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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.

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systems biology

Systems Biology

Ophelia Venturelli

CS374 December 6, 2005

definition systems biology
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
Features of complex systems
  • Nonlinearity

global properties not simple sum of parts

features of complex systems5
Features of complex systems
  • Open systems (dissipation of energy)

Flagella uses energy:

features of complex systems6
Features of complex systems
  • Memory (response history dependent)

adaptation = shift in curve

requires memory!

Response

Chemical concentration

features of complex systems7
Features of complex systems
  • Nested (modules have complexity)
what is systems biology
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
Principle 1: Modularity
  • Module
    • interacting nodes w/ common function
    • constrained pleiotropy
    • feedback loops, oscillators, amplifiers
principle 2 recurring circuit elements
Principle 2: Recurring circuit elements
  • Network motifs
    • histidine kinase & response regulator
principle 3 robustness
Principle 3: Robustness
  • Robustness
    • insensitivity to parameter variation
  • Severe constraints on design
    • robustness not present in most designs
aims of systems biology
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 biology13
Aims of systems biology
  • Tier 1
    • get parts list
  • Tier 2 & 3
    • enumerate biochemistry
aims of systems biology14
Aims of systems biology
  • Tier 2 & 3
    • enumerate biochemistry
    • define network/mathematical relationships
    • compute numerical solutions
aims of systems biology15
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 biology16
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
Tier 1: Static interactome analysis
  • Protein-protein
    • Signal transduction
    • Cell cycle
  • Protein-DNA
    • Gene regulation
  • Metabolic pathways
    • Respiration
    • cAMP
tier 1 static interactome analysis18
Tier 1: Static interactome analysis
  • Goals
    • Determine network topology
    • Network statistics
    • Analyze modular structure
tier 1 static interactome analysis19
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)

tier 1 static interactome analysis20
Tier 1: Static interactome analysis
  • Analysis methods
    • Functional Genomics
      • expression analysis
      • network integration
    • Graph Theory
      • scale free
      • small world
recap
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

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…
tier 2 deterministic modeling
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 modeling24
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 modeling25
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
Experimental Design
  • Is exact adaptation robust to substantial variations in biochemical parameters?
  • Systematically varied concentrations of chemotaxis-network proteins and measured resulting behavior
distinguish between robust adaptation and fine tuned models of chemotaxis
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

conclusions from study
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

recap30
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
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 analysis32
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 analysis33
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
Tier 3: Ensemble Noise
  • Transcriptional bursting
    • Leaky transcription
    • Slow transitions between chromatin states
  • Translational bursting
    • Low mRNA copy number
tier 3 temporal noise
Tier 3: Temporal Noise

Canonical way of modeling molecular stochasticity

slide36

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)
recap37
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
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 limitations39
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
Software
  • Tier 1: Interactomes
    • Graphviz, Bioconductor, Cytoscape
  • Tier 2: Deterministic
    • Matlab (SBtoolbox), Mathematica (PathwayLab)
  • Tier 3: Stochastic
    • R, Stochsim
algorithms
Algorithms
  • High-performance algorithms to solve systems of PDE’s
    • Virtual Cell
  • Automated parsing of networks into stochastic and deterministic regimes
    • H-GENESIS
    • STOCK
slide42

Conclusion

  • Three tiers
    • Interactomes
    • Deterministic
    • Stochastic
  • Principles which cross tiers
    • Modularity
    • Reuse
    • Robustness

Interactome (Tier 1)

Deterministic (Tier 2)

Stochastic (Tier 3)