Mathematical Biophysics

<p>Preface</p><p>Part I Basic models in mathematical biophysics</p><p>Chapter 1 Growth and catalysis models<br>Unlimited growth. Exponential growth. Self-catalysis (Auto-catalysis) <br>Limited growth. The Verhulst equation<br>Constraints with respect to substrate. Models of Monod and Michaelis–Menten<br>Competition. Selection<br>Jacob and Monod trigger system<br>Classic Lotka and Volterra models<br>Models of species interactions<br>Models of the enzyme catalysis<br>Model of a continuous microorganism culture<br>Age structured populations<br>Leslie matrices<br>Continuous models of age structure</p><p>Chapter 2 Oscillations, rhythms and chaos in biological systems<br>Oscillations in glycolysis<br>Intracellular calcium oscillations<br>Deterministic Chaos<br>Chaos in the community of three species<br>Periodic supply of substrate in the system of glycolysis</p><p>Chapter 3 Spatiotemporal self-organization of biological systems<br>Waves of life<br>Autowaves and dissipative structures<br>Basic model “Brusselator” <br>Localized dissipative structures<br>Belousov–Zhabotinsky reaction</p><p>Chapter 4 Model of the impact of a weak electric field on the nonlinear system of trans-membrane ion transport<br>Transmembrane ion transport model<br>Bistable model<br>Auto –oscillating system</p><p>Part II Models of complex systems</p><p>Chapter 5 Oscillations and periodic space structures of pH and electric potential along the cell membrane of algae Chara corallina<br>Kinetic model of the proton ATPase (pump) <br>Equation, describing dynamics of proton concentration in the vicinity of the cell<br>Equation for potential dynamics<br>Oscillations in the local system<br>pH patterns along the cellular membrane<br>Dependence of the processes on light intensity. Hysteresis<br>Scheme of interactions of photosynthesis and ion fluxes leading to the nonlinear dynamics</p><p>Chapter 6 Models of Morphogenesis<br>Turing instability<br>Morphogenetic field<br>Model of a distributed trigger<br>Animal coat markings<br>Models of amoeba aggregation. The role of chemotaxis</p><p>Chapter 7 Autowave processes, nerve pulse propagation, and heart activity<br>Experiments and model of Hodgkin and Huxley<br>Reduced FitzHugh-Nagumo Model<br>Excited element of the local system<br>Running pulses<br>Detailed models of cardiomyocytes<br>Axiomatic models of excited medium. Autowave processes and cardiac arrhythmia</p><p>Chapter 8 Nonlinear models of DNA dynamics<br>Hierarchy of structural and dynamical models<br>Linear DNA theory<br>Simple linear model of an elastic bar<br>Nonlinear models of DNA mobility. Mechanical analogue<br>Mathematical model, simulating single DNA base’s nonlinear oscillations<br>Physical analogues of real DNA sequences<br>Long-range effects<br>Nonlinear mechanisms of transcription regulation</p><p>Part III Kinetic models of photosynthetic processes</p><p>Chapter 9 Models of photosynthetic electron transport. Electron transfer in a multienzyme complex<br>Organization of processes in photosynthetic membrane<br>Kinetic description of redox reactions in solution<br>Modeling electron transfer in a multienzyme complex<br>Electron transfer in a two-component complex<br>Electron transfer in a n-carrier complex<br>Electron transport via mobile carriers<br>Electron transport in an isolated photosynthetic reaction center</p><p>Chapter 10 Kinetic model of interaction of two photosystems<br>Types of regulation of photosynthetic processes<br>Model of PSI and PSII interaction<br>Subsystem PSII<br>Scheme of PSII states<br>Charge separation<br>Submodel of PSI<br>Description of the mobile carrier redox evolution<br>Relationships between total concentrations of electron carriers<br>Modeling of electron transport chain of wild type and mutant Arabidopsys thaliana</p><p>Chapter 11 Detailed model of electron transfer in PSIIFluorescence as an indicator of the state of the photosystem<br>Scheme of PSII states<br>Equations describing processes in PSII<br>Dependence of rate constants on thylakoid transmembrane electric potential<br>Energy loss processes<br>Experiment<br>Description of events in PSII electron transport system after a short light flash</p><p>Chapter 12 Generalized kinetic model of primary photosynthetic processes<br>The structure of the model<br>Photosystem II complex<br>Cytochrome b6f complex<br>Photosystem I complex<br>Mobile carriers in the kinetic model<br>Role of transmembrane electric potential<br>Transmembrane ion transfer and   generation<br>Buffer properties of lumen and stroma<br>Parameter values<br>Simulation of fluorescence transients at different light intensities<br>The role of different states of photosystem II in fluorescence induction<br>Simulation of   kinetics</p><p>Part IV Direct multiparticle models of processes in subcellular systems</p><p>Chapter 13 Method of direct multiparticle simulation of protein interactions<br>Restricted diffusion of mobile electron carriers in photosynthetic membrane<br>Direct model scene<br>Brownian dynamics of mobile carriers<br>Simulation of cyclic electron transport around photosystem I</p><p>Chapter  14 Modeling of protein complex formation in solution with diffusion and electrostatic interactions<br>Steps of redox protein interactions<br>Model of protein-protein interaction in solution<br>Protein diffusion. Approximation with ellipsoids of revolution<br>Simulation of geometric shape of proteins and their collisions<br>Electrostatic interactions<br>Simulation of complex formation<br>Docking rate constant dependence on ionic strength of solution<br>Comparative analysis of the interaction of Pc with Cyt f and PSI reaction centers in higher plants and cyanobacteria. Role of electrostatics</p><p>Chapter 15 Modeling of protein interactions in photosynthetic membrane<br>Interaction of Pc with Cyt f in thylakoid lumen<br>Modeling of Pc -PSI interaction considering membrane surface charge and multienzyme complexes embedded in the membrane<br>Modeling of Pc interaction with cyt f and PSI considering membrane surface charge and multienzyme complexes embedded in the membrane</p><p>Chapter 16 Spaciotemporal evolution of electrochemical potential ΔμH+ in photosynthetic membrane<br>Modeling of proton transfer<br>Model of proton release into lumen<br>Model of lateral diffusion of protons<br>Proton flow through the ATP-synthase and ATP synthesis<br>Computer simulation of proton gradient evolution and ATP creation</p><p>Conclusion<br>References<br>Index</p>