AMATH 882: Mathematical Cell Biology Dynamic modelling of biochemical, genetic, and neural networks Introductory Lecture, Jan. 7, 2013
Jan 05, 2016
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
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?