Chapter 3, Problem 2SQE

One of the important uses of the Nernst equation is in describing the flow of ions across plasma membranes. Ions move under the influence of two forces: the concentration gradient (given in electrical units by the Nernst equation) and the electrical gradient (given by the membrane voltage). This is summarized by Ohm’s law:

$I_x=G_x\left(V_m-E_x\right)$ which describes the movement of ion x across the membrane. I is the current in amperes (A); G is the conductance, a measure of the permeability of x, in Siemens (S), which is $\Delta I/\Delta V;V_m$ is the membrane voltage; and $E_x$ is the equilibrium potential of ion x. Not only does this equation tell how large the current is, but it also tells what direction the current is flowing. By convention, a negative value of the current represents either a positive ion entering the cell or a negative ion leaving the cell. The opposite is true of a positive value of the current.

a. Using the following information, calculate the magnitude of ‘Na

${\left[{\text{Na}}^{\text{+}}\right]}_{\text{0}}\text{=145}\text{}\text{mM,}{\left[{\text{Na}}^{\text{+}}\right]}_{\text{i}}=15\text{mM},G_{\text{na}}+=1\text{nS},V_{\text{m}}=-70\text{mV}$

b. Is ${\text{Na}}^{\text{+}}$ entering or leaving the cell?

c. Is ${\text{Na}}^{\text{+}}$ moving with or against the concentration gradient? Is it moving with or against the electrical gradient?