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Computational Modeling of Genome-wide Transcriptional Regulation Center for Comparative Genomics and Bioinformatics, PSU, UP, 2005 Frank Pugh Department of Biochemistry and Molecular Biology Yousry Azmy Department of Mechanical & Nuclear Engineering The Pennsylvania State University

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CCBG Presentation PSU, University Park, July 13, 2005 2 of 12 Department of Mechanical and Nuclear Engineering 1. Motivation Ultimate goal of systems biology: Virtual cell Model cell as series of coupled chemical reactions Computationally predict its behavior in response to environmental perturbations Enable in silico drug interaction testing Guide experimental inquiry This project is an early step to achieve this goal: Establish smaller definable systems Construct computational models for these systems Experimentally test & validate (hopefully!) the models

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CCBG Presentation PSU, University Park, July 13, 2005 3 of 12 Department of Mechanical and Nuclear Engineering 1. Model Foundation Define cell in terms of massive series of coupled reactions: Genetic networks: describe circuitry of how genes influence expression of other genes, … Protein networks: describe physical interactions among all proteins in a cell Transcriptional regulation: thousands of genes, each potentially regulated by the combinatorial actions of hundreds of transcription regulatory proteins Starting point for network model: View network as series of reversible events that dynamically move: Forward: transcription machinery assembly Backward: disassembly or inhibition Transcriptional output: net flux of these forward and reverse events

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CCBG Presentation PSU, University Park, July 13, 2005 4 of 12 Department of Mechanical and Nuclear Engineering 1. Project Objectives Phenomenological model of yeast biochemical processes: Construct model that replicates changes in gene expression in response to experimental perturbations of transcription machinery Implies strong coupling between construction (computation) & validation (experiment) Large number of potential experiments to fully test all possible response permutations precludes exhaustive investigation Simplifying compromise: Construction/validation mode: Employ existing experimental results Portion of the data construct model, i.e. computing its parameters Remaining data validate and refine the constructed model Predictive mode: Execute model for new experimental settings & verify measured values If new cases break model compute new model parameters If new set of parameters cannot be found deficiency of model Seek & verify new connection scheme: Repeat validation sequence Prospective mode: Guide future experiments Identify new experiments deemed interesting to biochemistry/biology

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CCBG Presentation PSU, University Park, July 13, 2005 5 of 12 Department of Mechanical and Nuclear Engineering 2. TBP Model Model TATA binding protein (TBP) regulatory interactions Crystallographic structures of TBP and its regulators arranged according to their expected assembly/disassembly pathway. TAF1 is not shown This is way more biochemistry than I know!

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CCBG Presentation PSU, University Park, July 13, 2005 6 of 12 Department of Mechanical and Nuclear Engineering 2. Model Assumptions Initial model is phenomenological not quantitative: Determine sense of change not magnitude Ignore indirect effects due to one output affecting another output: Supported by experimental observation Only two-states on/off mechanisms are included in initial model Model distinguishes between state of: Switches: Binary on/off experimental control Flow: Three state in/out/no-flow depending on potential drop

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CCBG Presentation PSU, University Park, July 13, 2005 7 of 12 Department of Mechanical and Nuclear Engineering 2. Analogy to Electric Circuit Computational model based on analogy to electric circuit

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CCBG Presentation PSU, University Park, July 13, 2005 8 of 12 Department of Mechanical and Nuclear Engineering 2. Construction of Model An electric circuit is fully determined by: Connection scheme: Consequence of biochemistry Model parameters: Voltage at each external node: v n Resistors: r n Setting of switches: s n Applying Kirchoff’s laws to each switch setting combination internal voltages q n & currents k n 5800 Replicas of electric circuit: Each represents one gene: Yields circuit output i 0 All circuits in initial model possess the same ~10 switches Each circuit will possess a unique set of model parameters: v n & r n Voltage at output point arbitrarily set to zero (ground) Same switch setting for all circuits (genes) in given experiment

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CCBG Presentation PSU, University Park, July 13, 2005 9 of 12 Department of Mechanical and Nuclear Engineering 3. Illustration of Model Construction Given the 5-switch TBP circuit depicted on slide 7: (/gene) Total number of currents: 14 internal + 8 external = 22 Total number of internal node voltages: 12 Kirchoff’s laws 34 linear equations in 34 unknowns For given switch setting = { s 1, s 2, s 3, s 4, s 5 }, s n = 0,1 Solve for circuit output i 0 ( , v, r ) in terms of 29 unknown model parameters: v = { v n, n =1,…,7} r = { r n, n =0,…,21} Total number of switch states (experimental i 0 ) = 2 5 = 32 Overdetermined system of nonlinear relations in model parameters: Least-squares fit? Expect imbalance between number of relations & unknowns to grow with circuit complexity

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CCBG Presentation PSU, University Park, July 13, 2005 10 of 12 Department of Mechanical and Nuclear Engineering 3. Computational Challenges Yeast transcription machinery possesses: At least 100 switches that can be controlled one at a time About 5,800 circuits each with a single measurable output 2 100 possible experiments: combinations of on/off switch states This is 10 30 possibilities, each producing ~ 5,800 measured values! Discount ~99% as biochemically irrelevant 10 28 experiments to fully validate or refine the model Computationally prohibitive proposition! Initial proposal: Examine ~ 10 interactions centered around TBP Large symbolic problem: Numerical solution algorithm? Inverse problem syndrome: Solution sensitivity Accounting for experimental errors in model parameters Anything else?

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CCBG Presentation PSU, University Park, July 13, 2005 11 of 12 Department of Mechanical and Nuclear Engineering 4. Current Status Unguided data acquisition in Pugh’s lab Proof of principle study of computational model: Employ 5-switch circuit model of TBP interactions Obtain symbolic expression for i 0 ( , v, r ): Mathematica NoteBook composed Runs out of memory due to large expression!

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CCBG Presentation PSU, University Park, July 13, 2005 12 of 12 Department of Mechanical and Nuclear Engineering 4. Remaining Research Implement computational model in modular code: User access via GUI: Access & modify data, visualize circuit,… Parallelization via MPI Experiment with preliminary circuit in code Develop solution algorithm for given set of experimental data Develop algorithm to accommodate amended set of experimental data Code verification & model validation: Design & conduct new experiments likely to test validity of model Success: Sufficient number of experimental results not involved in computing model parameters are predicted by computer code Automate model refinement process to achieve validation: Develop algorithm to isolate pipe connections causing model failure Design interface to permit user to view possible modifications and select one or more for testing Design and conduct guided experiments

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CCBG Presentation PSU, University Park, July 13, 2005 13 of 12 Department of Mechanical and Nuclear Engineering Reduced Model k 16 r 16 i6i6 q8q8 k8k8 r8r8 i1i1 s1s1 k 10 r 10 q 10 k 12 r 12 r 13 k 13 q 15 k 14 r 14 i3i3 s3s3 q 14 q 12 i4i4 s4s4 i7i7 q9q9 k9k9 r9r9 i2i2 s2s2 k 11 r 11 q 11 k 19 r 19 k 17 r 17 q 13 k 15 r 15 k 18 r 18 q 17 k 20 r 20 q 18 q 16 q 19 k 21 r 21 i5i5 s5s5 i0i0

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