Modeling of Genetic Regulatory Networks

8/7/2019 Modeling of Genetic Regulatory Networks

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Mathematical Modelingof

Genetic Regulatory Networks

Dr.S.S.D.PandeyGlobal Synergetic Foundation

[email protected] June 2009
mailto:[email protected]:[email protected]


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Overview

1. Genetic regulatory networks

2. Modeling and simulation of genetic regulatory networks

3. Modeling and simulation approaches:differential equationsstochastic equations

4. Conclusions


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Genes and proteins

Genes code for proteins that are essential for developmentand functioning of organism: gene expression

DNA

RNA

Protein

protein andmodifier molecule

transcription

translation

post-translationalmodification


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Regulation of gene expression

Regulation of gene expression on several levels

Gene expression controlled by proteins produced by other genes:regulatory interactions


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Genetic regulatory network

Genetic regulatory network consists of set of genes, proteins,small molecules, and their mutual regulatory interactions

Development and functioning of organisms cell emerges frominteractions in genetic regulatory networks


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Bacteriophage l infection of E. coli

Response of E. colito phage linfection involves decisionbetween alternativedevelopmental pathways:lytic cycle and lysogeny

Ptashne, 1992


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Genetic regulatory network phage l

Choice between alternative developmental pathways controlledby network of genes, proteins, and mutual regulatoryinteractions

McAdams & Shapiro, 1995


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Computational approaches

Most genetic regulatory networks are large and complex

Cells have many components that can interact in complex ways

Dynamics of large and complex genetic regulatory processes

hard to understand by intuitive approaches alone

mathematical methods for modeling and simulation arerequired:

precise and unambiguous description of network ofinteractionssystematical derivation of behavioral predictions

Practical application of mathematical methods requires userfriendlycomputer tools


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Mathematical modeling approaches

Mathematical modeling has developed since the 1960s and iscurrently attracting much attentionBower and Bolouri, 2001; Hasty et al., 2001; McAdams and Arkin,1998;Smolen et al., 2000; de Jong, 2002

Two approaches to computer modeling and simulation

discussed in this session:differential equationsstochastic equations

Jean-Luc Gouz will discuss class of piecewise-lineardifferential equations central to this project in more detail


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Differential equation models

Cellular concentration of proteins, mRNAs, and other moleculesat time-point trepresented by continuous variable

v Regulatory interactions modeled by kinetic equations

where is rate law

Rate of change of variable xiis function of other concentrationVariables

Differential equations are major modeling formalism inmathematical biology

Segel, 1984; Kaplan and Glass, 1995; Murray, 2002


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Negative feedback system

Gene encodes a protein inhibiting its own expression:negative feedback

Negative feedback important for homeostasis, maintenance ofsystem near a desired stateThomas and dAri, 1990


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Model of negative feedback system


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Steady state analysis

No analytical solution of nonlinear differential equationsdescribing feedback system

System has single steady state at

Steady state is stable, that is, after perturbation system willreturn to steady state (homeostasis)


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Transient behavior after perturbation

Numerical simulation of differential equations shows transientbehavior towards steady state after perturbation

Initial values correspond to perturbation


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Positive feedback system

Gene encodes a protein activating its own expression:positive feedback

Positive feedback important for differentiation, evolutiontowards one of two alternative states of system


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Model of positive feedback system


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Steady state analysis

No analytical solution of nonlinear differential equationsdescribing feedback systemSystem has three steady states

Two stable and one unstable steady state. System will tend toone of two stable steady states (differentiation)


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Transient behavior after perturbation

Depending on strength of perturbation, transient behaviortowards different steady states


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Model of time-delay feedback system

Time to complete transcription and translation introduces timedelay in differential equations

Time-delay feedback systems may exhibit oscillatory behavior


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More complex feedback systems

Gene encodes a protein activating synthesis of another proteininhibiting expression of gene: positive and negative feedback

Interlocking feedback loops give rise to models with complexdynamics: numerical simulation techniques necessary


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Application of differential equations

Differential equations have been used to model a variety ofgenetic regulatory networks:

circadian rhythms in Drosophila(Leloup and Goldbeter, 1998)

phage infection of E. coli(McAdams and Shapiro, 1998)

segmentation of early embryo of Drosophila(Reinitz and Sharp, 1996)

cell division in Xenopus(Novak and Tyson, 1993)

Trp synthesis in E. coli(Santilln and Mackey, 2001)

induction of lacoperon in E. coli(Carrier and Keasling, 1999)

developmental cycle of bacteriophage T7 (Endy et al., 2000)

Modeling of Genetic Regulatory Networks

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