Genetic Algorithms and Genetic Programming for Multiscale Modeling
Modeling of Genetic Regulatory Networks
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Transcript of 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)