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Mathematical Modelling in Systems Biology: An Introduction by Brian Ingalls

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Mathematical Modelling in Systems Biology: An Introduction written by Brian Ingalls, Applied Mathematics, University of Waterloo.

Mathematical Modelling in Systems Biology: An Introduction written by Brian Ingalls cover the following topics.

• 1 Introduction
1.1 Systems Biology and Synthetic Biology
1.2 What is a Dynamic Mathematical Model?
1.3 Why are Dynamic Mathematical Models Needed?
1.4 How are Dynamic Mathematical Models Used?
1.5 Basic Features of Dynamic Mathematical Models
1.6 Dynamic Mathematical Models in Molecular Cell Biology
1.6.1 Drug target prediction in Trypanosoma brucei metabolism
1.6.2 Identifying the source of oscillatory behaviour in NF-?B signalling
1.6.3 Model-based design of an engineered genetic toggle switch
1.6.4 Establishing the mechanism for neuronal action potential generation

• 2 Modelling Chemical Reaction Networks
2.1 Chemical Reaction Networks
2.1.1 Closed and open networks
2.1.2 Dynamic behaviour of reaction networks
2.1.3 Simple network examples
2.1.4 Numerical simulation of differential equations
2.2 Separation of Time-Scales and Model Reduction
2.2.1 Separation of time-scales: the rapid equilibrium assumption
2.2.2 Separation of time-scales: the quasi-steady state assumption
2.4 Problem Set

• 3 Biochemical Kinetics
3.1 Enzyme Kinetics
3.1.1 Michaelis-Menten kinetics
3.1.2 Two-substrate reactions
3.2 Regulation of Enzyme Activity
3.2.1 Competitive inhibition
3.2.2 Allosteric regulation
3.3 Cooperativity
3.4 Compartmental Modelling and Transport
3.4.1 Diffusion
3.4.2 Facilitated transport
3.5 *Generalized Mass Action and S-System Modelling
3.7 Problem Set

• 4 Analysis of Dynamic Mathematical Models
4.1 Phase Plane Analysis
4.1.1 Direction fields
4.1.2 Nullclines
4.2 Stability
4.2.1 Stable and unstable steady states
4.2.2 Linearized stability analysis
4.3 Limit Cycle Oscillations
4.4 Bifurcation Analysis
4.5 Sensitivity Analysis
4.5.1 Local sensitivity analysis
4.5.2 Determining local sensitivity coefficients
4.6 *Parameter Fitting
4.8 Problem Set

• 5 Metabolic Networks
5.1 Modelling Metabolism
5.1.1 Example: a pathway model
5.1.2 Sensitivity analysis of metabolic networks: Metabolic Control Analysis
5.2 Metabolic Pathways
5.2.1 Flux control of unbranched pathways
5.2.2 Regulation of unbranched pathways
5.2.3 Branched pathways
5.3 Modelling Metabolic Networks
5.3.1 Model construction
5.3.2 Case study: modelling regulation of the methionine pathway
5.4 *Stoichiometric Network Analysis
5.4.1 Metabolic pathway analysis
5.4.2 Constraint-based modelling: metabolic flux analysis
5.6 Problem Set

• 6 Signal Transduction Pathways
6.1 Signal Amplification
6.1.1 Bacterial two-component signalling pathways
6.1.2 G-protein signalling pathways
6.2 Ultrasensitivity
6.2.1 Zero-order ultrasensitivity
6.3.1 Bacterial chemotaxis
6.4 Memory and irreversible decision-making
6.4.1 Apoptosis
6.5 Frequency Encoding
6.5.1 Calcium-induced calcium oscillations
6.6 *Frequency Response Analysis
6.6.1 Definition of the frequency response
6.6.2 Interpretation of the frequency response
6.6.3 Construction of the frequency response
6.8 Problem Set

• 7 Gene Regulatory Networks
7.1 Modelling Gene Expression
7.1.1 Unregulated gene expression
7.1.2 Regulated gene expression
7.1.3 Gene regulatory networks
7.2 Genetic Switches
7.2.1 The lac operon
7.2.2 The phage lambda decision switch
7.2.3 The Collins toggle switch
7.3 Oscillatory Gene Networks
7.3.1 The Goodwin oscillator
7.3.3 Synthetic oscillatory gene networks
7.4 Cell-to-Cell Communication
7.4.1 Bacterial quorum sensing
7.4.2 Engineered cell-to-cell communication
7.4.3 Synchronization of oscillating cells
7.5 Computation by Gene Regulatory Networks
7.5.1 Promoters as logic gates
7.5.2 Digital representations of gene circuits
7.5.3 Complex gene regulatory networks
7.6 *Stochastic Modelling of Biochemical and Genetic Networks
7.6.1 A discrete modelling framework
7.6.2 The chemical master equation
7.6.3 Gillespie’s stochastic simulation algorithm
7.6.4 Examples
7.8 Problem Set vii

• 8 Electrophysiology
8.1 Membrane Potential
8.1.1 The Nernst potential
8.1.2 The membrane model
8.2 Excitable Membranes
8.2.1 Voltage-gated ion channels
8.2.2 The Morris-Lecar model
8.3 Intercellular communication
8.3.1 Synaptic transmission
8.4 *Spatial modelling
8.4.1 Propagation of membrane voltage
8.4.2 Passive membrane
8.4.3 Excitable membrane: action potential propagation
8.6 Problem Set

• A Molecular Cell Biology
A.1 Cells
A.2 The Chemistry of Life
A.3 Macromolecules
A.4 Model Organisms

• B Mathematical Fundamentals
B.1 Differential Calculus
B.2 Linear Algebra
B.3 Probability

• C Computational Software
C.1 XPPAUT
C.2 MATLAB
C.2.1 The MATLAB Systems Biology Toolbox
D Exercise Solutions

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