1. AMATH 882: Computational Modeling of Cellular Systems
Dynamic modelling of biochemical, genetic, and neural networks
Introductory Lecture, Jan. 4, 2017

2. Dynamic biological systems -- multicellular

3. Dynamic biological systems -- cellular
Neutrophil chasing a bacterium

4. Dynamic biological systems -- intracellular
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

10. Enzyme-Catalysed Reactions

11. Allosteric Regulation

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

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

16. Signal Transduction pathway

17. Bacterial Chemotaxis http://www.aip.org/pt/jan00/images/berg4.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
AB/GG/induction.html

21. Phage Lambda http://fig.cox.miami.edu/Faculty/Dana/phage.jpg

22. Lysis/Lysogeny Switch

23. Circadian Rhythm

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

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.

26. http://www. nature. com/cgi-taf/DynaPage. taf

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 Vol. 2,

28. Synchronized Relaxation oscillators (Hasty Lab)

29. 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)

30. Excitable Cells Resting potential Ion Channel

31. Measuring Ion Channel Activity: Patch Clamp

32. Measuring Ion Channel Activity: Voltage Clamp

33. Action Potentials

34. voltage gated ionic channels
heart.med.upatras.gr/ Prezentare_adi/3.htm
../hodhuxneu/hh2.htm

35. Hodgkin-Huxley Model

36. Neural Computation

37. 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

38. Differential Equation Modelling
rate of change of concentration
rate of production
rate of degradation
From Chen, Tyson, Novak Mol. Biol Cell pp

39. Differential Equation Modelling

40. Differential Equation Modelling: Numerical Simulation

41. 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

42. sensitivity analysis:

43. 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

44. unstable
stable

45. 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

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