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A parallel computation framework for EONS synaptic modeling platform for parameter optimization and drug discovery

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A parallel computation framework for EONS synaptic modeling platform for parameter optimization and drug discovery

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Content A PARALLEL COMPUTATION FRAMEWORK FOR EONS SYNAPTIC MODELING PLATFORM FOR PARAMETER OPTIMIZATION AND DRUG DISCOVERY by Sushmita Lakshmi Allam __________________________________________________________ A Thesis Presented to the FACULTY OF THE USC VITERBI SCHOOL OF ENGINEERING UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE (BIOMEDICAL ENGINEERING) August 2008 Copyright 2008 Sushmita Lakshmi Allam ii ACKNOWLEDGEMENTS I wish to thank everyone who were directly and indirectly involved in the successful completion of my dissertation work. I express my sincere gratitude to Dr.Michel Baudry who introduced me to this project and led me through its successful completion. I was fortunate to work under his esteemed guidance filled with a lot of understanding and flexibility. I would like to immensely thank Dr.Ted Berger who extended his support whenever I needed and for letting me be a part of his lab. My heartfelt thanks to my committee member Dr.David Z. D’Argenio for his time in reviewing my work. Words are not enough to express my gratitude towards my mentor Dr.Jean-Marie Bouteiller, without whose support and motivation, this project would not have been possible. I profusely thank him for his patience during the numerous discussions that streamlined my thought process and his valuable contributions at every stage of this work. I thank Dr.Serge Bischoff who always inspired me through his hard work and Renaud Greget for his kind help in results acquisition. I sincerely thank Dr.Sageev George for sparing his precious time in helping me get started and working with the cluster, Dr.Walter Yamada and Shivani Pandya for providing me with access to the computing resources during crunch times and Ken Johnston for the administrative help. I thank all members of Dr.Berger’s lab, who provided an amicable environment to work in. iii I would like to thank our department chair Dr.Michael C K Khoo, faculty members of the Biomedical department, graduate advisors Mischal Diasanta, Chris Noll and my classmates in Biomedical Engineering who made these two years a memorable experience. I am extremely grateful to my friends Preeti, Smita and Shweta for being such wonderful companions in sharing the joy and caring through tough times. It was the unconditional love and support I received from all my family members, my dearest cousins Nirmala, Rajeev and Siritha who were always there for me and my two little sweethearts Abhi and Snigdha who always bring a smile on my face. I have no words to acknowledge the warm affectionate love, constant inspiration, encouragement I received from my beloved parents and my younger brother Tejaswi. This work is affectionately dedicated to them, as they are the architects of my past and present. Above all, I am thankful to the Almighty God for having showered his blessings upon me to achieve this proud moment. iv TABLE OF CONTENTS Acknowledgments ii List of Tables v List of Figures vi Abstract viii I. Chapter 1 – Introduction 1.1 Computational neuromodeling ………………………………………………..1 1.2 EONS………………………………………………………………………….2 1.3 Purpose………………………………………………………………………...3 1.4 Statement of the problem……………………………………………………....4 1.5 Significance………………………………………………………………………5 1.5.1 Parameter Optimization…………………………………………………..6 II. Chapter 2 – EONS Synaptic Modeling Platform 2.1 Background…………………………………………………………………….8 2.1.1 EONS Technology………………………………………………………..9 2.2 A tour of the user-interactive modeling platform……………………………….11 III. Chapter 3 – Methodology 3.1 Overall Description……………………………………………………………20 3.2 Implementation…………………………………………………………………22 3.2.1 Input data model XML…………………………………………………….23 3.2.2 Accessing the input data model……………………………………………24 3.2.3 Generation of multiple configuration files…………………………………25 3.2.4 Parallel Computing using multiple nodes of cluster……………………….26 3.2.4.1 PBS Commands…………………………………………………...28 3.2.5 Design of a database – MySQL……………………………………………29 3.2.6 Results retrieval and analysis……………………………………………32 IV. Chapter 4 – Conclusion 4.1 Applications……………………………………………………………………33 4.1.1 Application 1: Parameter Evaluation…………………………………......34 4.1.2 Application 2: Drug Discovery…………………………………………40 4.2 Conclusion……………………………………………………………………43 4.3 Future work……………………………………………………………………44 4.4 Discussion………………………………………………………………………45 References………………………………………………………………………………46 Bibliography……………………………………………………………………………..50 v LIST OF TABLES Table 2.1: Features of the EONS synaptic modeling platform. 10 Table 3.1: Structure and Content of the EONS Results DATABASE. 31 Table 4.1: Computation time on ordinary processors (vs.) cluster 44 node processors. vi LIST OF FIGURES Figure 1.1: Simulation modeling platforms in the CNS hierarchy. 2 Figure 2.1 The Stimulus Panel of the platform provides access to 12 the input depolarization parameters. Figure 2.2 Kinetic schema representation of AMPA/glutamate 13 7 states model. Figure 2.3 Kinetic schema representation of AMPA/glutamate 13 5 states model. Figure 2.4: Representation of NMDA receptor in 11 probable states 14 including its open and desensitized states. Figure 2.5: NMDA Receptor Panel contained in the postsynaptic 15 parameters Panel. Figure 2.6: Synaptic geometry panel to modify cleft parameters 17 Figure 2.7: Visual Feedback of calcium diffusion in the presynaptic 18 terminal and glutamate diffusion inside the cleft. Figure 2.8: Output responses for EPSP (b), neurotransmitter 18 concentration in the cleft at the location of release (c), Total postsynaptic calcium current (d), obtained for an action potential type input pulse (a), for simulation duration of 10 msec and default parameters at the interface. Figure 3.1: Schematic representation of the implementation on a 21 multi-node environment. Figure 3.2: A representation of the input data file in XML format. 24 Figure 3.3: Entity Relation Diagram of ‘eonsjan’ DB. 30 Figure 4.1: EPSP responses elicited by a single pulse stimulus as a 35 function number of AMPA receptors. Figure 4.2: EPSP responses elicited by a paired pulse stimulus as a 35 function of number of AMPA receptors. vii Figure 4.3: Maximum EPSP responses elicited by the first and second 36 pulses of a paired pulse stimulus as a function of number of AMPA receptors. Figure 4.4: EPSPs elicited by varying inter pulse intervals of paired 37 pulse stimulation. Figure 4.5: Maximum EPSP elicited by the first and second pulse 38 of the paired pulse stimulation. Figure 4.6: Patch-Clamp responses for NMDA receptors at different 39 magnesium concentration levels. Figure 4.7: EPSP values and their normalized values for a combined 42 effect of two compounds X and Y. viii ABSTRACT EONS modeling platform is a resourceful learning and research tool to study the mechanisms underlying the non–linear dynamics of synaptic transmission with the aid of mathematical models. Mathematical modeling of information processing in CNS pathways, in particular modeling of molecular events and synaptic dynamics, have not been extensively developed owing to the complex computations involved in integrating a multitude of parameters. In this paper, we discuss the development of a strategy to adapt the EONS synaptic modeling platform to a multi-node environment using a parallel computational framework to compute data intensive long simulations in a shorter time frame. We describe how this strategy can be applied to (i) determine the optimal values of the numerous parameters required for fitting experimental data, (ii) determine the impact of all parameters on various aspects of synaptic transmission (under normal conditions or conditions mimicking pathological conditions) and (iii) study the effects of exogenous molecules on both healthy and pathological synaptic models. 1 CHAPTER 1 INTRODUCTION 1.1 Computational neuromodeling Computational modeling approach was always looked upon with skepticism by experimental neuroscientists, as they believe that models are often far from reality and are too idealized compared to the highly complex real in-vivo conditions [1]. Nonetheless, quantitative modeling approaches are very promising in their ability to test proposed hypotheses. The very need for quantitative models arises, when the system under investigation is highly complex with too many counter intuitive inferences. However building realistic biological models faces many challenges, due to the numerous parameters to be integrated in the models and the complexity of the computations required to solve the large number of equations describing the individual events involved [2] . The difficulty in accessing a nascent synapse through experimentation has been previously discussed [3]. It is not an easy task to experimentally study certain aspects of synaptic dynamics; however we postulate that, through validated simulations models, it will be possible to analyze the roles of various parameters that contribute to synaptic mechanisms. However, it is difficult to intuit model behavior, due to the large number of parameters involved and the existence of multiple non-linear interactions; it is therefore necessary to quantify model sensitivity to variations in inputs and to identify parameters that are most likely to influence model behavior. Such parameter optimization and sensitivity analysis techniques need powerful computation resources. Recent advances in distributed computing and quantitative modeling approaches allowed modeling of systems biology in the entire hierarchy of CNS (Fig.1.1) from a synapse to the brain [4]. Some simulators in the domain are MCELL at the lowest in the hierarchy, NEURON, GENESIS and the high end Blue Brain project[5, 6]. EONS modeling platform belongs to the synaptic end defining molecular mechanisms regulating information processing in the CNS [7]. in-silico MCELL EONS NEURON GENESIS BLUE BRAIN --------------------------------------------------------------------------------------------- in-vivo Figure 1.1: Simulation modeling platforms in the CNS hierarchy [41, 42] 1.2 EONS The EONS (Elementary Objects of the Nervous System) synaptic modeling platform simulates the features of a generic glutamatergic synapse by incorporating many molecular mechanisms known to participate in and regulate synaptic transmission [7]. This web interface was developed to explore the roles of non-linear dynamics underlying synaptic mechanisms and receptor activity at the sub-synaptic level [8]. It involves mathematical models representing the dynamics of individual molecular events taking place at synapses and incorporates geometrical features 2 3 of synapses as well as second messenger pathways that participate in synaptic regulation and plasticity. 1.3 Purpose: The currently available user interface version of this EONS synaptic modeling platform allows users to analyze synaptic mechanisms defined by only a single set of input data for one instance of simulation. However for sensitivity analysis and parameter optimization required for model validation [9], simulations with multiple input data sets need to be run. This becomes quite challenging computationally, due to the speed and memory constraints of ordinary processors and also mechanistically, as it requires repetitive user intervention for data input. To overcome the above stated constraints of the current implementation, we developed a parallel computational framework to run a series of simulations simultaneously with different input datasets on a supercomputer/multinode system. This parallel framework allows for a complete characterization of the models studied and their interaction in parameter space: - A thorough validation of the models by comparing different simulation outputs to experimental data. - Sensitivity Analysis: The determination of the respective impact of every parameter on various outputs and the identification of the most critical parameter(s) for a specific output [9]. 4 - Parameter optimization: The determination of optimal parameter values by comparing different simulation outputs to various sets of experimental data (i.e., agonist concentration, optimal molecular mechanisms on kinetic binding/unbinding/desensitization etc.) 1.4 Statement of the problem The users will not be able to make comparative analysis between numerous outcomes elicited by varying quantities of input parameters easily with the current implementation of the platform. It becomes mechanistically challenging for the user to run simulations one after the other and save results within the available disk space on the user’s computer. The entire course of data input and acquisition for wide range input analysis on ordinary processors is extremely time- consuming. EONS uses ordinary differential equations (ODEs) to describe the mathematical models of synaptic mechanisms. The computations become data intensive with stepwise calculations and tougher with the integration of more parameters. While a simulation (an actual in-silico experiment) of a single pulse stimulation lasting about 20 ms provides information related to simple synaptic mechanisms, simulation of events of longer duration such as those taking place during the induction of long term potentiation (LTP) or those involving the effects of pharmacological agents interacting with targets incorporated in the platform would require much longer computational time. An ordinary Pentium PC with a single processor (4GHz, 2GB RAM) requires about 4 minutes to process a 5 simulation of 150 msec duration with a single dataset, thereby challenging the use of this system for longer simulations such as the 1.0 sec stimulation used experimentally to induce LTP and secondly to run multiple simulations to test hypotheses for a wider range of input data for parameter optimization. 1.5 Significance: This platform allows us to answer various questions/hypotheses raised in previously published material relating to synaptic dynamics. In particular, while much has been learned regarding the mechanisms involved in LTP, the precise mechanisms underlying the long lasting changes in synaptic efficacy remain to be fully characterized [10]. The goals of the present work based on parallel simulations are to provide an analysis of the synaptic events elicited by input parameters for a broader data range, to determine the optimal parameters to match simulated and experimental data, and to make interesting predictions regarding specific mechanisms underlying LTP and the effects of pharmacological agents. This approach will help model molecular processes with the best parameters to understand the contribution of individual molecular events to the mechanisms underlying LTP/LTD, learning and memory. 6 1.5.1 Parameter Optimization Mathematical models are used to describe a number of processes defined by sets of equations, parameters and variables to characterize the system/process under investigation. The output responses are influenced by the interplay of these input parameters, and it is highly essential to fit the best parameters into the model to get outcomes close to experimental data. Mathematical models mainly consist of three main components: decision variables, objective function and constraints. Decision variables are involved in decision making as these unknown quantities provide an optimal solution to the problem. Constraints are limitations of the problem, usually defined by functions and constants related by equality/in- equality sign [11]. Our parameters of interest are the coefficients of the objective function which define the goal of the objective function, which can be maximized, minimized or optimized to arrive at the best solution. For example, at the sub cellular level when the agonist binds to the receptor, it drives the receptor into different states corresponding to various functional configurations, i.e., sensitization/desensitization/open [12]. The receptor’s probability of existing in different states is calculated using Markov’s state models [1]. The binding kinetics of the agonist/antagonist/allosteric compounds are generally sufficient to compute the probability of opening/closing states of the receptor. With the multinode framework, we can vary the kinetic values of the model over a broad range to obtain optimal values, which may hold the key to 7 understand the modulatory effects of allosteric compounds regulating receptor sensitization/desensitization [13]. This approach can not only provide answers to specific questions based on the quantitative values of parameters but also generate their qualitative significance to the system under study through sensitivity analysis. This work mainly focuses on the development of the non-interface version of the EONS synaptic modeling platform, which can be launched simultaneously multiple times with multiple input sets on a high performance computing cluster. Thus the framework developed is computationally superior in running simulations of longer durations in a very short time requiring minimal user intervention. Such framework laid foundation to explore new applications like drug discovery and parameter evaluation, which will be discussed in the last chapter. The next chapter gives a brief description of the features of the platform and a tour of the interface version of the modeling platform. Chapter 3 describes the methodology adopted in building a non-interface version, the standard XML format to create input data files, the launching of multiple simulations on the cluster nodes, and the transfer of outputs to a centralized database. 8 CHAPTER 2 EONS –SYNAPTIC MODELING PLATFORM 2.1 Background A synapse is an important site of communication between two neurons. The molecular machinery within these specialized junctions plays a key role in regulating mechanisms involved in learning and memory processes. An understanding of these mechanisms in more intricate details will allow the study of brain dysfunctions and help develop therapeutic approaches for treating various nervous system disorders. Here is a brief summary of the main steps in synaptic transmission [14]: 1) An action potential depolarizes the pre-synaptic terminal. 2) Activation of voltage gated calcium channels results in inward flow of calcium into the cell. 3) Calcium diffusion promotes the fusion of vesicles to the plasma membrane and triggers the release of neurotransmitter molecules in the cleft. 4) Diffusion of neurotransmitter (ex.glutamate) takes place across the cleft followed by binding to the receptors on the postsynaptic cell membrane. 5) Based on the type of neurotransmitters, excitatory or inhibitory responses cause depolarization or hyperpolarization in the postsynaptic cell. However the underlying mechanisms are quite complex as binding of the neurotransmitter to the receptors, depend on affinity, concentration, receptor kinetics in binding/unbinding, etc. It is not an easy task to experimentally study certain aspects of synaptic dynamics; thus we postulate that, through validated 9 simulation models, it will be possible to analyze the role of various parameters that contribute to synaptic mechanisms. The conception of this EONS synaptic modeling platform was motivated by the need to develop simulation tools to systematically explore various non-linear dynamics of synaptic transmission and to develop models of Long Term Potentiation (LTP) [7]. In the past few years, significant work was carried out in Dr.Ted Berger’s lab by Dr.Jean-Marie Bouteiller in a fruitful collaboration with Dr.Michel Baudry for developing an online glutamatergic modeling platform for students and experienced modelers of the scientific community to explore mechanisms involved in regulating synaptic efficacy. The following chapter gives a brief overview of the features of the graphical user interface version of the modeling platform available on the World Wide Web at www.synaptic-dynamics.com [15]. 2.1.1 EONS Technology EONS (Elementary Objects of the Nervous System) is a synaptic modeling platform accessible on the web that was developed as a learning and research tool to understand mechanisms underlying glutamatergic transmission [7]. It contains input parameters (depolarization characteristics, synaptic morphology, number and distribution of receptors, etc.), which can be modified by the user through interactive components like labels, buttons, text fields, etc. The simulation output responses are displayed in the form of graphs on a separate panel. Users can evaluate the influence of each of the input values used for a specific simulation on 10 the dynamic behavior of a synapse, by examining various outputs, such as post- synaptic potential, calcium current from individual postsynaptic receptors or total calcium current in the post-synaptic cell. For example, through this modeling tool, one can observe changes in synaptic responses elicited by changes in the number or distribution of receptors, responses that are not always accessible to experimentation or deductive reasoning. With EONS, one can test hypotheses regarding pre- and post-synaptic mechanisms, integrating the kinetic parameters regulating receptor opening probabilities while preserving the effects of synaptic geometry like relative locations of presynaptic Ca channels, neurotransmitter release sites and relative locations of various post synaptic receptor sites [7]. Table 2.1: Features of the EONS synaptic modeling platform Inputs Mechanisms Outputs • Depolarization Pulse • Intracellular and Extracellular Ionic concentrations • Cleft geometry • Density and position of various receptors • Kinetic binding/unbinding parameters of receptors • Various ligand concentrations • Calcium diffusion in the pre synaptic terminal Ca L, N, T Types • Neurotransmitter release inside the cleft • Receptor channel probable states sensitized/ desensitized/open: AMPA5, AMPA7, AMPA13,NMDA7, NMDA11. • Other modulatory and feedback mechanisms • Neurotransmitter release profile • Probabilities of receptor in different equilibrium states • Calcium concentration, NMDA, AMPA currents • Excitatory postsynaptic currents and Potentials. 11 The mechanisms involved are dynamic in nature, they are time dependent and the models are rarely in steady state. The rates of change of the model’s variables from one state to another are represented by differential equations. Since a model is often composed of more than one variable, the system is described by a system of ordinary differential equations ODEs [1]. 2.2 A tour of the user interactive modeling platform: As a primary step, a presynaptic depolarization is selected from a menu comprising various types of depolarization (duration, amplitude, etc.) as the input stimulus. Currently there are four types of input pulses that can be provided to the system: single pulse, paired pulse, train pulse (or train of trains used to replicate the experimental conditions used for LTP induction [16]) and action potential. The user can specify delay, duration and frequency of these pulses by modifying the corresponding parameters in the interface (Fig. 2.1). Figure 2.1: The Stimulus Panel of the platform provides access to the input depolarization parameters Following the sequence of events occurring at the synaptic level in-vivo, the depolarization pulse triggers the entry of calcium into the presynaptic terminal through voltage-dependent Ca channels. EONS incorporate calcium entry, diffusion and buffering mechanisms, which are, described by Gaussian absorption profiles in two dimensions. ] ) ( ) ( exp[ 2 ) , ( 2 2 0 2 2 0 sigY y y sigX x x sigXsigY rate y x f − − − − = π 12 The current platform provides the flexibility for the user to change the initial buffering rate and location (x 0 ,y 0 ) of the calcium buffer. Diffusion of calcium inside the synaptic terminal is calculated using finite difference equations [17]. Following calcium diffusion, glutamate is released inside the cleft. The postsynaptic receptors (AMPA, NMDA, and mGluR) undergo different state transitions when glutamate and other agonist(s) (i.e., glycine for NMDA) bind to them [18]. The conductance of AMPA channels is determined by agonist occupancy and its kinetic binding characteristics to the receptor [19, 20]. EONS modeling platform incorporates mathematical models of AMPA receptor in 5 (Fig 2.3), 7 and 13 states [13]. The schematic below illustrates the transition of the receptor between various states following binding of an agonist A. The AMPA 7-states model (Fig. 2.2) has two binding sites for AMPA/glutamate and AMPA-13 has four. We can choose from any of the models to run simulations. Figure 2.2: Kinetic schema representation of AMPA/glutamate 7 states model. Figure 2.3: Kinetic schema representation of AMPA/glutamate 5 states model. 13 bGly aGlu R represents NMDA receptor bound with ‘a’ glutamate molecules and ‘b’ glycine molecule in sensitized state with a, b ∈{0, 1,2}. 2 2 Gly Glu D represents NMDA receptor bound with 2 glutamate and 2 glycine in desensitized state O represents open NMDA receptor Figure 2.4: Representation of NMDA receptor in 11 probable states including its open and desensitized states. Users have can modify the kinetic binding constants, which determine the probabilities of the various states of the receptor/channel. This is a significant modality which will allow us to test models for temperature dependent kinetic changes [21] and also allows us to evaluate hypotheses regarding the mechanisms underlying expression/maintenance of LTP (Long Term Potentiation) dependent on the kinetic rate constants regulating channel gating probabilities [10]. 14 Following is a brief summary of the NMDA receptor model implemented (Fig. 2.5). Figure 2.5: NMDA Receptor Panel contained in the postsynaptic parameters Panel The probability of the NMDA receptor to reach its open state is driven by the binding of glycine and glutamate to their specific binding sites. The receptor states at every step are determined by calculating the product of the coefficient matrix, which contains the product of kinetic rate constants and the equilibrium values of receptor’s initial states. A choice of several solvers is available (Back Euler, Forward Euler and Runge Kutta [1] second and fourth order) to solve this set of differential equations. 15 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ Gly Glu Gly Glu Gly Glu Glu Gly Glu Gly Glu Glu Gly Gly D R R R R R R R R R dt d 2 2 2 2 2 2 2 2 0 = [M]. ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ Gly Glu Gly Glu Gly Glu Glu Gly Glu Gly Glu Glu Gly Gly D R R R R R R R R R 2 2 2 2 2 2 2 2 0 Equation 2.1: Matrix used to determine the equillibrium states of NMDA receptor following binding/unbing with glycine and glutamate Similar calculations are performed to determine the probability states at every step of the simulation for all implemented receptors. The platform offers the flexibility to add new elements to the default specified values by increasing the number of L, N and T type calcium channels and the number of receptors thus allowing users to analyze changes in post-synaptic responses resulting from changes in the number and the location of the receptors. The synaptic cleft width can be modified, along with the position and number of receptors within the synapse; all these elements can be varied by moving the respective receptor icons along the membrane in the ‘Synaptic Geometry’ panel, making it convenient for the user to visualize their positions. The location and the number of receptors are recorded and incorporated as inputs to run the rest of the simulation. 16 Figure 2.6: Synaptic geometry panel to modify cleft parameters In the final step, we specify the duration of the simulation as well as its temperature (this speeds up or slows down biochemical processes [21]). Once the simulation is run, the user can visualize calcium diffusion and glutamate diffusion, and more importantly access a wide range of output data from the output parameters values of elementary models (e.g. activation rate ‘m’ and inactivation rate ‘h’ for Hodgkin Huxley voltage-dependent calcium channels, intermediate states probabilities, etc..) to global synaptic outputs (e.g. total postsynaptic current, total postsynaptic calcium current, postsynaptic potential, etc..), all displayed in the form of graphs in a separate panel. The corresponding data can be stored on the client machine for subsequent analysis. 17 Figure 2.7: Visual Feedback of calcium diffusion in the presynaptic terminal and glutamate diffusion inside the cleft (a) (b) (c) (d) Figure 2.8: Output responses for EPSP (b), neurotransmitter concentration in the cleft at the location of release (c), Total postsynaptic calcium current (d), obtained for an action potential type input pulse (a), for simulation duration of 10 msec and default parameters at the interface. 18 19 Though this java-based user interface provides excellent interactive features, it fails to provide a way to test different sets of data simultaneously due to the slow processing speed and the memory constraints of ordinary processors. To bypass the current limitations, we decided to adapt the platform to a multi- node environment, therefore enabling it to deal with multiple sets of input and output data. The primary interest in adapting this parallel framework is to find optimal input parameters from a wider data range, and subsequently to determine the ones among these input parameters that most significantly affect output responses. Secondly, this approach takes advantage of the processing speed of dedicated processors operating in parallel especially when simulations of longer duration are required, for example to study the induction of LTP. Hence the computational framework using parallel computers was developed with a vision that in the future, any number of input parameters can be varied in multiple combinations to derive their corresponding output. This in turn allows us to (i) calibrate the parameters to best fit experimental results (calibration purposes) and (ii) determine optimal values of input parameters that generate a specific output response (e.g. a stronger LTP induction). These calibration and optimization practices strongly increase the predictive power of the modeling platform hence guiding the design of experimental protocols. 20 CHAPTER 3 METHODOLOGY 3.1 Overall Description: The features of the EONS modeling platform and the purpose of extending it to a multinode computing environment were discussed in the previous chapters. This chapter focuses on describing the individual building blocks that constructed this computational framework. By adapting the existing platform to a high performance computing cluster [22], users are able to run simulations in parallel with different input datasets on multiple nodes of the cluster. The memory exploitation and calculation power of these dedicated processors of the cluster significantly decrease the total time required to run the simulations and thus, facilitate testing hypotheses for a wide range of input data in a shorter time frame. The cluster nodes have neither monitor, nor keyboard, but they have powerful processors and large amounts of RAM memory. The platform can no longer be accessed using a user interface with components implemented in the current platform like buttons, checkboxes, frames, labels, scrollbars, text fields etc., which will be affected if a display device, keyboard, or mouse is not supported in which case the corresponding java class constructors throws a ‘Headless Exception’ error (“Thrown when code that is dependent on a keyboard, display, or mouse is called in an environment that does not support a keyboard, display, or mouse”.)[23]. Hence the current platform needed to be transformed to a platform with an automated data access, no user intervention and finally no graphic variables to execute inside the cluster environment. The implementation of a parallel computation framework to address the above issues is discussed below (See Fig.3.1). At the front end, the user generates multiple datasets by executing a PERL [24] script specifying the names of the input parameters to be varied and their minimum and maximum range values on the head node of the cluster. This algorithm will generate multiple configuration files in standard XML [25, 26] format, with each file containing a different value of the parameter of interest. Similarly, the XML files will record metadata (data descriptive of file content, to understand, characterize and manage data) with contents like date and time of file creation, file index number, author name and other user-defined data, which will be used for reference at a later stage for data retrieval and analysis. Figure 3. 1: Schematic representation of the implementation on a multi-node environment 21 22 The number of configuration files generated is based on the ranges of parameter values chosen. Execution of a simple bash script with PBS (Portable Batch System) commands submits jobs to the cluster [27] . A job in this context refers to one long simulation run with a unique set of data from one configuration file. A directory for each node file, where the job is being executed is created on the user’s home directory. Each node receives a copy of the XML configuration file generated. An instance of the EONS modeling platform is automatically placed on each node when the PBS script is executed. The application parses the parameter values from the XML file to run the simulations with the required input parameters. The node file is updated with the execution status of the job, which can be accessed by the user at any point of time. At the termination of the program, each node reports the results of the simulation and inserts them into a centralized MySQL database [28]. The user can remotely connect to this database to query and analyze the desired results of interest. 3.2 Implementation: EONS is a GUI (Graphic User Interface) application and requires user intervention to change the default parameters within the interface, especially when the user wants to test hypotheses with various input data sets. When several instances of this program are launched on multiple nodes, it is an impossible option to have the user input parameters at every single node, which does not have a display device or a keyboard. Data availability to every node should be automated in such a way that user intervention at the node level is minimized. 23 This can be facilitated by creating a file that contains all the input parameters required by the application to run the simulation. Thus the primary step of implementation is the generation of multiple configuration files. 3.2.1 Input Data Model– XML A file is a resource where information is stored. The file content can be organized in a raw format or structured in a way, where the text content is surrounded by data descriptive of the content. The structured format offers the flexibility to create user-defined elements for easy communication and exchange of data. One such format, which offers flexibility and hierarchical organization with data descriptive elements, is the XML file format. XML has been widely accepted because of its simplicity and flexibility [25]. Due to their self –descriptive natures, programs can parse documents easily. The tags define the data objects called language elements, and the hierarchy of relationships among the language elements can be used to create XML schema. Since XML follows strict rules it is easy to implement parsers that are simply efficient and easy to create and use. The input files accessible by the application instance on each of the computing nodes of the grid environment are in standard XML format as shown in Fig 3.2. This XML file contains all the information with the required set of parameters to run a simulation by the application instance on the cluster node. Figure 3.2: A representation of the input data file in XML format. 3.2.2 Accessing the input data model A parser is one of the components in an interpreter or compiler that checks the document for a structured format and validity where it retains the implied hierarchy of the input text and transforms it into a form suitable for further processing [25]. XML parser exposes the contents of an XML document through an API (Application Programming Interface). A client application reads an XML document through this API. As well as reading the document and providing the contents to the client application, if it finds an error, it informs the client application. The structure and semantics of an XML document is encoded in the document’s markup, its tags and its attributes, a tool that is needed to recognize 24 25 and understand this structure to report any possible errors in this structure. This tool is called an XML parser. In this work a Document Object Model (DOM) parser’s, which is a component API of the Java API for XML Processing, is adapted. In a Document Object Model [25, 29] the whole document is stored as an object into the memory before processing. Invoking a custom made method called getValuefor (“String”), the value between the tagged element is returned as a string, which is used as input parameter by the program. 3.2.3 Generation of multiple configuration files Since the files need to be distributed on the cluster, it saves time if the XML/ input data files are created on the head node itself and are automatically distributed to the other computing nodes of the network. To generate multiple files, we use a PERL script owing to its powerful text processing features. PERL software is freely distributed and available on the cluster. The execution of the script provides a point of centralization because apart from generating different configuration files with different input data it also generates metadata inside the XML files like session date, simulation File number, and simulation description on its execution. All such data generated at this point will provide necessary information for data retrieval at a later stage. For example, files created with a Session Name 20080123_1545 correspond to the set of simulations which were launched simultaneously on the cluster around 23 rd Jan 2008 at 15:45 hours. The simulation input files created in this session contain the same session name and 26 this record serves as the prime identification to retrieve any results corresponding to that particular session. 3.2.4 Parallel computing using multiple nodes of cluster Parallel computing is used when there is a scope for dividing larger problem into smaller ones, and smaller computations are carried out simultaneously but at the end the results from these smaller computations are collected to address the larger problem. Parallel computing has been very resourceful over the past years in solving scientifically challenging and data intensive calculations [5, 30]. Distributed computing is one form of parallel computing where the distributed computer has processing elements connected by a network. Computing clusters are a sub class of these distributed computers composed of multiple stand alone machines, which carry out independent tasks concurrently thus offering better performance and speed. The speed up achieved with parallelization of tasks is explained by Gustafson’s law [31]. According to Gustafson’s law, large problems can be efficiently parallelized with the implementation on multiple processors. The degree to which the large task can be sped up is given by: S (P) = P − α * (P − 1) where P is the total number of processors, S is the speed up and α is the non- parallelizable part of the task. Since the instances of the program distributed on each of the nodes are independent of each other, the parallelization percentage is high in our case and 27 the maximum computation speed achieved is directly proportional to the no. of processors we use. A high performance computing environment with multiple processors connected to each other over a high speed network provides a powerful computational resource for handling huge data in scientific research. The current implementation was made possible with the availability of high performance computing cluster Wiglaf.usc.edu consisting of 257 nodes to support computationally complex simulations. This cluster offers 1482 GFlops performance. It follows the Beowulf architecture and has the following: 1) Head Node 2) Computing Nodes 3) A fast switching network interconnecting the individual cluster nodes with themselves and with the head node. Following are a few services supported on the cluster and only a few relevant to the current work are described here: i) Network File System (NFS), is to allow users to access home directories located on the cluster head node and to share files over the network. ii) Network Information System (NIS) is to centralize administration of the UNIX, thus allows the group of machines on the network to share a common set of configuration files, thereby giving access to the user with a valid account to all the computing nodes and the TORQUE submission system. 28 TORQUE is cluster resource manager software to control submission of computing tasks, or jobs on the cluster. Load balancing provides distribution of jobs onto available nodes using PBS commands [27]. iii) Network monitoring software, allows the examination of cluster network switch status. 3.2.4.1 PBS Commands PBS (Portable Batch System) A growing interest in parallel processing led to the development of job scheduling software. The PBS software [27] consists of client commands for submission, modification and monitoring of jobs. Some examples of PBS Commands are: qsub: The sub command will pass certain environment variables in the Variable_List attribute of the job, variables like HOME, LOGNAME, PATH, MAIL, SHELL, and their values will be made accessible to the job. qdel: The qdel command deletes jobs in the order in which their job identifiers are presented to the command. A job is deleted by sending a DeleteJob batch request to the batch server that owns the job. A job that has been deleted is no longer subject to management by batch services. qstat: The qstat command is used to request the status of jobs, queues, or a batch server. The requested status is written to standard out. These commands are simple in usage and provide a convenient way of executing and monitoring jobs on the cluster. 29 3.2.5 Design of a database –MySQL Database by definition means a structured collection of records stored on a computer system. It is highly essential to store and organize data especially when the data is extremely huge to handle and comes from different tasks or processors. A good database design and a DBMS (Database management system) allow multiple tasks to access and update the data simultaneously, while preserving database integrity. Database tables consist of columns and rows. Each column contains a different attribute and each row contains a different record. Each record is identified by a unique field known as the primary key. Records from other tables of the database are referenced through a foreign key. The following are steps necessary for a good database design [32]: 1) Composite fields should be broken into constituent parts. 2) A key field to uniquely identify each record should exist. 3) There should be no repeating groups of fields. 4) A separate table for any information that is used in multiple records and a key to link these tables to one another should be created. Database entity: An entity is a thing or an object of importance about which data must be captured. It should have attributes and relationships. DB entities appear in a data model as a box with a title. The title is the name of the entity. Entity Relation Diagram: Figure 3.3: Entity Relation Diagram of ‘eonsjan’ DB The java program communicates with the database through a JDBC [33, 34] (Java Database Connectivity) driver class implemented in the EONS source code itself, such that data generated from each program instance on the individual computing nodes are separately entered into the database as different records. 30 31 Table 3.1: Structure and Content of the EONS Results DATABASE Table Name Column Description Example SessionID Primary Key/Identification number for the session table 0001 SessionDescription Provides a brief description of the input parameters varied and their minimum and maximum values of the variation range for the current session. In the current session the value of variable A is varied from ‘min(A) to ‘max(A)’ and the value of variable B from ‘min(B) to ‘max(B)’. Session Name Unique identification in the yyyymmdd_hhmm format For the user to retrieve results. 200080312_1215 eons Version The current version of eons jar file used to run the simulations of this session eons_v1r79 User Notes Any notes user enters for reference at a later stage. Checking for epsp variations w.r.t no. of AMPA receptors User Name Name of the user working on this session. First name, Last name Cluster name The cluster on which the simulations are executed. Wiglaf/USC HPC Session Inputs The input parameters for which the session is run. Ach agonist, Gly agonist Session Outputs The outputs recorded from this session. CaConc, Ca Current, epsp. Session Session XML File SessionXMLFile: The entire XML file/ Parent file from which the children XML files are formed. Refer to Fig. 3.1 SimulationID Primary Key/Identification number for the simulation table 0001 Simulation Name SessionName followed by _Sim_ followed by simulation Number. This is to give a unique identification for each record of the session. 20080312_1215_Sim64 Simulation Simulation Description Simulation Description: Describes specifically the input values inputted from the current XML file for the simulation. In the current simulation the value of variable A is ‘min (A)’ and the value of variable B is ‘min (B)’. OutputID Primary key/ Identification number for the output table 0064 OutputName The output parameter’s name CaChannel OutputSubName The output sub-parameter name Ca Current Output Units Units of the output parameter nA, mV Output Output Content Holds he results from one simulation containing the time and result values and time values in an array. t and r followed by the simulation number. t64= [0 0.1 ……….1200.0] r64= [0.0 5e-4 …………1.1e-1] 3.2.6 Results retrieval and analysis The results for any desired combination of parameters can be retrieved from the database using simple SQL query statements [35] and data specific to output parameters of user’s interest can be selected for analysis. USE eonsjan; select o.outputContent from outputtbl o, simulationtbl S, sessiontbl SE where o.simulationTbl_simulationID = s.simulationID and S.sessionTbl_sessionID = SE.sessionID and SE.sessionName like '20080123_1048%' and o.outputSubName like 'PostSynaptic Potential%'; The above SQL Statement retrieves all the available sets of simulation data for the ‘PostSynaptic Potential’ from the session ‘20080123_1048’ contained in ‘eonsjan’ database. The database can be accessed from any PC or any machine with a command line interface or user interface with database query tools that execute simple SQL statements. All the results files are dumped into a text format or MATLAB m-file format as specified by the user. The file is further opened using MATLAB for analysis of data and plotting results. The data obtained, results and discussions are described in the following chapter. 32 33 CHAPTER 4 CONCLUSIONS In this chapter we discuss some results obtained using the new platform within the parallel computation framework on the high performance computing cluster. We also demonstrate how significantly the computational speed up in execution time and data acquisition is achieved with the adoption of this multinode framework. The overall goal that motivated the design and implementation of the simulation modeling platform was to provide a deeper understanding of the mechanisms underlying synaptic dynamics as well as the nonlinear interactions among these mechanisms. Moreover, simulation results could provide a successful complement to experimental results, which, due to current technological limitations, provide very limited quantitative information at the subsynaptic scale. 4.1 APPLICATIONS The platform with its user-interactive features, although successfully providing insights regarding the mechanisms underlying synaptic transmission, was however limited in its original design to simulate responses of a single instance of a glutamatergic synapse defined by a single input dataset. It became time consuming and impractical to run series of simulations in succession, by changing the input values each time at the user interface to study multiple responses. The extension of the platform and its adaptation to a parallel computational framework were motivated by the need to enhance the platform’s capabilities and to allow the exploration of a wide range of input parameters simultaneously. Direct 34 applications of such enhancements include model calibration (with respect to experimental/published data), parameters optimization and drug discovery (test of a wide range of exogenous compounds at different efficacy levels and their corresponding changes in kinetic constants). 4.1.1 Application 1: Parameter Evaluation To demonstrate the platform’s capability in calibrating input parameters contributing to the synaptic responses various experiments were conducted. One such experiment was to vary the number of AMPA receptors from 9 to 99, and to evaluate the changes in post-synaptic currents and other post-synaptic events. All the output responses were acquired in just a single batch of 11 simulations, which lasted 3 minutes. This could not have been possible with the previous platform’s features. Experiment 1: Previous attempts to explain LTP in correlation with an increase in AMPA receptors were not very successful through labeling studies [36, 37], due to the difficulty to access the number of receptors. In such cases we have to appreciate the features of simulation platforms, which offer the flexibility to vary parameters not available for experimental validation. In our first experiment, we studied changes in excitatory post-synaptic potentials (EPSPs) elicited in response to an increase in the number of AMPA receptors for both single pulse and paired pulse stimulation (Figs. 4.1 and 4.2). Figure 4.1: EPSP responses elicited by a single pulse stimulus as a function of number of AMPA receptors Figure 4.2: EPSP responses elicited by a paired pulse stimulus as a function of number of AMPA receptors 35 Figure 4.3: Maximum EPSP responses elicited by the first and second pulses of a paired pulse stimulus as a function of number of AMPA receptors Increasing the number of AMPA receptors linearly increased the maximum EPSP amplitude, as usually observed when the amount of LTP is minimal to average [36]. The relationship between maximal EPSP and number of AMPA receptors are linear for a single pulse and paired pulse stimulation. However the slope of maximal EPSP response evoked by the second pulse is larger. The paired pulse EPSP facilitation index (EPI) defined as the ratio of EPSP initial slope evoked by the second pulse to that evoked by first pulse indicates that synaptic response was enhanced by the second pulse, as demonstrated in in-vitro studies [38]. This observation is more significant in the case where the numbers of AMPA receptors are large (99) when compared to small (9). 36 It may be also interesting to note that multiple pulse stimulus like the train pulse will have different consequences as the tendency to fire increases with multiple spikes [38]. Experiment 2: In our next experiment we varied the time interval between the two pulses of a paired pulse. The inter stimulus interval was varied from 20 ms to 200 ms in steps of 20 ms. The EPSP responses obtained are shown below: Figure 4.4: EPSPs elicited by varying inter pulse intervals of paired pulse stimulation 37 Figure 4.5: Maximum EPSP elicited by the first and second pulse of the paired pulse stimulation The facilitation is maximum when the interval is 20 ms and declines with increase in the inter-pulse interval (IPI). Some studies of extracellular paired-pulse responses [38] indicate that paired pulse facilitation at 150 ms -200 ms inter pulse interval was smaller than that at 50-100 ms, which is quite evident from our simulation results. We may arrive at a conclusion that higher frequency pulses will lead to maximal facilitation as demonstrated by the 20ms IPI. Experiment 3: 38 EONS incorporates patch-clamp experiment modality as well. Our next experiment was to determine current responses evoked by NMDA receptors at various postsynaptic potentials. -120 -100 -80 -60 -40 -20 0 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 NMDA Current Responses Mg. Conc. 1.2mM Mg. Conc. 0.0012mM Figure 4.6: Patch-Clamp responses for NMDA receptors at different magnesium concentration levels. NMDA receptor dynamics are regulated by magnesium concentration [18] and we were able to reproduce with this multinode framework modality and with the use of the validated models implemented in EONS results obtained under various experimental conditions. In other simulation experiments, we also determined the effects of changing the number of AMPA receptors on NMDA receptor-mediated synaptic responses elicited paired pulse and train pulse simulations. However the above results will not be analyzed here, as we limit our discussion to an overall appreciation of how the new multinode simulation platform can contribute to the evaluation of input parameters for a wider range of data in a lesser time frame. The results thus obtained will provide a significant asset to 39 40 evaluate which parameters need calibration and their corresponding quantitative values for a desired output response. One interesting application that can be explored with this multinodal parallel framework is in drug discovery. We propose that we can effectively predict ligand efficacies at different concentration levels. The motivation behind this work is greatly stimulated by Rhenovia’s [39] drug discovery strategy (Rhenovia is a small bio-pharmaceutical company, which has obtained an exclusive licensing agreement from USC to exploit the EONS technology to perform service for drug discovery with pharmaceutical and biotechnology companies). 4.1.2 Application 2: Drug discovery There is a paradigm shift in the strategies adopted by pharmaceutical companies for drug discovery, assessment and development. The conventional experimental testing methods of the past no longer fit in today’s highly competitive markets and the need to fasten development of drugs already in the pipeline. Many simulation tools that provide in silico models of cellular/molecular processes allow analyzing various drug targets in a smarter way. “Simulations will not eliminate but might significantly reduce the number of lab experiments necessary to select a final drug target” [40]. Screening drug candidates by mathematically modeling their interactions with their endogenous biological target has been used for many years; however modeling drug interaction pathways with a more integrated biological system has been under evaluation for quite some time now, but has been challenged in 41 application and validity due to the numerous parameters involved in modeling and the underlying complexity (mechanistically and computationally) [2]. The EONS synaptic modeling platform, with the inclusion of complex mathematical models of receptors and drug interaction pathways is extended to address drug discovery by adapting the existing platform to the multiple nodes of the cluster. The framework used to launch simulations in parallel was addressed in the previous chapter. We present in this section an example of results obtained with the parallel platform to characterize the responses from two chemical compounds at varying efficacy levels. The concentration of the two different compounds X and Y was varied around their respective IC50 (half maximal inhibitory concentration) values to span a suitable range of concentration values. Simulation files were generated and each file contained distinct input (concentration) values for the two compounds. 81 Simulations with [9x9] input data sets were launched simultaneously on multiple nodes of the cluster. The output from all the simulations obtained were queried from the centralized database (where the outputs were automatically transferred after simulations stopped) and recorded into an m-file for further analysis and graphs were plotted using MATLAB. The maximal response of the post synaptic potential, total calcium current and calcium concentration obtained at varying concentration levels were recorded as below. Figure 4.6: EPSP values and their normalized values for a combined effect of two compounds X and Y Results Analysis: Predictions on the efficacies are better understood when normalized with the control values, responses recorded in absence of agonists. Normalized values are calculated using the following formula: ) ( ) ( base YR base XR base ZR Value Normalized − + − − = Where ZR is the value of the combined response, XR and YR are the individual responses in the presence of X and Y. Base value is the recorded response when no compound is added. If the normalized value is greater than unity, the two molecules at the specific concentration act synergistically, i.e., one influences the response obtained with the application of the other compound in a positive way at their respective concentration values. If the normalized value is 1 then we see an additive effect, while values between 0.5 and 1 may be considered as indicating the existence of an ‘overlap’ where the influence of one molecule over the other is minimal. Any values below 0.5 42 43 indicate an inhibitory effect, where the presence of one compound inhibits the response to the other. Not only do these results show potential synergistic, additive or inhibitory effects between compounds, they also provide significant information about the concentration values needed for the appropriate therapeutic dosages. The results presented here are currently being validated with in vitro and in vivo experiments. We believe that this drug discovery approach is very promising to test molecular compounds and combinations thereof developed for cognitive enhancement or the treatment of pathologies of the central nervous system. 4.2 CONCLUSION With the implementation of the platform in a parallel framework, the total execution time has decreased significantly, thus allowing users to run ‘n’ number of simulations in parallel without much intervention from data input and acquisition. However, the data acquisition time also depends on the number of nodes available for the user. If ‘n’ nodes are available to run ‘n’ simulations, then maximum speedup is achieved and data acquisition is done in a very minimal amount of time. 44 Computation Time: Table 4.1 Computation time on ordinary processors (vs.) cluster node processors Simulation Duration (in-silico experiment) *Execution time for 81 simulations (Ordinary processor) Execution Time for 81 Simulations (Dedicated Processors) 70 ms 202.5 minutes 3 minutes 140 ms 405 minutes 5 minutes 36 sec 300 ms 1863 minutes 11 minutes 40 sec 1200 ms 81 hours/~4 days 44 minutes *Execution time on the ordinary processor (4GHz, 2GB RAM) is a predicted output obtained by multiplying number of simulations with the execution time for one simulation. The database incorporated was designed and implemented to support large amounts of data. The database design was validated during more than four months of heavy successful usage. In a month’s time, we typically stored 46 sessions of data, which in average contains 2882 records of simulation data with 3 outputs per simulation; 8383 output records were uploaded to the database. The disk space occupied by the database was found to be 544710 kB (540 MB) for this time period. 4.3 FUTURE WORK Future work is initiated for optimizing our simulation program to achieve faster computation speed by incorporating variable step method and other numerical approaches. Secondly, other molecular mechanisms like AMPAkine modulatory effects, second messengers and drug interaction pathways will be integrated into the platform features to address broader questions to understand treatments for pathological models. 45 Ultimately, efforts will be made to incorporate this synaptic model into a neuron model to simulate small size neural networks. Parameter optimization and sensitivity analysis are not addressed to their full potential as a part of this thesis work due to time constraints but with the implementation of EONS on the grid this is not a formidable task. 4.4 DISCUSSION The computational framework developed thus allowed for a more complete characterization of the models studied and their interactions in the parameter space. Not only can we validate models when comparing different simulation outputs to experimental data but it also becomes possible: (i) to determine optimal parameter values and predict ligand efficacies at different concentration levels. (ii) to find optimal molecular mechanisms in kinetic binding/unbinding (iii) to study the effect of receptor desensitization etc in an automated manner and in a minimal amount of time The best outcomes of simulation data are selected for further in-vitro and in-vivo testing thus saving a lot of valuable time and resources. 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Abstract (if available)

Abstract EONS modeling platform is a resourceful learning and research tool to study the mechanisms underlying the non–linear dynamics of synaptic transmission with the aid of mathematical models. Mathematical modeling of information processing in CNS pathways, in particular modeling of molecular events and synaptic dynamics, have not been extensively developed owing to the complex computations involved in integrating a multitude of parameters. In this paper, we discuss the development of a strategy to adapt the EONS synaptic modeling platform to a multi-node environment using a parallel computational framework to compute data intensive long simulations in a shorter time frame. We describe how this strategy can be applied to (i) determine the optimal values of the numerous parameters required for fitting experimental data, (ii) determine the impact of all parameters on various aspects of synaptic transmission (under normal conditions or conditions mimicking pathological conditions) and (iii) study the effects of exogenous molecules on both healthy and pathological synaptic models.

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Asset Metadata

Creator Allam, Sushmita Lakshmi (author)

Core Title A parallel computation framework for EONS synaptic modeling platform for parameter optimization and drug discovery

School Viterbi School of Engineering

Degree Master of Science

Degree Program Biomedical Engineering

Publication Date 08/08/2008

Defense Date 06/26/2008

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

Tag cluster,CNS mathematical modeling,node,OAI-PMH Harvest,parallel computation,synaptic modeling,XML

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Baudry, Michel (committee chair), Berger, Theodore W. (committee member), D'Argenio, David Z. (committee member)

Creator Email allam@usc.edu,sushmita.allam@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1567

Unique identifier UC1203751

Identifier etd-Allam-2305 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-105275 (legacy record id),usctheses-m1567 (legacy record id)

Legacy Identifier etd-Allam-2305.pdf

Dmrecord 105275

Document Type Thesis

Rights Allam, Sushmita Lakshmi

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu