Introduction to Bioinformatics · Stochastic simulation Dynamic Bayesian networks Biochemical...

Introduction to Bioinformatics

Systems biology: modeling biologicalnetworks

Systems biologyp Study of ”whole biological systems”p ”Wholeness”: Organization of dynamic

interactionsn Different behaviour of the individual parts

when isolated or when combined togethern Systems cannot be fully understood by

analysis of their components in isolation

-- Ludwig von Bertalanffy, 1934(according to Zvelebil & Baum)

Outlinep 1. Systems biology and biological networks

n Transcriptional regulationn Metabolismn Signalling networksn Protein interactions

p 2. Modeling frameworksn Continuous and discrete modelsn Static and dynamic models

p 3. Identification of models from data

1. Systems biologyp Systems biology – biology of networks

n Shift from component-centered biology to systems ofinteracting components

Prokaryotic cell

Eukaryotic cell

http://en.wikipedia.org/wiki/Cell_(biology)Mariana Ruiz, Magnus Manske

http://en.wikipedia.org/wiki/Cell_(biology)

Interactions within the cellp Density of biomolecules in

the cell is high: plenty ofinteractions!

p Figure shows a cross-section of an Escherichiacoli celln Green: cell walln Blue, purple: cytoplasmic

arean Yellow: nucleoid regionn White: mRNA

http://mgl.scripps.edu/people/goodsell/illustration/publicDavid S. Goodsell

http://mgl.scripps.edu/people/goodsell/illustration/public

Paradigm shift from study of individualcomponents to systems

System size

Num

ber

ofdiffe

rent

syst

em

s

System 1

System 2

InteractionComponent

?

Paradigm shift from study of individualcomponents to systems

System size

Num

ber

ofdiffe

rent

syst

em

s

Level of model detail

Biological systems of networks

Transcriptional regulation

gene

regulatoryregion

transcription factor

co-operativeregulation

microarrayexperiments

Gene product (protein)

Metabolism

enzyme

metabolite

Signal transductionsignal molecule & receptor

activated relay molecule

inactivesignalingprotein

activesignalingprotein

end product of thesignaling cascade(activated enzyme)

Protein interaction networksp Protein interaction is the unifying theme of all

regulation at the cellular levelp Protein interaction occurs in every cellular system

including systems introduced earlierp Data on protein interaction reveals associations

both within a system and between systems

Protein interaction

2. Graphs as models of biologicalnetworksp A graph is a natural model for biological systems of

networksp Nodes of a graph represent biomolecules, edges

interactions between the moleculesp Graph can be undirected or directed

p To address questions beyond simple connectivity(node degree, paths), one can enrich the graphmodels with information relevant to the modelingtask at hand

Enriching examples: transcriptionalregulationp Regulatory effects can be

(roughly) divided inton activationn inhibition

p We can encode thisdistinction by labeling theedges by ’+’ and ’-’, forexample

p Graph models oftranscriptional regulationare called gene(tic)regulatory networks

Activation

Inhibition

gene 1

gene 2

gene 3

2 1 3

RepressorActivator

Enriching examples: more transcriptionalregulation

A gene regulatory network might be enriched further:In this diagram, proteins working cooperatively asregulators are marked with a black circle.

This network is a simplified part of cell cycle regulation.

Frameworks for biological networkmodelingp A variety of information can be encoded in graphsp Modeling frameworks can be categorised based

on what sort of information they includen Continuous and/or discrete variables?n Static or dynamic model? (take time into account?)n Spatial features? (consider the physical location

molecules in the cell?)

p Choice of framework depends on what we wantto do with the model:n Data explorationn Explanation of observed behaviourn Prediction

Static models Dynamic models

Discretevariables

Continuousvariables


Discretevariables

Continuousvariables

Plain graphs

Bayesian networks

(Probablistic)Boolean networks

Stochastic simulation

Dynamic Bayesiannetworks

Biochemical systemstheory (in steady-state)

Metabolic controlanalysis

Constraint-basedmodels

Differential equations

Biochemical systemstheory (general)


Discretevariables

Continuousvariables

Plain graphs

Bayesian networks









Dynamic models: differential equationsp In a differential equation model

n variables xi correspond to the concentrations ofbiological molecules;

n change of variables over time is governed by rateequations,

dxi/dt = fi(x), 1 i n

p In general, fi(x) is an arbitrary function (notnecessarily linear)

p Note that the graph structure is encoded byparameters to functions fi(x)

Properties of a differential equationmodelp The crucial step in specifying the model is

to choose functions fi(x) to balancen model complexity (number of parameters)n level of detail

p Overly complex model may need moredata than is available to specify

Example of a differential equation model oftranscriptional regulation

p Let x be the concentration of the target geneproduct

p A simple kinetic (i.e., derived from reactionmechanics) model could take into accountn multiple regulators of target gene andn degradation of gene products

and assume that regulation effects areindependent of each other

Example of a differential equation model oftranscriptional regulation

p Rate equation for change of x could then be

where k1 is the maximal rate of transcription ofthe gene, k2 is the rate constant of target genedegradation, wj is the regulatory weight ofregulator j and yj is the concentration ofregulator j

Number of parameters?

Differential equation model formetabolismp Likewise, rate equations can be derived for

differential equation models for metabolismp For simple enzymes, two parameters might be

enoughp Realistic modeling of some enzyme requires

knowledge of 10-20 parametersp Such data is usually not available in high-

throughput manner


Discretevariables

Continuousvariables

Plain graphs

Bayesian networks









Biochemical systems theory (BST)p BST is a modeling framework, where differential

rate equations are restricted to the followingpower-law form,

wheren i is the rate constant for molecule i andn gij is a kinetic constant for molecule i and reaction j

p BST approximates the kinetic system andrequires less parameters than the genetic kineticmodel


Discretevariables

Continuousvariables

Plain graphs

Bayesian networks









Interestingly, if we assume that the concentrationsare constant over time (steady-state), an analyticalsolution can be found to a BST model.

But then we throw away the dynamics of the system!

Steady-state modelingp Is the study of steady-states meaningful?p If we assume dxi/dt = 0, we restrict ourselves to

systems, where the production of a molecule isbalanced by its consumption

enzyme

metabolite In a metabolic steady-state, these twoenzymes consume and producethe metabolite in the middle at the same rate


Discretevariables

Continuousvariables

Plain graphs

Bayesian networks









Constraint-based modelingp Constraint-based

modeling is a linearframework, where thesystem is assumed tobe in a steady-state

p Model is representedby a stoichiometricmatrix S, where Sijgives the number ofmolecules of type iproduced in reaction jin a time unit.

2

1

3 4

1 2

3 4 5

6 7 89 10

12345678910

1 2 3 411

-1-1

12

-2-1

1

1-2

-11

Sij = 0 if valueomitted

Constraint-based modelingp Since variables xi are constant, the questions

asked now deal with reaction ratesp For instance, we could characterise solutions to

the linear steady-state condition, which can bewritten in matrix notation as

Sv = 0p Solutions v are reaction rate vectors, which for

example reveal alternative pathways inside thenetwork


Discretevariables

Continuousvariables

Plain graphs

Bayesian networks









Discrete models: Boolean networksp Boolean networks have been widely used in

modeling gene regulationn Switch-like behaviour of gene regulation resembles logic

circuit behaviourn Conceptually easy framework: models easy to interpretn Boolean networks extend naturally to dynamic modeling

Boolean networksA Boolean network

G(V, F) containsp Nodes V = {x1, …, xn},

xi = 0 or xi = 1p Boolean functions

F = {f1, …, fn}p Boolean function fi is

assigned to node xi

NOT AND

Logic diagramfor activity ofRb

Dynamics in Boolean networksp Dynamic behaviour can be simulatedp State of a variable xi at time t+1 is calculated by

function fi with input variables at time tp Dynamics are deterministic: state of the network

at any time depends only on the state at time 0.

Example of Boolean network dynamicsp Consider a Boolean network with 3 variables x1,

x2 and x3 and functions given byn x1 := x2 and x3

n x2 := not x3

n x3 := x1 or x2

t x1 x2 x30 0 0 01 0 1 02 0 1 13 1 0 14 0 0 1

...

Problems with Boolean networksp 0/1 modeling is unrealistic in many casesp Deterministic Boolean network does not cope well

with missing or noisy datap Many Boolean networks to choose from –

specifying the model requires a lot of datan A Boolean function has n parameters, or inputsn Each input is 0 or 1 => 2n possible input statesn The function is specified by input states for which

f(x) = 1 => 2^(2^n) possible Boolean functions


Discretevariables

Continuousvariables

Plain graphs

Bayesian networks









3. Model identification from datap We would like to learn a model from the data

such that the learned modeln Explains the observed datan Predicts the future data well

p Generalization property: model has a goodtradeoff between a good fit to the data andmodel simplicity

Three steps in learning a modelp Representation: choice of modeling framework,

how to encode the data into the modeln Restricting models: number of inputs to a Boolean

function, for example

p Optimization: choosing the ”best” model from theframeworkn Structure, parameters

p Validation: how can one trust the inferred model?

Conclusionsp Graph models are important tools in systems

biologyp Choice of modeling framework depends on the

properties of the system under studyp Particular care should be paid to dealing with

missing and incomplete data - choice of theframework should take the quality of data intoaccount

References and further readingp Florence d’Alché-Buc and Vincent Schachter: Modeling and

identification of biological networks. In Proc. Intl.Symposium on Applied Stochastic Models and DataAnalysis, 2005.

p Marketa Zvelebil and Jeremy O. Baum: Understandingbioinformatics. Garland Science, 2008.

p Hiroaki Kitano: Systems Biology: A Brief Overview. Science295, 2002.

p Marie E. Csete and John C. Doyle: Reverse engineering ofbiological complexity. Science 295, 2002.

p James M. Bower and Hamid Bolouri (eds): ComputationalModeling of Genetic and Biochemical Networks. MIT Press,2001.

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