**Surface charge density**

Membranes generally have a net negative surface charge because of the contribution of phospholipid sidechains. This gives the surface ionic properties which determine the distribution of ions and metabolites close to the surface. In general, the ions in solution take on a Boltzmann distribution near the surface, with the positively charged ions accumulated at the surface, and the negatively charged ions excluded from the surface.

A similar local distribution occurs around charged sites on macromolecules. However, in this case, an asymetric distribution of charge may gives the molecule a dipolar aspect, which can be important in:

Many reactions have been characterized in which evolution has taken advantage of the local charge effects to engineer specific features of importance in mechanism and control.

For example, in the reaction of cytochrome c with cytochrome oxidase
(or of cytochrome c_{2} with the photochemical reaction
center), a positively charged area surrounding the heme crevice of cytochrome
c docks with a complementary negatively changed surface on cytochrome oxidase.
In the case of of cytochrome c_{2} and the photochemical
reaction center, an X-ray crystal structure has been solved at low resolution
showing the docked cytochrome. In each of these cases, the complementary
surfaces act both to provide a force favoring complex formation, and to
provide an orienting force to guide the docking during the approach to
complex formation.

Another example is the change in aggregation of light harvesting complexes (LHCII) in chloroplasts which leads to the stacking of the grana. The charge on the LHCII is changed by phosphorylation in response to the state of the plastoquinone pool. The pool goes reduced when photosystem II delivers excitation faster than photosystem I. Reduction of the pool activates a kinase, which leads to phosphorylation by ATP. The phosphorylated LHCII dissociates from its aggregated state (and association with the photosystem), and the LHCII complexes drift away to the stroma, where they can act as an antenna to photosystem I. This has the effect of redistributing excitation so as to favor the oxidation of the pool.

**Effects of ionic strength**

The characteristic feature of such ionic interactions is the effect of ionic strength. As the concentration of ions increases, the surface charge is "masked"; the gradients of local potential fall off more rapidly due to the Boltzmann distribution from a higher initial concentration, and the small ions compete with the macromolecular charges for the complementary sites. At high ionic strength, the binding forces resulting from complementary attraction are therefore weaker, and physical parameters which depend on these change value. For example, the binding of cytochrome c (or c2) becomes weaker, and the rate constant for electron transfer (which depends on binding because the reaction proceeds from the bound state), changes from first-order (due to bound reactants) to second-order (as the complex dissociates), and the second-order rate constant decreases as ionic strength is further increased.

**Gouy-Chapman treatment**

The following is a brief description of the classical treatment of surface
potential.

1) We start with the Poisson equation which describes the falling off
of a local potential:

d^{2}y
/ dx^{2} = -4pr
/ e

here, y is the potential, x the distance
from the surface, r is the space charge density
(see below), and e is the dielectric constant
of the bulk phase.

2) The distribution of charged species in the potential gradient is
given by the Boltzmann equation:

c_{i} = c_{b}
exp(-z_{i}Fy /
RT)

where c_{i} is the concentration (or more
precisely, activity) of the ionic species i at a point where the potential
is y; c_{b} is
the concentration in the bulk phase where the potential is zero. (Note
that y here is eqivalent to Dy
in the Nernst equation, and the two equations are equivalent, with the
Nernst equation being the Boltzmann equation in log form).

3) The space charge density at any point is the sum of the charges at
that point, determined by the concentration and charge of each species:

r = S_{i}
z_{i}Fc_{i}

4) Combine equations 1) - 3) by substitution, and integrate:

(dy/dx)^{2}
= (-8pRT/e)(S_{i}
c_{b} [exp(-z_{i}Fy
/ RT) - 1])

5) Now we come to the surface.

s = ò_{o}^{¥}
rdx

The surface charge density, s, is determined
by integration of the space charge density in one dimension (the 1 dimensional
approximation, - because of local electroneutrality, each one dimensional
line of force at right angles to the membrane surface will be the same).

6) Substituting for r from the Poisson equation,
integrating, and solving for x=0:

s = (-e/4p)
ò_{o}^{¥}
(d^{2}y/dx^{2})dx
= (-e/4p)(dy_{s}/dx)_{x=0}

where dy_{s}
is the surface potential.

7) Combining eq. 4) and 6) for the case where y
= y_{s}

s = ±
|{(eRT/2p) (S_{i}
c_{b} [exp(-z_{i}Fy
/ RT) - 1])}|^{½}

8) Rearranging, and simplifying for the case where y_{s}
< 50 mV/z, and the salt is symetrical:

y_{s}
= (2pRT / F^{2}ec_{b})^{½}
s/z

©Copyright 1996, Antony Crofts, University of Illinois at Urbana-Champaign, a-crofts@uiuc.edu