'Preface
Part I Basic models in mathematical biophysics
Chapter 1 Growth and catalysis models
Unlimited growth. Exponential growth. Self-catalysis (Auto-catalysis)
Limited growth. The Verhulst equation
Constraints with respect to substrate. Models of Monod and Michaelis-Menten
Competition. Selection
Jacob and Monod trigger system
Classic Lotka and Volterra models
Models of species interactions
Models of the enzyme catalysis
Model of a continuous microorganism culture
Age structured populations
Leslie matrices
Continuous models of age structure
Chapter 2 Oscillations, rhythms and chaos in biological systems
Oscillations in glycolysis
Intracellular calcium oscillations
Deterministic Chaos
Chaos in the community of three species
Periodic supply of substrate in the system of glycolysis
Chapter 3 Spatiotemporal self-organization of biological systems
Waves of life
Autowaves and dissipative structures
Basic model "Brusselator"Localized dissipative structures
Belousov-Zhabotinsky reaction
Chapter 4 Model of the impact of a weak electric field on the nonlinear system of trans-membrane ion transport
Transmembrane ion transport model
Bistable model
Auto -oscillating system
Part II Models of complex systems
Chapter 5 Oscillations and periodic space structures of pH and electric potential along the cell membrane of algae Chara corallina
Kinetic model of the proton ATPase (pump)
Equation, describing dynamics of proton concentration in the vicinity of the cell
Equation for potential dynamics
Oscillations in the local system
pH patterns along the cellular membrane
Dependence of the processes on light intensity. Hysteresis
Scheme of interactions of photosynthesis and ion fluxes leading to the nonlinear dynamics
Chapter 6 Models of Morphogenesis
Turing instability
Morphogenetic field
Model of a distributed trigger
Animal coat markings
Models of amoeba aggregation. The role of chemotaxis
Chapter 7 Autowave processes, nerve pulse propagation, and heart activity
Experiments and model of Hodgkin and Huxley
Reduced FitzHugh-Nagumo Model
Excited element of the local system
Running pulses
Detailed models of cardiomyocytes
Axiomatic models of excited medium. Autowave processes and cardiac arrhythmia
Chapter 8 Nonlinear models of DNA dynamics
Hierarchy of structural and dynamical models
Linear DNA theory
Simple linear model of an elastic bar
Nonlinear models of DNA mobility. Mechanical analogue
Mathematical model, simulating single DNA base's nonlinear oscillations
Physical analogues of real DNA sequences
Long-range effects
Nonlinear mechanisms of transcription regulation
Part III Kinetic models of photosynthetic processes
Chapter 9 Models of photosynthetic electron transport. Electron transfer in a multienzyme complex
Organization of processes in photosynthetic membrane
Kinetic description of redox reactions in solutionModeling electron transfer in a multienzyme complex
Electron transfer in a two-component complex
Electron transfer in a n-carrier complex
Electron transport via mobile carriers
Electron transport in an isolated photosynthetic reaction center
Chapter 10 Kinetic model of interaction of two photosystems
Types of regulation of photosynthetic processes
Model of PSI and PSII interaction
Subsystem PSII
Scheme of PSII states
Charge separation
Submodel of PSI
Description of the mobile carrier redox evolution
Relationships between total concentrations of electron carriers
Modeling of electron transport chain of wild type and mutant Arabidopsys thaliana
Chapter 11 Detailed model of electron transfer in PSIIFluorescence as an indicator of the state of the photosystem
Scheme of PSII states
Equations describing processes in PSII
Dependence of rate constants on thylakoid transmembrane electric potential
Energy loss processes
Experiment
Description of events in PSII electron transport system after a short light flash
Chapter 12 Generalize
Klappentext
This book presents concise descriptions and analysis of the classical and modern models used in mathematical biophysics. The authors ask the question "what new information can be provided by the models that cannot be obtained directly from experimental data?" Actively developing fields such as regulatory mechanisms in cells and subcellular systems and electron transport and energy transport in membranes are addressed together with more classical topics such as metabolic processes, nerve conduction and heart activity, chemical kinetics, population dynamics, and photosynthesis. The main approach is to describe biological processes using different mathematical approaches necessary to reveal characteristic features and properties of simulated systems. With the emergence of powerful mathematics software packages such as MAPLE, Mathematica, Mathcad, and MatLab, these methodologies are now accessible to a wide audience.
Provides succinct but authoritative coverage of a broad array of biophysical topics and models
Written by authors at Moscow State University with its strong tradition in mathematics and biophysics
Scope, coverage, and length make the book highly suitable for use in a one-semester course at the senior undergraduate/graduate level
