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

2. Dynamic biological systems -- multicellular http://megaverse.net/chipmunkvideos/

3. Dynamic biological systems -- cellular http://astro.temple.edu/~jbs/courses/204lectures/neutrophil-js.html Neutrophil chasing a bacterium

4. Dynamic biological systems -- intracellular http://stke.sciencemag.org/cgi/content/full/sigtrans;3/147/tr5/DC1 Calcium waves in astrocytes in rat cerebral cortex

5. Dynamic biological systems -- molecular

6. 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)

7. 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

8. 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)

9. Metabolic Networks http://www.chemengr.ucsb.edu/~gadkar/images/network_ecoli.jpg

10. Enzyme-Catalysed Reactions http://www.uyseg.org/catalysis/principles/images/ enzyme_substrate.gif

11. Allosteric Regulation http://courses.washington.edu/conj/protein/allosteric.gif

12. http://www.cm.utexas.edu/a cademic/courses/Spring200 2/CH339K/Robertus/overhe ads-3/ch15_reg- glycolysis.jpg

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

14. 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)

15. Transmembrane receptors http://fig.cox.miami.edu/~cmallery/150/memb/fig11x7.jpg

16. Signal Transduction pathway

17. Bacterial Chemotaxis http://www.aip.org/pt/ jan00/images/berg4.j pg http://www.life.uiuc.edu/crofts/ bioph354/flag_labels.jpg

18. Apoptotic Signalling pathway

19. 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)

20. Simple genetic network: lac operon www.accessexcellence.org/ AB/GG/induction.html

21. Phage Lambda http://de.wikipedia.org/wiki/Bild:T4- phage.jpg http://fig.cox.miami.edu/Faculty/Dan a/phage.jpg

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

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

24. Eric Davidson's Lab at Caltech (http://sugp.caltech.edu/endomes/) Large Scale Genetic Network

25. 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.

26. http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v420/n6912/full/nature01257_r.html

27. 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.

28. 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)

29. Excitable Cells http://users.rcn.com/jkimball.ma.ultran et/BiologyPages/E/ExcitableCells.html Resting potential Ion Channel http://campus.lakeforest.edu/ ~light/ion%20channel.jpg

30. Measuring Ion Channel Activity: Patch Clamp http://www.ipmc.cnrs.fr/~duprat/neurophysiology/patch.htm

31. Measuring Ion Channel Activity: Voltage Clamp http://soma.npa.uiuc.edu/courses/physl341/Lec3.html

32. 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

33. voltage gated ionic channels heart.med.u patras.gr/ Prezentare_ adi/3.htm www.syssim.ecs.soton.ac.uk/.../hodhuxneu/hh2.htm

34. Hodgkin-Huxley Model http://www.amath.washington.edu/~ qian/talks/talk5/

35. Neural Computation http://www.dna.caltech.edu/courses/cns187/

36. 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

37. 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

38. Differential Equation Modelling

39. Differential Equation Modelling: Numerical Simulation

40. 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

41. complete sensitivity analysis:

42. 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

43. unstable stable

44. 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

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