Systems Biology Ophelia Venturelli CS374 December 6, 2005

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

Features of complex systems Nonlinearity global properties not simple sum of parts

Features of complex systems Feedback loops

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

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

Features of complex systems Nested (modules have complexity)

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)

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

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

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

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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!

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

Tier 3: Temporal Noise Canonical way of modeling molecular stochasticity

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

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

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!!!

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

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

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

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