AMATH 882: Computational Modeling of Cellular Systems Dynamic modelling of biochemical, genetic, and neural networks Introductory Lecture, Jan. 4, 2017

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 astrocytes in rat cerebral cortex http://stke.sciencemag.org/cgi/content/full/sigtrans;3/147/tr5/DC1

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

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

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://fig.cox.miami.edu/Faculty/Dana/phage.jpg http://de.wikipedia.org/wiki/Bild:T4-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

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 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

Synchronized Relaxation oscillators (Hasty Lab)

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 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 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 rate of change of concentration rate of production rate of degradation From Chen, Tyson, Novak Mol. Biol Cell 2000. pp. 369-391

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

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

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