE) and avidin were obtained from Invitrogen (Carlsbad, California). Indium-tin oxide
(ITO)-coated glass was obtained from Delta Technologies (Stillwater, MN). PDMS was
obtained from Dow chemical corporation (Midland, MI). NoChromix was obtained from
35
Godax Laboratories (Cabin John, MD). All other chemicals were used as provided by
Sigma-Aldrich (St. Louis, MO).
3.2.2 Cleaning of glass cover slips
The procedures are the same as section 2.2.2.
3.2.3 GUV preparation and observation
GUVs formation was the same as described in section 2.2.3. To immobilize GUVs on
the glass surface, 10 wt% biotin-DPPE was added to the lipid mixture. For “cholesterol-
free” permeability measurements, GUVs were made from a 1:1 mixture of DPPC and
DOPC with 10 wt% biotin-DPPE added. 1 mg/mL fluorescein-dextran (40kDa) was
added to the 2 mM HEPES at pH 7.04 and 200 mM sucrose solution to indicate the
solution pH change.
After 4 h, the GUV suspension was removed from the cell and injected to a
microfluidic channel constructed from patterned PDMS bonded to a #1 cover slip. There,
GUVs were observed by SDCM. The channels were made from PDMS patterned via
standard polymer micromolding techniques (Kersten & Crommelin 1995). The patterned
PDMS and the cover slip were oxidized by corona treatment (BD-20AC, Elecro-Technic
Products, Chicago, IL) to bond them irreversibly (Gregoria.G et al. 1971). The PDMS
channel was a T-junction (Kamholz et al. 1999) configuration with two inlets and one
outlet. The channel used to observe the GUV had a width of 1 mm, depth of 100 µm, and
length of 1 cm.
36
The biotin-avidin interaction was used to immobilize GUVs on the glass surface as
previously described (Li et al. 2010). Briefly, after fusing biotin-DPPE-containing
liposomes onto the glass surface, the channel was flushed with avidin solution, and then
biotin-DPPE-containing GUVs were introduced (Figure 3-1).
SDCM was performed using a Yokogawa (Tokyo, Japan) CSUX confocal head on a
Nikon (Tokyo, Japan) TI-E inverted microscope. Illumination was provided by 50 mW
solid-state lasers at 491 or 561 nm. Fluorescein-dextran (40 kDa) was excited at 491 nm,
and emission was captured at 525 nm. TR-DPPE was excited at 561 nm, and emission
was captured at 595 nm. Images were captured at 100 ms intervals. Constant
illumination intensity, camera amplification, and 100 ms exposure time were used for all
images.
Figure 3-1: GUVs were immobilized on an avidin-functionalized glass surface
3.2.4 Acid transport experiments
Primary acid transport experiments were performed on a single GUV composed of
DPPC, DOPC, cholesterol, TR-DPPE, and biotin-DPPE and bound to the bottom of a
microfluidic channel. The two inlet channels were used to inject 200 mM glucose
buffered either with 2 mM HEPES at pH 7.04 or an acid-containing 2 mM HEPES buffer
37
at pH 6.45. Solutions were injected into either inlet using a syringe pump. The linear flow
velocity in the observation channel was 15 mm/s.
The solutions injected into the channel also contained 0.05 mg/mL fluorescein-dextran
to facilitate visualization of the acid concentration external to the GUV. In a permeation
experiment, an acid solution was pumped into the channel from one of the two inlets as
images were recorded. Then the pH 7.04 glucose solution containing 0.05 mg/mL
fluorescein-dextran was pumped into the channel from the second inlet to flush away the
acid solution and remove the acid that had been transported into the GUV. A syringe
containing a different acid solution was then connected to the first inlet and this new acid
was injected into the channel (Figure 3-2). This process was repeated for all acids that we
utilized here in.
Figure 3-2: PDMS channel used for immobilizing and observing acid permeation into GUVs.
3.2.5 Image analysis
Images were analyzed using ImageJ (freely available from the NIH;
http://rsbweb.nih.gov/ij/) and Matlab (The MathWorks, Inc., Natick, MA). To correct for
illumination heterogeneity, the images were flat-fielded pixel-by-pixel in reference to an
image of an empty (no GUVs) field at the same fluorophore concentration (Li et al.
2010).
38
For each vesicle permeation experiment, the acid solution pH and camera settings were
the same. In each image, the fluorescence intensities of six 2-3 μm diameter circles were
measured in the interior of the GUV. The mean of these measurements was used as the
internal intensity. The standard deviations of the internal fluorescence measurements
were propagated as errors throughout the data analysis.
For analyses in which the full diffusion profile of an acid was investigated, profiles
were based on fluorescence intensities measured along lines drawn through the GUV
center. The complete methodology for converting these intensity measurements to
concentration profiles is included in the 3.3.4.
3.2.6 Correlating fluorescence intensity to acid concentration
Fluorescein is a pH-sensitive dye, and can therefore be used to determine solution pH
based on fluorescence intensity. We carefully established relationships between
fluorescence intensity, solution pH, and acid concentration. Carboxylic acids were
titrated into 200 mM glucose, 2mM HEPES, pH 7.04 buffer solution to measure how the
solution pH changed with acid concentrations. Solution pH was measured using a
Beckman Φ340 pH/Temp meter (Brea, CA). To test how the fluorescence intensity
changes with pH, acids with fixed concentration were titrated into a 1 mL cuvette
containing 200 mM glucose buffered with 0.1 mg/mL fluorescein-dextran (40kDa) and 2
mM HEPES at pH 7.04. Fluorescence was measured using a Shimadzu RF-5301PC
spectrofluorophotometer (Kyoto, Japan).
39
3.2.7 Finite difference modeling
A one-dimensional finite difference model was implemented based on Fick’s second
law:
2
2
ii
cc
tx
3-1
To simplify the calculation process, dimensionless variables were used in the
calculation, where c
i
is the concentration of species i (acid anion A
-
or protonated acid
HA), D is the diffusion coefficient of the acid in water, t is dimensionless time, equal to
TD/r
2
, with T as dimensional time, r is GUV radius, and x is dimensionless distance from
the bulk exterior boundary, equal to X/r, with X as dimensional distance. At initial
conditions (t = 0), concentration was assumed to be zero everywhere. The boundary
condition at the vesicle exterior was a time-varying concentration as measured
experimentally. A no-flux boundary condition was used at the GUV center. At the
membrane, flux was based on the concentration gradient across the membrane as:
,,
()
omem i mem
dc
Pc c
dx
3-2
where P is dimensionless membrane permeability, equal to 3Pr/D, where P is the true
membrane permeability, and c
o,mem
and c
i,mem
are external and internal concentration
adjacent to the membrane.
As carboxylic acids are weak acids, both charged and uncharged species coexist in
solution. Only the uncharged species can permeate the lipid membrane. The
concentration ratio of charged and uncharged species at each point in the model was
based on pH and literature values of pKa (Grime et al. 2008). In the finite difference
40
model, spatial and time derivatives were discretized with time and space steps δT and δX.
In the model δT was set as 5 × 10
-6
s; δX was set as 10
-5
cm. The model and fitting routine
were run in Matlab.
3.2.8 Determining permeability
Finite difference models were run at a series of permeabilities using the measured
external concentration, pKa, and diffusivity for each acid. The model results in the
vesicle interior were compared with experimental data at each permeability to obtain a
2
value (Equation 3-3).
2
(c
i
i
)
2
i
2
3-3
where c
i
are the experimental concentrations, μ
i
are the model concentrations, and σ
i
are
the standard deviations of the experimental data, summed over all data points. As
described below, slow-permeating acids could be fit on the basis of a single uniform
interior acid concentration while fast-permeating acids required an explicit fit of the
entire concentration profile interior to the membrane. The
2
statistic describes the
differences between the model results and experimental data, weighted by the error of the
experimental data. Smaller
2
values represent a better fitting result. The best-fit
permeability P is at the minimum χ
2
value. Reported ranges of P are based on those
permeabilities that produced a χ
2
corresponding to a p-value of 0.1 or greater (see section
3.3.5).
41
3.3 Results and discussion
3.3.1 Acid transport into a single GUV
In each experiment, images were captured at a constant rate as acid solution was
injected into the microfluidic channel. A typical time series of images demonstrating acid
permeation into a GUV is shown in Figure 3-3(a). This time series shows that internal
fluorescence intensity gradually decreased as acid permeated into the GUV. Once
fluorescence intensity inside the GUV equilibrated to a constant level, neutral buffer
solution was pumped into the channel to flush away the acid solution. Images captured as
acid subsequently diffused out of the GUV are shown in Figure 3-3(b). During the
process of acid efflux, the internal fluorescence intensity of the GUV gradually increased,
eventually recovering its initial level. This demonstrates that the fluorescence decrease
upon exposure of the GUV to acid solution was caused by acid permeation rather than
photobleaching or fluorophore leakage.
Figure 3-3. Time series of SDCM images showing the fluorescence intensity (ex 491 nm, em 525 nm)
change when acetic acid is transported (a) into and (b) out of a GUV. Scale bar is 20 μm.
To guarantee accurate measurements, the pH gradient and flow rate were optimized.
The pH gradient must be sufficiently large to visualize, but an excessively large pH
gradient results in transport too fast to capture with SDCM. Similarly, the microfluidic
42
flow must be sufficiently fast to allow for rapid buffer exchange, but excessive flow rates
result in vesicle motion that make the observations impossible. After several trials, a pH
gradient from 6.45 (exterior) to 7.04 (interior) was selected. This relatively small pH
gradient also eliminates diffusion potential barriers to transport, leaving the membrane
itself as the sole barrier (Deamer & Nichols 1983). A linear flow rate of 15 mm/s was
found to be optimal.
Even at these fast buffer exchange rates, some acids were found to diffuse into the
GUV at a timescale similar to that of buffer exchange. To account for the effect of buffer
exchange rates on the transmembrane transport process, acid concentration outside of the
vesicle was measured as a function of time. Both the neutral buffer solution and the acid
solution contained fluorescein-dextran at about 1/10 the concentration of that inside the
GUV. The fluorescence intensity exterior to the vesicle was converted to solution pH and
acid concentration.
The solid and dot-dash lines in Figure 3-4 show how the solution pH changes inside
and outside the GUV with time as it is exposed to various acid solutions. It is
immediately obvious from these data that as the acyl chain length of the acid increases,
the rate of transport also increases. Formic acid has the lowest permeability; hexanoic
acid has the highest permeability. In other words, carboxylic acid permeability increases
monotonically with lipophilicity.
43
Figure 3-4. Solution pH change inside and outside the GUV with time for six carboxylic acids. The
solid line and the dot-dash line represent the pH change inside and outside GUV. The dashed lines
are finite difference modeling fitting results. (a) formic acid, (b) acetic acid, (c) propionic acid, (d)
butyric acid, (e) pentanoic acid, (f) hexanoic acid.
To establish the pH values shown on the y-axis of Figure 3-4, an empirical relationship
between fluorescent intensity and pH was established for each acid. The pH/intensity data,
as well as the empirical fit that was used to determine pH in the transport experiments,
are shown in Figure 3-5(a). The empirical relationship between relative intensity (I) and
pH shown here is:
- 2.0(6.10 - pH)
0.986
I=1-
1+e
. 3-4
We also determined the relationship between acid concentration in our buffer system
and pH. These relationships are shown in Figure 3-5(b) for each acid. Note that in the
experimental pH range (6.4 – 7.0) the acids all behave similarly in this buffer. In the
finite difference model described below, acid concentration was based on the empirical
fit of a fifth-order polynomial to these data (shown as the solid line in Figure 3-5(b)).
44
Figure 3-5. (a) Fluorescence intensity vs. experimental pH. (b) Solution pH vs. acid concentration.
3.3.2 Effect of flow rate
We measured the effect of varying flow rate on the apparent permeabilities for the
three fast-permeating acids. To quickly estimate how apparent permeability changes with
flow rate, we used Equation 3-5 to fit the intensity change inside the GUV.
()
1
1
kt a
I
e
3-5
where t is time, k and a are the parameters that need to be fit in the model, with k the
decay rate of the intensity which can be interpreted as the apparent permeability.
The results are shown in Figure 3-6, along with a representative fit. Clearly, all acids
do display the plateau behavior, reaching a regime where permeability does not depend
on flow rate.
45
Figure 3-6: (a) Fit of hexanoic acid permeation data at a single flow rate to obtain an apparent rate of
change of fluorescence inside the GUV. (b) The plateau behavior of this rate of change at high flow
rates for all three fast-permeating acids.
3.3.3 Determining permeability
In order to determine precise permeability values, it is necessary to fit these data to a
transport model. The slow-permeating acids (formic and acetic) are transported into the
GUV at a much slower timescale than that at which the acid solution is injected into the
channel. The more quickly permeating acids, however, such as pentanoic acid and
hexanoic acid, are transported into the GUV at a timescale similar to that at which
injection into the microchannel occurs. This means that in order to quantify permeability
of these acids, the change in external concentration must be accounted for. To accomplish
this, we used a simple one-dimensional finite difference model in which one boundary
condition was set by the experimentally measured external concentration.
This model was based on Fick’s second law of diffusion and membrane flux theory.
The GUV was modeled as a spherically symmetric structure, allowing for a model in one
spatial dimension. Model parameters—GUV diameter, acid diffusivities, acid pKa’s, and
distance of measured external concentration from the bilayer—were taken from
46
experimental conditions or literature values. The external boundary condition was set
using fluorescence data measured at 1.5 radii from the GUV center.
Figure 3-7 shows how this model is able to account for the transport behavior of the
system, including the finite speed of buffer exchange. This figure shows the modeled
change of concentration interior and exterior to the GUV with time for two different acid
species. The permeabilities used here for each acid are based on the results shown in
Figure 3-4. The permeation of acetic acid (total duration 63.0 s) is much slower than that
of hexanoic acid (total duration 2.5 s). For acetic acid the membrane permeation
represents the main transport resistance; nearly all the concentration gradient occurs at
the membrane. On the other hand, diffusive resistance outside of the membrane
represents a significant barrier for hexanoic acid. A significant concentration gradient
extends into bulk solution.
47
Figure 3-7. Modeled concentration profiles of (a) acetic acid and (b) hexanoic acid. The GUV
membrane is at 6.25 μm. The GUV center is at 19 μm. The origin of the x-axis represents the position
where the external fluorescence intensity was measured. Each line represents the concentration
distribution across GUV membrane at one time step. As time goes on, the concentration increases
from the bottom to the top. For acetic acid, the total model duration shown is 63.0 s, with a time step
of 4.5 s. For hexanoic acid , these values are 2.5 s and 0.157 s. (c) Best fit of the model to experimental
concentration profiles in the GUV interior for hexanoic acid at the initial time, final time, and 3 time
steps during the permeation process.
To fit the model and obtain permeability values for slow-permeating acids, with
concentration profiles such as that in Figure 3-7(a), a single uniform interior
concentration was used at each experimental time point. For acids that permeated the
membrane more quickly, producing profiles like that shown in Figure 3-7(b) (this
represents butyric, pentanoic, and hexanoic acids), the entire interior concentration
profile was fit at each time point. Concentration profile data, along with a best-fit model,
are shown in Figure 3-7(c). Details on data processing to produce concentration profiles
are included in section 3.3.4.
48
Another important factor the model takes into consideration is the
protonated/deprotonated states of the acids. Uncharged species HA and charged species
A
-
and H
+
coexist in solution. Previous studies show only uncharged molecular species
can penetrate through lipid membranes (Al-Awqati 1999). Protons, however, are so
small that they can also penetrate lipid membranes at an appreciable rate (Deamer 1987).
In our experiment, the acids were dissolved in 2mM HEPES buffer solution at no more
than 0.27 mM. Even if all of the acid molecules were dissociated, the buffer can accept
all dissociated protons, guaranteeing that there is no proton permeation through lipid
membrane in the experiment. The model calculated the concentrations of the protonated
and deprotonated species according to local solution pH and acid pKa. Both species were
allowed to diffuse, but only the protonated species could permeate the lipid membrane.
3.3.4 Fitting experimental concentration profiles to obtain
permeability
For acids with an observable diffusive gradient interior to the membrane (i.e. butyric,
pentanoic, and hexanoic acid) the entire diffusive profile, rather than simple a uniform
concentration value, was used as the basis for determining a best-fit permeability.
The first step in this process is converting the fluorescent signal across a vesicle to
an acid concentration profile. Figure 3-8 gives an example of the raw data used to obtain
diffusive profiles. This plot shows intensity line profiles through a vesicle during a
permeation experiment. Each time step line was obtained by averaging two perpendicular
intensity lines through the GUV. This particular time series shows the decrease in internal
fluorescence intensity as hexanoic acid crossed the lipid bilayer of a GUV.
49
Figure 3-8: Line intensity profiles drawn through the center of the GUV in different time for
hexanoic acid.
While it is tempting to interpret the fluorescent gradient between the edge and the
center of the vesicle as describing a concentration gradient, it is in fact the result of an
artifact of the SDCM configuration. The spinning disk does not perfectly reject light from
outside of the focal plane. In the regions near the GUV center, where the vesicle diameter
along the imaging axis is larger, there is a greater out-of-plane contribution. Hence, even
in the t = 0 data, when no acid has crossed the membrane, a fluorescence gradient is
observable.
To correct for this effect, the total detected fluorescence intensity was considered to
be composed of two parts: light from the focal plane (reporting on the local acid
concentration across the vesicle), and light from outside of the focal plane. The total
intensity across a line profile is then:
22
00
(, ) ( , ) (, ) ( ) I xt I x t I xt b r r x 3-6
50
where I(x,t) is the total observed fluorescence intensity across a line profile through the
center the GUV, I
0
(x,t) is the light from the focal plane, and
22
0
(, ) ( ) I xt b r r x is
the light from outside of the focal plane. The light from outside of the focal plane
depends on the distance through the GUV along the optical axis, as well as the
concentration of acid, reported by I
0
. The distance through the GUV along the optical
axis is the term under the square-root symbol; it is found by treating the GUV as a sphere.
Distance along the optical axis will then vary as distance x along the line profile. At the
center of the GUV (x = r), the distance through the GUV is the greatest. At the edge (x =
0), this distance goes to zero. Notice that we have defined the coordinate system here
such that the edge of the GUV is the x = 0 point for consistency with our finite difference
model, which puts the center of the GUV at the right-side boundary.
The empirical parameter b describes the fraction of out-of-plane light that
contributes to observed confocal fluorescence. This is assumed to be constant.
Initially, the focal plane intensity should be uniform, so I
0
(x,0) should be constant
with x. This condition was used to determine a value of b at t = 0. This value was then
used throughout the time series correct for out-of-plane light. The intensity profile at each
time was then converted to a concentration profile using the method described in this
chapter Figure 3-7(c).
The concentration profile was then compared with the simulation results at the initial
time, final time, and 3 time steps during the permeation process (Figure 3-9).
2
minimization was used to find a best-fit permeability (P) (Figure 3-10 (d), (e), (f)). Figure
51
3-9 shows the best-fit models along with experimental concentration profiles for the three
fast-permeating acids.
Figure 3-9: experimental and best-fit model concentration profiles for acid permeation. (a) butyric
acid, (b) pentanoic acid, (c) hexanoic acid.
3.3.5 Statistical behavior of models
We have analyzed the goodness of fit of our finite element models and identified a
best-fit permeability values from these models by assuming that each of k experimental
data points represents a random variable and that the sum of the squares of these
variables are distributed according to a
2
distribution with k degrees of freedom. By
minimizing the
2
statistic (see Equation 3-3), we can find the model permeability that
best explains the experimental data.
52
This approach further allows for us to find a most-likely permeability range, since the
probability of obtaining a given
2
value is a well-known function of the degrees of
freedom of the
2
distribution in question. We can therefore use a cut-off at an arbitrary
p-value (here, 0.1; note: the term “p-value” here describes the statistical measure, not
permeability (P)) to assign a most likely range.
Figure 3-10 shows the behavior of
2
for each fit of acid transport data to the finite
difference model as a function of permeability. Permeabilities are very well constrained
statistically for values less than the best-fit permeability. Values greater than the best fit
are not as well constrained, particularly for the fast-transporting species. The ranges
reported in the manuscript are based on a
2
cutoff corresponding to a p-value of 0.1.
53
Figure 3-10: χ
2
values changes with permeabilities for six carboxylic acids. (a) formic acid, (b) acetic
acid, (c) propionic acid, (d) butyric acid, (e) pentanoic acid, (f) hexanoic acid.
54
3.3.6 Modeling the effect of buffer species
To assure that the finite difference model used to measure permeability does not suffer
from any artifacts due to its lack of an explicit treatment of buffer species, we ran a
modified version with buffer at extreme permeability conditions.
In this model, the protonated acid species AH is the only species that can permeate the
membrane, so transmembrane flux (and permeability) is defined only for this species.
The buffer species HEPES is a zwitterion. It has both a negative and a positive charge at
neutral pH: the positive group is deprotonated at 7.55 and the negative group is
protonated at 3. All the HEPES in the system examined can therefore be considered as
charged and unable to cross the membrane.
To look for any potential effect of HEPES accumulation or the development of
diffusive gradients of HEPES, we constructed a model in with explicit HEPES acid-base
equilibrium as determined by these pKa values and diffusivity as determined (Missner et
al. 2008). Initially, HEPES concentration was set constant through the system to match
experimental conditions.
At each time step, the concentrations of the various HEPES species were calculated as
follows:
2 22 1 2
1
22 1 2
21 2
22 1 2
[]
[]
110 10
[]10
[]
110 10
[]10
[]
110 10
tot
pH pKa pH pKa pKa
pH pKa
tot
pH pKa pH pKa pKa
pH pKa pKa
tot
pH pKa pH pKa pKa
Hepes
HHepes
Hepes
HHepes
Hepes
Hepes
3-7
Here, pKa1 is 7.55 and pKa2 is 3.00.
55
We ran this model with the permeabilities determined to be best-fit permeabilities for
both acetic acid (a slow-transporting species) and hexanoic acid (a fast-transporting
species).
The resulting temporal development of HEPES concentration profiles is shown in
Figure 3-11 and 3-12. With HEPES included in the model, the best-fit permeability for
acetic acid increases from 5.906 × 10
-4
cm/s to 5.964 × 10
-4
cm/s. Best-fit hexanoic acid
permeability increases from 1.434 × 10
-1
cm/s to 1.439 × 10
-2
cm/s. We believe that this
is sufficient justification for neglecting HEPES in our model.
56
Figure 3-11: Concentration profiles of hexanoic acid and HEPES as hexanoic acid permeates through
the GUV membrane. (a) total acid. (b) total HEPES. (c) [H-HEPES]
+-
. (d) [HEPES]
-
. (e) [H
2
-
HEPES]
+
. The membrane is at 6.25 μm. The GUV center is at 19 μm. The origin of the x-axis
represents the position where the external fluorescence intensity was measured. Each line represents
the concentration distribution across GUV membrane at one time step. As time goes on, the
concentration for (a), (b), (c), and (e) increases from the bottom to the top, while for (d) time
progresses from the top to the bottom. The total model duration shown is 2.5 s, with a time step of
0.157 s displayed here.
57
Figure 3-12: Concentration profiles of acetic acid and HEPES as acetic acid permeates through the
GUV membrane. (a) total acid. (b) total HEPES. (c) [H-HEPES]
+-
. (d) [HEPES]
-
. (e) [H
2
-HEPES]
+
.
The membrane is at 6.25 μm. The GUV center is at 19 μm. The origin of the x-axis represents the
position where the external fluorescence intensity was measured. Each line represents the
concentration distribution across GUV membrane at one time step. As time goes on, the
concentration for (a), (b), (c), and (e) increases from the bottom to the top, while for (d) time
progresses from the top to the bottom. The total model duration shown is 63.0 s, with a time step of
4.5 s displayed here.
58
3.3.7 Model sensitivity to diffusivity
To determine the effect that the value of diffusivity (D) used in the model has on the
best fit permeability, we performed a sensitivity analysis. Best-fit permeability was
calculated while model diffusivity was varied around the literature values that we used to
determine the values of permeability reported in the table 3-4 (9.18 cm
2
/s for butyric acid,
8.17 cm
2
/s for pentanoic acid and 7.84 cm
2
/s for hexanoic acid). The results of this
analysis are shown in Table 3-2 and Figure 3-13. The best fit is relatively insensitive to
changes in diffusivity for butyric and pentanoic acids, and insensitive to increases in
diffusivity in all cases. The best-fit permeability for hexanoic acid is, however, quite
sensitive to decreases in diffusivity. Note, however, that we are able to place a lower limit
on hexanoic acid permeability, and that this lower limit clearly distinguishes between the
permeabilities of pentanoic and hexanoic acids. Best-fit permeabilities for slower
permeating acids were insensitive to model diffusivity.
Table 3-2: Calculated permeabilities as diffusion coefficients changes in the MATLAB program
(numbers with asterisks are the literature diffusion coefficients and corresponding permeabilities)
Butyric acid
D (×10
6
cm/s) 5.18 6.18 7.18 8.18 9.18* 10.18 11.18
P (×10
2
cm
2
/s) 0.79 0.77 0.74 0.72 0.68* 0.66 0.66
Pentanoic acid
D (×10
6
cm/s) 5.17 6.17 7.17 8.17* 9.17 10.17 11.17
P (×10
2
cm
2
/s) 9.64 6.78 5.50 5.00* 4.57 4.28 4.07
Hexanoic acid
D (×10
6
cm/s) 5.84 6.84 7.84* 8.84 9.84 10.84
P (×10
2
cm
2
/s) 61.76 27.42 20.00*15.90 12.15 11.02
59
Figure 3-13: Calculated best-fit permeabilities at varying diffusivity
3.3.8 Reproducibility across multiple vesicles
The experiments determining acid permeability were performed in a single vesicle for
all acids, eliminating much of the possible experimental variability. To test the
reproducibility of this method across different vesicles, the permeability of acetic acid
was measured in 10 GUVs with varying diameters. These diameters were uniformly
distributed in the range from 18.1 to 31.3 μm. Each permeation process was observed
twice. The standard deviation of the measured permeability over these experiments was
0.015 × 10
-2
cm/s.
3.3.9 The effect of liquid ordered-liquid disordered (l
o
-l
d
) phase
separation on the membrane permeability
Lipid compositions similar to the one used here are known to exhibit liquid ordered-
liquid disordered (l
o
-l
d
)
phase separation, with a typical transition temperature at 29
o
C
(Veatch & Keller 2003). While the results described above were obtained with a vesicle
60
showing no apparent phase separation, we also repeated the experiment at temperatures
spanning this miscibility transition temperature to probe whether potential unobservable
phase separation has an effect on weak acid transport (Figure 3-14). Permeation of acetic
acid was observed in a GUV at 27 and 32
o
C. The permeabilities at 27 and 32
o
C are
0.073 × 10
-2
cm/s and 0.078 × 10
-2
cm/s respectively (Figure 3-15). The difference (about
6% faster at the higher temperature) was within the measurement error, indicating that
any effect introduced by phase separation is too small to resolve by this technique, and an
insignificant effect in terms of comparing permeabilities across acid species.
Figure 3-14: GUVs labeled by Texas-Red-modified DPPE excited at 561 nm showing the lipid bilayer.
(a) without phase separtion. (b) with phase separation. Scale bars are 10 μm.
Figure 3-15: Solution pH change inside and outside the GUV with time for acetic acid at 27
o
C (left),
and 32
o
C (right).
61
3.3.10 Controlling for membrane lipid composition
We also considered the effect that the inclusion of cholesterol had on membrane
permeability. It has been reported that lipid membranes with cholesterol have
permeabilities 5-10 times smaller than cholesterol-free membranes (Finkelst.A & Cass
1967; Kroes & Ostwald 1971; Grunze & Deuticke 1974; Yeagle et al. 1977). In this work,
we focus on cholesterol-containing membranes because slower permeabilities allow for
more precise permeability measurements and because cholesterol-containing membranes
more closely resemble membranes of biomedical interest.
To examine how our technique captures the difference between cholesterol-containing
and cholesterol-free membranes, we repeated a set of our experiments in a cholesterol
free-GUV composed of DPPC, DOPC and biotin-DPPE. The permeation processes for
formic, acetic, and propionic acid were studied (Figure 3-16). The permeabilities for
these acids were measured as 0.37 × 10
-2
cm/s, 0.43 × 10
-2
cm/s, and 1.0 × 10
-2
cm/s. The
permeabilities are about 5-10 times larger than in a cholesterol-containing membrane. As
with cholesterol-containing membranes, acid permeability increases as alkyl chain length
increases.
Figure 3-16. Solution pH change inside and outside a cholesterol-free GUV with time for three
carboxylic acids. The solid inside line and the dotted outside line represent the pH change inside and
outside GUV. The dashed fit lines are finite difference modeling fitting results. (a) formic acid, (b)
acetic acid, (c) propionic acid.
62
3.3.11 The effect of GUV binding on membrane tension and
permeability
Since the GUVs used in this work were immobilized by binding to the bottom of a
microfluidic channel, we considered whether the immobilization process could alter
membrane tension sufficiently to modulate transport properties.
According to Bernard (Bernard et al. 2000) the membrane tension is
1cos
W
3-8
where Σ is the membrane tension, W is the adhesion energy which is evaluated to be 10
-7
N/m (Bernard et al. 2000), and θ is the contact angle.
The membrane line tension is
2
1
2
3-9
where τ is the membrane line tension caused by the attachment of the GUV membrane to
the supporting surface, and λ is the angular correlation length which is estimated as 10
-7
m.
In our case, the contact angle θ can be estimated from Figure 3-17 as 30
o
. So the
membrane tension Σ is 7.5 × 10
-7
N/m, and the line tension τ is 1.0 × 10
-14
N. The
membrane tension of a free-floating GUV is around 1.0 × 10
-7
N/m (Baumgart et al.
2003). The tension required to rupture a membrane is around 1~25 × 10
-3
N/m (Evans et
al. 2003).
63
Figure 3-17: left is 3-D image of an immobilized GUV. Right is GUV profile from top, left and front.
To demonstrate that the effect of attachment tension on membrane transport was
minimal, we repeated the acetic acid transport experiment using GUVs with lower
membrane biotin-DPPE concentrations. The ratio of biotin-DPPE in these membranes
was only 5 wt%, in contrast to the 10 wt% biotin-DPPE membranes described previously
in this chapter. For this experiment, we measured a permeability of 0.067 × 10
-2
cm/s.
3.3.12 Simulations to rule out potential convection-related artifacts
To learn how the convective flow pattern in the microfluidic channel might alter the
permeation process we are observing, we built a finite element model of our system in
COMSOL Multiphysics (COMSOL AB, Stockholm, Sweden).
The geometry was based on that of the experiment. A GUV with a diameter of 25 μm
was in a rectangular channel with length of 1 mm, width of 200 μm, and height of 100
μm. The flow rate in the channel was 1 mm/s (Figure 3-18). To simplify the problem, the
concentration of permeant in the flow stream was 1 mol/m
3
and we did not consider acid-
base equilibrium.
64
To look at the issue of limited convection around vesicles attached to the channel
surface, we simulated the GUV either attached to the bottom or fixed at center of the
channel. To look at the effect of flow, we studied permeation both in the presence (Figure
3-19) and absence of a flow stream.
We looked at both fast and slow permeabilities, setting the nominal permeability of the
membrane to either 10 μm/s or 0.1 μm/s.
Figure 3-18: Geometry of the COMSOL simulation
65
Figure 3-19: Concentration profile in the bulk solution and GUV with flow in the channel. The GUV
was attached to the bottom of the channel. The concentrations shown by the color bar on the right
are relative to a bulk concentration of 1. Flow is from left to right. This simulation snapshot is at a
flow rate of 1 mm/s and a permeability of 0.1 μm/s, 100 s after the start of the simulation.
We analyzed the time-dependent change of concentration inside the GUV in the
context of a simple permeability model:
6
() 1
P
t
d
io
ct c e
3-10
where c
i
is the average concentration inside the vesicle, c
o
is the concentration outside, P
is permeability, d is GUV diameter, and t is time (Figure 3-20). The manner in which
measured permeability changes with flow conditions is summarized in Table 3-3.
66
Figure 3-20: The concentration change in the center of GUV under three different conditions. The
maximum concentrations were normalized to 1. The left figure shows a GUV membrane with
nominal permeability of 0.1 μm/s, and the right figure is GUV membrane with nominal permeability
of 10 μm/s.
Table 3-3: Best-fit membrane permeability under three different conditions.
Nominal
Permeability ( μm/s)
flow, bottom flow, suspended no flow, suspended
0.1 0.1021 0.1026 0.1005
10 8.5826 8.8742 8.9233
As flow conditions and GUV locations change, measured permeability changes by no
more than 4%. Differences between nominal permeability and permeability measured by
fitting Equation 3-10 in the no-flow condition are due to nonuniform concentration inside
the vesicle which Equation 3-10 does not account for.
This 3D finite element model does demonstrate that the presence of convective flow
and the location of the vesicle in the channel have little effect on the transport process.
The finite difference model that we ultimately used to measure permeability captures
better the relevant details of weak acid transport by basing the outer concentration
boundary condition on measured concentrations and explicitly accounting for acid-base
equilibrium at each point. Statistical analysis of results is also much simpler for the 1D,
which only has a single free parameter.
67
3.3.13 Comparison to Overton’s rule
Permeabilities from various carboxylic acid permeation studies including this one are
listed in Table 3-1. From acetic acid to butyric acid the permeabilities are in the same
range as other results. For pentanoic acid and hexanoic acid, the permeabilities are higher
than most other studies. Permeabilities increase with acyl chain length of the acid
molecules: an agreement with Overton’s rule.
The octanol/water and hexadecane/water partition coefficients of these six acids are
listed in Table 3-4. This table also reports theoretical permeabilities P as calculated
according to partition-diffusion theory: P=KD/l, where D is the diffusivity of the
molecule in the membrane, K is the oil/water partition coefficient, and l is the membrane
thickness. That the measured permeabilities are consistent with the change in oil/water
partition coefficients demonstrates that Overton’s rule applies for this system. Figure 3-
21 shows trends in permeability for the series of acids studied here in terms of both acyl
chain length and partition coefficient.
Figure 3-21. Trends in permeabilities of a homologous series of carboxylic acids. (a) P vs. acyl chain
length. (b) P vs. octanol/water, hexdecane/water partition coefficient, K (log
10
scale).
68
Table 3-4: Comparison of Overton’s rule to experimental results, normalized to formic acid
Ratio
K
oct/water
K
hex/water
(10
-4
)
D (10
-5
cm
2
/s) pKa P=K
oct
D/l P=K
hex
D/l P
exp
Formic
acid
0.29
a
1.1
b
1.516
d
3.75
e
1 1 1
Acetic
acid
0.49
a
5.3
b
1.271
d
4.76
f
1.4 4.0 1.7
Propionic
acid
1.8
a
23
b
1.009
d
4.87
g
4.1 14.0 5.3
Butyric
acid
6.2
a
87
b
0.918
d
4.83
f
12.9 47.9 20.0
Pentanoic
acid
18.1
a
490
c
0.817
d
4.83
f
33.6 240.1 222.2
Hexanoic
acid
76
b
1400
b
0.784
d
4.85
f
135.5 658.2 638.9
a
from reference (Wolosin & Ginsburg 1975)
b
from reference (Walter & Gutknecht 1986)
c
from reference (Potts & Guy 1995)
d
from reference (Bidstrup & Geankoplis 1963)
e
from reference (Walter et al. 1982)
f
from reference (Grime et al. 2008)
g
from reference (Saracino et al. 2003)
3.4 Conclusions
Confocal microscopy was used to image the transport of carboxylic acids with
different lengths of carbon chains into a single GUV. By observing the change in
intensity from a pH-sensitive fluorophore encapsulated inside the GUV, it was possible to
directly observe the transport process. This technique combines rapid buffer exchange in
a microfluidic device with high-speed confocal microscopy to accurately observe rapid
transmembrane transport processes. All experiments were performed in a single GUV,
eliminating any experimental variation caused by vesicle polydispersity or lack of
uniformity in the membrane formation protocol.
69
While even a glance at the data reveals a clear monotonic trend relating acid length to
permeability, a finite difference model can be fitted to the experimental data to obtain
precise permeability values. The clear adherence to Overton’s rule observed here
contrasts other recent results. This technique promises to be useful in understanding with
greater detail how the molecular properties of drug-like molecules determine their
transport behavior into cells.
70
Chapter 4: Deformation and poration of lipid bilayer
membranes by cationic nanoparticles
(This work has been submitted for publication to Soft Matter)
4.1 Introduction
As nanotechnology moves from the research lab into consumer, biomedical, and
industrial applications, there is a need to understand the toxicology and environmental
health impacts of synthetic nanomaterials (Fischer & Chan 2007; Lewinski et al. 2008;
Nel et al. 2009; Fadeel & Garcia-Bennett 2010). This need is motivated in large part by
the long history of research on environmental nanoparticles such as ultrafine soot. These
environmental nanoparticles have been found to enter the bloodstream following
inhalation leading to adverse effects on cardiovascular and pulmonary systems
(Oberdorster 2001; Nemmar et al. 2002; Oberdorster et al. 2002; Nel 2005; Sun et al.
2005; Chan et al. 2011). Given the unique physicochemical properties of nanomaterials,
it is to be expected that particles engineered for various applications might share these
biological behaviors. In fact, studies of engineered nanoparticles have shown biologically
harmful effects, largely based on investigations of cytotoxicity in cell culture. Cytotoxic
effects have been observed for carbonaceous nanomaterials including C
60
(Sayes et al.
2005; Rouse et al. 2006) and carbon nanotubes (Manna et al. 2005; Bottini et al. 2006;
Magrez et al. 2006; Tian et al. 2006; Wick et al. 2007); for gold (Tkachenko et al. 2004;
Shukla et al. 2005; Pernodet et al. 2006) and silver (AshaRani et al. 2009) nanoparticles;
71
and for CdSe quantum dots (Duan & Nie 2007; Ryman-Rasmussen et al. 2007; Zhang &
Yang 2011). These issues are becoming especially urgent as biomedical applications of
nanoparticles are emerging: research has suggested that nanoparticles have applications
ranging from drug and gene delivery (Bielinska et al. 2000; Popielarski et al. 2005; Rosi
et al. 2006; Giljohann et al. 2010) to biomedical imaging. (Weissleder 2006; Dubavik et
al. 2009; Sanson et al. 2011) A complete appreciation of the relationship between
nanoparticle properties and health effects must ultimately be based on a mechanistic
understanding of how nanomaterials interact with biological cells, tissues, and organs.
There is strong evidence that the biological effects of nanomaterials are closely related
to their surface properties, and particularly to how nanoparticles interact with, permeate,
and disrupt cell plasma membranes. A major mode of nanoparticle cytotoxicity may
involve the ability of nanoparticles to compromise the barrier properties of
biomembranes. It has long been known, for instance, that nanoparticles with positive
surface charge interact strongly with cell membranes, leading to internalization and
making them potentially potent drug delivery vehicles (Verma & Stellacci 2010; Yacobi
et al. 2010). Electrophysiological measurements show that these cationic nanoparticles
can radically increase the conductivity of live cell membranes, suggesting that pore
formation accompanies nanoparticle adsorption (Chen et al. 2009). These membrane-
permeating interactions can also lead to acute cytotoxicity (Fischer et al. 2003; Chen et
al. 2009). In planar lipid bilayer models, cationic nanoparticles synthesized from a wide
variety of materials are capable of inducing pore formation in the membrane (Hong et al.
2006; Leroueil et al. 2007; Leroueil et al. 2008; Roiter et al. 2008). Simulation studies
show that gold nanoparticles can directly penetrate lipid bilayers given a sufficiently high
72
cationic surface charge density (Lin et al. 2010). Polymeric nanoparticles are able to
permeate through intact layers of rat alveolar epithelium by passively crossing the
bilayer; this process is more pronounced for cationic particles (Yacobi et al. 2010).
The ability of nanoparticles to compromise membrane barrier properties is certainly
not limited to those particles with positive surface charges. For instance, dePlanque and
coworkers recently used electrophysiological measurements to show that nanoparticles
with a variety of surface chemistries can compromise lipid bilayer membranes (de
Planque et al. 2011). Granick and coworkers have shown that nanoparticles with both
negative and positive surface charges can bind to lipid membranes, inducing changes in
the membrane phase structure and leading to morphological deformations (Wang et al.
2008; Yu & Granick 2009). In cell culture-based investigations of nanoparticle toxicity,
membrane permeabilization is indicated by leakage of lactate dehydrogenase (LDH) from
the cells. This has been observed to occur with a wide variety of nanoparticles
(Tkachenko et al. 2004; Hussain et al. 2005; Muller et al. 2005; Sayes et al. 2005).
To better characterize the mechanism of membrane permeabilization induced by
nanoparticles, we used confocal microscopy to image the interaction of 20 nm-diameter
cationic polystyrene nanoparticles (PNPs) and GUVs. GUVs are synthetic biomembranes
that can be fabricated from a wide variety of lipid species to form spherical, single-
bilayer structures with diameters in the range of 5-100 µm (Angelova 1992; Moscho et
al. 1996; Rodriguez et al. 2005; Hu et al. 2011; Richmond et al. 2011). GUVs are ideal
model systems for investigating membrane shape deformation and transmembrane
transport processes (Yanagisawa et al. 2008; Li et al. 2010; Li et al. 2011). PNP
adsorption to the GUV surface was optically tracked in samples of GUVs co-incubated
73
with fluorescent nanoparticles. A high-molecular-weight polymer dye was encapsulated
in the GUV interior to track bilayer permeability due to the formation of nanoscale pores.
We found the cationic PNPs attached strongly to the GUV membrane, inducing
nanoscale pores, and, at high levels of adhesion, deforming the membrane into dendritic
protrusions.
4.2 Materials and methods
4.2.1 Materials
Dipalmitoylphosphatidylcholine (DPPC), dioleoylphosphatidylcholine (DOPC),
dioleoylphosphoethanolamine (DOPE), dioleoylphosphatidylserine (DOPS),
dioleoylphosphatidylglycerol (DOPG), and cholesterol were obtained from Avanti Polar
Lipids (Alabaster, AL). 1,1'-dioctadecyl-3,3,3',3'-tetramethylindodicarbocyanine
perchlorate (DiD) was obtained from Life Technologies (Grand Island, NY). Indium-tin
oxide (ITO)-coated glass was obtained from Delta Technologies (Stillwater, MN). PDMS
was obtained from Dow chemical corporation (Midland, MI). NoChromix was obtained
from Godax Laboratories (Cabin John, MD). All other chemicals were used as provided
by Sigma-Aldrich (St. Louis, MO).
4.2.2 Nanoparticles
Fluorescently labeled polystyrene nanoparticles (PNPs, Life Technologies, Grand
Island, NY) were used in the research. They were amidine-modified (i.e., positively
charged; diameters of 20 nm with 80.2 μEq of amide per g of polymer, and diameters of
120 nm with 39.7 μEq/g) and carboxylate-modified (i.e., negatively charged; diameters
74
of 20 nm with 304.3 μEq of carboxylate per g) nanoparticles. Here Eq represent
equivalent, and 1 equivalent is equal to 1 mole ion with +1 or -1 charge. The
concentration of all stock solutions was 9×10
14
# PNP/mL. Excitation /emission
wavelengths of amidine-modified PNPs are 490/515 nm, and of carboxylate-modified
PNPs are 580/605nm.
4.2.3 GUV preparation and observation
GUVs were made the same as described in part 2.2.2. For GUVs used in most
measurements the lipid composition was a 1:1:1 (molar ratio) mixture of DPPC, DOPC,
and cholesterol. Cholesterol-free membranes consisted of a 1:1 (molar ratio) mixture of
DPPC and DOPC. For the DOPE, DOPS, and DOPG membranes, the lipid compositions
were pure PE, PS, or PG lipids. All GUV membranes were doped with 1% DiD for
visualization. 1 mg/mL rhodamine-dextran (rh-dex, 155 kDa), or 1 mg/mL fluorescein-
dextran (fl-dex, 250 kDa, 500 kDa, and 2000 kDa), was added to 4 mM HEPES at pH 7.0
and 200 mM sucrose solution to detect the leakage of GUV membrane.
After 2 h, the GUV suspension was removed from the cell and deposited in a chamber
constructed from PDMS bonded to a #1 cover slip. There, GUVs were observed by
SDCM. The PDMS chamber was made by punching a hole with a diameter of 0.5 mm
and depth of 0.5 mm in the center of a cured PDMS slab. The PDMS and the cover slip
were oxidized by corona treatment (BD-20AC, Elecro-Technic Products, Chicago, IL) to
bond them irreversibly (Gregoria.G et al. 1971).
To avoid the rupture of GUVs on the glass surface, a lipid bilayer was first formed on
the glass surface by incubating the prepared GUVs suspension in the chamber on bare,
75
oxidized glass for 30 min. Any remaining unruptured GUVs were then flushed away with
a buffer solution containing 4 mM HEPES at pH 7.0 and 200 mM glucose. The chamber
was then filled with 80 µL of this solution and 3 μL of the as-prepared GUV suspension
was added. After these GUVs had settled to the bottom, the chamber was gently washed
by exchanging the glucose buffer 5 times.
SDCM was performed using a Yokogawa (Tokyo, Japan) CSUX confocal head on a
Nikon (Tokyo, Japan) TI-E inverted microscope. Illumination was provided by 50 mW
solid-state lasers at 491, 561, or 640 nm. PNPs and fl-dex were excited at 491 nm, and
emission was captured with a bandpass filter centered at 525 nm. Rh-dex 155 kDa was
excited at 561 nm, and emission was captured with a bandpass filter centered at 595 nm.
DiD was excited at 640 nm, and emission was captured with a bandpass filter centered at
660nm. Images were captured at 1 min intervals in 3 different color channels. Constant
illumination intensity, camera amplification, and exposure time were used for all images.
4.2.4 PNP attachment experiments
The PNP suspension as provided by the manufacturer was first sonicated for 30 min. 2
μL of this suspension was added to the chamber containing 80 μL glucose buffer with
GUVs. The contents of the chamber were stirred very gently until the attachment
reached equilibrium. Then another 2 μL of PNP suspension was added to the chamber.
This process was repeated until the GUV membrane ruptured. An initial image was
captured before the addition of any PNPs to the GUV suspension. Subsequent images
were taken at regular intervals thereafter. Images were analyzed using MATLAB.
Membrane fluorescence intensity was measured at 360 spots evenly distributed around
76
the GUV membrane and is reported as a mean. GUV interior intensity was measured near
the center of the GUV. Each experiment was repeated three times.
4.3 Results and discussion
4.3.1 Adhesion of PNP to lipid membrane
GUVs were fabricated according to the standard electroformation protocol (see
Supporting Information) (Angelova et al. 1992). In initial experiments, cationic PNPs
(Life Technologies, Grand Island, NY) were gradually added to a suspension of GUVs
fabricated from 1:1:1 (molar) DPPC:DOPC:cholesterol. A typical GUV over the time
course of such an experiment is shown in Figure 4-1. Figure 4-1(a) shows the GUV, with
a red dye in the lipid bilayer, prior to the addition of any PNPs. 2 μl of a PNP suspension
(9×10
14
# PNP/mL) was added to a 80 μl GUV solution; the mixture was stirred very
gently until the adhesion reached equilibrium (judged by constant nanoparticle
fluorescence on the membrane, around 20 min). This process was repeated until GUV
membrane ruptured. As the PNP concentration increased, nanoparticle adhesion to the
GUV membrane was apparent as green fluorescence associated with the membrane
(Figure 4-1(b)). At high PNP concentrations, dendritic protrusions began to extend from
the membrane (Figure 4-1(c) and (d)). Note that these protrusions include both the green-
labeled nanoparticles and the red-labeled lipid bilayer (Figure 4-1(e)). As these
protrusions formed, the GUV started to shrink and the encapsulated rhodamine-dextran
(rh-dex, 155 kDa molecular weight) leaked out (indicated by a decrease in the orange
77
fluorescence in the GUV interior). Eventually, at high PNP concentration, the membrane
collapsed completely.
Figure 4-1: Confocal microscopy images of PNP adhesion to a GUV. (a) 0 min, no PNPs, (b) 50 min,
1.35 × 10
14
# PNP/mL equilibrated for 20 min, (c) 100 min, 1.8 × 10
14
# PNP/mL equilibrated for 20
min, (d) 140 min, 2.25 × 10
14
# PNP/mL. (e) Detailed structure of protrusions from the GUV surface
induced by PNP adhesion to the membrane. Main image shows red-labeled lipids; inset shows green-
labeled PNPs. Scale bars are 10 μm for a-d and 5 μm for e (including the inset).
To determine the critical PNP concentration necessary to result in morphological
deformation of GUV membranes, we performed a set of experiments in which
suspensions of GUVs were incubated with various concentrations of PNPs and allowed to
equilibrate for 3 hours. 50 to 100 GUVs in each sample were then observed and the
number demonstrating morphological deformation by formation of protrusions was
counted. Figure 4-2 shows that as the PNP concentration increased, more GUVs were
deformed. A concentration of 1.8 × 10
14
# PNP/ml, seems to represent a concentration
above which nearly all the GUVs were deformed.
78
Figure 4-2: Fraction of GUVs deformed at various PNP concentrations after a 3 h incubation. Error
bars are ± one standard deviation over three trials at each concentration.
4.3.2 Time course of PNPs adhesion and membrane deformation
We studied the time course of nanoparticle adhesion and membrane deformation by
incubating the GUV suspension with a fixed concentration of nanoparticles above this
critical concentration. The time course of changes in a typical GUV incubated with a 2.25
× 10
14
# PNP/ml PNP suspension is shown in Figure 4-3. The top panel shows
nanoparticle adhesion (solid) and GUV diameter change (dotted). The bottom panel
shows the decrease in fluorescence intensity of encapsulated rh-dex (solid) along with the
results of an experiment to control for photobleaching (dashed). Note that dextran
leakage (indicating pore formation) commences almost simultaneously with the initial
changes in GUV diameter, at relatively low levels of PNP adhesion (compare with Figure
4-1(b)). This indicates that membrane poration occurs much earlier than the formation of
any dendritic protrusions and can be induced by relatively small PNP concentrations on
the membrane.
79
Figure 4-3: The time course of nanoparticle binding as determined by PNP fluorescence intensity on
the membrane and changes to GUV diameter are shown on the top panel. Corresponding changes to
fluorescence intensity of encapsulated rh-dex are shown as the solid line in the bottom panel. The
dashed line in the bottom panel represents a separately run control in which the fluorescent intensity
of GUV-encapsulated rh-dex is monitored in the absence of PNPs to demonstrate that there is no
significant photobleaching.
4.3.3 Mechanism behind the PNPs/lipid membrane interaction
To better understand the mechanistic details of the observed nanoparticle/lipid bilayer
phenomena, we sought to identify the nature of the adhesive interaction. First, we ran a
set of experiments in which PNP adsorption to a GUV membrane was quantified
according to PNP fluorescence on the membrane at a range of solution ionic strengths.
Experiments were performed in buffer solution containing concentrations of 0, 5, or 33
mg/ml NaCl. As the salt concentration increased, PNP adsorption decreased (Figure 4-
4(a)). This is a strong indication that PNP attachment to the bilayer is an electrostatically
mediated interaction; as salt concentration increased, the electrostatic driving force for
adhesion is screened. Note that this electrostatic interaction occurs between cationic
particles and zwitterionic phosphatidylcholine lipids.
Various lipid bilayer compositions were also studied. Binding experiments were run on
membranes without cholesterol, which should have decreased fluidity (Vanblitterswijk et
80
al. 1987); on membranes where the phosphatidylcholine lipids were replaced with
dioleoylphosphatidylethanolamine (DOPE), replacing the bulky cationic choline group
with a more compact primary amine; and phosphatidylserine and phosphatidylglycerol
lipids (DOPS and DOPG), which have net negative, rather than net neutral, head groups.
In no case was the binding process significantly altered. These results suggest that the
key interaction is between the cationic nanoparticle and the phosphate group of the lipid,
as described by Wang and coworkers (Wang et al. 2008).
DPPC:DOPC:cholesterol GUVs were also incubated in suspensions of 20 nm anionic
PNPs, 120 nm cationic PNPs, and 25kDa branched polyethylenimine (PEI). In the
anionic PNP solution, the GUV membranes did not undergo any morphological changes.
The lack of accumulation of anionic PNPs on the membrane indicates that the interaction
between the negatively charged nanoparticles and phosphatidylcholine groups is weaker
than in the case of cationic particles. While the 120 nm cationic NPs adsorbed to the
membrane to an extent similar to the 20 nm particles described above, they resulted in
fewer and less prominent protrusions. PEI dendrimers, with a hydrodynamic diameter of
5 nm, attached to the GUV membrane and induced GUV shrinkage and leakage. Instead
of forming extended dendritic protrusions as in the case of 20 nm cationic nanoparticles,
PEI caused membrane budding and collapse, as has also been observed by Vanderlick
and coworkers (Beales et al. 2011). These results all suggest that particle size and charge
state are key determinants in the particle-membrane interaction and the capacity of
particular nanoparticles to induce membrane mechanical deformation.
81
Figure 4-4: Nanoparticle fluorescence intensity on a GUV membrane as a function of PNP
concentration for GUVs (a) in varying NaCl concentration (0 mM, 5 mM, and 33 mM) and (b) with
different lipid compositions (1:1 DPPC:DOPC, 1:1:1 DPPC:DOPC:cholesterol, pure DOPE, pure
DOPS, pure POPG). In both panels, ‘background’ indicates the PNP fluorescence intensity of the
image background away from the membrane at varying PNP concentration.
4.3.4 Leakage of high molecular weight dextran from GUV
Perhaps the most biologically relevant phenomenon we observed during the interaction
of GUV membranes with 20 nm cationic PNPs was leakage of the high molecular weight
dextran species from the vesicle interior (See Figure 4-3, lower panel). As noted above,
this leakage begins to occur at low levels of PNP binding to the membrane, before the
onset of any significant morphological deformation. The fact that the leaking species is of
82
a high molecular weight indicates that membrane permeabilization in this case occurs
through pore formation. The fact that it occurs at low levels of PNP binding indicates that
it is a process with potential physiological relevance that can take place even at low
solution concentrations of nanoparticles. We set out to characterize the membrane pores
induced by PNPs by studying different molecular weights of encapsulated fluorescein-
dextran (fl-dex).
We investigated fl-dex molecular weights of 2000 kDa, 500 kDa and 250 kDa, with
hydrodynamic diameters of 54 nm, 28 nm, and 21 nm respectively (Venturoli & Rippe
2005). For each molecular weight of fl-dex, GUVs were prepared with the dextran
species encapsulated in the interior. Each GUV preparation was incubated with a
suspension of 2.25 × 10
14
# PNP/ml cationic 20 nm PNPs. As PNPs bound to and
deformed the membrane, the fluorescent intensity of the GUV interior, corresponding to
the encapsulated f-dex species, was recorded. Representative records are shown in Figure
4-5. Note that as GUV diameter decreases, GUV volume also decreases. This means that
fl-dex concentration will increase if the membrane remains impermeable to fl-dex. In
fact, this is what is observed in the case of 2000 kDa fl-dex (black squares, small images
(a) and (b) in Figure 4-5). This suggests that the pores formed in the GUV membrane are
too small to permit efflux of the 2000 kDa species. On the other hand, the 250 kDa
species leaked from the GUV in a manner similar to the 155 kDa rh-dex species shown in
Figure 4-3. For the 500 kDa fl-dex, the rate of efflux balanced the rate of vesicle
shrinkage to result in an approximately constant concentration. As polymer size
approaches pore size, the diffusion coefficient of the polymer in the pore will decrease,
which means the leakage of the polymer through the pore will become slower (Bohrer et
83
al. 1984; de Gennes 1999). Since dextran is a deformable polymer, it can pass through a
pore with a size 1/3 to 1/2 of its hydrodynamic diameter (Deen et al. 1981). From these
results, we can estimate a maximum pore diameter in the range of 18-27 nm. The ‘PNP
background’ trace in Figure 4-5 shows the fluorescence contribution from the
nanoparticles (determined in an experiment with a GUV containing no encapsulated
dextran), and indicates that the measured fl-dex concentrations are not distorted by the
presence of similarly labeled nanoparticles.
Figure 4-5: Time course of leakage of 2000 kDa, 500 kDa, and 250 kDa fl-dex from GUVs interacting
with PNPs. (a) and (b) are the initial and final images of a GUV containing 2000 kDa fl-dex. PNP
background represents the fluorescence contribution from the nanoparticles (determined in an
experiment with a GUV containing no encapsulated dextran). Scale bars are 10 μm.
To demonstrate that intensity changes in fl-dex experiments were caused by the
membrane leakage instead of photobleaching, the fluorescent intensity of GUV-
encapsulated fl-dex (250, 500, and 2000 kDa) was monitored in the absence of PNPs over
the experimental time frame, using the same illumination conditions and capture rate
used in the experiment. No significant photobleaching could be observed (Figure 4-6).
84
Figure 4-6: Fluorescent intensity change of GUV-encapsulated fl-dex (250 kDa, 500 kDa, 2000 kDa)
monitored in the absence of PNPs.
4.3.5 PNPs binding increased membrane steric pressure and surface
tension
Figure 4-7: Confocal microscope image of a phase-separated GUV during early stages of PNP
binding. The GUV undergoes a budding-like transformation consistent with reduced line tension at
the phase interface. Scale bar is 10 μm.
There have been several observations of protein binding processes to lipid membranes
resulting in the formation of tubular or dendritic protrusions or invaginations. For
instance, Römer and coworkers found that Shiga toxin B-subunit could alter local lipid
curvature to induce tubular invaginations, providing a potential viral entry route (Romer
85
et al. 2007). To investigate the mechanistic details of similar processes, Stachowiak and
coworkers have developed a system whereby nickel chelation-mediated protein binding
to a GUV membrane induces the formation of membrane protrusions similar to the ones
we see here (Stachowiak et al. 2010; Stachowiak et al. 2011; Stachowiak et al. 2012).
They have proposed a steric pressure mechanism whereby local protein crowding on the
membrane surface consumes any excess membrane area and applies a surface tension to
the membrane, stretching it into extended protrusions. It is likely that a similar
phenomenon is taking place in our experiments, with nanoparticle binding to the
membrane driven by nonspecific electrostatic interactions rather than His-tag chelation.
The formation of pores in the membrane is a likely result of the surface tension
imposed by steric pressure of nanoparticles packing onto the membrane surface. As
demonstrated by Brochard-Wyart and coworkers, surface tension imposed on a
membrane can lead to transient pores (Sandre et al. 1999). These pores are driven closed
by line tension at the pore edge; reduced line tension stabilizes membrane pores
(Karatekin et al. 2003). Figure 4-7 shows an example of a GUV in which liquid-
ordered/liquid-disordered phase separation could be observed during early stages of PNP
binding. This vesicle is undergoing a morphological transformation consistent with
reduced line tension, as described by Hutchison and coworkers (Hutchison et al. 2012).
This observation suggests that cationic nanoparticle binding may reduce pore line
tension, stabilizing transient pores and facilitating the leakage of GUV contents.
86
4.3.6 PNPs with different sizes and charges
In addition to the 20 nm cationic particles described in detail in the main text, GUVs
were also incubated with 20 nm anionic carboxylate-modified polystyrene PNPs, 120 nm
cationic amidine-modified polystyrene PNPs, and 25 kDa branched polyethylenimine
(PEI) solutions. The zeta potentials of these NPs were 71, -45, 67, and 56 mV
respectively for 20 nm cationic PNPs, 20 nm anionic PNPs, 120 nm cationic PNPs, and
PEI. Typical results are shown in Figure 4-8. For the anionic PNPs (orange fluorescence)
solution, the GUVs membranes (red fluorescence) did not display any morphological
changes (Figure 4-8(a)). There is in fact no significant accumulation of anionic NPs on
the GUV surface, indicating that any interaction of anionic PNPs with the
phosphatidylcholine group is weak. The 120 nm cationic NPs (green fluorescence)
adhered to the GUVs membrane (red fluorescence) as shown in Figure 4-8(b). There are
some structures protruding the membrane, but these are not as prominent or numerous as
in the case of 20 nm cationic PNPs. As PEI (no fluorescence) attached to the GUV
membrane (red fluorescence), the GUV started to shrink and the Rh-dex 155 kDa (dim
orange fluorescence in Figure 4-8(c)) leaked out of the GUV. Instead of forming
dendridic protrusions, PEI caused membrane budding and collapse.
87
Figure 4-8: Confocal images of GUVs interacting with various polymeric nanomaterials. (a) GUV
with 20 nm anionic NPs, (b) GUV membrane with 120 nm cationic NPs, (c) GUV membrane with
PEI. The scale bar is 10 μm in each image.
4.4 Conclusions
In this chapter, we showed that 20 nm polystyrene nanoparticles with cationic surfaces
can adhere strongly to zwitterionic lipid membranes. The interaction is nonspecific,
driven by an electrostatic interaction between the lipid phosphate group and the
nanoparticle surface. Nanoparticle binding to the membrane is accompanied by the
permeabilization of the membrane to high-molecular-weight polymers, indicating that the
nanoparticles induce membrane pore formation. At high levels of nanoparticle-membrane
binding, the membrane is drawn into dendritic protrusions, indicating that the
nanoparticles may be exerting a force on the membrane via a steric crowding mechanism
and increasing membrane surface tension, which leads to the formation of transient pores.
Since the mechanism of membrane-nanoparticle interaction is general, and pore
formation occurs at even low levels of binding, the pore formation observed here is
potentially a physiological relevant mode of interaction between nanoparticles and
biomembranes, and may help explain observed plasma membrane permeabilization in the
presence of broad classes of nanoparticles.
88
Chapter 5: Permeation of CO
2
through lipid membrane
Carbon dioxide is one of the most important compounds in nature. It plays a central
role in respiration, photosynthesis, and acid-base balance. In the cellular respiration
process, cells break down sugars, fats and amino acids with oxygen to generate energy,
producing carbon dioxide (Kaufman & Franz 1993). This process is essential to all plants,
animals, many fungi and some bacteria. In plants carbon dioxide is absorbed from
atmosphere by photosynthesis process. In animals carbon dioxide generated from body
tissues transport through blood and exhaled through the lungs. CO
2
is taken in blood in
three different ways. Most (about 70% to 80%) is converted to bicarbonate ions HCO
3-
by the enzyme carbonic anhydrase (CA) in the red blood cells. 5% - 10% is dissolved in
the plasma, and 5% - 10% is bound to hemoglobin as carbamino compounds
(Christiansen et al. 1914).
Because of its physiological importance, the permeation of CO
2
through cell
membranes has been studied a lot in different systems. Carbon dioxide is soluble in water
with 33.0 mM solubility at 25
o
C (Munjal & Stewart 1971). CO
2
exists in several
different chemical forms in water, CO
2
, H
2
CO
3
, HCO
3
-,
and CO
3
2-
. Carbon dioxide
reversibly converts to H
2
CO
3
(carbonic acid) in water. The hydration equilibrium
constant K
h
of carbonic acid is [H
2
CO
3
]/[CO
2
] = 1.70 × 10
-3
(Kern 1960), so most
carbon dioxide remains as CO
2
molecules not affecting the water pH, instead of
converting into carbonic acid. Carbonic acid has two acid dissociation constants, pK
a1
=
6.36, and pK
a2
= 10.33 (Butler 1982). The whole reaction equation of CO
2
in water is
shown below:
89
a1 a2 h
pK pK K
+- 2- +
22 2 3 3 3
CO + HO HCO H + HCO CO + H
5-1
Among these species, HCO
3
-
and CO
3
2-
can not easily permeate through most cell
membranes. But they often dominate the total CO
2
diffusion in the two sides of the cell
membranes (Gutknecht et al. 1977). So the transport of CO
2
across a cell membrane
include not only the permeation of dissolved CO
2
gas across the membrane, but also
reactions among several aqueous chemical forms of CO
2
as shown in Figure 5-1.
Figure 5-1: Diffusion of CO
2
across a lipid bilayer includes several steps (from left to right). First the
protonated and deprotonated forms of all participating molecules diffuse from the bulk across the cis
unstirred water layer (USL) to the membrane surface. Here HCO
3
-
and CO
3
2-
get protonated to form
CO
2
. The buffer AH provides an additional proton source. Following Overton’s Rule uncharged CO
2
permeates the membrane and gets deprotonated on the other side. The buffering molecule A
-
at the
transmembrane surface now serves as proton sink. Finally the protonated and deprotonated forms of
all species diffuse across the trans USL into the bulk. Copied from reference (Missner et al. 2008).
To exactly test the permeability of CO
2
through cell membrane, the permeation of
carbonic acid need to be eliminated. The dehydration of carbonic acid to CO
2
is a
relatively slow process (t
1/2
≈ 14s) (Gutknecht et al. 1977). The carbonic anhydrases (CA)
belongs to an enzyme family widely existing in animals and plants that rapidly catalyze
the interconversion of carbonic acid to carbon dioxide and water (Badger & Price 1994).
90
One of the enzyme functions is to interconvert CO
2
and bicarbonate to maintain acid-base
balance in blood and tissues, and to help transport CO
2
out of tissues. The reaction rate is
one of the fastest among all the enzymes between 10
4
– 10
6
reactions per second
(Lindskog 1997). CA removes a water molecule from carbonic acid (equation 5-2).
23 2 2
HCO CO + HO
Carbonic anhydrase
5-2
CA has been used a lot by researchers in the studying permeation of CO
2
through lipid
membrane. The enzyme activity increases when solution pH increases between 6.0 to 8.5
(Figure 5-2). If CO
2
is the primary product in solution and the solution pH is low (like pH
5.0), CA doesn’t have an obvious effect because at that pH CO
2
does not form
bicarbonate to an appreciable extent. If pH > 7.0, CA will help accelerate the rate of CO
2
conversion to H
2
CO
3
, but the effect is limited. When H
2
CO
3
or HCO
3
-
is the primary
product, CA will accelerate the production of CO
2
if solution pH is near neutral. At pH
above 8.0, the formation of CO
2
from bicarbonate decreases until it becomes negligible.
CA thereafter is not very effective. As pH approaches 6.0 to 5.0, the rate of the
uncatalyzed decomposition of H
2
CO
3
is very rapid. So the effect of CA is also not
obvious.
Figure 5-2: Effect of pH on stability of purified carbonic anhydrase. The pH stability of the enzyme
was determined by incubating the enzyme in different buffers for 24 h at room temperature. The
91
residual enzyme activity was measured according to the standard enzyme assay. 100% CA activity
was equivalent to 11.00 U/mg protein. Copied from reference (Sharma et al. 2009).
Although the CO
2
permeability has been estimated for a variety of membrane systems,
the molecular mechanisms of CO
2
transport are not well understood. The permeation of
CO
2
through cell membranes has been studied in epithelia, single cells, lipid bilayers,
soap films and monolayers. According to Overton’s rule, a molecule’s membrane
permeability is proportional to its membrane solubility. Simon and Gutknecht tested the
solubility of CO
2
in organic solvent and lipid bilayer membranes (liposome) (Simon &
Gutknecht 1980). The partition coefficient of CO
2
into octanol, hexadecane, and olive oil
is 1.3, 1.5 and 1.7 (ml CO
2
/ml lipid)/(ml CO
2
/ml saline) at 25
o
C. The partition
coefficient of CO
2
into liposomes of egg lecithin is smaller at 0.95, and the value
decreases by 25% upon addition of an equimolar amount of cholesterol. Endeward and
Gros tested the permeability of CO
2
through epithelial membranes of guinea-pig and
human red cell membrane (Endeward & Gros 2005; Endeward et al. 2006). They found
the permeability for epithelial membranes is 0.77 - 1.5 × 10
-3
cm/s, more than 100 times
lower than human red cell membrane, which is 0.06 - 0.15 cm/s. For human red cell
membrane, the membrane with channel protein aquaporin 1 (AQP1) has permeability 2
times larger than membrane without the protein. So they think that the membrane protein
AQP1 serves as a major pathway for CO
2
transport across the human membrane. Missner
and coworkers found the permeability of CO
2
is 20 times larger around 3.2 cm/s based on
planar lipid membranes and Madin-Darby canine kidney (MDCK) cells (Figure 5-3). So
they proposed that the uptake of CO
2
into cells is mainly limited by the diffusion in the
unstirred water layer (USL) near the membrane.
92
Figure 5-3: CO
2
concentration and pH shifts adjacent to the membrane at bulk pH 7.5 as CO
2
permeate through planar lipid bilayer. Copied from reference (Missner et al. 2008).
In an attempt to clarify the discrepancies in reported values of membrane permeability,
in our next research step, we will use the same measurement technique based on confocal
microscopy and immobilized GUVs in a microfluid channel to detect the permeability of
CO
2
through lipid membranes. The pH-sensitive dye fluorescein-dextran (40 kDa) will be
encapsulated in the GUV to visualize the transport of CO
2
. CA will be also added to
buffer solution to ensure CO
2
is the majority species.
93
Chapter 6: Conclusions
In this study, small molecules’ permeation through lipid membrane was studied. Short
chain PEG-NBD, carboxylic acids were taken as model molecules. Interaction between
cationic PNPs and lipid membrane was also studied to show how this kind of
nanoparticles were able to decrease the membrane barrier function and increase the
membrane permeability.
We have developed a system that combines high-speed microscopy of model lipid
membranes with image analysis and computer modeling to resolve important questions
about the mechanism of transport of molecules across lipid bilayers. SDCM of GUVs
allows for fluorescent molecules to be tracked as they permeate the lipid bilayer
membrane and enter the GUV interior, and further allows us to establish the complete
time course of the evolution of the concentration profile. Precise membrane permeability
can be determined easily from the transient concentration profile data by fitting the data
to a mathematical permeation model.
A series of molecules of increasing hydrophiliciy was constructed by covalently
modifying the dye NBD with PEG having 4, 8, or 12 repeating units. Transport of
modified NBD molecules was observed by tracking NBD fluorescence as the molecules
passed through the GUV membrane. An analytical passive transport model was devised,
image intensity data was regressed to the model, and permeability was calculated for each
species. Membrane permeability data show that longer chain PEG molecules, which have
a smaller octanol-water partition coefficient, permeate more slowly. This trend is
94
consistent with Overton’s rule, though it does not seem to fit a simple partition-diffusion
model of membrane transport.
We use confocal microscopy to image the transport of carboxylic acids with different
lengths of carbon chains into GUVs. Fluorescein-dextran (40kDa) was encapsulated in
GUVs to trace the transport of acid. GUVs were immobilized on the surface of a PDMS
microchannel by biotin-avidin binding. This PDMS channel allows the changing of
buffer solution to acid solution quickly and uniformly, avoiding nonuniform solution
mixing problems which would otherwise introduce artifacts to membrane permeability
measurements. Confocal microscopy allows for the interior of GUVs to be trivially
distinguished from their exterior. The results showed that as the chain lengths of acids
increase, their permeation through lipid membrane become faster. The permeabilities are
consistent with literature octanol-water partition coefficients and demonstrate that
Overton’s rule applies for this class of molecules.
Synthetic lipid bilayers in a GUV format were used to study potentially harmful
interactions between nanoparticles and biomembranes. Confocal fluorescence
microscopy shows that 20 nm polystyrene nanoparticles with cationic surfaces adhere
strongly to these lipid bilayer membranes. This adhesion is sensitive to the ionic strength
of the surrounding medium and is independent of the lipid composition of the membrane,
indicating that it is driven by nonspecific electrostatic interactions. Nanoparticles bound
to the GUV membrane form extended protrusions that incorporate the membrane lipids.
As the membrane material is pulled into these protrusions, the diameter of the GUV
shrinks. This process is accompanied by the formation of transient pores in the membrane,
95
as indicated by the leakage of high-molecular weight polymers from the GUV interior.
The membrane pore diameter was estimated as 18-27 nm. These results suggest that
nanoparticle adhesion imposes surface tension on biomembranes via a steric crowding
mechanism, leading to poration. The phenomenon is potentially a physiological relevant
mode of interaction between nanoparticles and biomembranes, and may help explain
observed plasma membrane permeabilization in the presence of broad classes of
nanoparticles.
Carbon dioxide is one of the most important compounds in nature. But the molecular
mechanisms of CO
2
transport are not well understood. Reported membrane
permeabillities to CO2 span two orders of magnitude. In an attempt to clarify the
discrepancies in reported values of membrane permeability, we will use the same
measurement technique based on confocal microscopy and immobilized GUVs in a
microfluid channel to detect the permeability of CO
2
through lipid membranes.
96
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Abstract (if available)
Abstract
The ability of a molecule to pass through the plasma membrane without the aid of any active cellular mechanisms is central to that molecule’s pharmaceutical characteristics. Passive transport has been understood in the context of Overton’s rule, which states that more lipophilic molecules cross membrane lipid bilayers more readily. Standard techniques including planar lipid membrane, liposome, and cell monolayer to observe passive transport processes are flawed and lack reproducibility. ❧ This research describes assays based on spinning-disk confocal microscopy (SDCM) of giant unilamellar vesicles (GUVs) that allow for fluorescent molecules to be tracked as they permeate the lipid membrane. This approach allows for the temporal development of the concentration field to be directly observed. Precise membrane permeability can be determined from by fitting the data to a mathematical permeation model. ❧ A series of molecules of increasing hydrophilicity was constructed by conjugating 4-nitrobenzo-2-oxa-1,3-diazole (NBD) with poly(ethylene-glycol) (PEG). An analytical passive transport model was devised, image intensity data was regressed to the model, and permeability was calculated. The result shows that longer chain PEG molecules which are more hydrophilic permeate more slowly. This trend is consistent with Overton’s rule, though it does not seem to fit a simple partition-diffusion model of membrane transport. ❧ Low-molecular-weight carboxylic acids have crucial effects on cellular processes. We studied the transport of carboxylic acids with different carbon chains lengths into GUVs. Fluorescein-dextran was used to trace the transport of acid. GUVs were immobilized on the surface of a poly(dimethylsiloxane) (PDMS) microchannel which allows the changing of buffer solution quickly and uniformly. The results showed that the permeabilities are consistent with octanol-water partition coefficients and demonstrate that Overton’s rule applies for this class of molecules. ❧ Synthetic lipid bilayers were used to study potentially harmful interactions between nanoparticles and biomembranes. Twenty nm polystyrene nanoparticles with cationic surfaces adhere strongly to lipid membranes. Adhesion is driven by nonspecific electrostatic interactions between the lipid phosphate groups and the nanoparticles. Nanoparticle adhesion leads to membrane morphological deformation and the formation of transient nanoscale pores. These results suggest that nanoparticle adhesion imposes surface tension on biomembranes via a steric crowding mechanism, leading to poration.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Li, Su
(author)
Core Title
Imaging molecular transport across and nanomaterial interaction with lipid membranes
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Chemical Engineering
Publication Date
01/25/2013
Defense Date
12/12/2012
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
cationic nanoparticles,confocal microscopy,giant unilamellar vesicle,membrane deformation,OAI-PMH Harvest,Overton’s rule,passive membrane transport
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Malmstadt, Noah (
committee chair
), Kim, Kwang-Jin (
committee member
), Wang, Pin (
committee member
)
Creator Email
lisu01@gmail.com
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c3-131221
Unique identifier
UC11291581
Identifier
usctheses-c3-131221 (legacy record id)
Legacy Identifier
etd-LiSu-1407.pdf
Dmrecord
131221
Document Type
Dissertation
Rights
Li, Su
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Tags
cationic nanoparticles
confocal microscopy
giant unilamellar vesicle
membrane deformation
Overton’s rule
passive membrane transport