Amath 382 computational modeling of cellular systems
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AMATH 382: Computational Modeling of Cellular Systems. Dynamic modelling of biochemical, genetic, and neural networks. Introductory Lecture, Jan. 6, 2014. Dynamic biological systems -- multicellular. http://megaverse.net/chipmunkvideos/. Dynamic biological systems -- cellular.

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Amath 382 computational modeling of cellular systems

AMATH 382:Computational Modeling of Cellular Systems

Dynamic modelling of biochemical, genetic, and neural networks

Introductory Lecture, Jan. 6, 2014


Dynamic biological systems multicellular
Dynamic biological systems -- multicellular

http://megaverse.net/chipmunkvideos/


Dynamic biological systems cellular
Dynamic biological systems -- cellular

Neutrophil chasing a bacterium

http://astro.temple.edu/~jbs/courses/204lectures/neutrophil-js.html


Dynamic biological systems intracellular
Dynamic biological systems -- intracellular

Calcium waves in astrocytes in rat cerebral cortex

http://stke.sciencemag.org/cgi/content/full/sigtrans;3/147/tr5/DC1



Our interest intracellular dynamics
Our interest: intracellular dynamics

  • Metabolism: chemical reaction networks, enzyme-catalysed reactions, allosteric regulation

  • Signal Transduction: G protein signalling, MAPK signalling cascade, bacterial chemotaxis, calcium oscillations.

  • Genetic Networks: switches(lac operon, phage lambda lysis/lysogeny switch, engineered toggle switch), oscillators (Goodwin oscillator, circadian rhythms, cell cycle, repressilator), computation

  • Electrophysiology: voltage-gated ion channels, Nernst potential, Morris-Lecar model, intercellular communication (gap junctions, synaptic transmission, neuronal circuits)


Our tools dynamic mathematical models
Our tools: dynamic mathematical models

  • Differential Equations:models from kinetic network description, describes dynamic (not usually spatial) phenomena, numerical simulations

  • Sensitivity Analysis:dependence of steady-state behaviour on internal and external conditions

  • Stability Analysis:phase plane analysis, characterizing long-term behaviour (bistability, oscillations)

  • Bifurcation Analysis: dependence of system dynamics on internal and external conditions


  • Metabolism: chemical reaction networks, enzyme-catalysed reactions, allosteric regulation

  • Signal Transduction: G protein signalling, MAPK signalling cascade, bacterial chemotaxis, calcium oscillations.

  • Genetic Networks: switches(lac operon, phage lambda lysis/lysogeny switch, engineered toggle switch), oscillators (Goodwin oscillator, circadian rhythms, cell cycle, repressilator), computation

  • Electrophysiology:voltage-gated ion channels, Nernst potential, Morris-Lecar model, intercellular communication (gapjunctions, synaptic transmission, neuronal circuits)


Metabolic networks
Metabolic Networks

http://www.chemengr.ucsb.edu/~gadkar/images/network_ecoli.jpg


Enzyme catalysed reactions
Enzyme-Catalysed Reactions

http://www.uyseg.org/catalysis/principles/images/enzyme_substrate.gif


Allosteric regulation
Allosteric Regulation

http://courses.washington.edu/conj/protein/allosteric.gif


http://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpghttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg


Metabolic networks1
Metabolic Networkshttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg

E. Coli metabolism

KEGG: Kyoto Encyclopedia of Genes and Genomes (http://www.genome.ad.jp/kegg/kegg.html)


  • Metabolismhttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg: chemical reaction networks, enzyme-catalysed reactions, allosteric regulation

  • Signal Transduction: G protein signalling, MAPK signalling cascade, bacterial chemotaxis, calcium oscillations.

  • Genetic Networks: switches(lac operon, phage lambda lysis/lysogeny switch, engineered toggle switch), oscillators (Goodwin oscillator, circadian rhythms, cell cycle, repressilator), computation

  • Electrophysiology:voltage-gated ion channels, Nernst potential, Morris-Lecar model, intercellular communication (gapjunctions, synaptic transmission, neuronal circuits)


Transmembrane receptors
Transmembrane receptorshttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg

http://fig.cox.miami.edu/~cmallery/150/memb/fig11x7.jpg


Signal transduction pathway
Signal Transduction pathwayhttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg


Bacterial chemotaxis
Bacterial Chemotaxishttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg

http://www.aip.org/pt/jan00/images/berg4.jpg

http://www.life.uiuc.edu/crofts/bioph354/flag_labels.jpg


Apoptotic signalling pathway
Apoptotic Signalling pathwayhttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg


  • Metabolismhttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg: chemical reaction networks, enzyme-catalysed reactions, allosteric regulation

  • Signal Transduction: G protein signalling, MAPK signalling cascade, bacterial chemotaxis, calcium oscillations.

  • Genetic Networks: switches(lac operon, phage lambda lysis/lysogeny switch, engineered toggle switch), oscillators (Goodwin oscillator, circadian rhythms, cell cycle, repressilator), computation

  • Electrophysiology:voltage-gated ion channels, Nernst potential, Morris-Lecar model, intercellular communication (gapjunctions, synaptic transmission, neuronal circuits)


Simple genetic network lac operon
Simple genetic networkhttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg: lac operon

  • www.accessexcellence.org/ AB/GG/induction.html


Phage lambda
Phage Lambdahttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg

http://de.wikipedia.org/wiki/Bild:T4-phage.jpg

http://fig.cox.miami.edu/Faculty/Dana/phage.jpg


Lysis lysogeny switch
Lysis/Lysogeny Switchhttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg

http://opbs.okstate.edu/~Blair/Bioch4113/LAC-OPERON/LAMBDA%20PHAGE.GIF


Circadian rhythm
Circadian Rhythmhttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg

http://www.molbio.princeton.edu/courses/mb427/2001/projects/03/circadian%20pathway.jpg


Large Scale Genetic Networkhttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg

Eric Davidson's Lab at Caltech (http://sugp.caltech.edu/endomes/)


Genetic toggle switch
Genetic Toggle Switchhttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg

Gardner, T.S., Cantor, C.R., and Collins, J.J. (2000). Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342.

http://www.cellbioed.org/articles/vol4no1/i1536-7509-4-1-19-f02.jpg


http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v420/n6912/full/nature01257_r.htmlhttp://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v420/n6912/full/nature01257_r.html


Construction of computational elements logic gates and cell cell communication
Construction of computational elements (logic gates) and cell-cell communication

Genetic circuit building blocks for cellular computation, communications, and signal processing, Weiss, Basu, Hooshangi, Kalmbach, Karig, Mehreja, Netravali. Natural Computing. 2003. Vol. 2, 47-84.

http://www.molbio.princeton.edu/research_facultymember.php?id=62


  • Metabolism cell-cell communication: chemical reaction networks, enzyme-catalysed reactions, allosteric regulation

  • Signal Transduction: G protein signalling, MAPK signalling cascade, bacterial chemotaxis, calcium oscillations.

  • Genetic Networks: switches(lac operon, phage lambda lysis/lysogeny switch, engineered toggle switch), oscillators (Goodwin oscillator, circadian rhythms, cell cycle, repressilator), computation

  • Electrophysiology:voltage-gated ion channels, Nernst potential, Morris-Lecar model, intercellular communication (gapjunctions, synaptic transmission, neuronal circuits)


Excitable cells
Excitable Cells cell-cell communication

Resting potential

Ion Channel

http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/E/ExcitableCells.html

http://campus.lakeforest.edu/~light/ion%20channel.jpg


Measuring ion channel activity patch clamp
Measuring Ion Channel Activity: Patch Clamp cell-cell communication

http://www.ipmc.cnrs.fr/~duprat/neurophysiology/patch.htm


Measuring ion channel activity voltage clamp
Measuring Ion Channel Activity: Voltage Clamp cell-cell communication

http://soma.npa.uiuc.edu/courses/physl341/Lec3.html


Action potentials
Action Potentials cell-cell communication

http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/E/ExcitableCells.html

http://content.answers.com/main/content/wp/en/thumb/0/02/300px-Action-potential.png


Voltage gated ionic channels
voltage gated ionic channels cell-cell communication

heart.med.upatras.gr/ Prezentare_adi/3.htm

www.syssim.ecs.soton.ac.uk/. ../hodhuxneu/hh2.htm


Hodgkin huxley model
Hodgkin-Huxley Model cell-cell communication

http://www.amath.washington.edu/~qian/talks/talk5/


Neural computation
Neural Computation cell-cell communication

http://www.dna.caltech.edu/courses/cns187/


Our tools dynamic mathematical models1
Our tools: dynamic mathematical models cell-cell communication

  • Differential Equations:models from kinetic network description, models dynamic but not spatial phenomena, numerical simulations

  • Sensitivity Analysis:dependence of steady-state behaviour on internal and external conditions

  • Stability Analysis:phase plane analysis, characterizing long-term behaviour (bistability, oscillations)

  • Bifurcation Analysis: dependence of system dynamics on internal and external conditions


Differential equation modelling

rate of degradation cell-cell communication

rate of change of concentration

rate of production

Differential Equation Modelling

From Chen, Tyson, Novak Mol. Biol Cell 2000. pp. 369-391


Differential equation modelling1
Differential Equation Modelling cell-cell communication



Our tools dynamic mathematical models2
Our tools: dynamic mathematical models cell-cell communication

  • Differential Equations:models from kinetic network description, numerical simulations

  • Sensitivity Analysis:dependence of steady-state behaviour on internal and external conditions

  • Stability Analysis:phase plane analysis, characterizing long-term behaviour (bistability, oscillations)

  • Bifurcation Analysis: dependence of system dynamics on internal and external conditions


complete sensitivity analysis: cell-cell communication


Our tools dynamic mathematical models3
Our tools: dynamic mathematical models cell-cell communication

  • Differential Equations:models from kinetic network description, numerical simulations

  • Sensitivity Analysis:dependence of steady-state behaviour on internal and external conditions

  • Stability Analysis:phase plane analysis, characterizing long-term behaviour (bistability, oscillations)

  • Bifurcation Analysis: dependence of system dynamics on internal and external conditions


unstable cell-cell communication

stable


Our tools dynamic mathematical models4
Our tools: dynamic mathematical models cell-cell communication

  • Differential Equations:models from kinetic network description, numerical simulations

  • Sensitivity Analysis:dependence of steady-state behaviour on internal and external conditions

  • Stability Analysis:phase plane analysis, characterizing long-term behaviour (bistability, oscillations)

  • Bifurcation Analysis: dependence of system dynamics on internal and external conditions


Why cell-cell communicationdynamic modelling?

allows construction of falsifiable models

in silico experiments

gain insight into dynamic behaviour of complex networks


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