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Identification of Predictive Dynamic Models for Systems Biology Jörg Stelling [email protected] IMA Workshop Biological Systems and Networks Minneapolis / MN, November 2015
Identification of Predictive Dynamic
Models for Systems Biology
Jörg Stelling
IMA Workshop Biological Systems and Networks
Minneapolis / MN, November 2015
Network Identification: Dual Challenges
Complexity:
Many components
Dynamic interactions
Self-modifying system
Spatial organization
Uncertainty:
Incomplete inventory
Few quantitative data
Conflicting hypotheses
Molecular noise
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Aim: Mechanistic Model Development
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Reaction listPictogram Approximations
Pathway diagram Differential equations
Aim: Mechanistic Model Development
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Co-Design of Experiments and Models
Exploitation of prior knowledge → Few, targeted experiments.
Model ensembles representing uncertain prior knowledge.
Challenges: Model discrimination & experimental design.
Experiment
Model ensembles
Prior knowledge:
(Conflicting) hypotheses.
Few experimental data.
Qualitative data.
Remember that all models are wrong; the practical
question is how wrong do they have to be to not be useful.
G.E. Box
Remember that all models are wrong; the practical
question is how wrong do they have to be to not be useful.
G.E. Box
Science may be described as the art
of systematic over-simplification.
K. Popper
Coarse Identification: Network Structure
A.-P. Oliveira et al. (2015) Mol. Syst. Biol. 11: 802.
Example: Yeast Nutrient Signaling
TOR
PKA
De Virgilio & Loewith, Oncogene 25:6392 (2006).
Problem: Identifying fundamental signaling mechanisms,
such as specific input signals to nutrient sensing pathways.
Challenge: Data Integration & Causal Inference
Oliveira et al., Mol.. Sys. Biol. 11:802 (2015).
Identification of causal relations (metabolic input signals):
Design of informative experiments and data integration.
Metabolites
Transcripts
TOR
Conceptual Idea: Network Motifs
Approach: Decompose a network (graph) into smaller subunits.
Network motifs: "Patterns of interconnections that recur ... at
frequencies significantly higher than ... in randomized networks.”
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Network Motif-Based Causal Inference
Oliveira et al., Mol.. Sys. Biol. 11:802 (2015).
Approach: 'Prototypic' interactions and qualitative causal
model → Experimental design enables model selection.
Metabolites
Transcripts
TOR
Network Motif-Based Causal Inference
Approach: 'Prototypic' interactions and qualitative causal
model → Experimental design enables model selection.
Network Motif-Based Causal Inference
Approach: 'Prototypic' interactions and qualitative causal
model → Bayesian approach & integration over methods.
TOR Input Signals: Experimental Design
Idea: Co-design of inference method and perturbation
experiments → Consistent, large-scale dynamic data set.
TOR Input Signals: Inference Results
Motif-based assignment of metabolite functions: Robust
(integration over methods) and 'plausible' inference results.
TOR Input Signals: Inference Results
Motif-based assignment of metabolite functions: Robust
(integration over methods) and 'plausible' inference results.
Generalization of the Approach?
Difficulties: Feature and experiment selection according to
(biological) hypothesis space; motif identifiability analysis.
'Downstream' motifs
excluded by prior knowledge
'Downstream' motifs
that cannot be discriminated
Detailed Identification: Toward Mechanisms
M. Sunnaker et al. (2013) Sci. Signaling ra41.
Prior Work: Ensemble Models for Yeast TOR
Set of ODE models: 24-29 species (states), 30-50 parameters.
Problem: Combinatorial explosion (models and parameters).
L. Kuepfer et al., Ensemble modeling for analysis of cell signaling dynamics. Nat. Biotechnol. 25: 1001 (2007).
Core model (CM, 1)Core model (CM, 1)
Original ensemble (19)Original ensemble (19)
Ensemble of kineticallydecoupled models (13)Ensemble of kineticallydecoupled models (13)
Ensemble with multiple phosphorylation (12)
Ensemble with multiple phosphorylation (12)
Computational Analysis Experimental Analysis
Assembly of type 2A phosphatases
Assembly of type 2A phosphatases
Tip41p complex formationwith type 2A phosphatasesTip41p complex formationwith type 2A phosphatases
- Model extensions
- Model discrimination- Cross-validation- Critical experiments- Key control mechanisms
- Model refinement
Topological Filtering: Concept
Formulation of all hypotheses in
a 'supermodel', specification of
models Mi via parameters.
Model reduction: Projection for
elimination of single parameters.
Model evaluation by Bayes
factors / posteriors given data Y:
M. Sunnaker et al., A method for automatic generation of predictive dynamic models …, Science Signaling, ra41, 2013.
Topological Filtering: Method
Dynamic (ODE) system, Gaussian measurement noise:
Likelihood function for model M, given parameter point Θ and
data Y, measurement covariance matrix S, residuals ε:
Bayes factors by integration over 'viable' volume (we do not
need to know the 'true' model for this computation):
Topological Filtering: Sampling Algorithm
Characterization of parameter spaces as a key ingredient.
Improved scaling: Novel (hybrid MCMC) sampling algorithm.
E. Zamora Sillero et al., Efficient characterization of high-dimensional parameter spaces ... BMC Syst. Biol. (2011).
Application: Yeast Stress Response
Short-term control of stress responsive genes via TF Msn2.
Glucose addition after starvation: Input cAMP peak, output
Msn2 phosphorylation and translocation to the cytoplasm.
Input Output
Application: Yeast Stress Response
Ensemble of 192 candidate topologies → 12 feasible models.
Iterations of (optimal) experimental design, data integration,
and posterior computations for mechanistic identification.
Iteration 1Iteration 2Iteration 3
Application: Yeast Stress Response
Example iteration: Confirmation of fast predicted Msn2
phosphorylation dynamics by targeted phosphoproteomics.
nucleus
cytoplasm
Application: Yeast Stress Response
Analysis of most plausible (>99% relative posterior) model:
Fast switching of phosphorylation state in nucleus.
High constitutive turnover of phosphorylation.
Switching through minor differences in net rates.
Msn2, nuc. = redMsn2, cyt. = greenMsn2P, nuc. = greyMsn2P, cyt. = blue
Nuclear rates = blackCytoplasmic rates = green
Nuclear net rates = greyCytopl. net rates = blue
Application: Yeast Stress Response
Msn2 system can act as differential sensor of cAMP input.
faster normal slower
Application: X Activity Control
Steady-state (simple) model, constant kinase input u:
Relation between phosphorylation and localization.
Switch between two (constitutive) transport cycles.
Cytoplasm
Nucleus
X CPX C
X NPX N
Nuclear X
Phosphorylated X
Steady-state (simple) model, constant kinase input u:
Relation between phosphorylation and localization.
Switch between two (constitutive) transport cycles.
Application: X Activity Control
Cytoplasm
Nucleus
X CPX C
X NPX N
Nuclear X
Phosphorylated X
Scaling: Modularity & Numerical Methods
M. Lang et al. (2014) Biophys. J. 106: 321.
M. Lang & J. Stelling (2015) SIAM J. Sci. Comput., under review.
C. Schillings et al. (2015) PLOS Comp. Biol. e1004457.
Modularization for experimental design (purpose-driven):
Given: Network with n hypotheses (existence of interactions).
Enumerate all modularizations that insulate hypotheses from each other → Combinations of n states to be measured.
Approach 1: Modularization for Design
M. Lang et al., Cutting the wires ... (2014) Biophys. J. 106: 321.
Modularization for experimental design (purpose-driven):
Given: Network with n hypotheses (existence of interactions).
Enumerate all modularizations that insulate hypotheses from each other → Combinations of n states to be measured.
Approach 1: Modularization for Design
Modularization for experimental design (purpose-driven):
Given: Network with n hypotheses (existence of interactions).
Enumerate all modularizations that insulate hypotheses from each other → Combinations of n states to be measured.
Approach 1: Modularization for Design
Modularization for optimization (parameter estimation):
Idea: Replace module inputs by experimental measurements.
Use two-level optimization procedure: Multiple-shooting approach by partitioning networks (instead of time domain).
Approach 2: Modularization for Optimization
Modularization for optimization (parameter estimation):
Idea: Replace module inputs by experimental measurements.
Use two-level optimization procedure: Multiple-shooting approach by partitioning networks (instead of time domain).
Approach 2: Modularization for Optimization
Characterization of system behavior in parameter space → Addressing the 'curse of dimensionality' problem:
Idea: Sparse, adaptive polynomial approximations of systems behavior with guarantees on accuracy (mass-action kinetics).
Approach 3: Sparse Polynomial Approximations
First-order(sensitivities)
Adaptivesparsegrids
x
Characterization of system behavior in parameter space → Addressing the 'curse of dimensionality' problem:
Small-scale example (10 parameters) and in general: Improved scaling of accuracy for number of simulations.
Approach 3: Sparse Polynomial Approximations
Characterization of system behavior in parameter space → Addressing the 'curse of dimensionality' problem:
EGFR signaling model (50 parameters): Numerical performance and questioning 'sloppy parameters' concepts.
Approach 3: Sparse Polynomial Approximations
Conv. 0.75
Conclusions & Perspectives
For network inference, co-design of experiments with
(purpose-driven) mathematical models is critical.
Formal models of different granularity can be employed
for data / hypothesis integration and interpretation.
Many conceptual (generalization of network motifs?) and
computational (scaling to large dynamic models?)
challenges need to be addressed.
Acknowledgments
Sotiris Dimopoulos, Mikael
Sunnaker, Elias Zamorra-Sillero,
Moritz Lang
Ana-Paula Oliveira, Reinhard
Dechant, Alberto Bussetto,
Andreas Wagner, Ruedi Aebersold,
John Lygeros, Joachim Buhmann,
Uwe Sauer, and others ...
Sean Summers, Claudia Schillings,
Christoph Schwab
