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Effect of ionic polarizability on electrodiffusion in lipid bilayer membranes

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Summary

Ion-carrier complexes and organic ions of similar size and shape have mobilities in lipid bilayer membranes which span several orders of magnitude. In this communication, an examination is made of the hypothesis that the basis for this unusually wide range of ionic mobilities is the potential energy barrier arising from image forces which selectively act on ions according to their polarizability. Using Poisson's equation to evaluate the electrostatic interaction between an ion and its surroundings, the potential energy barrier to ion transport due to image effects is computed, with the result that the potential energy barrier height depends strongly on ionic polarizability.

Theoretical membrane potential energy profile calculations are used in conjunction with the Nernst-Planck electrodiffusion equation to analyze the available mobility data for several ion-carrier complexes and lipid-soluble ions in lipid bilayer membranes. The variation among the mobilities of different ions is shown to be in agreement with theoretical predictions based on ionic polarizability and size. Furthermore, the important influence exerted by image forces on ion transport in lipid bilayer membranes compared to the frictional effect of membrane viscosity is established by contrasting available data on the activation energy of ionic conductivity with that for membrane fluidity.

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Abbreviations

A :

spherical conductor radius

c :

ionic concentration in the membrane

c w :

ionic concentration in the aqueous solution

E :

electric field strength/(RT/ℱL)

e :

elementary charge

F :

image force

ΔH η :

activation energy for microviscosity

ΔH k :

activation energy for electrodiffusion

J :

current flux

k :

electrodiffusion rate constant for lim ψ→0 defined byJ=ckψLℱ

k s :

modified electrodiffusion rate constant

L :

membrane width

P :

arbitrary image charge from one of Eqs. (14)–(17)

Q :

ionic charge

R :

gas law constant

r :

ionic radius

S :

sum of image charges within spherical conductor

T :

absolute temperature

u :

Stokes-Einstein mobility (footnote 1)

α:

polarizability

β:

(εI−εII)/(εI+εII)

γ:

see Fig. 2

δ:

see Fig. 2

ε:

dielectric constant

ε0 :

permittivity of free space

ζ:

radial space coordinate/L

η:

microviscosity relative to di(18∶1)-PC

θ:

see Fig. 2

Θ:

ionic charge/e

Λ:

constant defined in Eq.(44)

λ:

A/L

μ:

Poisson's equation constant

ξ:

axial space coordinate/L

P:

image charge/e

ϱ:

space charge density/(e/L 3)

Φ:

effective potential energy barrier

φ:

potential energy/RT

χ:

separation distance between an arbitrary charge and a charged spherical conductor

ψ:

electric potential/(RT/ℱ)

∇2 :

Laplacian

ℱ:

Faraday constant

D :

Stokes-Einstein diffusivity

ℓ:

L/L(di(18∶1)-PC)

C :

chemical

E :

electrostatic

M, N :

image charge indices

Q :

refers to ion (source charge)

R :

refers to location of ion binding site within the membrane

I, II, III:

dielectric regions

*:

denotes maximum potential energy, ϕ * E

TPhB− :

tetraphenylboride anion

DPA− :

dipicrylamine anion

CCCP− :

carbonylcyanidem-chlorophenylhydrazone anion

egg PC:

phosphatidyl choline from egg yolk

di(N∶1)-PC:

diacylphosphatidyl choline of an N-carbon mono-unsaturated fatty acid

GMO:

glyceryl monooleate

GMER:

glyceryl monoerucin

CHL:

cholesterol

PI:

phosphatidyl inositol

PS:

phosphatidyl serine

DPPC:

dipalmitoyl phosphatidyl choline

BPE:

bacterial phosphatidyl ethanolamine

PE:

phosphatidyl ethanolamine

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Authors and Affiliations

  1. Department of Chemical Engineering, Stanford University, 94305, Stanford, California

    Robert W. Bradshaw & Channing R. Robertson

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  1. Robert W. Bradshaw
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Bradshaw, R.W., Robertson, C.R. Effect of ionic polarizability on electrodiffusion in lipid bilayer membranes. J. Membrain Biol. 25, 93–114 (1975). https://doi.org/10.1007/BF01868570

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  • DOI: https://doi.org/10.1007/BF01868570

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