Basic modeling approaches for biological systems. Mahesh Bule

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1 Basic modeling approaches for biological systems Mahesh Bule

2 The hierarchy of life from atoms to living organisms

3 Modeling biological processes often requires accounting for action and feedback involving a wide range of spatial and temporal scale

4 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 (10 8 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

5 Integrative systems biology involving the iterative cycle of wet and dry laboratory research

6 Modeling approaches in biology Bottom up and top down

7 Approach for multi-scale model development in biology

8 Hierarchy of scale, related mechanisms and modeling approaches

9 Relation of modeling approach, scale and experimental procedure

10 Comparison of systemic and molecular views of the same metabolic system on the example of the photosynthetic apparatus of purple bacteria

11 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

12 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

13 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 )

14 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

15 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

16 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

17 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

18 Typical aspects of biological systems and corresponding models Modularity interacting nodes w/ common function constrained pleiotropy feedback loops, oscillators, amplifiers

19 Network versus Elements A system consists of individual elements that interacts and thus form a network

20 Robustness insensitivity to parameter variation Severe constraints on design robustness not present in most designs

21 Three basic approaches used for modeling biological process Interactome (Tier 1) Deterministic (Tier 2) Stochastic (Tier 3)

22 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?

23 Out put of different tiers during model development Tier 1 get parts list Tier 2 & 3 enumerate biochemistry

24 Out put of different tiers during model development Tier 2 & 3 enumerate biochemistry define network/mathematical relationships compute numerical solutions

25 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

26 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

27 Tire 1: Static interactome analysis Protein-protein Signal transduction Cell cycle Protein-DNA Gene regulation Metabolic pathways Respiration camp

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

29 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)

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

31 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)

32 Tier 2: Deterministic Modeling Results Robust Chemotaxis MinCDE Oscillation Feedback in Signal Transduction Output time series plots (ODE) condition on parameter values

33 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

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

35 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

36 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!

37 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

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

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