Exploring the nature of the translocon-assisted protein insertion

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EXPLORING THE NATURE OF THE TRANSLOCON-
ASSISTED PROTEIN INSERTION

by

Anna Rychkova

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
(CHEMISTRY)

August 2013

Copyright 2013 Anna Rychkova
ii

ACKNOWLEDGMENTS
I would like to thank my advisor Prof. Arieh Warshel for his mentoring during my
graduate studies and his enormous contribution to all the research progress in the group.
His lifelong passion for science, intuition and outstanding memory helped me to
overcome numerous problems in my research and keep pushing the project forward.
I would also like to thank my screening, qualifying and dissertation committee members
– Profs. Anna Krylov, Ian Haworth, Lin Chen and Xiaojiang Chen for their service in
advance to my candidacy. Special thanks to Prof. Ian Haworth for his willingness to help
in my job search process and being my recommender.
I am grateful to all past and current Prof. Warshel’s group members for their help and
support and being good examples of hardworking scientists. I would like specially thank
Dr. Zhen T. Chu for lots of his help with coding and debugging MOLARIS and Dr.
Spyridon Vicatos for helping me to learn programming and his passion and devotion to
the Coarse Grained model development.
Finally, I would like to thank my dearest family. My dad, Dr. Sergey Denisenko, for his
support during my school and undergrad years and making me get only the good marks.
My mom, Mariia Denisenko, for her love and care and lots of help with my studies,
especially the toughest ones – high school essay writing, so that I was able to get only the
good marks. My brother, Dr. Alexander Denisenko, for being the first in our family who
entered the world of physics. My husband, Dmitry Rychkov, for his constant support
during so many years, for his positive attitude and courage, that helped me to be where I
am now. And finally my son, Ivan Rychkov, who keeps reminding me what is the most
important in my life.

iii

TABLE OF CONTENTS
Acknowledgments............................................................................................................... ii
List of Tables .......................................................................................................................v
List of Figures .................................................................................................................... vi
Abstract ............................................................................................................................ viii
Chapter 1. The MOLARIS Coarse Grained Model .............................................................1
1.1. The Free Energy
side
∆G ................................................................................2
1.1.1. The van der Waals Interactions....................................................................2
1.1.2. The Side Chain Electrostatic Interactions ....................................................3
1.1.3. The Side Chain Polar Interactions ...............................................................7
1.1.4. The Side Chain Hydrophobic Interactions ...................................................8
1.2. The Free Energy
main
∆G ..............................................................................9
1.2.1. Calculation of
tor
G
ϕ ψ −
∆ ..................................................................................9
1.2.2. Calculation of
Solv
main
G ∆ ................................................................................10
1.2.3. Calculation of
total
HB
G ∆ ................................................................................11
1.3. The Free Energy
main side
G
−
∆ .......................................................................12
1.4. The Free Energy Terms Used in the Current Study ...................................13
Chapter 2. On the Energetics of the Translocon Assisted Insertion of Charged
Transmembrane Helices into Membranes .........................................................................14
2.1. Introduction ................................................................................................14
2.2. Systems ......................................................................................................16
2.3. Results ........................................................................................................19
2.4. Discussion ..................................................................................................23
Chapter 3. On the Mechanism of the Translocon-Assisted Protein Insertion ....................26
3.1. Introduction ................................................................................................26
3.2. Background ................................................................................................28
3.2.1. General Background ..................................................................................28
3.2.2. On ∆G
app
....................................................................................................30
3.2.3. On the “Positive Inside” Rule and on Topology Constraints ....................31
iv

3.2.4. On the Effective Barrier .............................................................................33
3.3. The CG Method, Energy Contributions and Calibration ...........................34
3.4. Results ........................................................................................................36
3.4.1. The Energetics of the Translocon-Assisted Membrane Insertion and
Translocation..............................................................................................39
3.4.2. The Effect of Mutations on the Energetics of the TR-assisted
SP Insertion ................................................................................................44
3.4.3. The Effect of the Ribosome on the Energetics of the TR-assisted SP
Insertion .....................................................................................................44
3.4.4. The Effect of the Tail .................................................................................46
3.5. Conceptual Analysis ..................................................................................48
3.5.1. The Justification of the Model ...................................................................48
3.5.2. Insertion Models Analysis .........................................................................50
3.5.3. Analyzing the Origin of ∆G
app
...................................................................56

3.5.3.1. Examining the LFER for Membrane Insertion ....................................59
3.5.3.2. Analyzing the Small Barriers Case ......................................................61
3.6. Concluding Remarks ..................................................................................64
Bibliography ......................................................................................................................66

v

LIST OF TABLES
Table 1 Estimating ∆G
app
........................................................................................22
Table 2 Examination and calibration of the helix insertion energy ........................35
Table 3 Energetics of the insertion process for the different systems ....................41
Table 4 Examining possible LFER in the insertion process ...................................60

vi

LIST OF FIGURES
Figure 1 Trimming of an originally fully atomistic side chain representation, with
the Coarse Grained representation ...............................................................1
Figure 2 A schematic description of feasible insertion process ...............................17
Figure 3 A hypothetical structural model generated for the open translocon and
three TM helixes ........................................................................................18
Figure 4 The system free energy of the two helices, TM1 and H, in the membrane
as a function of helices rotation .................................................................19
Figure 5 The energetics of different feasible steps for the insertion of helices into
the membrane – translocon system and the ∆∆G
app
= ∆∆G
app
(Ala→Arg)
associated with the contribution of Arg (relative to that of Ala) to the
insertion of the H helix to the system at the given configuration ..............21
Figure 6 The sequences of the model proteins used to study the membrane protein
topogenesis .................................................................................................36
Figure 7 The CG model of the RR SP inside the TR (at X=0) ................................38
Figure 8 Justifying the use of the helical model .......................................................38
Figure 9 The CG free energy profiles for insertion into the TR (blue lines), into the
membrane (red lines) and translocation (green lines) for the RR SP in the
N
in
(solid line) and N
out
(dashed line) orientations ....................................39
Figure 10 Examining the correlation between different calculated and observed
effects .........................................................................................................43
Figure 11 The effect of the ribosome on the TR insertion profile .............................45
vii

Figure 12 The observed dependence of the percentage of the translocated C-
terminus, which is proportional to the in/out ratio, on the SP
hydrophobicity and the N-terminal positive charge...................................47
Figure 13 Qualitative free energy profiles for different insertion pathways ..............52
Figure 14 Kinetic schemes for different insertion models .........................................54
Figure 15 A kinetic scheme for the analysis of ∆G
app
................................................56
Figure 16 Analysis of the interplay between the limiting energetics and the
corresponding consequences in the final partition .....................................58
Figure 17 The CG free energy profiles for H-helices with a central Arg, Glu and Leu
and examination of the LFER idea using the correlation between ∆∆g
‡
and
∆∆∆G .........................................................................................................59

viii

ABSTRACT
The main subject of the current dissertation is related to the fundamental question of
membrane protein folding. Membrane proteins represent an important class of proteins
that is abundant in the most genomes (20-30% of all genes encode membrane proteins
1
)
and has significant pharmaceutical interest (target of over 50% of all modern medicinal
drugs). Protein misfolding is increasingly recognized as a factor in many diseases,
including cystic fibrosis, Parkinson’s, Alzheimer’s and atherosclerosis
2
. Many proteins
involved in misfolding-based pathologies are membrane-associated. Therefore,
understanding the mechanism that governs membrane protein folding may aid in curing
such diseases.
The vast majority of membrane proteins get inserted into the lipid bilayer through the
protein-conducting channel called translocon. The translocon is evolutionary conserved
in all kingdoms of life – its homologues are found in eukaryotes, bacteria and archaea
3
. In
bacteria the translocon consists of the heterotrimeric SecYEG complex (where “Sec”
originates from the name of the corresponding gene sec, which stands for secretion). The
insertion of proteins into the translocon is performed by a motor protein. For
posttranslational protein translocation, the translocon interacts with the cytosolic motor
protein SecA that drives the ATP-dependent stepwise translocation of unfolded
polypeptides across the membrane. For the cotranslational integration of membrane
proteins, the translocon interacts with ribosome-nascent chain complexes and membrane
insertion is coupled to polypeptide chain elongation at the ribosome. Together, the
complex of SecYEG with the motor protein is termed ‘‘preprotein translocase’’ as it
suffices for protein translocation. There are some translocase-associated auxiliary
proteins that are known to participate in protein insertion into the lipid bilayer by
transiently interacting with the translocon (e.g., the heterotrimeric SecD-FyajC complex
and the YidC protein).
There are many puzzling questions in the field of membrane proteins. One of such
questions involves the discrepancy between the experimental and theoretical estimates for
the apparent free energy of inserting charged residues into the lipid bilayer. Here we
ix

explore the nature of ∆G
app
, asking what should be the value of this parameter if its
measurement represents equilibrium conditions. This is done using a coarse grained
model with advanced electrostatic treatment. Estimating the energetics of ionized
arginine of a transmembrane (TM) helix in the presence of neighboring helixes and/or the
translocon provide a rationale for the observed ∆G
app
of ionized residues. It is concluded
that the apparent insertion free energy of TM with charged residues reflects probably
more than just the free energy of moving the isolate single helix from water into the
membrane. The present approach should be effective not only in exploring the
mechanism of the operation of the translocon but also for studies of other membrane
proteins.
The much more advanced question involves the elucidation of the molecular nature of the
protein insertion and understanding the mechanisms that govern final membrane protein
topology. Here we tried to challenge ourselves and to estimate the complete free energy
profile for the translocon-assisted protein translocation and membrane insertion. At
present it is not practical to explore the insertion process by brute force simulation
approaches due to the extremely long time of this process and the very complex
landscape. Thus we use here our previously developed coarse grained (CG) model and
explored the energetics of the membrane insertion and translocation paths. The trend in
the calculated free energy profiles is verified by evaluating the correlation between the
calculated and observed effect of mutations as well as the effect of inverting the signal
peptide that reflects the “positive inside” rule. Furthermore, the effect of the tentative
opening induced by the ribosome is found to reduce the kinetic barrier. Significantly, the
trend of the forward and backward energy barriers provides a powerful way of analyzing
key energetics information. Thus it is concluded that the insertion process is most likely a
non-equilibrium process. Furthermore, we provided a general formulation for the analysis
of the elusive apparent membrane insertion energy, ∆G
app
, and concluded that this
important parameter is unlikely to correspond to the free energy difference between the
translocon and membrane. Our formulation seems to resolve the controversy about ∆G
app

for Arg.
x

Having the complete free energy profile for the translocon-assisted membrane protein
insertion in hands allowed us to approach an intriguing question about the biphasic
pulling force of the translocon
4
. In our current project we are trying to explore the nature
of the coupling between the stalling of the elongation of proteins in the ribosome and the
insertion through the TR. The origin of this long range coupling is elucidated by coarse
grained simulations that combine the TR insertion profile and the effective chemical
barrier for the extension of the nascent chain in the ribosome. Our simulation seems to
indicate that the coupled TR/chemistry free energy profile accounts for the biphasic
force. Apparently, although the overall elongation/insertion process can be depicted as a
tug of war between the forces of the TR and the ribosome, it is actually a reflection of the
combined free energy landscape.
The results of the current work were published in two PNAS papers:
• A. Rychkova, S. Vicatos, A. Warshel, On the energetics of translocon-assisted
insertion of charged transmembrane helices into membranes, PNAS, 2010, 107(41),
17598-603
• A. Rychkova, A. Warshel, Exploring the nature of the translocon-assisted protein
insertion, PNAS, 2013, 110(2), 495-500
and presented in several conferences, including 2012 Gordon Research Conference
“Protons & Membrane Reactions”, Biophysical Society 55
th
and 56
th
Annual Meetings,
the 241
st
ACS National Meeting and the 24
th
Annual Symposium of the Protein Society.

1

CHAPTER 1
THE MOLARIS COARSE GRAINED MODEL

The present work uses a Coarse Grained (CG) model that describes the main chains by an
explicit model and represents the side chains as a simplified united atom model (see Fig.
1). This CG model provides a more advanced treatment of electrostatic effect than most
current CG models. More specifically, this model expresses the overall free energy as:
total side main main-side
∆ = ∆ + ∆ +∆ G G G G (1)

Fig. 1. Trimming of an originally fully atomistic side chain representation, with the
Coarse Grained representation (the figure is taken from ref
5
).
2

1.1. THE FREE ENERGY
side
∆G
The most important part of our CG treatment is the
side
∆G term which is given by
vdw elec hyd
side side side side side
∆ = ∆ + ∆ + ∆ + ∆
polar
G G G G G (2)

1.1.1. THE VAN DER WAALS INTERACTIONS
The first term of equation 2 describes the effective van der Waals interactions between
simplified side chains.
vdw
side
∆G consists of two components: a) the interactions between
the protein residues simplified side chains,
vdw
side-prot
∆G and b) the interactions between side
chains and membrane grid atoms,
vdw
side-mem
∆G . Van der Waals interactions between the
membrane grid atoms are considered to be equal to zero.
vdw vdw vdw
side side prot side-mem
∆ = ∆ + ∆ G G G (3)
vdw
side-prot
G ∆ is described by a "8-6" potential of the form:
( ) ( )
8 6
vdw 0 0 0
side-prot
3 / 4 /
ij ij ij ij ij
i j
G r r r r ε
<
 
∆ = −
 
 
∑
(4)
where
0 0 0
ij i j
ε = ε ε and
0 0 0
ij i j
r = r r . The parameters
0
ij
ε and
0
ij
r define, respectively, the well
depth and equilibrium distance. These parameters were refined by minimizing the root-
mean-square deviations between the calculated and observed values of both the atomic
positions and the protein size (i.e., the radii of gyration) for a series of proteins. The
corresponding refined parameters can be found in the MOLARIS manual
6
.
The van der Waals interactions between side chains and membrane grid atoms are treated
in a quite different way. The membrane grid is treated with continuous derivatives in
order to reduce the need for generating a new grid when the protein is displaced or
changes its structure. This was done by building a continuous membrane (instead of
3

deleting membrane points that appears in direct contact with the protein). Accounting for
the fact that the membrane grid should be deleted upon contact with the simplified side
chain protein atoms, we replaced the standard van der Walls interaction between the
protein and the membrane by:
vdw
side-mem 6 2 6
( ) α α
<
 
∆ = −
 
+ +
 
 
∑
ij ij
i j
ij ij
A B
G
r r
(5)
where A
ij
and B
ij
are parameters for interacting i
th
side chain and j
th
membrane grid atom,
r
ij
is the distance between the two atoms, and α is a vdw cutoff parameter.
0 0 12
0 0 6
4 ( )
4 ( )
ε
ε
=
=
ij ij ij
ij ij ij
A r
B r
(6)
where
0 0 0
ij i j
ε ε ε = ,
0 0 0
1
( )
2
ij i j
r r r = + are, respectively, the well depth and equilibrium
distance for the pair of atoms i and j. Note the different way of calculating
0
ij
r , compared
to the one used for
vdw
side-prot
G ∆ . Parameter α is equal to 7452.75.

1.1.2. THE SIDE CHAIN ELECTROSTATIC INTERACTIONS
The second term of equation 2,
elec
side
∆G , is given by the following equation:
elec
side ,
2.3 ( ) ∆ = − − + ∆ + ∆
∑
w
i a i QQ self
i
G RT Q pK pH G G (7)
where i runs over the protein’s ionized residues,
,
w
a i
pK is the pK
a
of the i
th
residue in
water and
i
Q is the charge of the i
th
residue in the given ionization state. ∆
QQ
G

is the
charge-charge interaction free energy, which is given (in kcal/mol) by:
i j
QQ
i< j
ij eff
Q Q
∆G = 332
r ε
∑
(8)
4

where the distances and charges are expressed in Å and electronic charge units, and
eff
ε
is the effective dielectric for charge-charge interaction, which reflects the idea established
in many of our earlier works (e.g. refs
7,8
) that the optimal value is large even in protein
interiors (namely
eff
ε > 20). This type of dielectric has been found to provide very
powerful insight in recent studies of protein stability (see refs
7,9
). The ionization state of
the protein residues were determined by the Metropolis Monte Carlo approach of ref
5
for
the given pH.
The above electrostatic treatment involves a self-consistent treatment of the
interdependent self-energy, charge-charge interaction and the external pH (where the
ionization state is determined by a Monte Carlo treatment of the energetics of equation
7).
A key element in our approach is the treatment of the self energy, ∆
self
G , associated with
charging each ionized group (residues ASP, GLU, LYS, ARG and HIS) in its specific
environment. This term is given by:
( ) ( ) ( ) ( )
∆ = + +
∑
np np p p mem mem
self self i self i self i
i
G U N U N U N (9)
Where U designates effective potential, i runs over all ionized residues,
np
self
U ,
p
self
U and
mem
self
U are the contributions to the self-energy from non-polar (np) residues, polar (p)
residues and membrane (mem) atoms (more precisely, membrane grid points as clarified
below), respectively. Here
np
i
N ,
p
i
N and
mem
i
N are, respectively, the number of non-polar
residues, polar residues and membrane atoms in the neighborhood of the i
th
residue. Note
that the non-polar contribution for the membrane is taken into account separately in the
hydrophobic term (described below).
The empirical functions
p
self
U and
np
self
U are given by:
5

( )
2
( ) max max
( ) max
exp , 0
( )
,
α
  
− − < ≤

 
 
=


>

self np np np np np
np i self i i
np np
self i
self np np
np i i
B N N N N
U N
B N N
(10)
and
( )
2
( ) max max
( ) max
exp , 0
( )
,
α
  
− − < ≤

 
 
=


>

self p p p p p
p i self i i
p p
self i
self p p
p i i
B N N N N
U N
B N N
(11)
The number of non-polar residues neighboring the i
th
ionized residue is expressed by the
analytical function:
( )
( )
=
∑
np
i ij
j np
N F r (12)
with
( )
( )
2
1,
exp ,
ij np
ij
np ij np ij np
r r
F r
r r r r α
≤ 

=

 
− − >

 
  
(13)
where
ij
r is the distance between the simplified side chains of ionizable residue (i) and
non-polar residue (j),
np
r and α
np
are the parameter radius and factor, respectively, that
determine the effect of the non-polar residues. The same equations 12 and 13 were used
for the calculation of the number of polar residues neighboring the i
th
ionized residue
(with the parameters
p
r andα
p
) and for the number of membrane grid points
neighboring the i
th
ionized residue (with parameters
mem
r andα
mem
). The relevant
parameters for equations 10-13 are given in the MOLARIS manual
6
.
The reasoning behind equations 10-13 is the following. For the calculation of the non-
polar neighbors
np
i
N for each ionizable residue (i) and for a specified radius
np
r of the
center of the simplified side chain of (i), any non-polar residue whose simplified side
chain is within this radius is considered a neighbor of (i). Non-polar residues whose side
6

chain distance from (i) is larger than
np
r are still interacting with (i) (thus contributing to
the total
np
i
N ) but with an exponentially decaying function, described in equation 13.
( )
np np
self i
U N and ( )
p p
self i
U N are calculated, by using equations 10 and 11. The values for
max
p
N and
max
np
N have been estimated, by observing the values of neighbors in a set of
diverse proteins
9
. For specific values of
p
r and
np
r shown in the MOLARIS manual
6
and
used extensively in our previous work
5,9–13
, we have observed that less than 5% of
ionizable residues have more than
p
i
N =6. The same feature occurs for the non-polar
neighbors: less than 5% of the ionizable residues have more than
np
i
N =15, and those who
are, are deeply buried inside the interior part of the contained protein.
Our model was also applied to membranes which are represented by grids of unified
atoms and this grid is used in evaluating N
mem
by the equivalent of equations 12 and 13.
The membrane grid is used in calculating
self ,0
mem
U where we have:
( )
max 2 max
( )
,0
max
( )
exp ( ) , 0
,
self mem i i
mem i self mem mem mem mem
self i
mem mem
self i
mem i mem mem
B N N N N
U N
B N N
α
   − − < <
  
=

≥


(14)
The value of
( )
,0 self i
mem mem
U N , would be the contribution of the membrane grid atoms to the
ionizable residue (i), if its side chain is fully inside the membrane grid. To get the
dependence of the free energy from the position within the membrane,
( )
,0 self i
mem mem
U N has
to be treated with an additional exponential function, that accounts for the magnitude of
the burial inside the membrane grid (i.e how deep into the membrane grid is the side
chain located). This treatment is described below:
( )
2
,0
,0
2
exp ,
2
,
2
  
  −
   − ≤
 

 
 
 
  =

 

>


solvent
self solvent mem mem
mem
self i
s
mem mem
burried
self solvent mem
mem
R W W
U R
L
U N
W
U R
(15)
7

solvent
R is the distance to the closest solvent molecule, which is determined by a water
grid around the system, and using the distance to the closest water grid point.
mem
W is the
width of the membrane atoms grid.
s
L is a parameter that determines the effect of the
burial of residue (i), and in our recent works
11–13
its suggested value is one quarter of the
membrane grid width
mem
W . For a membrane grid spacing
o
spacing
D 2A = and width
o
36 A =
mem
W , the value of L
s
used was 9Ǻ (see ref
11–13
for more details).

1.1.3. THE SIDE CHAIN POLAR INTERACTIONS
The third term of equation 2,
side
∆
polar
G , is treated with equations identical to the ones used
to calculate the self energies of the ionizable residues:
( ) ( ) ( )
 
∆ = + +
 
∑
polar np np p p mem mem
side polar i polar i polar i
i
G U N U N U N (16)
where i runs over all polar residues (SER, THR, TYR, CYS, ASN, GLN),
np
i
N ,
p
i
N and
mem
i
N are the number of non-polar residues, polar residues, and membrane atoms in the
neighborhood of the i
th
residue. They are calculated by using equation 12 and 13, with
parameters listed in the MOLARIS manual
6
. The functions
np
polar
U ,
p
polar
U and
mem
polar
U are
given by the same expression as in equations 10-11, 14-15, and the corresponding
parameter
pol
p
B ,
pol
np
B and
pol
mem
B for each polar residue are given in the MOLARIS
manual
6
.

8

1.1.4. THE SIDE CHAIN HYDROPHOBIC INTERACTIONS
The last term of equation 2,
hyd
side
∆G , is treated by adopting similar model used in the self
energy and polar free energy calculations, as follows:
( ) ( ) ( )
 
∆ = + +
 
∑
hyd np Ring p p mem mem
side hyd i hyd i hyd i
i
G U N U N U N (17)
Where i runs over all non-polar residues (ALA, LEU, ILE, VAL, PRO, MET, PHE,
TRP),
p
i
N and
mem
i
N are the number of non-polar residues and membrane atoms in the
neighborhood of the i
th
residue. They are calculated by using equations 12-13, with
parameters listed the MOLARIS manual
6
. The functions
p
hyd
U and
mem
hyd
U are given by the
same expression as in equation 11 and 14-15 with the corresponding parameters (see
ref
6
).
The term
np
hyd
U however, is being treated in a different way, compared to its counterparts.
np
hyd
U is calculated as follows:
( )
( )
exp 1.4( )   = −
 
np Ring np Ring Water
hyd i hyd i i i
U N B N N (18)
where
( )
np
hyd i
B is a constant, similar in nature with the constants described in equation 10.
Ring
i
N is the number of implicit water grid points within a certain radius from the side
chain center.
Water
i
N is a constant, that reflects total number of implicit water grid points
that this specific residue is surrounded with, when it is by itself in a water environment.
To calculate
Ring
i
N for each non polar residue (i), an implicit water grid is created, which
surrounds residue (i). Then, the grid points which collide with protein main chain atoms
are eliminated. Finally, the grid points that are within the volume between the spheres of
radiuses r
hydro (i)
and r
hydro (i)
+ 4Ǻ from the center of residue (i)’s simplified side chain’s
atom, are kept, and the rest of the grid points are eliminated. The total number of these
9

grid points, is the value of
Ring
i
N . r
hydro (i)
is the radius of residue (i) that corresponds to the
size of its simplified side chain.

1.2. THE FREE ENERGY
main
∆G
The main chain free energy
main
∆G is given by:
Solv total qq
main bond angle tor itor tor main HB main
G G G G G G G G G
ϕ ψ −
∆ = ∆ + ∆ + ∆ + ∆ + ∆ + ∆ + ∆ + ∆ (19)
where ∆
bond
G , ∆
angle
G , ∆
tor
G , and ∆
itor
G are contributions from the regular ENZYMIX
force field. Also, the last term of equation 19, ∆
qq
main
G , is the charge-charge interaction
free energy between the main chain atoms, which is calculated by equation 8 and a
dielectric constant
eff
ε = 10. The additional terms will be discussed below.

1.2.1. CALCULATION OF
tor
G
ϕ ψ −
∆
Since the secondary structure of proteins depends strongly on the solvation of the main
chains we added the correction potential
tor
G
ϕ ψ −
∆ that is used to modify the gas phase
potential. This solvation potential is given by
( ) ( )
4
i i i i
tor i 0 0 0 0
i 1
G A g , g ,
ϕ ψ
ϕ ϕ ω ψ ψ ω
−
=
∆ = − −
∑
(20)
where
( ) ( ) ( ) ( ) ( )
g x, ω = exp 0.693 1 cos x / sin ω / 2 − − (21)
The values of
i
0
ϕ and
i
0
ψ are chosen to represent the minima of the α-helix and β-sheet
regions of the Ramachandran plot, while
i
A and
i
0
ω have been selected to tune the
10

simple model α-helix and β-sheet regions to match those of the explicit model. The
specific values of these parameters can be found in ref
6
.

1.2.2. CALCULATION OF
Solv
main
G ∆
The main chain solvation term is given by
Solv
main solv ,i
i
G B U
α
∆ = −
∑
(22)
( )
2
i max
i max
,i
i max
e ,
U
1,
θ
α θ θ
α
θ θ
θ θ
− −

<


=


≥


(23)
where
solv
B = −2 and (i) runs over all residues in the sequence. The function θ, which
reflects the percentage of polar residues around the C
α
atom of a given residue i, is given
by
( )
max max max
np,i mem,i p mem p
i max
p
N N N N N
N
θ θ θ
θ
θ
+ −
= (24)
with
max
p
N
θ
= 27 and
max
mem
N
θ
=33.
max
p
N
θ
is the maximum number of polar residues around
C
α
atom (checked for translocon system);
max
mem
N
θ
is the maximum number for membrane
atoms around C
α
atom (checked for Ala in a membrane with simplified membrane
spacing of 4Ǻ).
np,i
N and
mem,i
N are the number of nonpolar and membrane residues
around residue i, which are calculated by the same approach as for the self energy
calculation. The only difference is that we count the residues around the C
α
and not the
C
β
atom, as done for the calculation of the self energy contributions.

11

1.2.3. CALCULATION OF
total
HB
G ∆
The Hydrogen Bond function is given by
( )
total water i j mem i j
HB HB HB
G G U U G 1 U U
α α α α
∆ = ∆ ⋅ ⋅ + ∆ ⋅ − ⋅ (25)
where we have
( )
( )
2
HB ij HB
r r
water CG,0 regular
HB water HB HB
G A G G e
µ − −
∆ = ⋅ ∆ + ∆ + (26)
and where
( )
mem CG,0 regular
HB mem HB HB
G A G G ∆ = ⋅ ∆ + ∆ (27)
with
HB
µ = 22.2 and
HB
r =2.9Ǻ,
water
A = 0.044 and
mem
A = 0.22.
regular
HB
G ∆ is the regular HB
function used in the standard MOLARIS force field.
The scaling factors
water
A and
mem
A are calculated, based upon the function
( )
i j
A 1 0.8U U 4.5
α α
= − (28)
When in water, U
α

for all residues is equal to 1, therefore from equation 28, we have
( )
water
A 1 0.8 1 4.5 0.2 / 4.5 0.044 ≈ − ⋅ = =
(29)

When in membrane, U
α
for all residues is equal to 0, therefore from equation 28, we
have
( )
mem
A 1 0.8 0 4.5 1/ 4.5 0.22 ≈ − ⋅ = =
(30)

12

1.3. THE FREE ENERGY
main side
G
−
∆
main side
G
−
∆ consists of two parts, the electrostatic and the van der Waals parts:
elec vdw
main side main side main side
G G G
− − −
∆ = ∆ + ∆ (31)
The electrostatic part,
elec
main side
G
−
∆ is treated with the same electrostatic interactions as in
equation 8, but with the
eff
ε = 10.
The van der Waals for main-side interactions,
vdw
main side
G
−
∆ consists of two parts, a) the one
where the side chain is a regular protein side chain,
vdw
main side protein
G
−
∆ and b) the one where
the side chain is a membrane grid atom,
vdw
main side mem
G
−
∆ .
vdw vdw vdw
main side main side protein main side mem
G G G
− − −
∆ = ∆ + ∆ (32)
vdw
main side protein
G
−
∆ is treated as a regular 12-6 potential, only that side chain is treated as a
carbon atom. Again, the van der Waals interactions of membrane grid atoms,
vdw
main side mem
G
−
∆ , are handled with the same treatment as
vdw
side-mem
∆G of equations 5-6:
vdw
side-mem 6 2 6
( ) α α
<
 
∆ = −
 
+ +
 
 
∑
ij ij
i j
ij ij
A B
G
r r
(33)
=
=
ij i j
ij i j
A A A
B B B
(34)
where A
i
, A
j
and B
i
, B
j
are the vdw parameters for main chain atoms i and membrane grid
atoms j. Parameter α for this case is equal to 2871.33.

13

1.4. THE FREE ENERGY TERMS USED IN THE CURRENT STUDY
For the calculation of the absolute free energies it is important to include all the possible
terms. However when we are interested in the relative effects, like the ones considered in
this study, it is essential to include only those terms that give different contributions for
different states of the system, i.e. determine the final effect. For this reason the free
energy of different states considered in Chapter 2 was calculated as:
elec hyd
tot side side
G G G ∆ = ∆ + ∆ (35)
Trying to get more accurate profile for the processes of peptide insertion from water to
protein-membrane system, we included two extra terms – main chain solvation and
corrected hydrogen bond term, so that the total free energy was calculated as:
elec hyd solv total
tot side side main HB
G G G G G ∆ = ∆ + ∆ + ∆ + ∆ (36)

14

CHAPTER 2
ON THE ENERGETICS OF THE TRANSLOCON ASSISTED INSERTION OF
CHARGED TRANSMEMBRANE HELICES INTO MEMBRANES

2.1. INTRODUCTION
The insertion of transmembrane (TM) proteins into membranes is a subject of great
current interest
14–19
. It is known that the recognition of proteins is performed by the
translocon complex that ensures both the translocation of globular proteins across
membranes and the integration of membrane proteins into membranes
20
. Biochemical
studies have provided major information about the insertion process and structural studies
have provided key hints about the actual insertion mechanism
14,21–23
. Furthermore, clever
experiments by von Heijne, White and their coworkers
18
have determined a scale that
reflects the apparent energetic of the inserting a TM helix into a membrane in biological
conditions. These workers took the sequence of the double-spanning protein (bacterial
leader peptidase) and added to two TM helixes of this protein (TM1 and TM2) additional
helix (the H-helix), which was flanked by two acceptor sites for N-linked glycosylation.
The degree of membrane integration of the H-helix was then analyzed by the number of
glycosylated sites, and the apparent equilibrium constants, K
app
= f
1g
/f
2g
(where f
1g
and f
2g

were determined by the fractions of singly and doubly glycosylated proteins,
respectively) were calculated. This values were then converted to the relevant apparent
free energies, ∆G
app
= -RTlnK
app
. Decomposing ∆G
app
to the contribution from different
amino acids provided the insertion scale for the H-helices, with each of the twenty
naturally occurring amino acids placed in the middle of the 19-residue hydrophobic
stretch (see ref
18
and section 2.3 for more details).
The experimental determination of the ‘biological’ hydrophobic scale
18
challenges one to
rationalize the origin of this important scale. In particular one would like to understand
the reason for the small values of the free energy associated with the insertion of charge
residues. This presents a significant problem, as the free energy of placing a charge in a
15

non polar environment is expected to be very large
24
, and since some attempts to simulate
the relevant free energy penalty lead in most cases to a significantly larger estimate of the
∆G
app
(by more than 10 kcal/mol)
25,26
than the observed one (2-4 kcal/mol)
18
. Different
justifications have been given to the observed values, including the effect of water
penetration, the effects of the lipid head groups, position of the charge in the membrane,
and even membrane distortion
26
. However, these justifications cannot fully account for
the energetics of ionized groups in the center of a TM helix at the center of the
membrane. Thus, this issue remains a major open problem, where it seems that the
observed scale may reflect more than just the free energy of moving different residues to
the center of the membrane environment, even with possible effects that can account for a
part of the discrepancy.
It must also be mentioned that the experimental analysis that led to the ∆G
app
scale is
extremely complex and it is not entirely clear if we are dealing with a rigorous
quasiequilibrium conditions (this issue is analyzed in the discussion section 2.4).
Very recent all atom simulation
27
indicated that the energetics of ionized residues can
change in a drastic way if such residues are in a membrane with some protein content
rather than in a pure membrane environment. Furthermore, the calculated solvation free
energy profile for the Arg close to the translocon and 20 Å away from it, indicated that
the desolvation penalty for a charged residue close to the lateral gate is quite low (3-5
kcal/mol) and thus comparable to the experimental value. The increase in stabilization of
the ionized Arg near the translocon or near membrane protein segments has been found to
be partially due to water molecules in the protein interior. These results provided an
interesting possible rationale for the value of ∆G
app
, although the likelihood that the
system would be near the translocon or in any specific insertion step was not explored,
and the effect of the relationship to the actual system used for deducing ∆G
app
was not
modeled. Finally, it was also suggested that helix-helix interaction can account for the
low apparent energy
28
, but no estimate of this effect was given.
At present it seems to us that the elucidation of the nature of insertion free energies by
direct all atom simulations is extremely challenging, since the structural characteristics of
16

the TM/translocon system are not completely clear and since a converging sampling of
such a complex system is extremely challenging. Thus one of the most promising options
may be opened by the use of coarse grained (CG) models of the type introduced in ref
29

for general folding problems and subsequently for folding studies of helical proteins
30
.
Advances in CG simulations of membrane proteins and some examples of such
simulations are summarized in a recent review
31
, whereas the general development of CG
models in simulation of different biological systems are reviewed in ref
10
.
The augmentation of our early CG models with more recent electrostatic modifications
5

make them particularly suitable for studying the above fundamental problem. Thus we
explore here the origin of ∆G
app
of ionized residues by using a coarse grained (CG)
model for the TM insertion process. This model allows us to analyze the energetics of
different configurations, where the insertion of the H helix with a charged Arg residue is
assisted by contacts with other helixes and/or the translocon. Our analysis accounts for
the trend in the observed ∆G
app
(assuming that it follows quasiequilibrium relationship)
and indicates that this quantity probably reflects stabilization by other helixes and
perhaps by the translocon.

2.2. SYSTEMS
As stated above, the uncertainty about the structural changes of the translocon and the
complexity of the insertion process suggest that the use of fully explicit model is not an
optimal strategy. Thus it is tempting to exploit CG models of the types considered in
refs
29,30
and other reviewed in ref
31
, and to focus on electrostatic effects
5
.
The type of structural models considered in the present work are depicted schematically
in Fig 2, where we followed tentatively the sequence of events proposed by Rapoport and
coworkers
19
. This description is relevant to the insertion process used in establishing
∆G
app
18
. Namely, the three TM helices used in our simulations correspond to the integral
membrane protein leader peptidase (Lep) with an engineered third H-segment.
17

In examining the energetics of possible insertion steps and the corresponding states of the
system, we faced the problem of limited structural information. Thus we generated the
relevant structures (see below) starting from the X- ray structure of the heterotrimeric
membrane protein complex SecY (PDB ID 3DIN)
23
and using MD with the CG model to
generate tentative models for the required relaxed structures. A typical structure that will
be considered in this work is given as an example in Fig 3. It should be noted, in this
respect, that the considered structures will not represent the sequence of insertion events,
but rather possible quasiequilibrium configurations in this process. In fact the overall
competition between translocation and insertion is very complex and unresolved. The
considered configurations are well consistent with the relevant experiments
19,32
,
indicating that: (i) two TMs can be presented in the channel – one in the pore and one
intercalated into the lateral gate; (ii) during the synthesis of a multispanning membrane
protein, the TMs could leave the translocon one by one or in pairs; (iii) one TM can
facilitate the exit of another TM by returning to the channel to associate with the second
TM.
Fig. 2. A schematic description of feasible insertion process (based on a proposal by
Heinrich et al.
19
)
18

We also like to clarify that there are other works that attempted to model the translocon
structure and its opening (e.g. ref
27,33,34
), but the exact structure is not known and the
effect of the possible ionization states presents an additional challenge, thus the use of
CG model is probably the best current strategy for addressing energy issues.
Our strategy of exploring the energetics of the different feasible states is demonstrated in
Fig. 4 for a system of two helixes embedded in the membrane. In this case we considered
the energy of the CG model for different rotational angels of the helixes with a helix-
helix distance of 14 Å (this distance was necessary in order to prevent the clashing of the
Arg side chain with the second helix during the rotation of the H helix). The
corresponding free energy surface is described in Fig. 4, where we take the lowest free
energy values as our estimate of the free energy of the given system. The same approach
Fig. 3. A hypothetical structural model generated for the open translocon and three
TM helixes. The positioning of the helices corresponds to model 11 on Fig. 5. The
translocon is shown in orange, TM1 in yellow, TM2 in blue and H in red, membrane
in gray. Part of the membrane is removed in order to make the proteins visible.
19

has been used for the different constructs we examined. All the calculations were
performed with the program package MOLARIS
35
, using the simplified folding module.

2.3. RESULTS
In the first stage we explored in a very tentative way the general issue of the mechanism
of insertion of TM helixes through the translocon. This was done by following the
insertion sequence featured in Fig 2. The energetic of each step was examined using the
CG model, considering only the energetics of inserting the helixes in the relaxed protein.
These calculations did not attempt to fully optimize the protein structure or to explore its
deformation free energy and was mainly needed for estimating the energetics of states
Fig. 4. The system free energy of the two helices, TM1 and H, in the membrane as a
function of helices rotation. TM1 has polar regions and H has positively charged Arg.
As can be seen from the graph the energy goes down when the charged Arg points
toward the TM1 helix, so that the exposure of charge to the membrane is reduced. The
minimum of the system free energy is 0.19 kcal/mol at (240
0
, 180
0
) when the Arg is
stabilized by the interaction with hydrophilic residues of TM1.
20

where the H helix touches the translocon. In general the missing deformation energy will
make the total energy of states where the helixes are out of the translocon more stable.
A much more detailed analysis was done in examining the nature of the energetics of the
H helix and the corresponding ∆G
app
, (under the conditional assumption of
quasiequilibrium), focusing on the case where Arg residue is in the center of the H helix.
More specifically, in order to estimate ∆G
app
we examined the change in free energy,
∆∆G
wat→sys
(H), of transferring the H-helix from water to different likely configurations
(states) that can be generated during the insertion process. For each of the possible
options we evaluated the lowest energy obtained by keeping the helixes rigid and
mapping the energy of the system as a function of the relative orientation of the helixes
involved. This was done while not allowing the helixes to move in the z direction. The
corresponding procedure is illustrated in Fig 4. In each case we evaluated the total free
energy of the full system (translocon and helices in the membrane), ∆G
tot
=∆G
sys
(all), at
the lowest energy configuration. We repeated this calculation for the same system
without the H helix, ∆G
sys
(all-H), and for the isolated H helix in water, ∆G
wat
(H). Using
these values we expressed the apparent free energy of inserting the H helix as:
( ) ( ) ( ) ( ) ( )
app wat sys sys sys wat
G H G H G all G all H G H
→
∆ = ∆ = ∆ − ∆ − − ∆ (37)
We then calculated the ∆G
app
(H) for the H helix with central Arg and with central Ala
and obtained corresponding difference:
( ) ( _ / ) ( _ / )
app app app
G Ala Arg G H c Arg G H c Ala ∆∆ → = ∆ − ∆ (38)
where c/Arg designates central Arg. This treatment allowed us to conveniently evaluate
the apparent free energy of Arg residue relative to that of Ala and to compare the
calculated results to the corresponding experimental value
18
. The resulting ∆G
app
are
given in Fig. 5 and Table 1. The figure also provides the total energy of each system and
thus we can focus only on those systems with the lowest ∆G
tot
. In the present case only
system 17 and 19 contribute since these are the only system with low total energy and
non-negligible probability (see, however, below).
21

As seen from the figure and the table the lowest free energies correspond to the case
where the insertion is assisted by the polar parts of either the translocon or the other
helixes. In particular the lowest energy configuration (state 17) gives ∆∆G
app
=4.01
kcal/mol in a reasonable agreement with the observed value of 2.47 kcal/mol. In principle
we have to consider the free energy weighted average of configuration 17, 19 and 16 and
this will reduce the calculated ∆G
app
. Although the results are quite stable and do not
change significantly with small change of the parameters used, the agreement might be
coincidental and the validity of our finding requires further verification. However, the
results seem to indicate that the biological insertion scale reflects more complex situation
than just the energetic of helices in solution.

Fig. 5. The energetics of different feasible steps for the insertion of helices into the
membrane – translocon system and the ∆∆G
app
= ∆∆G
app
(Ala→Arg) associated with
the contribution of Arg (relative to that of Ala) to the insertion of the H helix to the
system at the given configuration. The figure also provides the total energy of each
system ∆G
tot
(relative to that of the system in state 1).
22

# ∆G
(1)
∆G
(2)
∆G
(3)
∆G
app
∆∆G
app

10a -39.5 -31.1 -8.8 0.4 3.6
10b -35.5 -31.1 -1.2 -3.2
11a -35.8 -21.8 -8.8 -5.2 4.8
11b -33.0 -21.8 -1.2 -10.0
12a -39.7 -31.0 -8.8 0.1 3.9
12b -36.0 -31.0 -1.2 -3.8
13a -49.5 -38.7 -8.8 -2.0 3.5
13b -45.4 -38.7 -1.2 -5.5
14a -48.3 -38.3 -8.8 -1.1 3.9
14b -44.5 -38.3 -1.2 -5.0
15a -47.3 -38.4 -8.8 -0.1 4.4
15b -44.1 -38.4 -1.2 -4.6
16a -59.0 -38.7 -8.8 -11.5 4.2
16b -55.6 -38.7 -1.2 -15.7
17a -62.0 -41.8 -8.8 -11.4 4.0
17b -58.4 -41.8 -1.2 -15.5
18a -47.7 -37.1 -8.8 -1.8 16.0
18b -56.1 -37.1 -1.2 -17.8
19a -61.6 -40.9 -8.8 -12.0 0.8
19b -54.8 -40.9 -1.2 -12.8
20a -55.0 -44.4 -8.8 -1.8 16.0
20b -63.4 -44.4 -1.2 -17.8

Table 1. Estimating ∆G
app
. All the energies are given in kcal/mol. The table includes
only the results for models 10-20. The models with the letter “a” and “b” have charged
Arg and Ala, respectively on the H-helix. ∆G
(1)
= ∆G
sys
(all) = ∆G
tot
is the free energy
of the full model (translocon and helices in the membrane) relative to the model 1.
∆G
(2)
= ∆G
sys
(all-H) is the free energy of the full model without H-helix. ∆G
(3)
=
∆G
wat
(H) is the free energy of the H-helix in water. ∆G
app
= ∆∆G
wat→sys
(H) =
∆G
sys
(all)-∆G
sys
(all-H)-∆G
wat
(H) is the apparent free energy of the H-helix. ∆∆G
app
=
∆∆G
app
(Ala→Arg) = ∆G
app
(H_c/Arg)-∆G
app
(H_c/Ala) is the difference between the
apparent free energies for Arg and Ala (can be compared to experimental value). The
free energy values highlighted in bold are used in Fig. 5. Glu on TM2 was found to be
protonated in pH=7 inside the membrane.
23

2.4. DISCUSSION
Understanding the molecular determinants of protein insertion through membrane is a
problem of major current interest. Experimental estimates of the relevant energetics
provided a major insight about the contributions of different residues. However, the
complexity of the insertion process and the uncertainty in the exact nature of the
structural changes makes it very challenging to generate a detailed molecular picture of
the insertion mechanism and the origin of ∆G
app
.
Here the use of simplified CG model seems to provide an excellent compromise,
allowing one to explore large range of the configurational changes and to obtain
reasonable conclusions in the case of relatively “fuzzy” structural information.
Furthermore, the CG model can be used when we gain more information as an optimal
reference potential for studies of the energetics of explicit models
31
.
A recent interesting study
34
explored the role of hydrophobic residues in the energetic of
the lateral gating of the translocon and has attempted to address the partition of helixes
between the membrane and the translocon issue, and in some respects the origin of ∆G
app
.
However, ref
34
has not explored the partition between the membrane and water or an
alternative measures of the relationship between translocation and insertion in addressing
the nature of ∆G
app
, and instead looked at the partition of the helix between the translocon
and the membrane. This approach may be related to the possibility that ∆G
app
(or other
insertions parameters) reflects somehow kinetic effects when, for example, the assumed
equilibrium is not reached during the glycosylation experiments. However, the kinetic
proposal has not been formulated by workers in the field in a physical (energy based)
considerations.
Our analysis tends to favor a mechanism where the calculated ∆G
app
of Arg
+
reflects
helix-helix interaction in the membrane more than the stabilization of this ionized group
by the translocon. Nevertheless, at present the difference between the total energy of
configurations 17 (or 19) and 13 may need more careful assessment (as we deal with
significantly different situation). Furthermore, it may be beneficial to quantify the CG
findings by using our approach of evaluating the free energies for transformation from
24

the CG to the explicit model
5
, and such studies will be conducted in the future. In this
respect we note that Johansson and Lindahl
27
considered the general effect of having an
Arg near the translocon and in the membranes with different concentration of helixes, but
have not explored the relative probability or the relationship to the insertion experiment.
An exciting recent experimental study of Spiess and coworkers
36
indicated quite clearly
that mutations of the translocon change ∆G
app
for hydrophobic residues. This finding was
assumed to lend some support to the kinetic control proposal, suggesting that catalytic
contribution should not affect equilibrium. However, it is more likely that the interaction
between the translocon and the H helix reaches a quasiequilibrium at the different stages
of insertion (e.g. some contribution of state 13 in Fig. 5), and that this determined the
fraction of the H helix in the membrane. Such an effect has no relationship to the forward
and backward barriers for the insertion and translocation unless some of these barriers are
more that 20 kcal/mol, where it would become (according to transition state theory) rate
limiting with a rate constant of about 1 min
-1
. If the glycosylation experiment takes one
hour, then the only way that we have a kinetic mechanism is the vectorial mechanism.
Thus it is more likely that the finding of different ∆G
app
for different systems is not
correlated with a kinetic model but with a possible complex with the translocon.
Mutational studies of the type described by Spiess and coworkers
36
and by von Heijne,
White and coworkers
37
can be very instrumental in validating or improving the present
finding. They can clearly tell us if the H helix still touches the translocon during the
partition between the membrane and solution. More specifically modifying the other two
helices with a “belt” of non polar residues in their center can be used to find out whether
the H helix, with an ionized group in its center, is in contact with the other helixes. In this
respect we note that the current experiments
37
are not conclusive enough.
Recent attempts to derive an implicit model for membrane proteins
38
and to explore the
insertion energy by CG simulations
39
have provided some interesting insights. However,
such an approach suffers from major problems when it is applied to charged residues, as
it does not explore the effect of stabilization by polar groups considered here. The
problem is that the CG models considered do not seem to reproduce explicit simulations
25

(and other estimates) of oil water transfer free energy of ionized residues. What is
missing are more consistent attempts to model the energetics of insertion process, where
possible protein-protein or helix–helix interactions are explored (as was done here), or
full atomistic calibration of the CG electrostatic parameters.
Regardless of the exact explanation of the origin of ∆G
app
of charged residues, it seems to
us that CG models offer a powerful way to progress in analyzing the key experimental
information and eventually in progressing in the detailed understanding of the complex
insertion process. That is, one of the most promising directions of the current approach is
its potential in providing information about the sequence of event in the insertion of
membrane proteins, since we can evaluate the energetic of different steps (e.g. the steps
presented in Fig 2) and even explore the barriers for alternative paths. Combining such
simulations with experimental studies is expected to be quite useful.

26

CHAPTER 3
ON THE MECHANISM OF THE TRANSLOCON-ASSISTED PROTEIN INSERTION

3.1. INTRODUCTION
The establishment of the correct functional topology of membrane proteins is a subject of
great current interest (e.g. refs
40–42
). It is known that the protein-conducting channel
named translocon (TR) plays a vital role in membrane proteins biogenesis
20
. Although
biochemical and structural (e.g. refs
23,43
) studies have provided crucial information about
the insertion process, the understanding of this process is still limited. The difficulties in
gaining detailed understanding are also apparent from the emerging problem in fully
defining the molecular meaning of the intriguing results about the apparent free energy,
∆G
app
. That is, the concept of ∆G
app
,introduced by Hessa et al.
18
for the assessment of
inserted versus secreted helical domains (see section 3.2.1), appeared in recent years to be
more complex than previously thought. More specifically, the most logical implication of
the original descriptions of ∆G
app
has been that it represents an equilibrium result of the
partition between membrane and water. In fact, this was implied by the attempts to
correlate ∆G
app
with the water-membrane partitions. However, different works
34,44,45

implied that the corresponding equilibrium constant corresponds to the equilibrium
between the TR and the membrane (see also section 3.2). Unfortunately, none of these
works has offered a clear physical rationale for why one has to consider such equilibrium
without considering the transfer to water. We note that even the interesting discussion in
ref
45
does not provide a verifiable model (that can be rejected or accepted), since it does
not provide a kinetic diagram with assumed reaction rates and activation barriers (of the
type that will be given in this work). Furthermore, the fact that the insertion is driven by
ATP hydrolysis or ribosome induced vectorial process has not been connected to the
analysis of ∆G
app
, except in our study
13
which considered a possible rationale for the
non-equilibrium process. However, this was a hypothetical exercise, rather than a
structure/energy based study.
27

In addition to the problem in rationalizing ∆G
app
there are other key sources of yet
unresolved experimental constraints, such as the “positive inside“ rule and different
mutational effects (see below) that can help in guiding the challenging task of
understanding the TR effect. However, in the absence of key information about the
energetics and structure of intermediates along the insertion path, one must attempt to use
simulation approaches to gain a clearer understanding. In principle one may try brute
force all-atom simulations, but such efforts have not led to a progress in understanding
the insertion barrier, which is far too high for even millisecond simulations. Here the
insight about possible path for the beginning of the insertion
46
cannot help in telling us
about the rate determining processes. One may also try to obtain the relevant potential of
mean force (PMF) with an all-atom model, but the corresponding landscape is very
complex and the convergence is expected to be problematic. Thus we believe that it is
crucial to use Coarse Grained (CG) models in studying the insertion energetics and then
to augment such studies by considering the effect of mutations on the directionality of the
signal peptide (SP) insertion and on other observations.
CG models were introduced in protein modeling in 1975
29
and have become since then
very powerful tools for modeling biological systems
10,47
. In fact a CG model has already
been used by us in a study
13
of ∆G
app
(see section II). A very recent work
48
used a
drastically simpler CG model and explored the insertion rate for SPs of variable sizes.
This study probably captured effects that are determined by very coarse features.
However, the model has not explored the relevant energetics, and we believe that
understanding the nature of the free energy landscape rather than dynamical features is
crucial here. Thus, it seems to us that our CG model that is focused on a realistic
description of the electrostatic energetics provides the optimal current strategy for this
challenging task, and such a study is described here.
Although the current CG study cannot provide fully quantitative insertion free energy
profile, combining the profile with systematic analysis of the effect of SP and TR
mutations and using it to identify energetics constraint, shads a new interesting light on
the TR insertion process. This includes reproducing several key observations and
highlighting the role of the kinetic control by the barrier for the insertion process.
28

Furthermore, the CG analysis appears to provide a very powerful way of analyzing the
origin of ∆G
app
.

3.2. BACKGROUND

3.2.1. GENERAL BACKGROUND
In analyzing the TR assisted insertion process it is important to address the key
experimental observations. Here we start with the elegant experiments of von Heijne,
White, and their coworkers
18
where they determined a scale that reflects the apparent
energetic of inserting a TM helix into a membrane in biological conditions. These
workers generated a construct with two TM helixes of this protein (TM1 and TM2) and
an additional helix (the H helix), flanked by two acceptor sites for N-linked
glycosylation. The degree of membrane integration of the H helix was then determined
by the number of glycosylated sites and the apparent equilibrium constant, K
app
= f
1g
⁄f
2g

(where f
1g
and f
2g
are the fractions of singly and doubly glycosylated proteins,
respectively). This value was then converted to the relevant apparent free energy, ∆G
app
=
−RT lnK
app
, which was then decomposed to the contribution from each of the 20
naturally occurring amino acids placed in the middle of the H helix.
The basic question in exploring the molecular meaning of ∆G
app
and the TR mediated
insertion process is the nature of the relevant energetics and insertion paths. The original
implication has been that the translocon effect is relatively small and that the
experimental findings are related to the energetics of the specific amino acid in the center
of the membrane. This issue is important in view of attempts to point out the possibility
that the experiments have not established the central position of the Arg positive charge,
and thus an obvious possibility would be to tilt the Arg side chain towards the membrane
surface and use this idea in explaining the low ∆G
app
25,44,45
. We point out in this respect
that the one can use a more trivial suggestion, just saying that the center of the helix is
moving and placing the central charge closer to the membrane surface. However, it seems
29

to be clear from the heated arguments in the field that the insertion is related to the Arg
energy when it is in the center of the membrane. In fact, once it is asserted that ∆G
app

corresponds to the water membrane partition then this must be related to the energy of
being at the center of the membrane. This issue is further addressed in the section 3.2.2.
We would also like to clarify that our CG finding about the importance of helix-helix
interaction in reducing the ∆G
app
for Arg cannot be overlooked by arguing that Meindl-
Beinker et al. experiment
37
show very little effect of mutating the helixes (see section
3.2.2).
At any rate, the difficulties of reproducing the assumed energetic of Arg at the center of
the membrane led to the implication that the observed energy corresponds to the motion
from the TR to the membrane
34,44,45
. Unfortunately, as stated above, we are not aware of a
clear justification for this assumption. Thus the relatively clearly defined issue of the
energetic of charges in the center of the membrane forces one to move to the far more
challenging issue of the energetics of the whole insertion process.
The pioneering studies of von Heijne (e.g. ref
49
) have established the “positive-inside”
rule, which identified the retention of the positively charged N-terminus on the
intracellular part of the membrane. It has been found that positively charged amino acids
are important elements in targeting peptides that direct proteins into mitochondria, nuclei,
and the secretory pathways of both prokaryotic and eukaryotic cells. The exact structure
base origin of this effect becomes an open question.
In both prokaryotic and eukaryotic cells, proteins are allowed entry into the secretory
pathway only if they are endowed with a specific targeting signal - a signal peptide
(SP)
50
. Goder and Spiess
40
performed systematic and elegant studies of the in/out ratio in
the insertion of SPs with a helical segment and a tail of different length and provided
intriguing information about the insertion process. In particular, it has been found that
increasing the positive charge in the N-terminal increases the percentage of the C-
translocated peptides (N
in
), while increasing the length of the helix decreases this
percentage. Furthermore, the fraction of C-translocated peptides increases upon moving
30

from short tails to longer tails, until reaching a fixed fraction (see Fig. 12). Reproducing
and rationalizing these experimental trends is clearly a worthwhile challenge.

3.2.2. ON ∆G
APP

This paper put significant emphasize on the origin of the ∆G
app
. Here it is important to
avoid some assertions that were discussed in the main text, and because of space
limitation we add here some additional discussion. For example, we would like to point
out that our CG finding about the importance of helix-helix interaction in reducing the
∆G
app
for Arg cannot be overlooked by arguing that Meindl-Beinker et al. experiment
37

show very little effect of mutating the helixes. In fact, the experiments were done with
Asp and Asn but never with Arg, which would have led to a more conclusive finding.
That is, in the case of an Asp residue the desolvation penalty could easily lead to the
protonation of an Asp, since (pK
a
w
–pH) is relatively small. In fact, in our previous
study
13
we found Glu residue being protonated inside the membrane at pH=7. Thus it
seems to us that the experiments of Meindl-Beinker et al.
37
are not conclusive enough in
this respect and cannot be used to rule out the importance of helix-helix interaction for
insertion of charged residues into the membrane.
It is also important to further clarify the controversy about the ∆G
app
proposal as this adds
important background for the motivation of this work. The original implications that
∆G
app
for Arg corresponds to the equilibrium between a charge in the center of the
membrane and in water has been rather obvious, since otherwise it does not make senses
to talk on the thermodynamic scale of insertion of amino acids from water to membrane.
Of course, one can offer many suggestions of how the Arg in the actual experiment
cannot be at the center of the membrane (e.g. refs
51,52
) or to argue that the system cannot
hold the charges in the center of the membrane. However, as pointed out in the main text
the question has been logically related to the rationalization of very small apparent
energy of a charged Arg at the center of the membrane.

31

3.2.3. ON THE “POSITIVE INSIDE” RULE AND ON TOPOLOGY CONSTRAINTS
In considering the “positive-inside” rule we also note that for the ER signals the charge
difference between the two flanking regions of the signal core, rather than the positive
charge per se, correlates with the signal sequence orientation
53
. Because there is no
general electrical potential across the ER membrane, the charge rule is likely to be due to
the interactions of charges in the signal with those at or near the translocon
54
.
It is interesting to mention that the positive-inside rule applies even to organisms with
reversed membrane potential (i.e. inside-positive instead of negative)
55
. In these cases the
retention of positive charges in the cytoplasm can’t be determined by membrane
potential. Cases like these suggest the importance of the insertion process by itself in
determining the final membrane protein topology.
Goder et al.
54
argued that the TR charges are not solely responsible for the positive-inside
rule, and that other subunits of the translocon complex may as well contribute to the
charge rule. Due to the lack of the electrical potential across the ER membrane in
eukaryotes lipids may still influence the “positive-inside rule” by asymmetrically
accessing the lateral gate of the TR, thus creating the charge imbalance between the two
sides of the membrane. Some experiments suggest even more tricky tools, like changing
lipid composition and Ca
+
concentration, that cell might utilize in establishing the charge
rule
56
.
The proteins synthesized by the ribosome are allowed to enter into the secretory pathway
only if they are endowed with a specific targeting signal - a signal peptide (SP)
50
. The SP
is in most cases a transient extension to the amino terminus of the protein and is removed
by one of a small class of enzymes known as signal peptidases once its targeting function
has been carried out. The studies of the SP insertion performed by Goder and Spiess
40
led
to the interesting suggestion of the retention and inversion models. In the first model the
positive side of the SP is retained in the cytoplasm by interaction with the negative
charges at or near the TR, thus the SP inserts into the TR with predefined orientation and
doesn’t change it during the protein synthesis. In the second model the SP enters the TR
with either N
in
or N
out
orientation and then inverts its orientation to position positive part
32

of the SP facing the cytoplasm. There are several experimental studies that support both
retention and inversion models
40,41,57,58
. The recent multiple CG trajectories analysis of
Zhang and Miller
48
suggested that the SP may utilize both types of mechanism.
More evidence appears in the literature suggesting that the first signal peptide is not the
sole determinant of the whole polytopical membrane protein topology. As was shown in
ref
59
, the topology of the protein containing five transmembrane helices could be
controlled by a single positively charged residue placed at the very end of the protein.
This result suggested that the protein remains “topologically uncommitted” until the last
residue is synthesized. Since the size of the translocon pore seems to only allow the
accommodation of one helix, membrane proteins should use other mechanisms to flip
their orientation in the lipid bilayer. Analysis of membrane protein structure database also
suggested that transmembrane helices must reposition during folding and
oligomerizations
60
.
Multiple studies conducted by Dowhan’s group (e.g. refs
61,62
), indicated that lipid
composition is important for the membrane protein orientation. It seems that the
interaction of the nascent polypeptide chain with the translocon only determine the initial
orientation of the TM domain. The final protein orientation depends on short-range
interactions between the protein and the lipid environment and long-range interactions
within the protein during final folding events. This means that the membrane protein
organization can be changed post-assembly depending on changes in the lipid
environment. This leads to an interesting possibility of lipid environment, which changes
along the protein secretory pathway, to activate initially latent membrane proteins.
Some TR mutations are known to affect the topology of membrane proteins
43
. For
example, Spiess and coworkers identified a class of such mutants and found that all of
them have a prl phenotype. This type of mutants allows proteins with defective or absent
signal sequence to be translocated. Based on the translocon structure information Smith
et al.
63
proposed that prl mutations either destabilize the closed state of the channel or
stabilize the open form, thus allowing the channel to open without triggering events of
the signal sequence binding.
33

3.2.4. ON THE EFFECTIVE BARRIER
In this work we assess the barrier for the TR insertion starting from the estimate of ref
41

that the SP reaches its final orientation in ~50s during the ribosome-driven insertion
process. Unfortunately this estimate is based on the ribosome translation rate of about 5
amino acids/s, thus implying that the TR barrier is designed so that the rate of transfer
trough the TR will be similar to the rate of exit from the ribosome. Although this is
clearly a very tentative assumption it represents all the currently available information
and thus we consider here an estimate of a transfer of about 3Å in (1/5)s. Now assuming
that the TR barrier has an effective width of around 15 Å we can obtain a rough estimate
of the effective activation barrier by using transition state theory (TST) with a
transmission factor correction (e.g. ref
64
):
( )
12
6 10 exp / k g RT κ ≈ ⋅ ⋅ −∆
‡
(39)
where

∆g
≠
is the activation barrier in kcal/mol and RT is 0.6 kcal/mol at room
temperature. The transmission factor, κ
,
is given by the number of time the targectory,
that arives to the transition state (TS) and ends at the product state , moves back and forth
on the TS. The tratment of equation 39 can become less valid when we have a low
activation barrier and when we have a diffusive porcess. In the case of the insertion
process we belive that the activation barrier is sufficintly high to be treated by TST with
some transmisison factor coefficient. We also note that the diffusion constant used by
ref
48
(which is related to the transmission factor) presents very significant overestimate.
At any rate, with a transmision factor of 0.5 we estimate the activation barrier to be in the
range of 20 kcal/mol. If the transmission factor is around 0.01 we have to reduce the
activation barrier by about 2.5 kcal/mol but it is still in the range used in the present
work. Obviously unless we have a realistic structural model with the ribosome we cannot
get a sufficiently accurate PMF to push for more well defined activation barrier.
However, at some stage it will be worthwhile to use our renormalization approach
10
and
to obtain a realistic effective friction and effective activation barrier.

34

3.3. THE CG METHOD, ENERGY CONTRIBUTIONS AND CALIBRATION
CG models appeared to be very effective in elucidating protein functions (e.g. ref
10
) and
the CG model has already been used by us in a study
13
of the assumption that ∆G
app

reflects an equilibrium process. A recent work
48
used a drastically simpler CG model
(turning each 3 residues into one effective residue in a 2-D model). This CG study
provided captured effects that are probably determined by very coarse features. However,
this model has not explored the relevant energetics, and we believe that understanding the
nature of the free energy landscape rather than dynamical features is crucial for a better
description of the control of the insertion process and for the elucidation of the nature of
∆G
app
. In fact, except in the very unlikely case that the insertion is a completely diffusive
event, the corresponding kinetics is controlled by the free energy barriers and minima
whose knowledge is a key to a clear description. Thus, it seems to us that our CG that is
focused on a realistic description of the electrostatic energetics provides the optimal
current strategy and such a model was used here.
Our CG model, whose details were given elsewhere
12
, has been continuously refined
5,12
,
considering a benchmark of absolute protein stability (an extension of the set considered
in ref
60
where we used the PDLD/S model) and also other relevant features such as pKa’s
and the energies of inserting charges into membrane. Recent examination of the effect of
the main chain and hydrogen bond terms on the agreement between calculated and
observed absolute stability of proteins led to a modification of the terms given in ref
12
.
The current terms and parameters are given in the MOLARIS Manual
6
.
Since the energy of insertion to the membrane plays an important role in our analysis, we
explored the performance of the CG model in evaluating the water to membrane insertion
energy and report the corresponding results in Table 2. Unfortunately, there is only one
direct experimental observation and a couple of direct simulation result (see Table 2), and
the calculated results significantly overestimate the values obtained from ∆G
app
. The
same well known problem occurs with other CG or physically based models
65,66
. At
present it is unclear what the origin of this problem is and it might reflect the following
three factors. (i) The value of ∆G
app
does not correspond to water-membrane equilibrium
35

(this issue is analyzed in great length in the main text). (ii) The overestimate of water-
membrane free energy difference can be in part due to the missing entropic effects
66
and
possibly due to having the helix in the water phase stabilized by the membrane surface
65
.
(iii) In the case of the TR-mediated experiments it is possible that the bound glycan in the
glycosylation site stabilizes the helix in the water phase by around 5 kcal/mol. The
corresponding effects were taken into account in part as a feasible limit in our second
estimate in Fig. 14. However, we must mention that our main conclusions do not change
by this scaling.

model ∆G
elec
∆G
hyd
∆G
solv
∆G
HB
∆G
tot
∆∆G
tot
(wat→mem)
∆∆G
est
(wat→mem)
polyA_wat 0.00 -4.44 -12.65 -5.12 -22.21
polyA_mem 0.00 -16.36 -0.49 -9.90 -26.75 -4.55 -(4÷5)

M2δ_wat -0.74 -4.96 -19.24 -0.23 -25.17
M2δ_mem 0.16 -26.13 -6.25 -2.17 -34.40 -9.22 -(6.0÷11.3)

polyL_wat 0.00 -5.24 -8.52 -2.15 -15.91
polyL_mem 0.00 -34.72 -0.39 -5.11 -40.23 -24.32 -3.0

RR_wat 0.45 -11.99 -19.82 -3.91 -35.27
RR_mem 1.18 -54.82 -7.47 -7.88 -68.99 -33.72 —

Table 2. Examination and calibration of the helix insertion energy. Energies in
kcal/mol. ∆G
tot
, ∆G
elec
, ∆G
hyd
, ∆G
solv
and ∆G
HB
are, respectively, the total free energy
(relative to state A), the electrostatic energy , the hydrophobic contribution, the main
chain solvation and the hydrogen bond contribution. ∆∆G
tot
(wat→mem) is the free
energy change for moving the peptide from water to membrane. ∆∆G
est
(wat→mem)
designated estimated values of the free energy change, which includes: the observed
value for the 20mer polyA
78,79
, the value for the 23-amino-acid M2δ segment of the
nicotinic acetylcholine receptor, estimated by other CG calculations
66,80
, the value for
the 12mer polyL estimated from microscopic simulations
81
.
36

3.4. RESULTS
Our studies starts with a focus on the SP sequences studies by Goder and Spiess
40
. These
SP’s generated mixed topologies in experiment where the partitioning depended on the
flanking charges and the signal hydrophobicity. In our calculations we truncated the C-
terminal to 4 residues and used the sequences shown in Fig. 6 (we also performed
calculations that considered the tail).
The TR was modeled by using as a starting point the SecY structure of the SecA-bound
form
23
(PDB ID 3DIN). The SP structure was created by PyMOL
67
from an arbitrary
helix of 30 residues by mutating the amino acids to the required sequence. The generated
SP was inserted into the TR by first placing it in the lateral gate (according to the recent
electron cryomicroscopy data
68,69
) and then relaxing the system, applying torsion and
hydrogen bond constrains on the helical part of the SP (22 oligo-leucine) to prevent it
from unfolding. The resulting model is depicted in Fig. 7.
In order to explore the origin of the observed
40
dependence of the in/out ratio on the
flanking charges of the SP, we calculated the barriers for the SP insertion into the TR for
Fig. 6. The sequences of the model proteins used to study the membrane protein
topogenesis. RR, PR and PH are the mutants of H1∆Leu22 SP truncated to 30
residues. The extra 21-residues were added to the C-terminal of H1∆Leu22 mutants to
estimate the effect of the tail on the CG profile. The names of the experimental
constructs 60[H1](+1) and 40[Leu16](+5) SP’s were kept, although they were
truncated to 40 and 51 residues, respectively. Charged residues are shown in bold. The
N-terminal charge of the H1∆Leu22 mutants was added to the first amino acid.
37

three SP’s named here RR, PR and PH (Fig. 6). We started with a targeted molecular
dynamics (TMD) treatment were we pulled the SP from the inside of the TR into the
cytoplasm (to reflect the reversed TR insertion process), into the membrane and into the
exoplasm (to reflect the translocation process). All the TMD runs constrained the helical
region of the SP to prevent it from unwinding (the reason for this will be discussed
below). Next we took the TMD insertion path and evaluated the CG energies at different
points along the path. The rational for this simplification is justified in section 3.5.1. We
only note here that even with the CG model we still have major convergence problems
since we are interested in stable results in order to analyze the relevant but small
experimentally observed free energy differences. Thus the current protocol that also
includes specialized mutational treatment (see section 3.5.1) is arguably the optimal
current strategy. In imposing the helical constraint we considered the fact that exploring
the insertion of a non helical system will drastically reduce the reliability of the
calculations. Thus we focused on the helical system whose energetics provides a
qualitative limit to the energetics of other insertion processes (see Fig. 8). We also note
that a recent work
4
concluded, by length estimates, that the inserted system in related
cases is at least partially helical. It was also found that the energetics of a helical
construct and a construct where the helix is perturbed by a central proline residue is quite
similar, indicating that non helical and helical insertion should have similar barriers.
The reaction coordinate (X) for the TR insertion and translocation was taken as the RMS
of the first and last amino acid of the SP respectively, and as the RMS of the first and last
residues of the helical part of the SP for the membrane insertion. Zero reaction coordinate
corresponds to the SP positioned inside the lateral gate of the TR, X
ins/transl
<0 – SP inside
the cytoplasm, X
ins
>0 – SP inside membrane, X
transl
>0 – SP in the extracellular part.
Although the insertion process is complicated and is driven by a vectorial process (e.g.
the ribosome) we started examining the energetics of the insertion without the ribosome
and then explored some aspect of the ribosome-assisted insertion and the effect of the
tail. Furthermore, we focused on the ∆∆G, namely the difference between the effects of
mutations on each of SP helical configurations (rather than on the difference between the
energies of the relaxed configuration of each mutant).
38

Fig. 7. The CG model of the RR SP inside the TR (at X=0). SP is shown in purple, TR
in orange with TM 2b and 7 forming lateral gate in green, membrane in gray. Part of
the membrane is removed for better protein visibility.
Fig. 8. Justifying the use of the helical model. The picture depicts tentative free
energy profiles for constrained helical peptide (solid line), for unconstrained peptide
(dashed and dot-dashed lines) and for TR insertion in the presence of the ribosome
(dashed line). In the case of the unconstrained peptide we depicted two possible
trends. Overall the figure reflects the assumption that the helical model provides a
qualitative way of estimating the trend in the profile for the real process that involves
relaxation from the helical structure.
39

3.4.1. THE ENERGETICS OF THE TRANSLOCON-ASSISTED MEMBRANE INSERTION AND
TRANSLOCATION
The calculated profile for translocon-assisted membrane insertion and translocation of
RR SP is shown in Fig. 9, where the data points are plotted relative to the ∆G
tot
(A
in
) of
the corresponding SP in N
in
orientation. It should be noted that ∆G
tot
(A
out
) appears shifted
up for RR SP, although the free energy of the system where the SP is fully positioned in
water should be the same independently of the SP orientation. The shift is due to the
Fig. 9. The CG free energy profiles for insertion into the TR (blue lines), into the
membrane (red lines) and translocation (green lines) for the RR SP in the N
in
(solid
line) and N
out
(dashed line) orientations. All profiles are plotted relative to the free
energy of the N
in
SP in water (at the very negative X). The data points were obtained
from the calculations for the SP without the tail. The effect of the tail is discussed in
the text. Note that the difference between the energy of C
(in)
and C
(out)
is an artifact
due to the fluctuations in the distance between the SP and the TR as well as due to the
limited membrane spacing. The energy in the membrane is most probably too negative
as discussed in the section 3.3 and indicated by the tentative gray lines.
40

electrostatic interaction of the SP with the overall field from the TR. This effect decreases
when the charge of the SP is reduced. Overall we find that two positive charges on the N-
terminus side of the RR SP create the highest barrier for the insertion into the TR. We can
also see the reduction in the free energy of the SP positioned inside the TR (state B) when
the charges are eliminated (see Table 3).
To explore the consistency of the different models we compared the difference in the
barrier heights for the TR insertion (∆∆g
‡
(A
`
out
→A
`
in
)) and the difference in the free
energies inside the TR (∆∆G(B
out
→B
in
)) of the SP’s in the N
in
and N
out
orientations with
the corresponding experimental values (∆∆G
exp
(N
out
→N
in
)) (Table 3 and Fig. 10A). Both
sets have a reasonable correlation with the experiment. However, the calculated effects
are significantly larger than the corresponding observed effect. This trend is due in part to
the missing compensating contributions associated with the use of a fixed helix and an
identical path for N
in
and N
out
(note that the apparent dielectric effect reflects factors that
are not explicitly included in the simulations
70
), as well as to the missing effect of the tail,
which will be considered below.

41

SP system ∆g
‡
(A`
in
) ∆g
‡
(A`
out
) ∆∆g
‡

(A`
out
→A`
in
)
∆G(B
in
) ∆G(B
out
) ∆∆G

(B
out
→B
in
)
∆∆G
exp
(N
out
→N
in
)
H1∆Leu22
RR 25.11 29.49 -4.38 -7.03 -5.65 -1.38 -0.82
PR 23.72 26.36 -2.64 -9.17 -9.11 -0.06 -0.12
PH 21.42 22.25 -0.83 -11.01 -12.06 1.05 1.30

60[H1](+1)
R74(74)E 15.91 23.71 -7.80 -7.94 -2.08 -5.86 -0.62
K264(284)E 17.76 25.12 -7.36 -6.06 -0.67 -5.39 -0.50
wt 17.73 24.57 -6.84 -6.64 -1.10 -5.54 -0.26
Q234(261)R 17.51 24.07 -6.56 -7.10 -1.59 -5.51 -0.07
Q93(93)R 19.37 24.95 -5.58 -5.98 -0.59 -5.39 0.17

40[Leu16](+5)
K37(65)E 31.11 29.04 2.07 -3.50 5.37 -8.87 -1.02
D6(34)R 31.33 26.17 5.16 -2.90 3.44 -6.33 -0.98
K264(284)E 30.54 23.46 7.08 -6.86 0.35 -7.20 -0.29
R74(74)E 27.11 22.95 4.16 -9.07 1.90 -10.96 -0.12
wt 29.28 22.26 7.02 -7.89 0.80 -8.68 0.10
Q234(261)R 28.87 21.65 7.22 -8.66 1.13 -9.78 0.47
Q93(93)R 29.58 21.85 7.73 -7.23 1.75 -8.97 0.62

42

Table 3. Energetics of the insertion process for the different systems. Mutation data
for the three SP’s: H1ΔLeu22, 60[H1](+1) and 40[Leu16](+5). The three mutants of
the H1ΔLeu22 peptide studied were: RR, PR and PH (see sequence in Fig. 6). The
system name indicates the relevant TR mutation. The residue number represents its
position in SecY, were the corresponding position in Sec61 given in parentheses. For
the 40[Leu16](+5) peptide the effect of the SP mutations was studied in addition to
the TR mutations. The residue number for the SP mutation is for the simulated SP (see
sequence in Fig. 6) were the corresponding position in the original peptide is given in
parentheses. ∆g
‡
(A`
(in)
) and ∆g
‡
(A`
(out)
) are the barrier heights for the SP insertion into
the TR in N
in
and N
out
orientations respectively. ∆G(B
(in)
) and ∆G(B
(out)
) are the free
energies of the SP inside the TR in N
in
and N
out
orientations respectively.
∆∆G
exp
(N
out
→N
in
) is the preference of the N
in
orientation versus the N
out
obtained
from the experimental results of Goder and Spiess
40
, who reported the percentage data
for C-terminus translocated SP’s. To get the free energy we first converted the
insertion probability (P=f(N
in
)/(f(N
in
)+f(N
out
)), where f(N
in
) and f(N
out
) are the
fractions of SP’s with N
in
and N
out
orientations respectively) to the equilibrium
constant, K=f(N
in
)/f(N
out
). The result can be converted to the free energy using the
relationship ∆G=-RTlnK. The resulting free energy would represent the free energy of
inserting SP in N
in
orientation with respect to the one in N
out
orientation, which we
denote as ∆∆G
exp
(N
out
→N
in
). It should be noted that experiment was done with yeast
Sec61p translocon, whereas in calculations we used bacterial SecY structure from
23

(PDB ID 3DIN). Energies are in kcal/mol.
43

Fig. 10. Examining the correlation between different calculated and observed effects.
∆∆g
‡
(N
out
→N
in
) is the difference in the TR insertion barrier heights for the N
in
and
N
out
orientations of the SP, ∆∆G(N
out
→N
in
) is the difference in the free energy of the
SP positioned inside the TR in N
in
and N
out
orientations. And ∆∆G
exp
(N
out
→N
in
) is the
experimental estimate of the difference between the free energies of the two
orientations. (A) The correlation plots for the insertion of the different SPs. (B) The
correlation plots for the insertion of the 60[H1](+1) SP . The data points are obtained
for the wild type SecY TR and the R74E, Q93R, Q234R and K264E mutants. (C) The
correlation plots for the insertion of the 40Leu16(+5) SP. The data pointes are for the
wild type and 4 mutant SecY structures (R74E, Q93R, Q234R and K264E) as well as
for the mutations of the SP (D6R and K37E).
44

3.4.2. THE EFFECT OF MUTATIONS ON THE ENERGETICS OF THE TR-ASSISTED SP
INSERTION
Next we calculated the effect of TR mutations on the energetics of the SP insertion,
considering the experimental data from
43,54
. The SP models were derived from
60[H1](+1) and 40[Leu16](+5) peptides, while truncating the N- and C-terminals of the
SP’s (Fig. 6). The peptide models were built in a way similar to that described above. The
experimental results for the TR mutations were taken from studies of the yeast S.
cerevisiae Sec61 TR
43,54
. To check the effect of similar mutations in the T. maritima
SecY system, we also used the sequence alignment data from
71
considering data from
conserved residues in both organisms. The calculated results are summarized in Table 3
and the correlations of ∆∆g
‡
(A
`
out
→A
`
in
) and ∆∆G(B
out
→B
in
) with ∆∆G
exp
(N
out
→N
in
) are
given in Fig. 10B and 10C. As can be seen from Fig. 10B, ∆∆g
‡
(A
`
out
→A
`
in
) of the
60[H1](+1) SP has better correlation with experiment than ∆∆G(B
out
→B
in
). On the other
hand, for the 40[Leu16](+5)CPY ∆∆G(B
out
→B
in
) is uncorrelated with ∆∆G
exp
(N
out
→N
in
)
(see discussion below). Finally, we found that the effect of the TR mutations that change
the in/out ratio was independent from the tail effect.

3.4.3. THE EFFECT OF THE RIBOSOME ON THE ENERGETICS OF THE TR-ASSISTED SP
INSERTION
In the absence of direct estimate of the time for the insertion process we took the
estimate
41
of a translation rate of about 5 amino acids per second. We note however, that
this estimate does not tell us what exactly the actual barrier in the TR is and that it is
taken in the absence of alternative information. At any rate, this time constant can be
converted to an activation barrier of 20 kcal/mol based on transition state theory. This
must present a significant acceleration above the rate of insertion without such an
external help, indicating that the insertion process is only feasible with the help of
activating systems. The ribosome can act just by its direct electrostatic effect or by
changing the structure of the TR and thus reducing the barrier. To explore these options
we examined first how the ribosome charges may affect the barrier for the SP insertion.
45

This was done by adding 16 negative charges 5 Å away from the membrane surface in a
position similar to rRNA H59 helix of the ribosome using the data from the cryo-EM
structure of the ribosome-SecY complex
68
. The addition of the negative charges reduces
the barriers for RR TR insertion in N
in
and N
out
orientations by about 2 kcal/mol. Next,
we explored the possible indirect effect of the ribosome induced TR structural changes on
the SP insertion. For this purpose we used the cryo-EM structure of the SecY. Now (see
Fig. 11) we obtained very significant reduction in the barrier heights for the RR SP
insertion into the ribosome-bound TR: ∆g
‡
(A
`
in
)=6.3 kcal/mol and ∆g
‡
(A
`
out
)=9.3
kcal/mol. Although the high resolution structure of the ribosome-TR complex is not
available and our modeling does not involve the simulation of a protein chain growing
inside the ribosome, we believe that we captured the trend in the real effect. We also note
that despite the fact that the X-ray structure with SecA does not show the large structural
change used here it may also have an activated open structure (see
23
). However, it is very
likely that the movement from the SecA-bound to the ribosome-bound TR structure
presents a significant overestimate of the actual opening. Thus we considered in Fig. 11
(and in the subsequent discussion) a profile that takes 55% of the SecA-bound and 45%
Fig. 11. The effect of the ribosome on the TR insertion profile. RR SP was inserted
into the SecA-bound SecY TR (solid line) and ribosome-bound Sec61 TR (dotted
line) in N
out
orientation. The profiles are plotted with the respect to the system
structure with the SP in water (X ≈ -74Å). The intermediate profile was generated by
scaling the TR-bound and the ribosome-bound profiles by 0.55 and 0.45, respectively,
in order to obtain the experimental value of ∆g
‡
=20 kcal/mol (dashed line).
46

of the ribosome-bound TR insertion profiles to reproduce the rough experimental
estimate of ∆g
‡
(A
`
in
) (20 kcal/mol) of the barrier of the insertion process. The idea is that
in this way we capture the some of the tentative effect of the ribosome while still having
a reasonable barrier. We are also well aware that the role of SecA includes an active ATP
driven process (see Fig. S2 of ref
13
). However, in the present case we only include this
effect implicitly.

3.4.4. THE EFFECT OF THE TAIL
In order to explore the qualitative effect of the tail residues we added 21 residues to the
C-terminus of RR, PR and PH SP’s, using the sequence of the H1∆Leu22 protein
40
with a
limited relaxation. Here, we considered first the effect of a short tail case (see Fig. 12)
were we used the actual sequence of the 21-residue tail with its ionizable groups. In this
case we reproduced the observed trend of Fig. 12 and rationalize its origin (see
concluding discussion). For the long tail limit we have not performed any simulations,
but, it is reasonable to assume that the longer tail will increase the hydrophobicity effect
in the N
in
insertion. The consideration of the tail also helped to rationalize the
overestimate of ∆∆g
‡
(A
`
in
→A
`
out
) obtained for an isolated helix, since the tail charges
destabilize N
in
.
Moving from a short helix to a long one without the tail gives an equal decrease in the
hydrophobicity (about -4 kcal/mol) to N
in
and N
out
. Furthermore, the addition of the tail
with its charges increases the energy of the TS for N
in
(where the tail passes near the
helix) by about 5 kcal/mol for both the short and long helix (note that the electrostatic
effect of the tail is an overestimate due to the incomplete stabilization of the charges of
the tail where a major sampling including exploring ion pair formation between the tail
charges would be required for improved absolute values). However, the addition of the
tail reduces the hydrophobicity effect in moving from a sort to a long helix by about 1
kcal/mol in the N
in
case. Thus ∆∆g
‡
for N
in
going to N
out
decreases by 1 kcal/mol,
moving from a short to a long helix, which is consistent with the experimental trend of
the reduction in the in/out ratio.
47

We have not performed simulation studies in the long tail limit. However, it is reasonable
to assume that a longer tail would increase the hydrophobicity effect on the N
in
path and
stabilize the top of the barrier more than with a short tail, for a fixed helix length.
Another interesting issue is the nature of the barrier for moving the tail to the endoplasm
in the N
in
case. The corresponding barrier is unlikely to be rate limiting, as the effect of
the helix charges changes the in/out ratio and this cannot happened at the stage when the
Fig. 12. The observed dependence of the percentage of the translocated C-terminus,
which is proportional to the in/out ratio, on the SP hydrophobicity and the N-terminal
positive charge. The figure describes the main trend obtained in the experiment of
ref
40
, and also presents the corresponding calculated trend. The calculated effect of
moving down vertically (from a shot helix to a long one) is consistent with the
reduction of the in/out ratio, whereas moving horizontally is consistent with the
observed increase in the in/out ratio (see text for details).
48

tail goes to the outside, unless the helix is still in the TR (or between the TR and the
membrane) in the stage of the tail exit. However, this would reflect the interaction
between the helix charges and the tail rather than between the helix charge and the TR,
which is found here. In particular the fact that the in/out ratio does not change when the
tail becomes long enough, indicates that the helix insertion is the rate limiting in these
cases.

3.5. CONCEPTUAL ANALYSIS

3.5.1. THE JUSTIFICATION OF THE MODEL
The present study may seem to some readers as an extremely oversimplified collection of
qualitative assumptions. In fact, some readers may assume that all atom TMD studies
must be much more reliable than the current calculations. This, however, may reflect the
familiar confusion of the rigor of a model with its ability to converge and to give
meaningful results. In fact CG models are at present significantly more reliable that full
atomistic models in capturing the action of, for example, molecular motors
72,73
.
In fact when we started the present study we explored the performance of the PMF of the
CG model and found them (not surprisingly) to involve major instabilities. The problem
is that we are looking on almost a folding problem and that we are interested in small
energy differences such as the effects of mutations (see also below). Attempts to take the
points generated in the preparing the PMF calculations and to average the corresponding
CG energies provided better but still unstable results for our purpose of estimating
mutational effect. Here we note that the main strength of the CG is in obtaining the
electrostatic energy of the simplified side chains since the main chain is described
explicitly with the regular instability of all atom models. In fact the main power of the
CG model is in looking on stabilities of proteins in folded structures or in exploring the
energetic in well-defined paths without significant fluctuations of the main chain (e.g. the
remarkable successes in modeling the landscape of F1-ATPase
73
). It also appeared that
49

the interaction with the L6/7 and L8/9 loops of the TR added to the instability, since in
the SecA-bound TR structure these loops locate on top of the TR channel (in contrast to
ribosome-bound TR structure, where these loops are tilted away from the channel axis by
the interaction with the ribosome). Eventually we found out that the instability can be
reduced drastically by performing a short TMD without significant relaxation and then
evaluating the CG effective energy (which actually corresponds to the free energy) at
each point along the TMD path. The next crucial step in obtaining stable results was
made by fixing all the TR residues, since otherwise the calculated results become rather
unstable and uninformative. Similarly in exploring the in and out energies we found it
essential to use the same geometries of the SP main chain and only mutated the side
chains to reverse their order.
Of course, we are very well aware of the need for sampling; we also introduced many key
studies of sampling with explicit (e.g. ref
74
) and implicit (e.g. ref
75
) protein model, but the
whole point of the CG model is that it already captures a large part of the averaging
process (the same is true with the use of a proper effective dielectric). At any rate, the
present study did focused on the most effective ways of obtaining stable results and
reproducing mutational trend rather than on the most rigorous treatment (which at present
cannot provide what is needed here).
Of course part of the difficulties in moving to more explicit treatment reflected the fact
that the ribosome was not included explicitly, the fact that the tail was sometimes
truncated and the fact that we considered just the insertion of a preformed helix. The
effect of the ribosome was estimated by considering the effect of its charges, as well as
and its effect on the TR structure. It was found that the effect of the ribosome on the
in/out distribution is not likely to account for the mutational effects considered here.
Similarly, we have considered the effect of the tail and showed that it also does not
account for the mutational effects either. The justification of using a preformed helix
model was given in the section 3.4.
50

Overall we believe that calculations are sufficiently reliable to (a) establish qualitatively
the general shape of the insertion profile and (b) to show that the calculated electrostatic
effect of some key mutations occurs at or near the barrier of the insertion profile.
3.5.2. INSERTION MODELS ANALYSIS
Although the present CG profile does not provide a quantitative tool of estimating the
activation barriers for the insertion process, there are elements of the calculations that are
quite reliable and robust, at least in establishing the relative trends. Current work for the
first time supplies a relatively clear way of formulating energy based insertion problem
and relating it to the available experiments. This can be done by considering the energy
diagrams of Figs. 13 and 14, where we provide estimates of the barriers for the different
feasible paths. Here we used the scaled results mentioned above with ∆g
‡
(A
`
out
) set at 20
kcal/mol. Furthermore, the energy values in the membrane were treated as discussed in
the section 3.3. Thus we obtained the second set of energies used in Fig. 14.
In considering Figs. 13 and 14 we can reach several tentative conclusions. The first is that
the insertion is most probably irreversible since the barrier for going back from the
membrane to the initial state is higher than the forward barrier. That is, the forward
barrier in the ribosome-assisted process can be estimated to be about 20 kcal/mol,
whereas the stabilization by the membrane is most probably more than 10 kcal/mol. Thus
the back reaction is at the range of 30 kcal/mol, which is not accessible at biological
times. This conclusion is supported by the analysis of the mutation experiments where we
found much better correlation between the calculated and observed results for the forward
activation barrier that for the equilibrium free energy.
Now despite the above conclusion we still have to ask whether the equilibration between
the in and out configurations may involve state B as an intermediate. To explore this
issue we note that that the barrier for moving to the membrane (B
(in)
→ C
(in)
or B
(out)
→
C
(out)
) is relatively small (in agreement with other calculations
34
). Thus the retention
model (Fig. 13A) leads to the conclusion that state C
(out)
can move to state D. In fact, the
model also allows for movement from D to C
(in)
trough B
(in)
. However, this is inconsistent
with the fact that the in/out equilibrium is not determined by the final states (C
(out)
and
51

C
(in)
) since this states are likely to have very similar energies (unless somehow the SP
inserted to the membrane stays near the TR or the ribosome). It is also likely that we
underestimate the D to B barrier but it would not change our conclusions. Considering
the alternative inversion model (Fig. 13B), we can also see the same problem
(equilibration between the two inserted configurations). Interestingly, the second
inversion model (Fig. 13C) seems to be inconsistent with the observed in/out partition,
since the barrier for A to B (or A`) is identical for the in and out paths and this should
lead to 50% ration which is not observed experimentally in most cases. However, it may
be possible that the second barrier becomes higher than the first barrier in the case of a
short tail. In such a case we will have a very small in/out ratio for a short tail and a ratio
of 50% (which is the result of having the same rate limiting barrier) only for a longer tail.
Yet, since we did not observe exactly 50% this would mean that such a scenario is only
possible if the path of Fig. 13C is not the only path. At any rate, the crucial point is that
all models are consistent with a kinetic control by ∆g
‡
(A`
in
) and none seems to reflect the
equilibrium between the TR and membrane (see also concluding discussion).
52

53

Fig. 13. Qualitative free energy profiles for different insertion pathways. (A) The
profiles for the retention model. The SP insertion in N
in
(solid line) and N
out
(dashed
line) orientations consist of TR insertion (in blue), membrane insertion (in red) and
translocation (in green) parts. State A corresponds to the SP in the cytoplasm, state B
– to the SP inside the TR, state C – to the SP inserted into the membrane, and state D
– to the SP in the exoplasm. (B) SP insertion model where inversion to N
in
orientation
occurs simultaneously with polypeptide synthesis (step A
(in)
→B
(in)
). (C) A model
where the head-on insertion (through A`
(in)
) is followed by the inversion to N
in

orientation (through A``
(in)
).
54

55

Fig. 14. Kinetic schemes for different insertion models. (A) A scheme for the
retention model. The numbers are taken from the calculation for RR SP after scaling
them by 0.68 to fit ∆g
‡
(A
(out)
→B
(out)
) to 20 kcal/mol. The numbers in parentheses
represent the estimated free energy after taking into account the missing effects
discussed in the section 3.3. (B), (C) The kinetic schemes for the two inversion
models depicted in Fig. 13.
56

3.5.3. ANALYZING THE ORIGIN OF ∆G
APP

The analysis of Fig. 13 is not directly related to the experiment that determined ∆G
app

(which used a different system). Thus we consider in Figs. 15 and 16 the process that
corresponds to the measurements of ∆G
app
. In generating these figures we took into
account the fact that both state H and G are likely to have similar values to within a few
kcal/mol, since otherwise (with the exception discussed below) the population in water
would not be observed experimentally. Thus we considered the limit of the second set of
the membrane water energies (see above) but also kept in mind the actual CG results.
Using these two limits we can reach the following conclusions (see Fig. 16): (i) If
∆∆G(H→G) is small and if the back barriers from H to F (
H F
g
→
∆
‡
) or G to F (
G F
g
→
∆
‡
)
are lower than the limiting barrier,

g
τ
∆
‡
(which is taken as the barrier that corresponds to
the time in the experimental measurements), we come back to the original idea that ∆G
app

reflects equilibrium between the membrane and the water systems (Fig. 16A). In this case
Fig. 15. A kinetic scheme for the analysis of ∆G
app
. The reported values are taken
from the CG calculations of the H-helix with a central arginine. The values in bracket
present an estimate that is within the limits considered in Fig. 16A. However, the
energies of H and G might to be significantly less negative. The numbers on the paths
and at each state represent the activation barriers and relative free energies,
respectively, and are given in kcal/mol. The figure also provides the rate constants for
the key steps discussed in the text.
57

the equilibration is independent of the energy of state F so it is not an equilibration
between the TR and the membrane. (ii) If ∆∆G(H→G) is large and
H F
g
→
∆
‡
and
G F
g
→
∆
‡

are higher than the g
τ
∆
‡
,

then we have a kinetic control, where we might have a linear
free energy relationship (LFER), where the product distribution is correlated with the
activation barriers (see section 3.5.3.1), so that the forward rates are correlated with
∆G
app
(Fig. 16B)) . (iii) In the less likely case that the ∆G of H and G is very different
(|∆∆G(H→G)| > 4 kcal/mol), the forward barriers from F must determine the populations
of G and F (otherwise one of them will not be observed) and in this case ∆G
app
must be
determined by LFER. The seemingly alternative option that |∆∆G(H→G)| > 4 kcal/mol
and that the barriers
H F
g
→
∆
‡

and
G F
g
→
∆
‡
are lower than would lead to the finding
of all the population in G (which is inconsistent with the experimental finding) (Fig.
16C). (iv) Finally in the case when the barriers are sufficiently small we can just focus on
the equilibrium problem with K
1
=W/TR and K
2
=M/TR (where M, W and TR correspond
to G, H and F, respectively), assuming that the experiment cannot determine whether the
H helix is in the membrane or in the TR region so that K
app
=(TR+M)/W. Now we can
show (see section 3.5.3.2) that K
app
=(1+K
2
)/K
1
and thus when K
1
and K
2
are much larger
than one we have K
app
= K
2
/K
1
= M/W and when K
2
<<1 we have K
app
=1/K
1
=TR/W.
Overall, none of the considered options is consistent with the currently popular
assumption that ∆G
app
is determined by the equilibrium between the TR and membrane.

g
τ
∆
‡
58

Fig. 16. Analysis of the interplay between the limiting energetics and the
corresponding consequences in the final partition. ( ) and (
) represent respectively, the activation barrier for moving back from water (or
membrane) to the TR and to the cytosol. is the limiting barrier that corresponds
to the length of the time in of the experimental measurements. ∆∆G is the actual free
energy difference between the water and membrane. The barriers are related to the
corresponding rate constant by transition state theory. In case (A) ∆G
app
can represent
water/membrane equilibrium. In case (B) we can only account for the observed ∆G
app
by assuming

LFER, whereas in case (C) we have a situation where all the H segments
will be inserted into the membrane, which is not observed experimentally. Additional
options are considered in the text .The energies of H and G might be significantly less
negative then the calculated values.
59

3.5.3.1.EXAMINING THE LFER FOR MEMBRANE INSERTION
Here we will examine the possibility of the LFER for membrane insertion based on the
information from the insertion profiles. Using our CG approach we examined the effect
of replacing central Leu residue on the H-helix designed in ref
18
by Arg and Glu residues
Fig. 17. (A) The CG free energy profiles for H-helices with a central Arg, Glu and
Leu (denoted as cR, cE and cL respectively). The simulated H-helix has the following
sequence: AAAALALALXLALALAAAA, where X is R, E or L. The energy in the
membrane is most probably too negative as indicated by the tentative dashed lines.
(B) Using the correlation between ∆∆g
‡
and ∆∆∆G to examine the LFER idea. ∆∆g
‡

is the change in the barrier height of the F→G and F→H parts of the profile when cL
is mutated to cR or cE peptide. ∆∆∆G is the change in the relative free energies of
states G and H when cL is mutated to cR or cE.
60

and calculated the TR insertion, translocation and membrane insertion profiles for each
protein (Fig. 17A). Using the data for the relative free energies of states G and H
(∆∆G(F→G) and ∆∆G(F→H)) and the barrier heights for F→G and F→H parts of the
profile (∆g
‡
(F→G) and ∆g
‡
(F→H)) we compared the changes in these values when
central Leu is mutated to Arg or Glu. The correlation plot for ∆∆g
‡
vs. ∆∆∆G (Fig. 17B)
showed a linear dependence, which is an indication of LFER. The results are summarized
in Fig. 17 and Table 4. As can be seen from Fig. 17 we have a reasonable LFER, which
may well be the origin of ∆G
app
. Note that LFER is a well-accepted concept in studies of
the related problem of protein folding
76
and in studies of chemical and enzymatic
reactions
64,77
. Thus one possibility is that ∆G
app
reflects LFER.

system ∆∆G
(F→G)
∆∆∆G
cL→i
(F→G)
∆∆G
(F→H)
∆∆∆G
cL→i
(F→H)
∆g
‡
(F→G)
∆∆g
‡
cL→i
(F→G)
∆g
‡
(F→H)
∆∆g
‡
cL→i
(F→H)
cR -19.76 -3.35 -4.38 -6.56 1.20 -0.25 4.06 -4.91
cE -18.04 -1.63 -2.06 -4.24 1.31 -0.14 4.70 -4.27
cL -16.41 2.18 1.45 8.97

Table 4. Examining possible LFER in the insertion process. ∆∆G(F→G) and
∆∆G(F→H) are, respectively, the free energies of states G and H relative to state F.
∆∆∆G
cL→i
(F→G) and ∆∆∆G
cL→i
(F→H) are, respectively, the differences in the
relative free energies of states G and H when cL is mutated to either cR or cE
(indicated as i). ∆g
‡
(F→G) and ∆g
‡
(F→H) are the barriers for moving H-helix from
the TR into the membrane and to the exoplasm. ∆∆g
‡
cL→i
(F→G) and ∆∆g
‡
cL→i
(F→H)
are the changes in barriers when cL is mutated to either cR or cE. Energies are in
kcal/mol.
61

3.5.3.2.ANALYZING THE SMALL BARRIERS CASE
We would also like to further clarify and extend the options (iv) considered above. To
simplify the analysis we can just concentrate on the part of moving from the TR to the
membrane and from the TR to water. Fig. 16 considers some of the key options but one
can also consider a few more cases. For example, one may suggest a case when the H
helix is more stable in the TR than in the membrane or in water. In this case (if the
activation barriers of going forward and backward are not too large) we will obtain a
partition between the H helix in water and the H helix in both the TR and the membrane,
which will be better described as equilibrium between the TR and water and that between
the TR and the membrane. We can, in fact, obtain a general solution once we assume that
the forward and backward rate constants from the TR to both the membrane (M) and to
water (W) are sufficiently large so that we have equilibration for each process. In this
case we can use TR, M and W for F, G and H, respectively and write:
1
2
/
/
1
K W TR
K M TR
TR M W
=
=
+ + =
(40)
We can also write
( ) /
app
K M TR W = + (41)
Note that here we added the fraction that is still in the TR as part of the membrane since
we cannot separate them experimentally. Solving equations 40 and 41 we get
2 1
(1 ) /
app
K K K = + (42)
This important result (which has not been pointed out before) corresponds to the
water/membrane equilibrium and not to the membrane/TR equilibrium. In the limit where
K
2
and K
1
are significantly larger than 1, we find that K
app
can be approximated by
K
2
/K
1
. In the other limit of K
2
<<1 we find that K
app
=1/K
1
. Interestingly, when K
app
is
approximately 1, which is the range chosen in designing the H helix of ∆G
app
, we can
have either K
2
≈ K1>>1, or K
2
<<1 and K
1
≈1. Thus it seems to us that the attempts to
62

invoke the membrane/TR equilibrium as the factor that determines ∆G
app
(K
app
=K
2
) is not
justified.
As much as the elusive question about ∆G
app
of Arg is concerned, we can make the
following analysis. (a) In the range of K
2
≈ K
1
>>1 we have ∆G
app
≈ RT ln(K
1
/K
2
). For
for the apparent free energy of Arg relative to Leu we can get
0 0 0
1 2 1 2
( ) ( ) ln( / ) ln( / )
app app app
G Leu Arg G Arg G RT K K K K   ∆∆ → = ∆ − ∆ ≈ −
 
(43)
where K
1
, K
2
and K
0
1
, K
0
2
are the equilibrium constants for the H-helix with central Arg
and Leu respectively. Using data from Table 4 we obtain
0
( ) ( ) ( ) 3.21 /
app Arg
G Leu Arg G W M G W M kcal mol ∆∆ → = ∆∆ → − ∆∆ → = (44)
This situation corresponds to the equilibrium between water and membrane. This might
be the case when Arg in the center of the membrane stabilized by other helixes in the way
considered in our previous work
13
, where we estimated the energy of moving Arg from
water to the membrane around 3-5 kcal/mol. A similar value will be obtained if we have
the combination of snorkeling, helix tilting and helix sliding
51,52
).
(b) In the range of K
2
<<1 we have K
app
=1/K
1
and ∆G
app
≈ RT ln(K
1
). Now the apparent
free energy of Arg relative to Leu will be
0 0
1 1
( ) ( ) ln( ) ln( )
app app app
G Leu Arg G Arg G RT K K   ∆∆ → = ∆ − ∆ ≈ −
 
(45)
and using data from Table 4 we will get
0
( ) ( ) ( ) 6.56 /
app Arg
G Leu Arg G W TR G W TR kcal mol ∆∆ → = ∆∆ → − ∆∆ → = (46)
In this case we have equilibrium between water and the TR. This corresponds to the
situation when Arg is in the center of the membrane and is not be stabilized by another
helix. In this case the energy of moving from water to membrane is about 20 kcal/mol,
which has been the origin of the controversy in the field. However, as we show here the
63

measurements cannot determine cases of extreme instability in the membrane since the H
helix will be in the TR. In both cases our estimates are at the observed range.
At any rate, our main point is that any actual proposal that the equilibrium between the
TR and the membrane determines ∆G
app
should be formulated in a similar way to the
present analysis, since otherwise such a proposal cannot be verified. Here obtaining the
free energy profile even in a very qualitative way forces one to formulate the problem in
a clear way.

64

3.6. CONCLUDING REMARKS
The present study focused on the qualitative CG exploration of the insertion free energy
landscape using the hints provided by biochemical studies, in view of the difficulties of
using brute force simulation to obtain relevant conclusions. The relative heights and
positions of the calculated CG barriers were found to be consistent with key mutational
information and with the “positive inside” rule. Furthermore, the tentative effect of the
TR opening induced by the ribosome is found to reduce the kinetic barrier. Equally
important is the fact that our systematic analysis indicated that the mutation studies of the
insertion process are much better correlated with ∆∆g
‡
that ∆∆G, indicating that we have
a kinetic control.
Our finding can be explained in rather clear qualitative terms, starting from our view that
the knowledge of the energetics of the system should provide the clearest way of
describing the kinetics and the partition results. For example, it must be obvious that the
positive inside rule is related to the interaction of the charge of the SP with some regions
of the overall system, but elucidating the relevant energy contributions is crucial for a
concrete understanding. Here the seemingly obvious suggestion would be the interaction
of positive charges with the negative ribosome charges that stabilizes the barrier for the
N
in
path. However, this cannot explain why mutations of the center of the TR change the
in/out ratio. In this case our calculations established that the TR electrostatic potential
stabilized a positive SP charge near the top of the free energy profile (the TS at A`
(out)
of
Fig. 13). Thus the most likely possibility is that the electric potential of the TR, at X of
approximately -40 Å, is responsible to the positive inside rule. Now if this is true then the
insertion is controlled by the height of the barrier, which is a non-equilibrium kinetic
control. Furthermore, our study seems to indicate that the effect of the mutations that
change the in/out distribution is independent on the ribosome effect.
This work reproduced the opposing trends in the effect of the hydrophobicity and polarity
on the in/out ratio. That is, the increase in positive charge increases the barrier for
insertion of the positive head and thus reduces the N
out
fraction. On the other hand,
increasing the hydrophobicity of the SP helix reduces the barriers for both the N
out
and
65

N
in,
but does it to a lesser extent in the case of N
in
, where the tail must also pass near the
inserted helix. This opposing trend is indicted in Fig. 12. Finally, we may also speculate
on the possible reason for the increase of the in/out ratio for long tails
41
(without
performing actual simulations). That is, with a long tail we probably have an increase in
hydrophobicity in the N
in
case and this is likely to lead to a decrease of the N
in
barrier and
an increased in/out ratio.
The most important advance in the present work is not so much in providing qualitative
free energy profiles but in forcing us to look at the alternative kinetic options in a well-
defined energy based logical way and to be able to incorporate experimental and
conceptual constraints in the overall analysis. In particular, the trend of the forward and
backward energy barriers provide a powerful way of analyzing key energetics
information such as the apparent membrane insertion energy ∆G
app
. It is concluded that
∆G
app
is unlikely to correspond to the difference between the free energies of the protein
inside the translocon and the membrane but in most limiting cases to the equilibrium
between the membrane and water or the equilibrium between the TR and water. The use
of our new formulation seems to resolve the controversy about ∆G
app
of Arg
.
Interestingly our calculated profile seems to provide a rational to the results found in the
recent exciting experiment of ref
4
.
Overall we view the present study as a demonstration of the need of a clear mechanistic
formulation in the study of the translocon-mediated insertion and of the ability to CG
modeling using the available experimental results as further constraints on the kinetic
analysis.

66

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Asset Metadata

Creator Rychkova, Anna (author)

Core Title Exploring the nature of the translocon-assisted protein insertion

Contributor Electronically uploaded by the author (provenance)

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Publication Date 07/23/2013

Defense Date 03/14/2013

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag apparent free energy,coarse grained model,membrane proteins,OAI-PMH Harvest,signal peptide,topology,translocon

Format application/pdf (imt)

Language English

Advisor Warshel, Arieh (committee chair), Haworth, Ian S. (committee member), Krylov, Anna I. (committee member)

Creator Email rychkova@usc.edu

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Abstract (if available)

Abstract The main subject of the current dissertation is related to the fundamental question of membrane protein folding. Membrane proteins represent an important class of proteins that is abundant in the most genomes (20-30% of all genes encode membrane proteins) and has significant pharmaceutical interest (target of over 50% of all modern medicinal drugs). Protein misfolding is increasingly recognized as a factor in many diseases, including cystic fibrosis, Parkinson's, Alzheimer's and atherosclerosis. Many proteins involved in misfolding-based pathologies are membrane-associated. Therefore, understanding the mechanism that governs membrane protein folding may aid in curing such diseases. ❧ The vast majority of membrane proteins get inserted into the lipid bilayer through the protein-conducting channel called translocon. The translocon is evolutionary conserved in all kingdoms of life - its homologues are found in eukaryotes, bacteria and archaea. In bacteria the translocon consists of the heterotrimeric SecYEG complex (where ""Sec"" originates from the name of the corresponding gene sec, which stands for secretion). The insertion of proteins into the translocon is performed by a motor protein. For posttranslational protein translocation, the translocon interacts with the cytosolic motor protein SecA that drives the ATP-dependent stepwise translocation of unfolded polypeptides across the membrane. For the cotranslational integration of membrane proteins, the translocon interacts with ribosome-nascent chain complexes and membrane insertion is coupled to polypeptide chain elongation at the ribosome. Together, the complex of SecYEG with the motor protein is termed ""preprotein translocase"" as it suffices for protein translocation. There are some translocase-associated auxiliary proteins that are known to participate in protein insertion into the lipid bilayer by transiently interacting with the translocon (e.g., the heterotrimeric SecD-FyajC complex and the YidC protein). ❧ There are many puzzling questions in the field of membrane proteins. One of such questions involves the discrepancy between the experimental and theoretical estimates for the apparent free energy of inserting charged residues into the lipid bilayer. Here we explore the nature of ΔG_app, asking what should be the value of this parameter if its measurement represents equilibrium conditions. This is done using a coarse grained model with advanced electrostatic treatment. Estimating the energetics of ionized arginine of a transmembrane (TM) helix in the presence of neighboring helixes and/or the translocon provide a rationale for the observed ΔG_app of ionized residues. It is concluded that the apparent insertion free energy of TM with charged residues reflects probably more than just the free energy of moving the isolate single helix from water into the membrane. The present approach should be effective not only in exploring the mechanism of the operation of the translocon but also for studies of other membrane proteins. ❧ The much more advanced question involves the elucidation of the molecular nature of the protein insertion and understanding the mechanisms that govern final membrane protein topology. Here we tried to challenge ourselves and to estimate the complete free energy profile for the translocon-assisted protein translocation and membrane insertion. At present it is not practical to explore the insertion process by brute force simulation approaches due to the extremely long time of this process and the very complex landscape. Thus we use here our previously developed coarse grained (CG) model and explored the energetics of the membrane insertion and translocation paths. The trend in the calculated free energy profiles is verified by evaluating the correlation between the calculated and observed effect of mutations as well as the effect of inverting the signal peptide that reflects the ""positive inside"" rule. Furthermore, the effect of the tentative opening induced by the ribosome is found to reduce the kinetic barrier. Significantly, the trend of the forward and backward energy barriers provides a powerful way of analyzing key energetics information. Thus it is concluded that the insertion process is most likely a non-equilibrium process. Furthermore, we provided a general formulation for the analysis of the elusive apparent membrane insertion energy, ΔG_app, and concluded that this important parameter is unlikely to correspond to the free energy difference between the translocon and membrane. Our formulation seems to resolve the controversy about ΔG_app for Arg. ❧ Having the complete free energy profile for the translocon-assisted membrane protein insertion in hands allowed us to approach an intriguing question about the biphasic pulling force of the translocon. In our current project we are trying to explore the nature of the coupling between the stalling of the elongation of proteins in the ribosome and the insertion through the TR. The origin of this long range coupling is elucidated by coarse grained simulations that combine the TR insertion profile and the effective chemical barrier for the extension of the nascent chain in the ribosome. Our simulation seems to indicate that the coupled TR/chemistry free energy profile accounts for the biphasic force. Apparently, although the overall elongation/insertion process can be depicted as a tug of war between the forces of the TR and the ribosome, it is actually a reflection of the combined free energy landscape. ❧ The results of the current work were published in two PNAS papers: *A. Rychkova, S. Vicatos, A. Warshel, On the energetics of translocon-assisted insertion of charged transmembrane helices into membranes, PNAS, 2010, 107(41), 17598-603