AMATH 382: Computational Modeling of Cellular Systems Dynamic modelling of biochemical, genetic, and neural networks Introductory Lecture, Jan. 6, 2014

Dynamic biological systems -- multicellular

Dynamic biological systems -- cellular Neutrophil chasing a bacterium

Dynamic biological systems -- intracellular Calcium waves in astrocytes in rat cerebral cortex

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

Enzyme-Catalysed Reactions enzyme_substrate.gif

Allosteric Regulation

cademic/courses/Spring200 2/CH339K/Robertus/overhe ads-3/ch15_reg- glycolysis.jpg

E. Coli metabolism KEGG: Kyoto Encyclopedia of Genes and Genomes ( 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

Signal Transduction pathway

Bacterial Chemotaxis jan00/images/berg4.j pg 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 AB/GG/induction.html

Phage Lambda phage.jpg a/phage.jpg

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

Circadian Rhythm

Eric Davidson's Lab at Caltech ( Large Scale Genetic Network

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.

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 Vol. 2,

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 et/BiologyPages/E/ExcitableCells.html Resting potential Ion Channel ~light/ion%20channel.jpg

Measuring Ion Channel Activity: Patch Clamp

Measuring Ion Channel Activity: Voltage Clamp

Action Potentials et/BiologyPages/E/ExcitableCells.html /thumb/0/02/300px-Action-potential.png

voltage gated ionic channels heart.med.u patras.gr/ Prezentare_ adi/3.htm

Hodgkin-Huxley Model qian/talks/talk5/

Neural Computation

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 pp 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?