1. 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

2. 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

3. 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

4. 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

5. 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!

6. 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

7. 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

8. 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

9. 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

10. 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?

11. 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!

12. 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

13. 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