Systems Biology

1. Systems Biology Ophelia Venturelli CS374 December 6, 2005

2. Definition: systems biology • Quantitative analysis of components and dynamics of complex biological systems Interactome (Tier 1) Deterministic (Tier 2) Stochastic (Tier 3)

3. Features of complex systems • Nonlinearity global properties not simple sum of parts

4. Features of complex systems • Feedback loops

5. Features of complex systems • Open systems (dissipation of energy) Flagella uses energy:

6. Features of complex systems • Memory (response history dependent) adaptation = shift in curve requires memory! Response Chemical concentration

7. Features of complex systems • Nested (modules have complexity)

8. What is Systems Biology? • quantitatively account for these properties • different levels of modeling • Three tiers • Interactomes • Deterministic • Stochastic • Principles which transcend tiers… Interactome (Tier 1) Deterministic (Tier 2) Stochastic (Tier 3)

9. Principle 1: Modularity • Module • interacting nodes w/ common function • constrained pleiotropy • feedback loops, oscillators, amplifiers

10. Principle 2: Recurring circuit elements • Network motifs • histidine kinase & response regulator

11. Principle 3: Robustness • Robustness • insensitivity to parameter variation • Severe constraints on design • robustness not present in most designs

12. Aims of systems biology • Tier 1: Interactome • Which molecules talk to each other in networks? • Tier 2: Deterministic • What is the average case behavior? • Tier 3: Stochastic • What is the variance of the system?

13. Aims of systems biology • Tier 1 • get parts list • Tier 2 & 3 • enumerate biochemistry

14. Aims of systems biology • Tier 2 & 3 • enumerate biochemistry • define network/mathematical relationships • compute numerical solutions

15. Aims of systems biology • Tier 2 & 3 • Deterministic: Behavior of system with respect to time is predicted with certainty given initial conditions • Stochastic: Dynamics cannot be predicted with certainty given initial conditions

16. Aims of systems biology • Deterministic • Ordinary differential equations (ODE’s) • Concentration as a function of time only • Partial differential equations (PDE’s) • Concentration as a function of space and time • Stochastic • Stochastic update equations • Molecule numbers as random variables • functions of time

17. Tier 1: Static interactome analysis • Protein-protein • Signal transduction • Cell cycle • Protein-DNA • Gene regulation • Metabolic pathways • Respiration • cAMP

18. Tier 1: Static interactome analysis • Goals • Determine network topology • Network statistics • Analyze modular structure

19. Tier 1: Static interactome analysis • Limitations: • Time, space, population average • Crude interactions • strength • types • Global features • starting point for Tier 2 & 3 typical interactome first time-varying yeast interactome (Bork 2005)

20. Tier 1: Static interactome analysis • Analysis methods • Functional Genomics • expression analysis • network integration • Graph Theory • scale free • small world

21. Recap • Tier 1: Interactome • which molecules talk to each other? • crude, large scale • global set of modules • Now zoom in on one module… • Tier 2: Deterministic Modeling • average case behavior of a module

22. lumped cell cell compartments continuous time & space (MinCDE oscillation) Tier 2: Deterministic Models • Goal • model mesoscale system • average case behavior • Three levels • ODE system • ODE compartment system • PDE (rare!) • data limited…

23. Tier 2: Deterministic Modeling • Results • Robust Chemotaxis (Barkai 1997) • MinCDE Oscillation (Howard 2003) • Feedback in Signal Transduction (Brandman 2005) • Output • time series plots (ODE) • condition on parameter values Brandman 2005

24. Tier 2: Deterministic Modeling • Example • Robustness in bacterial chemotaxis • Bacterial chemotaxis robust to parameter fluctuations! • Chemotaxis: bacterial migration towards/away from chemicals • Parameters • concentrations • binding affinities

25. Tier 2: Deterministic Modeling • Bacterial chemotaxis • model as random walk • Exact adaptation • change in concentration of chemical stimulant • rapid change in bacterial tumbling frequency… • then adapts back precisely to its pre-stimulus value!! Random walk

26. Experimental Design • Is exact adaptation robust to substantial variations in biochemical parameters? • Systematically varied concentrations of chemotaxis-network proteins and measured resulting behavior

27. Distinguish between robust-adaptation and fine-tuned models of chemotaxis Tumbling frequency IPTG inducer pUA4 pUA4 Adaption time pUA4 pUA4 E. Coli cheR -/- population Express CheR over a 100-fold range Adaption precision 1 mM L-aspartate Adaptation precision = ratio of steady-state tumbling frequency of unstimulated to stimulated cells Summary of results Tumbling frequency 0.3 ± 0.06 (20-fold) Adaption time 3 ± 1 (3-fold) Adaption precision 1.04 ± 0.07

28. Tumbling frequency as a function of time for wild-type cells

29. Conclusions from study • Exact adaptation is maintained despite substantial varations in network-protein concentrations • Exact adaptation is a robust property • …but adaptation time and steady-state behavior are fine-tuned CheR fold expression

30. Recap • Just saw Tier 2 • Deterministic modeling • average case behavior • robustness: canonical avg. case property • Tier 3 • Stochastic modeling • variance of system

31. Tier 3: Stochastic analysis • Fluctuations in abundance of expressed molecules at the single-cell level • Leads to non-genetic individuality of isogenic population

32. Tier 3: Stochastic Analysis • When stochasticity is negligible, use deterministic modeling… • Molecular “noise” is low: • System is large • molar quantities • Fast kinetics • reaction time negligible • Large cell volume • infinite boundary conditions

33. Tier 3: Stochastic Analysis • Molecular “noise” is high: • System is small • finite molecule count matters • Slow kinetics • relative to movement time • Large cell volume • relative to molecule size • Need explicit stochastic modeling!

34. Tier 3: Ensemble Noise • Transcriptional bursting • Leaky transcription • Slow transitions between chromatin states • Translational bursting • Low mRNA copy number

35. Tier 3: Temporal Noise Canonical way of modeling molecular stochasticity

36. Tier 3: Spatial Noise Finite number effect:translocation of molecules from the nucleus to the cytoplasm have a large effect on nuclear concentration Nucleus Cytoplasm • N = average molecular abundance • η (coefficient of variation) = σ/N • Decrease in abundance results ina 1/√N scaling of the noise (η=1/√N)

37. Recap • Three tiers • Interactomes • Deterministic • Stochastic • Principles which cross tiers • Modularity • Reuse • Robustness Interactome (Tier 1) Deterministic (Tier 2) Stochastic (Tier 3)

38. Major challenges and limitations • Measurement of chemical kinetics parameters and molecular concentrations in vivo • Differences between in vitro and in vivo data • Compartmental specific reactions • Data is the limit!!!

39. Major challenges and limitations • Data is the limit!!! • Functional genomic data (Interactomes) • E. Coli chemotaxis (Leibler, deterministic/robustness) • Important • parameter estimation • feedback based estimation methods Sachs 2005

40. Software • Tier 1: Interactomes • Graphviz, Bioconductor, Cytoscape • Tier 2: Deterministic • Matlab (SBtoolbox), Mathematica (PathwayLab) • Tier 3: Stochastic • R, Stochsim

41. Algorithms • High-performance algorithms to solve systems of PDE’s • Virtual Cell • Automated parsing of networks into stochastic and deterministic regimes • H-GENESIS • STOCK

42. Conclusion • Three tiers • Interactomes • Deterministic • Stochastic • Principles which cross tiers • Modularity • Reuse • Robustness Interactome (Tier 1) Deterministic (Tier 2) Stochastic (Tier 3)