1. BASIC BIOPHYSICS TOOLS AND RELATIONSHIPS

2. Basic Laws
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
Fick’s Law
Ohm’s Law

3. Fick’s Law
The flow of particles due to diffusion is along the concentration gradient with particles moving from high-concentration areas to low ones.

4. Fick’s Law
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

5. Ohm’s Law
Charged particles in a solution experience a force resulting from other charged particles and electric fields present.

6. Ohm’s Law 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).

7. Einstein Relationship
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

8. Einstein Relationship
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

9. Donnan Equilibrium
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

10. Goldman Equation
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