Incorporating Osmotic Balance

The example shown in Figure 4-2 illustrates how ionic equilibrium can be reached and how the Nernst equation can be used to calculate the value of the membrane potential at equilibrium. However, the simple situation in the example is not very similar to the situation in real animal cells. For one thing, animal cells are not enclosed in a box with rigid walls, and thus osmotic balance must be taken into account. An example of how equilibrium can be reached when water balance must be considered is shown in Figure 4-4a. In this example the rigid walls are removed, so that osmotic balance must be achieved in order to reach equilibrium. In addition, an impermeant intracellular solute, P, has been added. For now, P has no charge; the effect of adding a charge on the intracellular organic solute will be considered later.

In Figure 4-4a, it is assumed that the model cell contains 50 mM Na+ and 100 mM P. What must the concentrations of the other intracellular and extracellular solutes be in order for the model cell to be at equilibrium? The principal of electrical neutrality tells us that for practical purposes, the concentrations of

INSIDE 50 mM Na+

100 m/Vl1

Cell membrane rh

INSIDE

100 mM P Total osmolarity = 200 mOsm

Cell membrane

OUTSIDE

Na+ 100 mM

Cl- 100 mM

Total osmolarity = 200 mOsm ECl = -17.5 mV

Figure 4-4 A model cell in which both osmotic and electrical factors must be considered at equilibrium.

(a) The starting conditions, with initial values of some parameters provided.

(b) The values of all parameters required for the cell to be at equilibrium.

cations and anions within any compartment are equal. Thus, because P is assumed to have no charge, [Cl-]j = [Na+] = 50 mM. For osmotic balance, the external osmolarity must equal the internal osmolarity, which is 200 mOsm. The principal of electrical neutrality again requires that [Na+]o = [Cl-]o. This requirement, together with the requirement for osmotic balance, can be satisfied if [Na+]o = [Cl-]o = 100 mM. The model cell of Figure 4-4a can therefore be at equilibrium if the concentrations of intracellular and extracellular solutes are as shown in Figure 4-4b. At this equilibrium, the voltage across the membrane of the model cell (the membrane potential, Em) would be given by the Nernst equation for chloride:

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