Fundamentals of Biophysics (eBook)

Andrey B. Rubin (Autor)

eBook Download: EPUB

2014 | 1. Auflage
224 Seiten
Wiley-Scrivener (Verlag)
978-1-118-84275-1 (ISBN)

Infos

Biophysics is a science that comprises theoretical plotting and models based on contemporary physicochemical conceptions. They mirror physical specificity of the molecular organization and elementary processes in living organisms, which in their turn form the molecular basis of biological phenomena. Presentation of a complete course in biophysics requires vast biological material as well as additional involvement of state-of-the-art concepts in physics, chemistry and mathematics. This is essential for the students to 'perceive' the specific nature and peculiarity of molecular biological processes and see how this specificity is displayed in biological systems. This is the essence of the up-to-date biophysical approach to the analysis of biological processes.

Fundamentals of Biophysics offers a complete, thorough coverage of the material in a straightforward and no-nonsense format, offering a new and unique approach to the material that presents the appropriate topics without extraneous and unneeded filler material.

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 was head of the Department of Biophysics at MSU, Governer of the Task Force on Education in Biophysics, and a member of the RAS Council on Space Biology and Biological membrane since 2005. He has received many awards for his contributions to the science of biophysics, holds many patents and inventions, and authored of numerous papers. He is also on the editorial board of the journal, Biophysics, in the Russian language.

Inhalt

Preface vii

1 Dynamic Properties of Biological Processes 1

2 Types of Dynamic Behavior of Biological Systems 17

3 Kinetics of Enzyme Processes 35

4 Distributed Biological Systems. Chaotic Processes 45

5 Mathematical Models in Ecology 61

6 Thermodynamics of Irreversible Processes in Biological Systems Near Equilibrium 77

7 Thermodynamics of Systems Far from Equilibrium 93

8 Physicochemical Principles of Biopolymer Structure 101

9 Intramolecular Dynamics of Proteins 121

10 Physical Models of Protein Dynamic Mobility 133

11 Energy Migration and Electron Transport in Biological Structures 141

12 Mechanisms of Enzyme Catalysis 151

13 Physicochemical Features of Biological Membranes. Ionic Equilibria 157

14 Passive Transport of Substances Across Membranes 171

15 Channels and Carriers. Active Transport 179

16 Transport of Ions in Excitable Membranes 185

17 Primary Processes of Energy Transformation in Photosynthesis 191

18 Energy Transformation in Biological Membranes 199

Further Reading 207

Index 209

Textauszug

Chapter 1

Dynamic Properties of Biological Processes

Biological Kinetics. Intricate network of various reactions, specifically organized in time and space, underlie both cell exchange processes with the environment and internal metabolism. In biological systems, components interact continuously with each other, which for the most part specifies the nature of dynamic behavior of intact biological systems, mechanisms of their self-control and governing named kinetics of biological processes. As a result of such processes, concentrations of different substances, the number of individual cells and the biomass of organisms change; the other values may also vary, for instance the transmembrane potential in the cell. Upon description of the kinetics in biological systems, the basic initial prerequisites are generally the same as in chemical kinetics.

It is believed that changes of variables at every time moment can be described using corresponding differential equations. In addition to variable values, a kinetic system has a set of specific parameters that remain unchanged during its examination and characterize the conditions of reactions (temperature, humidity, pH, and electrostatic conductivity). As a rule, the constant values of the reaction rates are determined by such parameters.

Let us analyze an elementary example of closed cell population in which multiplication and death occur concurrently and which are abundant in nutrients. The questions arise: how is the number of cells changed in such a system with time, and can a stationary state eventually form in it when the number of cells remains the same? This kinetic problem may be solved with the use of differential equations. Let at moment t the concentration of cells in the environment be N. The rate of the cell concentration changes in the environment is the net sum of their multiplication rate (vmitipl) and death rate (vdeath).

In an ordinary case, the multiplication rate, which is the increase in the cell concentration per time unit, is proportional to their number at every moment, i.e.

where k1 is the proportionality constant dependent on the environmental conditions (temperature, the presence of nutrients, etc.)

Correspondingly

where k2 is the constant determining the intensity of processes of cell death. Hence it follows that

(1.1)

where k = k1−k2.

By solving the above equation we will see how the cell concentration is changed with time in the environment N = N(t). By integrating Eq. (1.1) we get

(1.2)

where N0 is the cell concentration at zero time t = 0 of the examining the system.

It can be seen that depending on the ratio of the death rate constant (k2) and multiplication rate constant (k1) the destiny of this closed population will be different. If k1 > k2, k > 0, the system will give rise to the unlimited growth of the cell number.

N(t) → ∞ at t → ∞.

If k1 < k2, the population will dye out with time

N(t) → ∞ at t → ∞.

And only in a particular case when k1 = k2 the number of cells will remain constant

N = N0.

Another example of the model of the population growth in the environment with a limited amount of nutrients is the known equation of a logistic curve. The Verhulst equation is as follows

(1.3)

Here Nmax is the maximal population number possible under such conditions. Curve N = N(t) described by the above equation is shown in Fig. 1.1. At the initial period of growth, when N << Nmax the curve is exponential. Then, after the inflection, the slope gradually decreases and the curve approaches the upper asymptote N = Nmax, i.e. the maximal attainable level under such conditions.

Figure 1.1 Logistic curve.

But as compared to the typical chemical kinetics, the biological kinetics has the following specificity.

1. The variables can be not only substance concentrations but also other values.

2. The variables change not only in time but also in space (diffusion of reagents across biomembranes).

3. A biological system is heterogeneous in space and the conditions of the reagent interaction can vary in different sites of the system).

4. There exist special mechanisms of self-regulation functioning by the feedback principle.

5. The power of the polynomial in the right-hand side of the differential equation is not always dependent on the reaction order.

As a rule, a hydrodynamic model of a vessel connected with liquid inflow and outflow fluxes passing simultaneously, is taken as a simple model of an open system. The liquid levels in the vessel are dependent on the rates of liquid inflow and outflow fluxes. When the rates are the same, the liquid level would remain constant and a stationary state forms in the system. A change in the rate of at least one flow would cause a corresponding shift in the stationary level of the liquid in the vessel.

The Feedback Principle. Let us provide our hydrodynamic model with a special device that can increase or decrease the rate of liquid outflow upon rotation of the faucet at the outlet of the vessel depending on the liquid level changes. Such a system is shown in Figure 1.2. An electromotor rotates the stopcock according to the signal received from the photocell. The electric current generated in the photocell is governed by the level of light absorption that changes parallel to the liquid level in the vessel. The photocell lamp and the electromotor are power supplied from a small turbine whose blades are rotated by the water outflow. In this model the feedback principle maintains to a certain extent the liquid level upon varying the water inflow as a result of self-regulation. In biological systems, the feedback principle is used to regulate many enzyme reactions where the activity of enzymes varies depending on the reagent concentration or external conditions. As a result the concentration of reaction products remains constant. Biological systems may have different stationary regimes depending on the values of controlling parameters. It is also possible that fluctuations at the stationary states appear when concentrations of intermediate substances change in time at regular intervals and fixed frequency. Finally, under certain combinations of chemical reactions and diffusion processes proceeding concurrently, a special type of three-dimensional structure may appear in the originally homogeneous system.

Figure 1.2 Hydrodynamic model of a feedback system. L, lamp; PE, photocell; S, stopcock; M, electromotor; T, turbine.

The cardinal problem for biophysicists is to obtain characteristics of various dynamic regimes in complicated systems and to study conditions and parameters when they are realized in living cells. This can be done by studying the properties of stationary regimes, their stability and transition to a stationary state.

Elementary Model of Open System. Let us analyze an elementary model of an open system which exchanges substances a and b with the environment, coupled to the reversible first order reaction of transformations . In Fig. 1.3, a and b are concentration variables within the system; A and B are constant concentrations of the same substances in the external vessels; and k1, k+2, k−2, and k3 are rate constants of the processes.

Figure 1.3 Open system: a model of metabolic processes in a cell.

Though being very simple, the model reflects the basic features of metabolic processes in a cell. The supply of the substrate and the release of metabolites into the environment are triggered by the reactions A → a, b → B, and the transformation corresponds to the processes of cell metabolism. For example, glucose and oxygen as substrates for respiration are supplied to a cell at stage A → a; stage b → B corresponds to the release of CO2 and H2O to the outside of the cell, and the entire metabolic respiratory cycle of the glucose molecule transformation can be described by reaction . The rate constant values are naturally phenomenological and generalized and therefore cannot be attributed to any particular biochemical stage. However, as we have seen, even such an utterly simplified model reveals basic features of a combination of metabolic reactions of a cell as an open system.

The kinetic equations for this system are as follows:

(1.4)

Inasmuch as at a stationary state, variables (a, b) are constant, then

Let us equate the right-hand side of eq. (1.4) to zero:

(1.5)

We get the system of algebraic equations:

(1.6)

from which stationary values and are known:

(1.7)

The above values do not depend on the initial conditions, i.e. on the initial values a = ao and b = bo at time t = 0 but depend only on the constant values and substance concentrations in the external vessels A and B. This means that whatever the initial state of the system is, the only stationary regime with a = , b = will be finally formed. The system of differential equations (1.4) is...

Produkt-Details

• Erscheint lt. Verlag: 11.9.2014
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Behavior • biological • Biological processes • Biophysics • Biophysik • Chaotic • dynamic • Ecology • Enzyme • Equilibrium • FAR • irreversible • Kinetics • Mathematical • Membranes • Models • Near • Passive • Physics • Physik • processes • Properties • substances • Systems • thermodynamics • Transport • Types
• ISBN-10: 1-118-84275-8 / 1118842758
• ISBN-13: 978-1-118-84275-1 / 9781118842751