AMATH 900:

Mathematical Cell Biology

Dynamic modelling of biochemical, genetic, and

neuronal networks

Dynamic biological systems -- multicellular

http://megaverse.net/chipmunkvideos/

Dynamic biological systems -- cellular

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

Neutrophil chasing a bacterium

Dynamic biological systems -- intracellular

http://www.bio.davidson.edu/courses/movies.html

Calcium Waves in Retinal Glia

Dynamic biological systems -- molecular

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

• 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 (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/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)

Metabolic Networks

• 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)

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.jpg

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

Apoptotic Signalling pathway

• 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)

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/Dana/phage.jpg

Lysis/Lysogeny Switch

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

Circadian Rhythm

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

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

Large Scale Genetic Network

Genetic Toggle Switch

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

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

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.

• 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)

Excitable Cells

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

ExcitableCells.html

Resting potential

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.ultranet/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.upatras.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: phase plane analysis, characterizing long-term behaviour (bistability, oscillations)

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

Differential Equation Modelling

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

rate of change of concentration

rate of production

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

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

complete sensitivity analysis:

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

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

unstable

stable

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

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

allows construction of falsifiable models

in silico experiments

gain insight into dynamic behaviour of complex networks

Why dynamic modelling?