Biological Membranes : Theory of Transport, Potentials and Electric Impulses

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Biological Membranes : Theory of Transport, Potentials and Electric Impulses

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  • 製本 Hardcover:ハードカバー版/ページ数 671 p.
  • 言語 ENG
  • 商品コード 9780521810180
  • DDC分類 571.64

基本説明

Translated from the Danish.

Full Description


This text, suitable for graduates and researchers in physiology and biophysics and medical students specializing in neurophysiology and related fields, provides a comprehensive discussion of biological mass transfer and bioelectrical phenomena. Emphasis has been given to the applicability of physics, physical chemistry and mathematics to the quantitative analysis of biological processes, with all the necessary mathematical grounding provided in Chapter 1. This book guides the student through the key stages needed for the formulation of biological models and interpretation of mathematical solutions, central to the understanding of cell membrane functions.

Table of Contents

Foreword                                           xix
Preface xxi
Mathematical prelude 1 (61)
Introduction 1 (1)
Basic concepts of differential calculus 2 (9)
Limits 2 (1)
Functions 2 (1)
The derivative 3 (3)
A few derived functions 6 (1)
Approximate value of the increment 6 (2)
Δy
Differential 8 (1)
The chain rule 9 (1)
The derivative of the inverse function 10 (1)
Basic concepts of integral calculus 11 (7)
Definite and indefinite integral 12 (2)
The fundamental law 14 (1)
Evaluation of a definite integral 15 (2)
The mean value theorem 17 (1)
The natural logarithm 18 (4)
Definition of the natural logarithm 18 (1)
Elementary properties of the logarithm 19 (1)
Logarithm of a product 20 (1)
Logarithm of a quotient 21 (1)
Logarithm of an exponential 22 (1)
The exponential function 22 (4)
Definition of the exponential function 22 (3)
Derivative and integral 25 (1)
Taylor's theorem 26 (8)
Taylor and Maclaurin series 26 (1)
Expansion of a polynomial 26 (1)
Expansion of an arbitrary function 27 (1)
The binomial series 28 (2)
Series of the logarithmic and exponential 30 (1)
functions
The logarithm 30 (1)
The exponential function 31 (1)
Approximate expressions of functions 32 (1)
Evaluation of an undetermined expression 33 (1)
0/0
Basic techniques of integration 34 (4)
The method of substitution 34 (2)
Partial integration 36 (2)
Functions of several variables 38 (11)
Geometrical representation 40 (1)
Partial derivatives 40 (3)
Total differential 43 (2)
The chain rule once more 45 (4)
Some ordinary differential equations 49 (8)
Four first-order differential equations 50 (1)
The equation y' + αy = 0 51 (1)
The equation y' + αy = K 52 (1)
The equation y' + αy = Q(x) 53 (1)
The equation y' + P(x)y = Q(x) 53 (2)
Two second-order differential equations 55 (1)
The equation y'' + k2y = 0 55 (1)
The equation y'' - k2y = 0 56 (1)
A note on partial differential equations 57 (5)
Migration and diffusion 62 (197)
Introduction 62 (3)
Flux 65 (1)
Types of passive transport 65 (1)
Migration 66 (4)
Friction coefficient and mobility 66 (2)
Migration flux 68 (2)
Diffusion 70 (110)
Phenomenological description 70 (3)
Diffusion flux (Fick's law) 73 (1)
The diffusion coefficient 74 (1)
A simple application of Fick's law 75 (1)
The diffusion equation 76 (1)
Diffusion with mass conservation 77 (2)
Diffusion with concurrent mass production 79 (1)
Classification of diffusion processes 79 (1)
Stationary diffusion processes 80 (1)
One-dimensional diffusion 81 (1)
Diffusion through a plate 81 (3)
Diffusion through two adjoining, 84 (3)
different media
Unstirred layers 87 (2)
Plate covered on one side by a membrane 89 (2)
of permeability P
Diffusion with mass consumption 91 (8)
Diffusion in a cylinder with radial 99 (1)
symmetry
The diffusion equation 100(3)
Diffusion through a cylindrical shell 103(2)
Diffusion in a cylinder with mass 105(3)
consumption
Diffusion from a cylinder into the 108(3)
surrounding medium with mass consumption
(Krogh's cylinder)
Diffusion with radial symmetry in a sphere 111(1)
The diffusion equation 111(3)
Diffusion through a spherical shell 114(1)
Sphere covered by a thin membrane, mass 115(2)
consumption in the interior
Time-dependent diffusion processes 117(1)
An extended initial distribution 117(6)
(Boltzmann's trick)
Diffusion from a region with constant 123(1)
concentration
Duhamel's integral 124(3)
An instantaneous surface distribution 127(3)
Green's function 130(1)
A varying initial distribution in space 130(3)
Initial uniform distribution in the 133(1)
infinite half-space
The effect of an impermeable barrier 133(2)
The effect of a matter-absorbing wall 135(2)
A variable flux into one half-space 137(2)
Molecular description of diffusion 139(1)
Brownian motion 140(3)
Diffusion from a statistical point of view 143(2)
Random walk 145(1)
The distribution function 146(7)
The mean displacement 153(1)
The mean displacement in one direction 154(1)
The root mean square displacement (the 154(3)
Einstein-Smoluchowski relation)
Two-dimensional random walk 157(2)
Three-dimensional random walk 159(2)
Random walk and Fick's law 161(1)
Einstein's simplified treatment 161(3)
A more exact derivation of Fick's law 164(5)
Random walk and the diffusion equation 169(6)
Random walk over an energy barrier 175(5)
Diffusion and migration superimposed 180(50)
The Smoluchowski equation 180(2)
An instantaneous plane source in infinite 182(2)
space
The concentration change with time at a 184(1)
fixed point in space
Driving the swarm towards a reflecting 184(6)
barrier: a case of sedimentation
``Random walk'' considerations 190(1)
The flux equation 190(3)
Random walk and the diffusion--migration 193(2)
equation
Migration over an energy barrier 195(4)
Kramers' equation 199(2)
Diffusion coefficient and mobility 201(1)
The Einstein relation 202(1)
Einstein--Stokes relation 203(3)
The ``driving force'' behind the 206(2)
diffusion process
Diffusion through membranes 208(1)
Permeability coefficient 209(1)
Kinetics of exchange 210(1)
Outer concentration kept at zero 211(1)
Outer concentration kept constant: cell 212(1)
concentration initially zero
Both phases comparable in size 213(5)
Compartment analysis 218(1)
Transport with passive membrane 218(1)
permeabilities
A step change in outer concentration 219(1)
Outer concentration grows asymptotically 220(1)
One-way transport 221(1)
Unidirectional flux 221(1)
Unidirectional transfer 222(2)
Passive influx and unidirected efflux 224(1)
Stationary diffusion with superimposed 224(1)
migration
Determination of the flux 225(3)
Unidirectional fluxes and flux ratio 228(1)
Concentration profile 229(1)
Convective and osmotic water movement 230(29)
through membranes
Convective water movement 231(2)
Osmotic water movement 233(1)
Osmotic pressure 233(2)
Colligative properties 235(1)
The underlying mechanism of osmotic water 236(1)
movement
The equation for the osmotic pressure 237(5)
Osmotic coefficient 242(1)
A simple dynamic model of osmotic 243(7)
equilibrium
The freezing-point depression 250(1)
The freezing-point depression and osmotic 251(1)
pressure
Osmolarity 252(2)
Reflection coefficient 254(1)
Water movement across cell membranes 255(4)
Membrane potentials 259(152)
Introduction 259(1)
Electric field and potential 260(5)
Transport of ions in solutions 265(12)
Migration 266(5)
Electrodiffusion (Nernst-Planck equations) 271(1)
Equivalent forms 272(2)
Poisson's equation 274(2)
Electroneutrality 276(1)
The constant field 277(1)
The equilibrium potential 277(36)
A qualitative description of the origin 278(3)
of the membrane potential across an
ion-selective permeable membrane
The Nernst equation 281(2)
The charge density of the excess charges 283(1)
on the two membrane sides
Derivation of Nernst's equation 283(3)
Establishing the electric contact to the 286(1)
electrolyte solution: electrodes
The galvanic cell 286(2)
Half-cells 288(1)
Electrode potentials 289(5)
Standard electrode potentials 294(1)
Non-equivalent electrode current 295(3)
Reversibility 298(1)
Two recording electrodes 299(1)
The silver-silver chloride electrode 299(2)
The calomel electrode 301(1)
The equivalent electric circuit for the 302(1)
ionic-selective membrane
Measurement of the current-voltage 302(2)
characteristic
Membrane current and membrane conductance 304(4)
The equivalent circuit diagram 308(3)
Membrane conductance and membrane 311(2)
permeability
The Donnan potential 313(23)
Qualitative description of the Donnan 314(2)
distribution
Quantitative treatment of the Donnan 316(4)
system
Low polyelectrolyte concentration 320(1)
High polyelectrolyte concentration 321(1)
Concentration and potential profiles 322(2)
The Poisson-Boltzmann equations 324(2)
Solving the Poisson-Boltzmann equations 326(1)
The solution for x ≥ 0 326(3)
The solution for x ≤ 0 329(2)
Binding the two solutions together 331(2)
A numerical example 333(2)
The total space charge 335(1)
Diffusion potentials 336(17)
Qualitative description of the diffusion 336(1)
potential
Collapse of the Donnan regime 336(1)
A binary electrolyte 337(1)
The salt bridge to eliminate the 338(1)
diffusion potential
Calculation of the diffusion potential 339(2)
for a binary monovalent electrolyte
Diffusion potential between solutions of 341(1)
different composition
The Planck regime 342(1)
Planck's general relations 343(2)
The electrical equivalent for the Planck 345(3)
regime
Planck's expression for the diffusion 348(1)
potential
The Henderson regime 348(3)
The salt bridge once again 351(2)
Electrodiffusion through membranes 353(31)
A single salt 353(1)
The diffusion potential 354(2)
The membrane resistance 356(1)
The potential profile 357(1)
The equivalent electric circuit 357(2)
Electroneutrality 359(1)
Ion-selective membranes 360(3)
The Goldman regime 363(2)
Derivation of the Goldman equation 365(5)
Concentration profiles 370(2)
Membrane conductance and membrane 372(1)
permeability
Concentrations equal on both sides 373(1)
Different surrounding concentrations: V ‾ 374(2)
Vj(eq)
V ≠ Vj(eq) 376(1)
Total current and membrane potential 377(2)
The mosaic membrane (the Millman equation) 379(5)
The membrane potential of a biological cell 384(19)
Measuring the membrane potential 385(3)
The origin of the membrane potential 388(3)
Membrane potential and ionic 391(1)
concentrations in the extracellular medium
Sudden changes of both VK(eq) and VCl(eq) 392(4)
Membrane potential with varying K+ in 396(2)
extracellular fluid in the absence of Cl-
Membrane potential with varying Na+ in 398(1)
the extracellular fluid
Membrane potential and active Na+/K+ 399(1)
transport
Absolute stationarity 400(2)
Total current is zero 402(1)
The mosaic membrane 403(1)
Flux ratio analysis 403(8)
Flux ratio and electrodiffusion 406(3)
Flux ratio and convective diffusion 409(2)
The nerve impulse 411(126)
Introduction 411(2)
Excitability 411(1)
The communication system 412(1)
Historical background 413(4)
The nerve signal recorded with external 417(10)
electrodes
The nerve signal 417(2)
The diphasic action potential 419(1)
The monophasic action potential 420(2)
Some elementary properties of the nerve 422(1)
signal
``All or nothing'' law 423(1)
Subliminal stimuli 424(2)
The refractory period 426(1)
Results from the giant axon of the squid 427(84)
Recording the resting membrane potential 427(4)
and action potential
The resting membrane potential 431(1)
Membrane potential and the Goldman regime 432(1)
Mobility of K+ ions in axoplasm 433(4)
The action potential 437(1)
Stimulation with an intracellular 437(1)
microelectrode
The internal electrode is a cathode 437(1)
The internal electrode is an anode 438(3)
Conductance changes attending the action 441(1)
potential
The effect of extracellular sodium 442(1)
concentration on the action potential
Perfused axons 443(4)
The experimental substantiation of the 447(1)
sodium hypothesis
Net movement of radioactive sodium and 447(2)
potassium during electric activity
The temporal resolution of the separate 449(1)
ionic current: voltage clamp technique
The control system 450(4)
Identification of the early 454(5)
inward-directed current
Identification of the outward-directed 459(2)
current
Calculation of the partial membrane 461(1)
conductances for sodium and potassium
The time course of the changes in sodium 461(2)
and potassium conductance during a
voltage clamp
The dependence of the conductance changes 463(1)
on the displacement of the membrane
potential
The inactivation process 464(6)
The membrane action potential: 470(2)
qualitative synthesis of the voltage
clamp experiments
The action potential 472(1)
Threshold phenomena 473(1)
Investigations on single Na+ channels 474(5)
Selective effects on the Na+ and K+ 479(1)
channels
Blocking the Na+ channel 480(1)
Blocking the K+ channel 481(2)
Destruction of Na+ inactivation 483(1)
The propagated action potential 484(1)
The local current loops 484(2)
The nerve as an electric cable 486(1)
Derivation of the cable equation 486(5)
The stationary state 491(1)
Time-dependent solutions 492(8)
Reconstruction of the action potential 500(1)
The Hodgkin--Huxley equations 501(2)
The propagated action potential 503(3)
Nerve impulse recorded with external 506(4)
electrodes
The conduction velocity 510(1)
Myelinated nerves 511(5)
Repetitive impulse transmission 516(4)
The Hodgkin--Huxley equations 520(17)
Empirical equations for the sodium and 520(2)
potassium conductances
Voltage clamp 522(6)
The membrane action potential 528(4)
The propagated action potential 532(5)
Impulse transmission across cell boundaries 537(47)
General characteristics of impulse 537(5)
transmission
The synapse 537(2)
Mechanisms of transmission 539(3)
Neuromuscular transmission: impulse 542(42)
transmission from nerve to muscle
Structure of the end-plate 542(2)
The course of the electrical transmission 544(2)
The synaptic delay 546(1)
The postsynaptic potential 546(2)
The end-plate potential 548(1)
End-plate potential and acetylcholine 549(4)
The time course of the end-plate potential 553(1)
Cholinesterase and anti-cholinesterase 554(2)
Ionic movements associated with the 556(9)
course of the end-plate potential
Quantal release of acetylcholine 565(1)
Miniature end-plate potentials 565(6)
End-plate potential and miniature 571(11)
potentials
The vesicle hypothesis 582(2)
Appendix A About the functions Erf {x}, Erfc 584(4)
{x} and calculation of the integral
Appendix B Solving the integral 588(2)
Appendix C Evaluation of 590(3)
Appendix D To demonstrate that the mean value 593(2)
<ξ2> of the displacements squared is
proportional to the number N of the
displacements
Appendix E Evaluation of the integral Eq. 595(4)
(2.5.191)
Appendix F Evaluation of the integral 599(2)
Appendix G Example of the application of the 601(3)
theory of Brownian motion
Appendix H A note on the physical meaning of 604(2)
the pressure gradient
Appendix I About hyperbolic functions 606(6)
Appendix J Evaluation of an integral of 612(4)
Duhamel's type
Appendix K Calculation of the potential 616(2)
profiles resulting from injection of a constant
current Io in the axon
Appendix L A note on the method of images 618(5)
Appendix M Cable analysis of the end-plate 623(5)
potential (Fatt & Katz, 1951)
Appendix N Measuring the electric parameters in 628(3)
a spherical cell
Appendix O Measuring the electric parameters in 631(7)
a cylindrical cell
Appendix P Electric parameters for a 638(3)
cylindrical unmyelinated axon
Appendix Q Surface recorded action potential 641(5)
and membrane action potential
Appendix R About concentration scales 646(2)
Appendix S Units and physical constants 648(2)
List of symbols 650(5)
References 655(7)
Index 662