Course Notes - AMATH/BIOL 382 Computational Modelling of...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: AMATH/BIOL 382 Computational Modelling of Cellular Systems Brian Ingalls Applied Mathematics University of Waterloo bingalls@uwaterloo.ca December 28, 2009 Contents 1 Biochemical Reaction Networks 3 1.1 Chemical Reaction Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.1 Closed and open networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.2 Dynamic Behaviour of Reaction Networks . . . . . . . . . . . . . . . . . . . . 5 1.1.3 Numerical Integration of Differential Equations . . . . . . . . . . . . . . . . . 16 1.2 Separation of Time Scales and Model Reduction . . . . . . . . . . . . . . . . . . . . 19 1.2.1 Separation of Timescales: The Rapid Equilibrium Assumption . . . . . . . . 20 1.2.2 Separation of Timescales: The Quasi-Steady-State Assumption . . . . . . . . 22 1.3 Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2 Biochemical Kinetics 28 2.1 Enzyme kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.1.1 Rates of Enzyme-Catalysed Reactions . . . . . . . . . . . . . . . . . . . . . . 29 2.2 Regulation of Enzyme Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2.1 Competitive Inhibition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2.2 Allosteric Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2.3 Cooperativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.3 Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3 Dynamic modelling tools 45 3.1 Phase plane analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.2.1 Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2.2 Oscillatory behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3 Bifurcations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.4 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.4.1 Local Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.5 Problem Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4 Metabolism 72 4.1 Pathway Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.2 Sensitivity Analysis of Metabolic Networks . . . . . . . . . . . . . . . . . . . . . . . 73 4.3 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3.1 Unbranched Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3.2 Negative feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 1 4.3.3 Branch points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Branch points ....
View Full Document

Page1 / 131

Course Notes - AMATH/BIOL 382 Computational Modelling of...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online