Stochastic Transport Processes in Discrete Biological Systems

ISBN-13: 9783540119647 / Angielski / Miękka / 1982 / 174 str.

Eckart Frehland

Opis

These notes are in part based on a course for advanced students in the applications of stochastic processes held in 1978 at the University of Konstanz. These notes contain the results of re- cent studies on the stochastic description of ion transport through biological membranes. In particular, they serve as an introduction to an unified theory of fluctuations in complex biological transport systems. We emphasize that the subject of this volume is not to introduce the mathematics of stochastic processes but to present a field of theoretical biophysics in which stochastic methods are important. In the last years the study of membrane noise has become an important method in biophysics. Valuable information on the ion transport mechanisms in membranes can be obtained from noise analysis. A number of different processes such as the opening and closing of ion channels have been shown to be sources of the measured current or voltage fluctuations. Bio- logical 'transport systems can be complex. For example, the transport process can be coupled to other processes such as chemical reactions and take place in discontinuous structures of molecular dimensions. Furthermore, since there are strong electric fields or high concentration gradients across biological membranes ion transport processes of biological relevance are mostly processes far from equilibrium. For these reasons the development of new theoretical concepts has been necessary. The concept of transport in discrete systems has turned out to be more appropriate than continuum models.

Spis treści

A. Stochastic Processes.- 1. Expectation Values, Moments, Variance, Correlations.- 2. Probabilities.- 2.1 Expectation Values and Probabilities.- 3. Binomial, Poisson, Normal Distributions.- 4. Stationarity and Ergodicity.- B. Analysis of Stationary Stochastic Processes.- 1. Basic Concepts of Noise Analysis.- 1.1 Spectral Density.- 1.2 Autocorrelation Function and Wiener-Khintchine Relations.- 2. Poisson Processes, Carson’s Theorem.- 2.1 Variance, Autocorrelation Function, Spectral Density.- 2.2 Special Examples.- 2.3 Ions Crossing Membranes: Shot Noise.- 3. The Master Equation Approach to Fluctuations.- 3.1 Markov Processes.- 3.2 Master Equation and Phenomenological Equations.- 3.3 Linearized Phenomenological Equations and Fundamental Solutions.- 3.4 Variances, Correlations, Spectra.- 3.5 Correlation and Spectra of Measurable Quantities.- 3.6 Direct Calculation of Fluctuations from the Fundamental Solutions of the Master Equation.- 3.7 Current Noise Generated by the Opening and Closing of Channels.- C. Transport Fluctuations Around Steady States.- 1. Introductory Remarks on Transport Fluctuations.- 1.1 Characterization.- 1.2 A simple Example: Channels with one Binding Site.- 2. The Concept of Transport in Discrete Systems.- 2.1 The Fluxes.- 2.2 Current as a Transport Observable.- 2.3 Conservative Systems, Open Systems.- 2.4 Interactions Neglected.- 3. Transport Fluctuations at Equilibrium.- 3.1 The Nyquist or Fluctuation-Dissipation Theorem.- 3.2 Voltage Dependence of the Rate Constants.- 3.3 Linear Response and Complex Admittance.- 4. Theory of Transport Fluctuations Around Equilibrium and Nonequilibrium Steady States.- 4.1 The Flux-Correlation Matrix.- 4.2 Autocorrelation Function and Spectral Density of Current Fluctuations.- 4.3 More Rigorous Treatment of the Time Correlation Matrix.- 5. Transport Fluctuations in Basic Membrane Transport Systems.- 5.1 Current Noise in Open Channels.- 5.2 The Influence of Voltage and Barrier Structure on the Fluctuations.- 5.3 Carrier Noise.- 6. Transport Fluctuations in More Sophisticated Channel Models.- 6.1 Single-File Diffusion Through Narrow Channels.- 6.2 Numerical Calculations of Single-File Noise in Open Channels.- 6.3 Single-File Noise: Coupling Between Transport and Open-Closed Kinetics of the Channels.- 7. Invalidity of the Fluctuation-Dissipation Theorem for Transport Fluctuations Around Nonequilibrium Steady States.- 7.1 Special Examples: Channel Noise, Carrier Noise, Noise Generated by Permanently Open Channels.- 7.2 Different Behaviour of Scalarand Vectorial Quantities at Nonequilibrium.- 8. Current Noise: The Limit of High Applied Voltage.- 8.1 Interactions Neglected: Shot Noise.- 8.2 Reduction of Noise as Consequence of Ionic Interactions in the Single-File Model.- D. Nonstationary Processes, Fluctuations at Transient States.- 1. A Simple Example: Identical, Independent Channels.- 2. Time-Dependent States in Markov Processes.- 2.1 General Equations for the Moments.- 2.2 One-Variable Birth-Death Processes.- 3. Linear Birth-Death Processes With One Variable.- 3.1 Expectation Value and Variance.- 3.2 Application: Linear Two State Channel Models.- 4. Nonlinear Processes.- 4.1 Approximation Procedures.- 4.2 Bilinear One-Variable Birth-Death Processes.- 4.3 Bimolecular Reactions: The Gramicidin Channel.- 5. Transport Noise at Transient States.- References.