Amath/Bio 382: Computational Modelling of Cellular

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Transcript Amath/Bio 382: Computational Modelling of Cellular

AMATH 882: Mathematical Cell Biology

Dynamic modelling of biochemical, genetic, and neural networks Introductory Lecture, Jan. 7, 2013

Dynamic biological systems - multicellular

http://megaverse.net/chipmunkvideos/

Dynamic biological systems - cellular

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

Dynamic biological systems - intracellular

Calcium Waves in Retinal Glia http://www.bio.davidson.edu/courses/movies.html

Dynamic biological systems - molecular

Our interest: intracellular dynamics • Metabolism: oscillations. chemical reaction networks, enzyme catalysed reactions, allosteric regulation • Signal Transduction: • Genetic Networks: • Electrophysiology: neuronal circuits) G protein signalling, MAPK signalling cascade, bacterial chemotaxis, calcium switches (lac operon, phage lambda lysis/lysogeny switch, engineered toggle switch), oscillators (Goodwin oscillator, circadian rhythms, cell cycle, repressilator), computation voltage-gated ion channels, Nernst potential, Morris-Lecar model, intercellular communication (gap junctions, synaptic transmission,

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: characterizing long-term behaviour (bistability, oscillations) phase plane analysis, • 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 (gap junctions, synaptic transmission, neuronal circuits)

Metabolic Networks

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

Enzyme-Catalysed Reactions

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

Allosteric Regulation

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

http://www.cm.utexas.edu/a cademic/courses/Spring200 2/CH339K/Robertus/overhe ads-3/ch15_reg glycolysis.jpg

Metabolic Networks

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

)

Transmembrane receptors

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

Signal Transduction pathway

Bacterial Chemotaxis

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

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

Apoptotic Signalling pathway

Simple genetic network

: lac

operon

•

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

Phage Lambda

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

http://fig.cox.miami.edu/Faculty/Dan a/phage.jpg

Lysis/Lysogeny Switch

http://opbs.okst

ate.edu/~Blair/ Bioch4113/LAC OPERON/LAM BDA%20PHAG E.GIF

Circadian Rhythm

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

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

Genetic Toggle Switch 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.html

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

Excitable Cells

Resting potential http://users.rcn.com/jkimball.ma.ultran

et/BiologyPages/E/ExcitableCells.html

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

Measuring Ion Channel Activity: Patch Clamp

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

Measuring Ion Channel Activity: Voltage Clamp

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

Action Potentials

http://users.rcn.com/jkimball.ma.ultran

et/BiologyPages/E/ExcitableCells.html

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

voltage gated ionic channels

heart.med.u

patras.gr/ Prezentare_ adi/3.htm

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

Hodgkin-Huxley Model

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

Neural Computation

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

Our tools: dynamic mathematical models • 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: characterizing long-term behaviour (bistability, oscillations) phase plane analysis, • Bifurcation Analysis: dependence of system dynamics on internal and external conditions

Differential Equation Modelling

rate of change of rate of concentration production 2000. pp. 369-391 rate of degradation

Differential Equation Modelling

Differential Equation Modelling: Numerical Simulation

Our tools: dynamic mathematical models • Differential Equations: models from kinetic network description, numerical simulations • Sensitivity Analysis: dependence of steady-state behaviour on internal and external conditions • Stability Analysis: characterizing long-term behaviour (bistability, oscillations) phase plane analysis, • Bifurcation Analysis: dependence of system dynamics on internal and external conditions

unstable stable

3 2.5

2 1.5

S1 4 3.5

1 0.5

0 1 1.5

2 2.5

3 q 3.5

4 4.5

Why dynamic modelling?

allows construction of falsifiable models in silico experiments gain insight into dynamic behaviour of complex networks