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
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, enzymecatalysed 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, enzymecatalysed 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_regglycolysis.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, enzymecatalysed 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.j
pg
http://www.life.uiuc.edu/crofts/
bioph354/flag_labels.jpg
Apoptotic Signalling pathway
• Metabolism:
chemical reaction networks, enzymecatalysed 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:T4phage.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
• Metabolism:
chemical reaction networks, enzymecatalysed 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.ultran
et/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.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:
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
rate of change of
rate of
degradation
concentration
production
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
A
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
S1
4
3.5
3
2.5
2
1.5
1
0.5
0
1
1.5
2
2.5
3
q
3.5
4
4.5
5
Why dynamic modelling?
allows construction of falsifiable models
in silico experiments
gain insight into dynamic behaviour of complex networks