Ionic Basis Of Membranes Potentials. I.

Effect of Ion Concentrations and Conductances on Membrane Potential (V_m)

Introduction

The membrane potential is so fundamental to what cells do that is crucial for you develop a thorough understanding of membrane potentials, how they're produced, how they're maintained, and how a membrane potential's value can be increased or decreased. Although not conceptually complicated, it can be a little tricky and frustrating to understand fully the process that produces the potential difference across plasma membrane ( = the membrane potential, V_m). The more exposure you get to the workings of the process, the better. The purpose of this set of experiments is to help you develop a good understanding of the ionic basis of V_m by allowing you to conduct experiments in which you quantify the effect of varying the factors that are most important in establishing V_m and setting its magnitude ( = its numerical value).

In lecture, you were introduced to the Goldman Equation, published by D.E. Goldman in 1943. Goldman's insight was that (i) V_m is the result of + and - charges being separated from one another by the membrane, and (ii) that it is the rate at which charges (specifically, + charges) move (diffuse) through the membrane that determines how many charges are separated at any given instant. Goldman realized that the rate of a given ion’s diffusion through the membrane (termed ion flux, or ion current, by physiologists) depended on two factors: the ion’s concentration on either side of the membrane and the conductance of the membrane for that ion. Based on principles of irreversible thermodynamics, Goldman incorporated both ion concentrations and conductances into his equation, thereby making it possible for researchers to calculate V_m, given values for those two easily measured parameters.

Since the amount of separated charge is what determines the magnitude of V_m, once you understand what controls the rate of charge flux through the membrane, you will understand most of what is involved in generating and maintaining the membrane potential. While conducting the following experiments and interpreting the resulting data, remember that the plasma membrane, in addition to being a semi-permeable membrane, also acts as a capacitor, meaning that it can separate and store + and - charges. It will also help if you keep in mind the relationship between ion concentration gradient (Dc), membrane conductance (g_m), the amount of charge (q_m) 'stored' by the membrane, and membrane potential (V_m):

Dc_i, g_m,i è J_i^net ( = J_iⁱⁿ - J_i^out) µ ln(g_m,ic_m,i/g_m,ic_m,o) ) è q_m,i è V_m,i ( = q_m,i/C_m )

Stated in words, this flow chart tells us that, for a given ion, i, the combination of concentration gradient (Dc_i) and membrane conductance (g_m,i) results in a net flux of i (J_i^net) through the membrane (which Goldman argued was proportional to ln(g_m,ic_m,i/g_m,ic_m,o)). The net flux of i through the membrane results in the net separation of q_m,i +/- charge pairs across the membrane. Since the plasma membrane exhibits the electrical properties of a capacitor, the + and - charges 'stored' along its outer and inner faces set up a potential difference between the two faces of the plasma membrane. The magnitude of the potential difference resulting from the flux of ionic species i through the membrane is ^V_m,i.

Before commencing this exercise, you may need some review about the meaning of some terms and concepts associated with the physics of electricity and the electrical behavior of R-C circuits. You may do this review now, or at any time you feel you need it

What Does The Membrane Potential Simulation Allow You To Do?

This simulation allows you to calculate q_m and display the resulting value for ^V_m, based on parameter values that you specify. During the experiments you will be conducting, you will vary the rate at which + and - charges are being separated from one another across a plasma membrane. You will do this in two ways:

a. by varying the concentration gradient for K⁺, Na⁺ and/or Cl^- by changing their intracellular and/or extracellular concentration, or

b. by changing the conductance of the membrane for one or more of the same three ions.

What Does The Membrane Potential Simulation's Display Look Like?

When you first start the simulation by clicking on the "Run The Simulation" link, depending on your computer's operating system, the size of its monitor, and the particular browser you're using, you will see a display that looks similar to:

Along the right side of the display you see a number of sliders, each with its associated textfield, that allow you to specify the external and internal concentrations of Na⁺ and K⁺, and to specify the values for g_Na+, g_K+, and g_Cl-. You may change any of these values independently of the others, or you may make changes in concert.

Three control buttons (Run, Clear, Reset) are provided. The function of these buttons is pretty much self-explanatory, except that clicking the Reset button will, in addition to resetting all parameters to their default values, cause the simulation to run one time and calculate V_m based on the default parameter values. Clicking the Clear button clears the display (including the legend) but leaves the parameter values unchanged.