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AMATH 882: Mathematical Cell Biology

AMATH 882: Mathematical Cell Biology. Dynamic modelling of biochemical, genetic, and neural networks. Introductory Lecture, Jan. 10, 2010. Dynamic biological systems -- multicellular. http://megaverse.net/chipmunkvideos/. Dynamic biological systems -- cellular. Neutrophil chasing a bacterium.

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AMATH 882: Mathematical Cell Biology

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  1. AMATH 882:Mathematical Cell Biology Dynamic modelling of biochemical, genetic, and neural networks Introductory Lecture, Jan. 10, 2010

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

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

  4. Dynamic biological systems -- intracellular Calcium Waves in Retinal Glia http://www.bio.davidson.edu/courses/movies.html

  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 (gapjunctions, 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/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpghttp://www.cm.utexas.edu/academic/courses/Spring2002/CH339K/Robertus/overheads-3/ch15_reg-glycolysis.jpg

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

  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 (gapjunctions, 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.jpg 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 (gapjunctions, 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/Dana/phage.jpg

  22. Lysis/Lysogeny Switch http://opbs.okstate.edu/~Blair/Bioch4113/LAC-OPERON/LAMBDA%20PHAGE.GIF

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

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

  25. 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

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

  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 (gapjunctions, synaptic transmission, neuronal circuits)

  29. 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

  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.ultranet/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.upatras.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. rate of degradation rate of change of concentration rate of production Differential Equation Modelling From Chen, Tyson, Novak Mol. Biol Cell 2000. pp. 369-391

  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

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

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