Download BASIC BIOPHYSICS TOOLS AND RELATIONSHIPS


Two basic biophysics tools and a relationship
are used to characterize the resting potential
across a cell membrane by quantitatively
describing the impact of the ionic gradients
and electric fields
1. Fick’s Law
2. Ohm’s Law

The flow of particles due to diffusion is along
the concentration gradient with particles
moving from high-concentration areas to low
ones.
 Specifically,
for a cell membrane, the flow of ions
across a membrane is given by
 where
J is the flow of ions due to diffusion, [I] is
the ion concentration, dx is the membrane
thickness, and D is the diffusivity constant in
m2/s. The negative sign indicates that the flow of
ions is from higher to lower concentration, and
d[I]/dx represents the concentration gradient

Charged particles in a solution experience a
force resulting from other charged particles
and electric fields present.
 The
flow of ions across a membrane is
given by
 where
J is the flow of ions due to drift in an
electric field , µ = mobility in m2/sV, Z =
ionic valence, [I] is the ion concentration, v
is the voltage across the membrane, and
dv/dx is electric field (-E).

The relationship between the drift of particles
in an electric field under osmotic pressure,
that is the relationship between diffusivity
and mobility, is given by

where D is the diffusivity constant, m is
mobility, K is Boltzmann’s constant, T is the
absolute temperature in degrees Kelvin, and
q is the magnitude of the electric charge
 An
accompanying principle is space charge
neutrality, which states that the number of
cations in a given volume is equal to the
number of anions.
 Thus,
in the equilibrium state ions still diffuse
across the membrane but each K+ that
crosses the membrane must be accompanied
by a Cl- for space charge neutrality to be
satisfied
 The
Goldman equation quantitatively
describes the relationship between Vm and
permeable ions but applies only when the
membrane potential or electric field is
constant. This situation is a reasonable
approximation for a resting membrane
potential.
 The
Goldman equation is used by
physiologists to calculate the membrane
potential for a variety of cells