Computational Modeling of Genome-wide Transcriptional Regulation

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

2. 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 CCBG Presentation PSU, University Park, July 13, 2005 2 of 12

3. 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 CCBG Presentation PSU, University Park, July 13, 2005 3 of 12

4. 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 a construct model, i.e. computing its parameters • Remaining data a validate and refine the constructed model • Predictive mode: Execute model for new experimental settings & verify measured values • If new cases break model a compute new model parameters • If new set of parameters cannot be found a deficiency of model • Seek & verify new connection scheme: Repeat validation sequence • Prospective mode: Guide future experiments • Identify new experiments deemed interesting to biochemistry/biology CCBG Presentation PSU, University Park, July 13, 2005 4 of 12

5. 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! CCBG Presentation PSU, University Park, July 13, 2005 5 of 12

6. 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 CCBG Presentation PSU, University Park, July 13, 2005 6 of 12

7. v1 v2 s1 s2 i2 r2 i1 r1 k10 k11 r6 r7 r8 q10 q12 q11 r9 v6 v7 q8 q9 r10 r11 k9 i6 i7 k8 r16 v3 k16 r19 k19 s3 r12 r4 k12 v4 q13 s4 i3 r3 i4 r13 r14 q16 q14 v5 q15 k13 k14 k20 r20 s5 i5 k17 r17 r5 r15 r18 r0 r21 v=0 q18 q17 q19 k21 k15 i0 k18 2. Analogy to Electric Circuit • Computational model based on analogy to electric circuit CCBG Presentation PSU, University Park, July 13, 2005 7 of 12

8. 2. Construction of Model • An electric circuit is fully determined by: • Connection scheme: Consequence of biochemistry • Model parameters: • Voltage at each external node: vn • Resistors: rn • Setting of switches: sn • Applying Kirchoff’s laws to each switch setting combination a internal voltages qn & currents kn • 5800 Replicas of electric circuit: • Each represents one gene: Yields circuit output i0 • All circuits in initial model possess the same ~10 switches • Each circuit will possess a unique set of model parameters: vn & rn • Voltage at output point arbitrarily set to zero (ground) • Same switch setting for all circuits (genes) in given experiment CCBG Presentation PSU, University Park, July 13, 2005 8 of 12

9. 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 a 34 linear equations in 34 unknowns • For given switch setting s = {s1, s2, s3, s4, s5}, sn = 0,1 • Solve for circuit output i0(s,v,r) in terms of 29 unknown model parameters: • v = {vn, n=1,…,7} • r = {rn, n=0,…,21} • Total number of switch states (experimental i0) = 25 = 32 • Overdetermined system of nonlinear relations in model parameters: Least-squares fit? • Expect imbalance between number of relations & unknowns to grow with circuit complexity CCBG Presentation PSU, University Park, July 13, 2005 9 of 12

10. 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 a 2100 possible experiments: combinations of on/off switch states • This is 1030 possibilities, each producing ~ 5,800 measured values! • Discount ~99% as biochemically irrelevant a 1028 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? CCBG Presentation PSU, University Park, July 13, 2005 10 of 12

11. 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 i0(s,v,r): • Mathematica NoteBook composed • Runs out of memory due to large expression! CCBG Presentation PSU, University Park, July 13, 2005 11 of 12

12. 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 CCBG Presentation PSU, University Park, July 13, 2005 12 of 12

13. s1 s2 i1 i2 k10 k11 i7 i6 r8 q10 q12 q11 r9 q8 q9 r10 r11 k9 k8 r16 k16 r19 k19 s3 r12 i4 k12 i3 q13 s4 r13 r14 q16 q14 q15 k13 s5 k14 k20 r20 i5 k17 r17 r15 r18 r21 q18 q17 q19 i0 k21 k15 k18 Reduced Model CCBG Presentation PSU, University Park, July 13, 2005 13 of 12