Compendium of Biophysics

Wiley-Scrivener (Verlag)
  • 1. Auflage
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  • erschienen am 13. Juli 2017
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  • 660 Seiten
E-Book | ePUB mit Adobe-DRM | Systemvoraussetzungen
978-1-119-16027-4 (ISBN)

Following up on his first book, Fundementals of Biophysics, the author, a well-known scientist in this area, builds on that foundation by offering the biologist or scientist an advanced, comprehensive coverage of biophysics. Structuring the book into four major parts, he thoroughly covers the biophysics of complex systems, such as the kinetics and thermodynamic processes of biological systems, in the first part. The second part is dedicated to molecular biophysics, such as biopolymers and proteins, and the third part is on the biophysics of membrane processes. The final part is on photobiological processes.

This ambitious work is a must-have for the veteran biologist, scientist, or chemist working in this field, and for the novice or student, who is interested in learning about biophysics. It is an emerging field, becoming increasingly more important, the more we learn about and develop the science. No library on biophysics is complete without this text and its precursor, both available from Wiley-Scrivener.

Andrey B. Rubin is a professor of biophysics at Lomonosov Moscow State University in the Department of Biophysics. Born in Russia, he is chair of the National Committee for Biophysics in the Russian Academy of Science. He has been head of the Department of Biophysics at MSU, Governor of the Task Force on Education in Biophysics, and a member of the RAS Council on Space Biology and Biological Membranes since 2005. He has received many awards for his contributions to the science of biophysics, and he holds many patents and inventions, as well as having been the author of numerous papers. He is also on the editorial board of the journal, Biophysics, in the Russian language.

  • Englisch
  • Somerset
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  • USA
  • 37,60 MB
978-1-119-16027-4 (9781119160274)
weitere Ausgaben werden ermittelt
  • Intro
  • Title page
  • Copyright page
  • Introduction
  • Part I: Biophysics of Complex Systems
  • I. Kinetics of Biological Processes
  • Chapter 1: Qualitative Methods for Studying Dynamic Models of Biological Processes
  • 1.1 General Principles of Description of Kinetic Behavior of Biological Systems
  • 1.2 Qualitative Analysis of Elementary Models of Biological Processes
  • Chapter 2: Types of Dynamic Behavior of Biological Systems
  • 2.1 Biological Triggers
  • 2.2 Oscillatory Processes in Biology. Limit Cycles
  • 2.3 Time Hierarchy in Biological Systems
  • Chapter 3: Kinetics of Enzyme Processes
  • 3.1 Elementary Enzyme Reactions
  • 3.2 Multiplicity of Stationary States in Enzyme Systems
  • 3.3 Oscillations in Enzyme Systems
  • 3.4 Mathematical Modeling of Metabolic Pathways
  • Chapter 4: Self-Organization Processes in Distributed Biological Systems
  • 4.1 General Characteristics of Autowave Processes
  • 4.2 Mathematical Models of Self-Organized Structures
  • 4.3 Chaotic Processes in Determined Systems
  • II. Thermodynamics of Biological Processes
  • Chapter 5: Thermodynamics of Irreversible Processes in Biological Systems Near Equilibrium (Linear Thermodynamics)
  • Chapter 6: Thermodynamics of Systems Far From Equilibrium (Nonlinear Thermodynamics)
  • Part II: Molecular Biophysics
  • III. Three-dimensional Organization of Biopolymers
  • Chapter 7: Three-dimensional Configurations of Polymer Molecules
  • 7.1 Statistical Character of Polymer Structure
  • 7.2 Volumetric Interactions and Globule-Coil Transitions in Polymer Macromolecules
  • 7.3 Phase Transitions in Proteins
  • Chapter 8: Different Types of Interactions in Macromolecules
  • 8.1 Van-der-Waals Interactions
  • 8.2 Hydrogen Bond. Charge-Dipole Interactions
  • 8.3 Internal Rotation and Rotational Isomerism
  • Chapter 9: Conformational Energy and Three-dimensional Structure of Biopolymers
  • 9.1 Conformational Energy of Polypeptide Chains
  • 9.2 Numerical Methods for Estimation of Conformational Energy of Biopolymers
  • 9.3 Predictions of Three-dimensional Structure of Proteins
  • 9.4 Peculiarities of Three-dimensional Organization of Nucleic Acids
  • 9.5 State of Water and Hydrophobic Interactions in Biostructures
  • 9.6 Protein Folding
  • IV. Dynamic Properties of Globular Proteins
  • Chapter 10: Protein Dynamics
  • 10.1 Structural Changes in Proteins
  • 10.2 Conformational Mobility of Proteins by the Data of Different Methods
  • Chapter 11: Physical Models of Dynamic Mobility of Proteins
  • 11.1 General Characteristic of Molecular Dynamics of Biopolymers
  • 11.2 Model of Limited Diffusion (Brownian Oscillator with Strong Damping)
  • 11.3 Numerical Modeling of Molecular Dynamics of Proteins
  • 11.4 Molecular Dynamics of Protein Myoglobin
  • 11.5 Dynamic Models of DNA
  • 11.6 Direct Modeling of Interactions of Proteins
  • Further Reading
  • Part III: Biophysics of Membrane Processes
  • V. Structure-functional Organization of Biological Membranes
  • Chapter 12: Molecular Organization of Biological Membranes
  • 12.1 Composition and Structure of Biological Membranes
  • 12.2 Formation of Membrane Structures
  • 12.3 Thermodynamics of Membrane Formation and Stability
  • 12.4 Mechanical Properties of Membranes
  • 12.5 Effect of Electric Fields on Cells
  • Chapter 13: Conformational Properties of Membranes
  • 13.1 Phase Transitions in Membrane Systems
  • 13.2 Lipid - Lipid Interactions in Membranes
  • 13.3 Lipid - Protein and Protein - Protein Interactions in Membranes
  • 13.4 Peroxidation of Biomembrane Lipids
  • VI. Transport of Substances and Bioelectrogenesis
  • Chapter 14: Nonelectrolyte Transport
  • 14.1 Diffusion
  • 14.2 Facilitated Diffusion
  • 14.3 Water Transport. Aquaporins
  • Chapter 15: Ion Transport. Ionic Equilibria
  • 15.1 Electrochemical Potential
  • 15.2 Ion Hydration
  • 15.3 Ionic Equilibrium on the Phase Interface
  • 15.4 Profiles of Potential and Concentrations at the Interface
  • 15.5 Double Electric Layer
  • Chapter 16: Electrodiffusion Theory of Ion Transport Across Membranes
  • 16.1 The Nernst - Planck Equation of Electrodiffusion
  • 16.2 Constant Field Approximation
  • Chapter 17: Induced Ion Transport
  • 17.1 Bilayer Lipid Membranes
  • 17.2 Mobile Carriers
  • 17.3 Channel-forming Reagents
  • 17.4 Effect of Surface and Dipole Potentials on the Ion Transport Rate
  • Chapter 18: Ion Transport in Channels
  • 18.1 Discrete Description of Transport
  • 18.2 Channel Blocking and Saturation
  • 18.3 General Properties of Ion Channels in Nervous Fibers
  • 18.4 Molecular Structure of Channels
  • 18.5 Electric Fluctuations of Membrane Properties
  • Chapter 19: Ion Transport in Excitable Membranes
  • 19.1 Action Potential
  • 19.2 Ion Currents in the Axon Membrane
  • 19.3 Description of Ionic Currents in the Hodgkin - Huxley Model
  • 19.4 Gating Currents
  • 19.5 Impulse Propagation
  • Chapter 20: Active Transport
  • 20.1 Calcium Pump
  • 20.2 Sodium-Potassium Pump
  • 20.3 Electrogenic Ion Transport
  • 20.4 Proton Transport
  • VII. Energy Transformation in Biomembranes
  • Chapter 21: Electron Transport and Energy Transformation in Biomembranes
  • 21.1 General Description of Energy Transformation in Biomembranes
  • 21.2 Mechanisms of Proton Translocation and Generation of ?µH+ in Respiratory and Photosynthetic Chains of Electron Transport
  • 21.3 ATPase Complex
  • 21.4 ATPase Complex as a Molecular Motor
  • Chapter 22: Physics of Muscle Contraction, Actin-Myosin Molecular Motor
  • 22.1 General Description of Energy Transformation in Systems of Biological Motility
  • 22.2 Basic Information on Properties of Cross-striated Muscles
  • 22.3 Structural Organization of Muscle Contractile and Regulatory Proteins
  • 22.4 Mechanochemical Transformation of Energy in Muscles. Lymn - Taylor Scheme
  • 22.5 Three-dimensional Structure of Actin and the Myosin Head
  • 22.6 Mechanism of the Work Cycle of the Actin-Myosin Motor
  • Chapter 23: Biophysics of Processes of Intracellular Signaling
  • 23.1 General Regularities of Intracellular Signaling
  • 23.2 Biophysics of Cellular Signaling
  • 23.3 Methods for Studying Cell Signaling
  • Further Reading
  • VIII. Electronic Properties of Biopolymers
  • Chapter 24: Fundamentals of Quantum Description of Molecules
  • 24.1 Introduction
  • 24.2 Stationary and Non-stationary States of Quantum Systems. Principle of Superposition of States
  • 24.3 Theory of Non-stationary Excitations - Theory of Transitions
  • 24.4 Model of a Hydrogen Molecule Ion. Nature of Chemical Bonds
  • 24.5 Method of Molecular Orbitals
  • 24.6 Manifestation of Electronic Properties of Biopolymers
  • Chapter 25: Mechanisms of Charge Transfer and Energy Migration in Biomolecular Structures
  • 25.1 Tunneling Effect
  • 25.2 The Charge Transfer Theory
  • 25.3 Role of Hydrogen Bonds in Electron Transport in Biomolecular Systems
  • 25.4 Dynamics of Photoconformational Transfer
  • 25.5 Mechanisms of Energy Migration
  • Chapter 26: Ion Transport in Excitable Membranes
  • 26.1 Physicochemical Description and Biophysical Models of Enzyme Processes
  • 26.2 Electron Conformational Interactions upon Enzyme Catalysis
  • 26.3 Electronic Interactions in the Enzyme Active Center
  • 26.4 Molecular Modeling of the Structure of an Enzyme - Substrate Complex
  • Part IV: Biophysics of Photobiological Processes
  • IX. Primary Processes of Photosynthesis
  • Chapter 27: Energy Transformation in Primary Processes of Photosynthesis
  • 27.1 General Characteristic of Initial Stages of Photobiological Processes
  • 27.2 General Scheme of Primary Processes of Photosynthesis
  • 27.3 Structural Organization of Pigment-Protein Antenna Complexes
  • 27.4 Mechanisms of Transformation of Excitation Energy in Photosynthetic Membrane
  • 27.5 Reaction Centers in Purple Photosynthesizing Bacteria
  • 27.6 Pigment - Protein Complex of Photosystem I
  • 27.7 Pigment - Protein Complex of Photosystem II
  • 27.8 Variable and Delayed Fluorescence
  • Chapter 28: Electron-Conformational Interactions in Primary Processes of Photosynthesis
  • 28.1 Studies of Superfast Processes in Reaction Centers of Photosynthesis
  • 28.2 Initial Charge Separation in RCs
  • 28.3 Mechanisms of Cytochrome Oxidation in Reaction Centers
  • 28.4 Conformational Dynamics and Electron Transfer in Reaction Centers
  • 28.5 Electron Transfer and Formation of Contact States in the System of Quinone Acceptors (PQA QB)
  • 28.6 Mathematical Models of Primary Electron Transport Processes in Photosynthesis
  • X. Primary Processes in Biological Systems
  • Chapter 29: Photo-conversions of Bacteriorhodopsin and Rhodopsin
  • 29.1 Structure and Functions of Purple Membranes
  • 29.2 Photocycle of Bacteriorhodopsin
  • 29.3 Primary Act of Bacteriorhodopsin Photoconversions
  • 29.4 Model Systems Containing Bacteriorhodopsin
  • 29.5 Molecular Bases of Visual Reception. Visual Cells (Rods)
  • 29.6 Primary Act of Rhodopsin Photoconversion
  • Chapter 30: Photoregulatory and Photodestructive Processes
  • 30.1 General Characteristics of Photoregulatory Processes
  • 30.2 Photoreceptors and Molecular Mechanisms of Photoregulatory Processes. Phytochromes
  • 30.3 General Characteristics of Photodestructive Processes
  • 30.4 Photochemical Reactions in DNA and Its Components
  • 30.5 Effects of High-intensity Laser UV Irradiation on DNA (Two-quantum Reactions)
  • 30.6 Photoreactivation and Photoprotection
  • 30.7 Ultraviolet Light Action on Proteins
  • 30.8 Sensitized Damage of Biomolecules in Photodynamic Reactions
  • 30.9 Photosensitized Effects in Cell Systems
  • Further Reading
  • Index
  • End User License Agreement

Chapter 1
Qualitative Methods for Studying Dynamic Models of Biological Processes

The functioning of the integrated biological system is a result of interactions of its components in time and space. Elucidation of the principles of regulation of such a system is a problem that can be solved only with the use of correctly chosen mathematical methods.

The kinetics of biological processes includes the time-dependent behavior of various processes proceeding at different levels of life organization: biochemical conversions, generation of electric potentials on biological membranes, cell cycles, accumulation of biomass or species reproduction, interactions of living populations in biocommunities.

1.1 General Principles of Description of Kinetic Behavior of Biological Systems

The kinetics of a system is characterized by a totality of variables and parameters expressed via measurable quantities, which at each instant of time have definite numerical values.

In different biological systems, different measurable values can play the role of variables: those are concentrations of intermediate substances in biochemistry, the number of microorganisms or their overall biomass in microbiology, the species population number in ecology, membrane potentials in biophysics of membrane processes, etc. Parameters may be temperature, humidity, pH, electric conductance of membranes, etc.

This is sufficient to construct a general mathematical model representing a system of n differential equations:


where c1(t), ., cn(t) are unknown functions of time describing the system variables (for example, substance concentrations); dci/dt are rates of changes of these variables; fi are functions dependent on external and internal parameters of the system. A comprehensive model of type (1.1) may contain a large number of equations, including nonlinear ones.

Many essential questions concerning the qualitative character of the system behavior, in particular, stability of stationary states and transition between them, oscillation modes and others, can be solved using methods of the qualitative theory of differential equations. These methods permit revealing important general properties of the model without determining explicitly the unknown functions c1(t), ., cn(t). Such an approach gives good results when analyzing the models that consist of a small number of equations and reflect the most important dynamic features of the system.

The key approach in the qualitative theory of differential equations is to characterize the state of the system as a whole by variables c1, c2, ., cn, which they aquire at each instant of time upon changing in accord with (1.1). If the values of variables c1, c2, ., cn are put on rectangular coordinate axes in the n-dimensional space, the system state will be described by some point M in this space with coordinates M(c1, c2, ., cn). The point M is called a representation point.

The change in the system state is comparable to the displacement of the point M in the n-dimensional space. The space with coordinates c1, c2, ., cn is a phase state; the curve, described in it by the point M, is a phase trajectory.

1.2 Qualitative Analysis of Elementary Models of Biological Processes

Let us consider qualitative methods of studying such systems represented as a system of two independent differential equations (the right-hand parts do not depend explicitly on time), that can be written as:


Here P(x, y) and Q(x, y) are continuous functions, determined in some range G of the Euclidean plane (x and y are Cartesian coordinates) and having continuous derivatives not lower than the first order.

The range may be both unlimited and limited. When variables x and y have a certain biological meaning (substance concentrations, species population number), some restrictions are usually superimposed on them. First of all, biological variables cannot be negative.

Accept the coordinates of the representation point M0 to be (x0, y0) at t = t0.

At every next instant of time t, the representation point will move in compliance with the system of equations (1.2) and have the position M(x, y), corresponding to x(t), y(t). The set of points on the phase plane x, y is a phase trajectory.

The character of phase trajectories reflects general qualitative features of the system behavior in time. The phase plane, divided in trajectories, represents an easily visible "portrait" of the system. It allows grasping at once the whole set of possible motions (changes in variables x, y) corresponding to the initial conditions. The phase trajectory has tangents, the slopes of which in every point M(x, y) equals the derivative value in this point dy/dx. Accordingly, to trace a phase trajectory through point M1(x1, y1) of the phase plane, it is enough to know the direction of the tangent in this point of the plane or the value of the derivative

To this end, it is required to have an equation with variables x, y and without time t in an explicit form. For that, let us divide the second equation in system (1.2) by the first one. The following differential equation is obtained


which is frequently much more simple than the initial system (1.2). Solution of equation (1.3) y = y(x, c) or in an explicit form F(x, y) = C, where C is the constant of integration, yields a family of integral curves - phase trajectories of system (1.2) on the plane x, y.

But generally, equation (1.3) may have no analytical solution, and then integral plotting should be done using qualitative methods.

Method of Isoclinic Lines. The method of isoclinic lines is typically used for qualitative plotting of a phase portrait of a system. In this case, lines, which intersect the integral lines at a certain angle, are plotted on the phase plane. The analysis of a number of isoclinic lines can show the probable course of the integral lines.

The equation of isoclinic lines can be obtained from equation (1.3). Suppose dy/dx = A, where A is a definite constant value. The value of A is a slope of the tangent to the phase trajectory and, consequently, can have values from -8 to +8. Substituting the A value instead of dy/dx in (1.3), we get the equation of isoclinic lines:


By giving different definite numeric values to A, we obtain a family of curves. In any point of each of these curves, the tangent slope to the phase trajectory, passing through this point, is the same value, namely the value of A, which characterizes the given isoclinic line.

Note that in the case of linear systems, i.e. systems of the type


isoclinic lines represent a bundle of straight lines, passing through the origin of coordinates:

Singular Points. Equation (1.3) determines directly the singular tangent to the corresponding integral curve in each point of the plane. Exclusion is the point of intersection of all isoclinic lines , at which the tangent direction is indefinite, because in this case the value of the derivative is ambiguous:

The points, in which time derivatives of variables x and y turn concurrently to zero


and in which the direction of tangents to integral curves is indefinite, are singular points. The singular point in the equation of phase trajectories (1.3) complies with the stationary state of system (1.2), because the rates of changes of variables in this point are equal to zero, and its coordinates are stationary values of variables .

For a qualitative study of a system, it is often possible not to go beyond plotting only some isoclinic lines on the phase plane. Of special interest are the so-called basic isoclinic lines: dy/dx = 0 is the isoclinic line of horizontal tangents to phase trajectories, the equation of which is Q(x, y) = 0, and the isoclinic of vertical tangents dy/dx = 8, which is in line with equation P(x, y) = 0.

The plotting of the basic isoclinic lines and the determination of their intersection point, the coordinates of which satisfy the following conditions


gives the intersection point of all isoclinic lines on the phase plane. As mentioned above, this point is a singular point and corresponds to the stationary state of the system (Fig. 1.1).

Figure 1.1. The stationary state is determined by the point of intersection of the basic isoclinic lines.

Figure 1.1 demonstrates the case of one stationary point of intersection of basic isoclinic lines of the system. The figure shows directions of the tangents...

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