basic modeling approaches for biological systems 595... · 2015-03-02 · modeling and biology...
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Basic modeling approaches for biological systems
Mahesh Bule
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The hierarchy of life from atoms to living organisms
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Modeling biological processes often requires accounting for action and feedback involving
a wide range of spatial and temporal scale
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Modeling and biology
• Life is one of the most complex phenomenon in the universe
• Biological systems are regulated at scales of many orders of magnitude in space and time, with space spanning from the molecular scale (10−10 m) to the living organism scale (1 m), and time from nanoseconds (10−9 s) to years (108 s)
• The systematic investigation of cells, organs, organisms and manly cellular processes such as communication, cell division, homeostasis and adaptation- is systems biology
• Systems biology offer chance to predict outcome of complex process e.g. cell growth, gene expression
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Integrative systems biology involving the iterative cycle of wet and dry laboratory
research
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Modeling approaches in biology
• Bottom up and top down
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Approach for multi-scale model development in biology
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Hierarchy of scale, related mechanisms and modeling approaches
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Relation of modeling approach, scale and experimental procedure
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Comparison of systemic and molecular views of the same metabolic system on the example of
the photosynthetic apparatus of purple bacteria
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Systems Biology is Modeling
• It relies on the integration of experimentation, data processing and modeling
• Modelling biological process focusses on increasing the depth of understanding and prediction of reliable results
• Development of tools to aid modelling can aid in understanding of processes
• Development of multi-scale modelling can allow “dry experiments” or “in-silico experiments” to be used as a form of validation which can save time and resources
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Systems Biology is Modeling
Properties of model
1. Model assignment is not unique
• Biological processes can be described in more than one way as follows: – A biological object can be investigated with different
experimental methods
– Each biological process can be described with different (mathematical) model
– The choice of a mathematical model or an algorithm to describe a biological object depends on problem
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Systems Biology is Modeling
2. System state
• Different modeling approaches have different representations of state e.g. – In differential equation model for a metabolic
network, the state is a list of concentrations of each chemical species
– In stochastic model, its is a probability distribution and /or list of current number of molecules of species
– In a Boolean model of gene regulation, the state is string of bits indicating for of each gene whether it is expressed (“1”) or not expressed (“0”)
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Systems Biology is Modeling
3. Steady state
• The concept of stationary states is important for the modeling of dynamical systems
• The asymptotic behavior of dynamic systems, i.e. the behavior after sufficiently long time, is often stationary
• Fast process often reach a quasi-steady state after short transition period
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Systems Biology is Modeling
4. Variables, Parameters, and Constants
• Constant is fixed value- natural number
• Parameters are quantities that are assigned a value, such as the Km value of enzyme in a reaction
• Variables are quantities with a changeable value for which the model establishes relations
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Systems Biology is Modeling
5. Modeling behavior
Two fundamental causes that determine the behavior of a system
• Influences from the environment (input)
• Processes within the system
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Systems Biology is Modeling
6. Process classification For modeling, processes are classified with respect to criteria. • Reversibility – determines whether process can proceed in
a forward and backward direction • Irreversible- the process which can proceed only in one
direction • Periodicity- indicates that a series of state may be assumed
in the time interval (t, t+∆t) • Deterministic approach- when the motion through all
following states can be predicted with known conditions • Discrete model- where values taken from a discrete set • Continuous model- where values are taken from a
continuum
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Typical aspects of biological systems and corresponding models
• Modularity
– interacting nodes w/ common function
– constrained pleiotropy
– feedback loops,
oscillators, amplifiers
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• Network versus Elements
– A system consists of individual elements that interacts and thus form a network
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• Robustness
– insensitivity to parameter variation
• Severe constraints on design
– robustness not present in most designs
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Three basic approaches used for modeling biological process
Interactome (Tier 1)
Deterministic (Tier 2)
Stochastic (Tier 3)
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Response measurment during model development
• 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?
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Out put of different tiers during model development
• Tier 1 – get parts list
• Tier 2 & 3 – enumerate biochemistry
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Out put of different tiers during model development
• Tier 2 & 3 – enumerate biochemistry
– define network/mathematical relationships
– compute numerical solutions
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• Tire 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
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Introduction to different models used
• 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
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Tire 1: Static interactome analysis
• Protein-protein
• Signal
transduction
• Cell cycle
• Protein-DNA
• Gene regulation
• Metabolic
pathways
• Respiration
• cAMP
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Tier 1: Static interactome analysis
• Goals – Determine network topology – Network statistics – Analyze modular structure
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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
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Tier 1: Static interactome analysis
• Analysis methods
– Functional Genomics
• expression analysis
• network integration
– Graph Theory
• scale free
• small world
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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)
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Tier 2: Deterministic Modeling
• Results – Robust Chemotaxis
– MinCDE Oscillation
– Feedback in Signal Transduction
• Output – time series plots (ODE)
– condition on parameter values
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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
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Tier 3: Stochastic analysis
• Fluctuations in abundance of expressed molecules at the single-cell level
– Leads to non-genetic individuality of isogenic population
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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
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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!
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Model development workflow in biology
Formulation of problem
Verification of available information
Selection of model structure
Establishing a simple model
Sensitivity analysis
Experimental test and model prediction
Iterative refinement of model
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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!!!
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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