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  • Fundamental Principlesof Membrane Biophysics

    David Njus

    Department of Biological SciencesWayne State University

    D. Njus, 2000

  • Table of Contents

    Chapter 1. Biological Membranes

    Chapter 2. Thermodynamics of Micelle Formation

    Chapter 3. The Fluid Mosaic Membrane

    Chapter 4. Membrane Electrostatics

    Chapter 5. Specific and Non-Specific Binding

    Chapter 6. Permeability and Conductance

    Chapter 7. Permeability and Conductance of Electrolytes

    Chapter 8. Channels and Excitable Membranes

    Chapter 9. Active Transport

    Chapter 10. Facilitated Diffusion

    Chapter 11. Coupled Transport

    Chapter 12. Energy Coupling

    Chapter 13. Epithelial Transport

    Appendices

    I. Glossary of Symbols

    II. Abbreviations

    III. Fundamental Constants

    IV. Conversion Factors

    V. Mathematical Formulae

  • Glossary of Symbols

    A areaC molar concentration, capacitancec velocity of lightcmc critical micelle concentrationD diffusion coefficientd derivativeE energy, reduction potentialE electric fielde electronic chargeF forceF Faraday constantf frictional coefficientf fugacityG Gibbs free energyg conductance, acceleration of gravityH enthalpyh Plancks constantI currentJ flowKi equilibrium constant for reaction iKp partition coefficientk Boltzmann constantki rate constant for reaction im mass, aggregation numberN Avogadro's numbern amount in molesP permeability coefficient, pressure, powerQ heatq chargeR gas constant, resistancer radiusS entropyT absolute temperaturet timeu mobilityV volumev velocityW workX mole fraction

    x distanceZ collision factorz valence

    activity coefficient difference dipole moment dielectric constanto permittivity of vacuum viscosity, efficiency wavelength of light electrochemical potential density reflection coefficient electrical potential

  • Abbreviations

    Angstromsatm atmospheresC degrees centigradecal caloriescoul coulombsD DebyesDa Daltonseq equivalentsesu electrostatic unitsF farads (coul/volt)g gramsj joulesK degrees Kelvinl litersM moles/literm metersmin minutesmol molesS Siemenssec secondsV volts

    k kilo 103c centi 10-2m milli 10-3 micro 10-6n nano 10-9p pico 10-12f femto 10-15a atto 10-18

  • Fundamental Constants

    Gas constant R = 8.3144 j.K-1.mol-11.9872 cal.K-1.mol-18.3144 x 107 ergs.K-1.mol-10.082054 l.atm.K-1.mol-1

    Boltzmann constant k = 1.38044 x 10-16 erg.K-1Avogadro's Number N = 6.0230 x 1023 molecules.mole-1Ice point To = 273.15 KFaraday constant F = 96,490 coul.eq-1Permittivity of vacuum o = 8.854 x 10-12 coul.m-1.volt-1Molar volume, ideal gas, 0C, 1 atm Vo = 22.4138 l.mol-1Electronic charge e = 4.80286 x 10-10 esu

    1.602 x 10-19 coulElectron mass me = 9.1083 x 10-28 gVelocity of light c = 2.997930 x 1010 cm.sec-1Standard acceleration of gravity g = 980.665 cm.sec-2Planck's constant h = 6.6252 x 10-27 erg.secVolume conversion factor = 103 l.m-3Collision factor Z = 1011 M-1.sec-1

    Conversion Factors

    1 atm = 760 mm = 1.01325 x 106 dyne.cm-21 cal = 4.184000 j1 j = 107 ergs = 1 volt.coul1 erg = 1 dyne.cm1 ev = 1.60206 x 10-12 erg1 l.atm = 24.22 cal1 = 10-10 m1 Debye = 10-18 esu.cm.molecule-1 = 2 x 10-6 coul.m.mol-11 kcal/eq = 0.043362 volts

  • Mathematical Formulae

    sinh x = 1/2 (ex - e-x)

    sinh x = x + x3/3! + x5/5! + x7/7! + ...

    ex = 1 + x + x2/2! + x3/3! + ...

    Surface AreaCylinder (minus ends) A = 2rhSphere A = 4r2

    VolumeCylinder V = r2hSphere V = (4/3) r3

  • Fundamental Principlesof Membrane Biophysics

    CHAPTER 1: BIOLOGICAL MEMBRANES

    David Njus

    Department of Biological SciencesWayne State University

    D. Njus, 2000

  • Page 1.1

    CHAPTER 1: BIOLOGICAL MEMBRANES

    Section 1.1. Biological MembranesBiological membranes maintain the spatial organization of life. Membranes

    defined the boundaries of the first living cells and still work to shield cellular metabolismfrom changes in the environment. Membranes prevent undesirable agents from enteringcells and keep needed molecules on the inside. They also organize the interior ofeukaryotic cells by separating compartments for specialized purposes. Membranes are notstatic barriers, but active structures. To function effectively, they must selectively passmolecules, ions, and signals from one side to the other.

    The strategy underlying biological membrane function is that the best barrierbetween aqueous compartments is a hydrophobic layer. The water-soluble compoundspresent within cells and in their environments are not soluble in the lipid milieu of themembrane and pass slowly or not at all through even a very thin lipid layer. Thismechanism has a number of advantages which life has exploited. First, the lipid bilayer isa natural structure and assembles spontaneously. Second, the structure is flexible andallows for growth and movement as well as for the insertion and operation of proteinmachinery. Finally, the structure has a low dielectric constant giving the membraneelectrical properties which are used in signalling, transport and energy transduction.

    To understand how biological membranes function, we will begin by analyzingtheir structure. The structure determines the fundamental properties of fluidity,permeability, and membrane potential. The origin and characterization of these propertieswill be analyzed next. Finally, we will discuss how these properties contribute to thevarious functions of biological membranes: signal transduction, energy transduction, andtransport.

    Life, like all other processes in our universe, obeys the laws of physics andchemistry. Consequently, the theoretical framework of physical chemistry providespowerful tools for understanding living systems. Especially important is the requirementimposed by the second law of thermodynamics: processes must result in a net decrease infree energy in order to occur spontaneously. Free energy changes govern all metabolicprocesses, but they are particularly apparent in common phenomena of biologicalmembranes. For example, membrane structure is governed by the distribution ofcompounds between the hydrophobic interior of the membrane and the aqueous spaces oneither side. Free energy also determines the movement of molecules and ions acrossmembranes in response to concentration gradients and membrane potentials. Becausemembranes have a well defined planar geometry, the mathematics is simpler than it mightotherwise be. Thus, to understand in depth the structure and function of biologicalmembranes, it is essential to understand and apply principles of physical chemistry. Thepurpose of this course is to construct a coherent framework to do that.

    Section 1.2. The Fluid Mosaic Model of Membrane StructureEarly on, it was recognized that hydrophobic compounds passed more readily than

    water-soluble compounds through biological membranes. This, coupled with theidentification of lipids as a major component, led to the notion that biological membraneshave a hydrophobic character. The calculation (erroneous, as it turns out) that the lipid

  • Page 1.2

    content was twice that needed for a single layer of lipid led to the concept (correct, as luckwould have it) of the lipid bilayer (Gorter and Grendel, 1925; Danielli and Davson, 1935).Lipids are amphiphilic compounds with a small hydrophilic headgroup attached to longhydrocarbon chains. In the lipid bilayer, lipids are aligned with the headgroups facing thewater on either surface of the membrane and the hydrophobic hydrocarbons sandwiched inbetween.

    The lipid bilayer concept did not establish the location of the protein components ofthe membrane. Originally, for lack of a better site, the proteins were stuck on to themembrane surface. This was not tenable, of course, because proteins are responsible formoving molecules and messages across membranes and they could not perform thosefunctions without being a integral part of the membrane itself. This realization gave rise tothe concept of integral and peripheral proteins. Peripheral proteins are loosely associatedwith the membrane and located on the surface of the lipid bilayer. Integral proteins areinserted into the membrane and pass all the way (or much of the way) across themembrane. Originally, the integral proteins were thought to form a well defined matrixwith the lipid bilayer filling in the spaces in between. In the late 1960's, however, itbecame clear that many proteins are not rigidly fixed in the membrane, but can diffuseacross the surfaces of cells relatively easily and independently. Membranes came to beviewed as fluid structures with proteins and lipids arranged in their thermodynamicallymost favorable structure. Lipids exist in a bilayer and provide the milieu in which theintegral membrane proteins float. The proteins are oriented so that their hydrophobicsurfaces are immersed in the hydrophobic interior of the lipid bilayer. Hydrophilic aminoacids are exposed only in the aqueous regions on either side of the membrane. Theorganization of the membrane is a direct consequence of the partitioning of its components,both lipid and protein, so that hydrophobic regions are kept within the membrane andhydrophilic parts are exposed to the water on either side. Because the components are notheld together by bonds, they are free to diffuse and move independently within the plane ofthe membrane. Singer and Nicolson (1972) captured this view in the fluid mosaic model.

    The fluid mosaic model persists as the accepted view of membrane structure. Therecognition of linkages between membrane proteins and components of the cytoskeletalsystem has mod

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