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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
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
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
CCBG Presentation
PSU, University Park, July 13, 2005
3 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
of the data a construct model, i.e. computing its parameters
 Remaining data a validate and refine the constructed model
 Portion
 Predictive mode: Execute model for new experimental settings &
verify measured values
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
 If
 Prospective mode: Guide future experiments
 Identify
new experiments deemed interesting to biochemistry/biology
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PSU, University Park, July 13, 2005
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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!
CCBG Presentation
PSU, University Park, July 13, 2005
5 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
CCBG Presentation
PSU, University Park, July 13, 2005
6 of 12
Department of Mechanical
and Nuclear Engineering
2. Analogy to Electric Circuit
 Computational model based on analogy to electric circuit
v1
v6
s1
v2
s2
i
r6 r1 1 r8 q10
q8
i6
k8
k10
r12 k12
q14
q12
r10
v3
s3
k16
r4
i
r13 r3 3 r14
q15
k13
k14
k15
i4
k9
v4
q17
s4
q16
r18
k18
CCBG Presentation
PSU, University Park, July 13, 2005
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q9
r7
v7
i7
r19 k19
r20 k20
r17 k17
i2
r2
q11 r9
r11
r16
q13
r15
k11
v5
i5
r21
q18
k21
s5
r5 r
0
q19
v=0
i0
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: 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
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 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
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
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
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 i0(s,v,r):
 Mathematica
NoteBook composed
 Runs out of memory due to large expression!
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PSU, University Park, July 13, 2005
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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
CCBG Presentation
PSU, University Park, July 13, 2005
12 of 12
Department of Mechanical
and Nuclear Engineering
Reduced Model
i1
s1
i6
s2
k10
r8 q10
q8
r10
k8
r12 k12
q14
i3
s3
r13
q12
k16 r16
q13
q15
r15
k15
i7
q11 r9
r11
k9
q9
r19 k19
i4
r14
k13
k11
i2
s4
q16
r20 k20 s5
k14
r17 k17
q17
i5
r18
k18
CCBG Presentation
PSU, University Park, July 13, 2005
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r21
q18
k21
q19 i
0
Department of Mechanical
and Nuclear Engineering