introduction to mathematical biology - tu dresden · introduction to mathematical biology osvaldo...

Introduction to Mathematical Biology

Osvaldo Chara Technische Universität Dresden, Germany

[email protected]

http://imc.zih.tu-dresden.de/imc/

Osvaldo Chara - SSIM - Dresden 2012 - Monday

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1. Modelling biological and biochemical process using ODEs Osvaldo Chara

Monday 13 and Tuesday 14, 9:00 to 10:30 h.

2. Modelling biological and biochemical process using PDEs Lutz Brusch

Wednsesday 15 and Thursday 16, 13:30 to 15:00 h.

Schedule


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1. Modelling biological and biochemical process using ODEs Osvaldo Chara

Monday 13

9:00 to 10:30 h.


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x

d

d

xyt

y

d

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the Lotka-Volterra model By the way, I am Vito Volterra

rxt

x

d

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the Malthus model

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x

d

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the logistic model


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Rashevsky, N. (Ed.), 1962. Physicomathematical Aspects of Biology: Proceedings of the International School of Physics “Enrico Fermi” XVI Course. Academic Press, New York.


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Rashevsky, N. (Ed.), 1962. Physicomathematical Aspects of Biology: Proceedings of the International School of Physics “Enrico Fermi” XVI Course. Academic Press, New York.


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Yeah, I am Nicolas Rashevsky


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molecules cells tissues organs organisms populations

Which is the spatial scale of the phenomenon under study?


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molecules cells tissues organs organisms populations

Which is the spatial scale of the phenomenon under study?


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modelling cellular processes

reactions transport


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reactions transport


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A + B C + D

reactants products

chemical reaction


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A + B C + D

reactants products

chemical reaction

1. stechiometry

2. directionality / reversibility


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A + B C + B

catalyst product

catalysis

substrate catalyst


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A + B C + B

catalyst product

catalysis

substrate catalyst


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A C

catalyst product

catalysis

substrate

B


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2H2O2 2H20 + O2

Catalase

just an example


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reactions transport


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reactions transport


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Apical membrane

Basolateral membrane

Paracelular path Transcelular path

lipid bilayer AQP cotransporter


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Apical membrane

Basolateral membrane

Paracelular path Transcelular path

lipid bilayer AQP cotransporter

AQPs!


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transport of water: osmosis


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Pickard WF. 2008. Modelling the swelling assay for aquaporin expression. J Math Biol 57:883–903. Chara et al., 2011. Regulatory volume decrease and P receptor signaling in fish cells: mechanisms, physiology, and modeling approaches. J Exp Zool A Ecol Genet Physiol. 315(4):175-202.


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The cup of coffee of SSIM 2012

coffee

sugar


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coffee

sugar


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coffee

sugar


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coffee

sugar


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a phenomenological explanation: the Fick's law

Imaginary membrane of area A and length x

Js

Cx

ADJ s

s


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transport of water and non-electrolyte solutes

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Kedem & Katchalsky, 1958. Thermodynamic analysis of the permeability of biological membranes to non-electrolytes. Biochim. Biophys. Acta 27, 229-246. Kedem & Katchalsky, 1961. A physical interpretation of the phenomenological coefficients of membrane permeability. J. Gen. Physiol. 45: 143-179. Katchalsky & Curran, 1965. Non-equilibrium Thermodynamics in Biophysics. Harvard University Press, Cambridge, MA, USA. Kleinhans, 1998. Membrane permeability modeling: Kedem-Katchalsky vs a two-parameter formalism. Cryobiology. 37(4):271-89.

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introduction to mathematical biology - tu dresden · introduction to mathematical biology osvaldo...

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