Mathematical Biophysics (eBook)

PrefacePart I Basic models in mathematical biophysicsChapter 1 Growth and catalysis modelsUnlimited growth. Exponential growth. Self-catalysis (Auto-catalysis) Limited growth. The Verhulst equationConstraints with respect to substrate. Models of Monod and Michaelis–MentenCompetition. SelectionJacob and Monod trigger systemClassic Lotka and Volterra modelsModels of species interactionsModels of the enzyme catalysisModel of a continuous microorganism cultureAge structured populationsLeslie matricesContinuous models of age structureChapter 2 Oscillations, rhythms and chaos in biological systemsOscillations in glycolysisIntracellular calcium oscillationsDeterministic ChaosChaos in the community of three speciesPeriodic supply of substrate in the system of glycolysisChapter 3 Spatiotemporal self-organization of biological systemsWaves of lifeAutowaves and dissipative structuresBasic model “Brusselator” Localized dissipative structuresBelousov–Zhabotinsky reactionChapter 4 Model of the impact of a weak electric field on the nonlinear system of trans-membrane ion transportTransmembrane ion transport modelBistable modelAuto –oscillating systemPart II Models of complex systemsChapter 5 Oscillations and periodic space structures of pH and electric potential along the cell membrane of algae Chara corallinaKinetic model of the proton ATPase (pump) Equation, describing dynamics of proton concentration in the vicinity of the cellEquation for potential dynamicsOscillations in the local systempH patterns along the cellular membraneDependence of the processes on light intensity. HysteresisScheme of interactions of photosynthesis and ion fluxes leading to the nonlinear dynamicsChapter 6 Models of MorphogenesisTuring instabilityMorphogenetic fieldModel of a distributed triggerAnimal coat markingsModels of amoeba aggregation. The role of chemotaxisChapter 7 Autowave processes, nerve pulse propagation, and heart activityExperiments and model of Hodgkin and HuxleyReduced FitzHugh-Nagumo ModelExcited element of the local systemRunning pulsesDetailed models of cardiomyocytesAxiomatic models of excited medium. Autowave processes and cardiac arrhythmiaChapter 8 Nonlinear models of DNA dynamicsHierarchy of structural and dynamical modelsLinear DNA theorySimple linear model of an elastic barNonlinear models of DNA mobility. Mechanical analogueMathematical model, simulating single DNA base’s nonlinear oscillationsPhysical analogues of real DNA sequencesLong-range effectsNonlinear mechanisms of transcription regulationPart III Kinetic models of photosynthetic processesChapter 9 Models of photosynthetic electron transport. Electron transfer in a multienzyme complexOrganization of processes in photosynthetic membraneKinetic description of redox reactions in solutionModeling electron transfer in a multienzyme complexElectron transfer in a two-component complexElectron transfer in a n-carrier complexElectron transport via mobile carriersElectron transport in an isolated photosynthetic reaction centerChapter 10 Kinetic model of interaction of two photosystemsTypes of regulation of photosynthetic processesModel of PSI and PSII interactionSubsystem PSIIScheme of PSII statesCharge separationSubmodel of PSIDescription of the mobile carrier redox evolutionRelationships between total concentrations of electron carriersModeling of electron transport chain of wild type and mutant Arabidopsys thalianaChapter 11 Detailed model of electron transfer in PSIIFluorescence as an indicator of the state of the photosystemScheme of PSII statesEquations describing processes in PSIIDependence of rate constants on thylakoid transmembrane electric potentialEnergy loss processesExperimentDescription of events in PSII electron transport system after a short light flashChapter 12 Generalized kinetic model of primary photosynthetic processesThe structure of the modelPhotosystem II complexCytochrome b6f complexPhotosystem I complexMobile carriers in the kinetic modelRole of transmembrane electric potentialTransmembrane ion transfer and   generationBuffer properties of lumen and stromaParameter valuesSimulation of fluorescence transients at different light intensitiesThe role of different states of photosystem II in fluorescence inductionSimulation of   kineticsPart IV Direct multiparticle models of processes in subcellular systemsChapter 13 Method of direct multiparticle simulation of protein interactionsRestricted diffusion of mobile electron carriers in photosynthetic membraneDirect model sceneBrownian dynamics of mobile carriersSimulation of cyclic electron transport around photosystem IChapter  14 Modeling of protein complex formation in solution with diffusion and electrostatic interactionsSteps of redox protein interactionsModel of protein-protein interaction in solutionProtein diffusion. Approximation with ellipsoids of revolutionSimulation of geometric shape of proteins and their collisionsElectrostatic interactionsSimulation of complex formationDocking rate constant dependence on ionic strength of solutionComparative analysis of the interaction of Pc with Cyt f and PSI reaction centers in higher plants and cyanobacteria. Role of electrostaticsChapter 15 Modeling of protein interactions in photosynthetic membraneInteraction of Pc with Cyt f in thylakoid lumenModeling of Pc -PSI interaction considering membrane surface charge and multienzyme complexes embedded in the membraneModeling of Pc interaction with cyt f and PSI considering membrane surface charge and multienzyme complexes embedded in the membraneChapter 16 Spaciotemporal evolution of electrochemical potential ΔμH+ in photosynthetic membraneModeling of proton transferModel of proton release into lumenModel of lateral diffusion of protonsProton flow through the ATP-synthase and ATP synthesisComputer simulation of proton gradient evolution and ATP creationConclusionReferencesIndex