Membranes, Channels, and Noise PDF
Preview Membranes, Channels, and Noise
MEMBRANES, CHANNELS, AND NOISE MEMBRANES, CHANNELS, AND NOISE Edited by Robert S. Eisenberg Rush Medical College Chicago, Illinois Martin Frank National Institutes of Health Bethesda, Maryland and Charles F. Stevens Yale University School of Medicine New Haven, Connecticut PLENUM PRESS • NEW YORK AND LONDON Library of Congress Cataloging in Publication Data Workshop on Noise Measurements as a Probe of Ionic Conductance (1981: Denver, Colo.) Membranes, channels, and noise. "Based on a Workshop on Noise Measurements as a Probe of Ionic Conductance held February 25, 1981, at the Biophysics Annual Meeting, in Denver, Colorado"-T.p. verso. Includes bibliographical references and index. 1. Membranes (Biology)-Electric properties-Congresses. 2. Ion channels-Congresses. 3. Electric noise-Measurement-Congresses. I. Eisenberg, Robert S. II. Frank, Martin, 1947- . Ill. Stevens, Charles F., 1934- . IV. Title. [DNLM: 1. Membrane Potentials -congresses. 2. Ion Channels-physiology-congresses. 3. Epithelium-congresses. QH 601 W926m 1981] QH60l.W67 1981 574.87'5 84-15083 ISBN-13: 978-1-4684-4852-8 e-ISBN-13: 978-1-4684-4850-4 DOl: 10.1007/978-1-4684-4850-4 Based on a Workshop on Noise Measurements as a Probe of Ionic Conductance, held February 25, 1981, at the Biophysics Annual Meeting, in Denver, Colorado © 1984 Plenum Press, New York Softcover reprint of the hardcover 18t edition 1984 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher PREFACE This volume is a collection of papers designed to increase awareness and utilization of fluctuation theory for the description of ionic events at the membrane. The papers are revised and updated versions of presentations made at a workshop entitled "Noise Measurements as a Probe of Ionic Conductance." As a result of discussions held at that meeting, the participants were asked to provide selected chapters designed to provide detailed descriptions of the theory and its application to a number of membrane channels. Fluctuation theory was developed initially to explain statistical fluctuations of ordinary physical quantities such as random collisions between gas molecules and walls. As knowledge of ionic pores has advanced, it has become apparent that randomized fluctuations could be utilized to characterize pore behavior in excitable and epithelial membranes. Because of the increased awareness of the applicability of fluctuation theory, the workshop participants were invited to contribute papers to this volume to provide them with an opportunity to teach others the essentials of noise measurements. The emphasis of this volume is on the practical steps which must be followed to make and interpret measurements of noise, both noise produced by natural fluctuatjons of the transport system, and noise which is the response to an applied stochastic signal. This collection of papers is meant to emphasize practical limitations as well as practical and theoretical advantages of such measurements. v PREFACE The original concept of a workshop on noise analysis was presented by the members of the Physiology Study Section, Division of Research Grants, National Institutes of Health. The workshop was organized by a committee consisting of Robert Eisenberg, Charles Stevens and Martin Frank and was held on February 25, 1981 as part of the Annual Meeting of the Biophysical Society held in Denver, Colorado. The support provided by the Program Committee of the Biophysical Society is gratefully acknowledged. The sponsorship of Caryl and Alan Erickson of the Dagan Corporation, Minneapolis, Minnesota is also greatly appreciated. Special thanks are extended to my wife, Cheryl, for her support during this project and to Mrs. Florence T. Turska and Mrs. Veronica Q. Heller for the preparation of the manuscript in its final form. Martin Frank CONTENTS Inferences About Molecular Mechanisms Through Fluctuation Analysis 1 Charles F. Stevens Nonstationary Noise Analysis of Membrane Currents • . . . •• 21 F.J. Sigworth Analysis of Membrane Properties Using Extrinsic Noise • • •• 49 .Richard T. Mathias "Stationary" Fluctuations of Na Current in Myelinated Nerve • . • • 117 Wolfgang Nonner Synaptic Noise l39 Vincent E. Dionne Noise Analysis of Transport Through Apical Sodium Channels of Tight Amphibian Epithelia 161 Bernd Lindemann and Jack H.-Y. Li The Information Content of Single Channel Data 197 Joseph Patlak Membranes and Channels Physiology and Molecular Biology 235 Robert S. Eisenberg Index • • . • • • • • • • • • • • • . • • • • • • • • • • •• 285 vii INFERENCES ABOUT MOLECULAR MECHANISMS THROUGH FLUCTUATION ANALYSIS Charles F. Stevens Section of Molecular Neurobiology Yale University School of Medicine New Haven, CT 06510 USA Membrane channels operate in an inherently probabilistic fashion because the world at a molecular level is chaotic. As a consequence of this molecular chaos, the number of open channels in an excitable cell's membrane varies incessantly around an average value and produces random fluctuations in membrane conductance. The statistical characteristics of these fluctuations are not identical for all channel types. but rather reflects those same physical processes that give rise to variety in behaviors between species of channels. Thus, one sort of channel may produce small and rapid fluctuations, whereas another may yield large, slow noise. The essence of fluctuation analysis --the study of a system's inherent noise--is this: channel noise reflects underlyin.g molecular mechanisms, so we can learn about these mechanisms by studying conductance fluctuations. In some situations, fluctuation analysis is simply an alternative to studying the average response to a perturbation, but in other instances we can gain information not otherwise available. For example, different molecular mechanisms can exhibit identical average behavior. but produce fluctuations with distinct characteristics. Fluctuation analysis can therefore be used to 2 C.F.STEVENS distinguish between various mechanisms underlying some macroscopic process. The goal of this paper is to present, in a simplified but relatively complete manner, the essentials of fluctuation analysis. The main discussion divides into three sections. In the first section, I will deal with the characterization of noise. The section contains a description of spectral analysis and the covariance function (nearly the same as the autocorrelation function). The second section treats the connection between molecular properties and inherent fluctuations. I will present a specific, simple molecular mechanism for channel gating, derive a probabilistic description of this mechanism, and calculate the spectrum of conductance fluctuations anticipated. The final section considers certain practical considerations in fluctuation analysis including a discussion of some physical sources of noise, and sampling theorem, and aliasing. NOISE IS CHARACTERIZED BY SPECTRAL ANALYSIS Figs. lB and 2B present two samples of noise--the samples might represent, for example, conductance fluctuations as a function of time--which are clearly different; the trace in Fig. 2B is obviously more rapidly varying than the one in Fig. lB, although the amplitude of the fluctuations appear similar. Any useful characterization, then, must in some way specify both amplitude and rapidity. One usual way of characterizing such noise samples is by spectral analysis. The basic idea of spectral analysis is a simple and natural one: noise records are decomposed into their constituent sine and cosine wave components, and the amplitude and frequency of these components are used as the required specification of noise properties. MOLECULAR MECHANISMS THROUGH FLUCTUATION ANALYSIS 3 A -26 .N:.z.:. 10 '" ::5 -27 +>>- . 10 ";;; <: -28 0Q I 10 'C +u'aQ>- I. . 10 -29 U> ! II! ! I 100 1000 FreCJuency (Hz) B ----------------------------------------- --------- I 10 pA ~msQc Fig. 1. A. Spectrum of noise samples (shown in B) presented in a double logarithmic plot. B. Sample of relatively slowly varying nojse. The rapidity of sinusoidal wiggles is specified by a single number, frequency, but two distinct measures of sinusoid size can be used. One size measure is the amplitude (one-half the peak to peak excursion) and the other is the RMS (root mean square) value. The FNS value is calculated by squaring the sinusoid (so that the positive and negative values cannot cancel in the averaging process) and finding the time average of this squared sinusoid. The RMS value is then the square root of this time average. Volt meters normally read RMS values rather than actual amplitudes because a sinusoid with a particular RMS value has the same power as a DC voltage of that amplitude. For example. the standard U.S.A. household voltage has a frequency of 60 Hz, an amplitude of about 160 volts, and an RMS value of about 110 volts with a power equivalent to a 110 volt DC source. 4 c. F. STEVENS A -26 'N 10 .:.J.:..: '"::s -27 .>, . 10 ..;;.; c: -28 "" 10 C..t,... -29 " 10 <Qn. . I! I! 100 1000 B Fr,;,qu,;,ncy (Hz) I 10 pll ~msQc Fig. 2. A. Double logarithmic plot of spectral density vs. frequency. Spectrum calculated from relatively rapidly varying noise displayed in B. The key to characterizing noise in terms of its constituent sinusoid components is Fourier analysis. According to Fourier's theorem any usual function of time can be decomposed into a sum of sine and cosine waves with various amplitudes. Let us suppose that we have a sample of a noise with zero mean, and further suppose that the noise contains no frequency components above 500 Hz. The original noise sample (with a duration of T seconds and amplitude y(t) at each time) can, according to Fourier's theorem, be written as y(t) Al cos ( 2;t) + BI sin ( 2;t) ) + A2 cos (2' 2;t) + B2 sin (2' 21r~ + A3 cos (3' 2;t) + B3 sin (3' 21r~)
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