## Model Cell that Looks Like a Real Animal Cell

The model cell of Figure 4-5b still lacks many features of real animal cells. For instance, as Table 2-1 shows, the internal organic molecules are charged, and this charge must be considered in the balance between cations and anions required by the principle of electrical neutrality. Recall that the category of internal anions, A-, actually represents a diverse group of molecules, including proteins, charged amino acids, and sulfate and phosphate ions. Some of these bear a single negative charge, others two, and some even three net negative charges. Taken as a group, however, the average charge per molecule is slightly greater than -1.2. Thus, the internal impermeant anions can be represented as A1.2-.

Figure 4-6 An example of a realistic model cell that is at both electrical and osmotic equilibrium. The compositions of ECF and ICF for this equilibrated model cell are the same as for a typical mammalian cell (see Table 2-1). (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.

In addition, the model cell of Figure 4-5b lacked Na+ inside the cell, while real ICF does contain a small amount of sodium. Addition of these complicating factors leads to the model cell of Figure 4-6a, which now contains all the constituents shown in Table 2-1. If the cell of Figure 4-6a is to be at equilibrium, what concentrations of the various ions in ECF and ICF would be required, and what would be the transmembrane potential? To begin, we will take some values from Table 2-1 and determine what the remaining parameters must be for the cell to be at equilibrium. Assume that [K+]o = 5 mM, [Na+]o = 120 mM, [Cl-] = 5 mM, and [A12-] = 108 mM. (Actually, it is not necessary to assume the concentration of A; it could be calculated from the other parameters. For mathematical simplicity, however, we will assume that it is known from the start.) Because Cl- is the sole external anion, the principle of electrical neutrality requires that [Cl-]o be 125 mM. Both K+ and Cl-can cross the membrane, so that the conditions for a Donnan equilibrium Equation (4-5) must be satisfied. This requires that [K+] = 125 mM. The equilibrated value of [Na+] can then be obtained from the requirements for osmotic balance; [Na+] must be 12 mM if internal and external osmolarities are to be equal. From the Nernst equation for either Cl- or K+, the membrane potential at equilibrium can be determined to be about -81 mV.

The equilibrium values for this model cell are shown in Figure 4-6b. Note that the concentrations of all intracellular and extracellular solutes are the same for the model cell and for real mammalian cells (Table 2-1). The values in Figure 4-6b were arrived at by assuming that the cell was in equilibrium, and

INSIDE

Cell membrane r4i

Total osmolarity = 250 mOsm

Cell membrane

this implies that the real cell, which has the same ECF and ICF, is also at equilibrium. Thus, the model cell, and by extension the real cell, will remain in the state summarized in Figure 4-6b without expending any metabolic energy at all. From this viewpoint, the animal cell is a beautiful example of efficiency, existing at perfect equilibrium, both ionic and osmotic, in harmony with its electrochemical environment. The problem, however, is that the model cell is not an accurate representation of the situation in real animal cells: real cells are not at equilibrium and must expend metabolic energy to maintain the status quo.

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