THE KINETICS OF PENETRATION : I. EQUATIONS FOR THE ENTRANCE OF ELECTROLYTES.
When the only solute present is a weak acid, HA, which penetrates as molecules only into a living cell according to a curve of the first order and eventually reaches a true equilibrium we may regard the rate of increase of molecules inside as See PDF for Equation where P(M) is the permeability of the protoplasm to molecules, M(o), denotes the external and M(i) the internal concentration of molecules, A(i) denotes the internal concentration of the anion A(-) and See PDF for Equation (It is assumed that the activity coefficients equal 1.) Putting P(M)F(M) = V(M), the apparent velocity constant of the process, we have See PDF for Equation where e denotes the concentration at equilibrium. Then See PDF for Equation where t is time. The corresponding equation when ions alone enter is See PDF for Equation. where K is the dissociation constant of HA, P(A) is the permeability of the protoplasm to the ion pair H(+) + A(-), and A(ie) denotes the internal concentration of A(i) at equilibrium. Putting P(A)KF(M) = V(A), the apparent velocity constant of the process, we have See PDF for Equation and See PDF for Equation When both ions and molecules of HA enter together we have See PDF for Equation where S(i) = M(i) + A(i) and S(ie) is the value of S(i) at equilibrium. Then See PDF for Equation V(M), V(A), and V(MA) depend on F(M) and hence on the internal pH value but are independent of the external pH value except as it affects the internal pH value. When the ion pair Na(+) + A(-) penetrates and Na(i) = BA(i), we have See PDF for Equation and See PDF for Equation where P(NaA) is the permeability of the protoplasm to the ion pair Na(+) + A(-), Na(o) and Na(i) are the external and internal concentrations of Na(+), See PDF for Equation, and V(Na) is the apparent velocity constant of the process. Equations are also given for the penetration of: (1) molecules of HA and the ion pair Na(+) + A(-), (2) the ion pairs H(+) + A(-) and Na(+) + A(-), (3) molecules of HA and the ion pairs Na(+) + A(-) and H(+) + A(-). (4) The penetration of molecules of HA together with those of a weak base ZOH. (5) Exchange of ions of the same sign. When a weak electrolyte HA is the only solute present we cannot decide whether molecules alone or molecules and ions enter by comparing the velocity constants at different pH values, since in both cases they will behave alike, remaining constant if F(M) is constant and falling off with increase of external pH value if F(M) falls off. But if a salt (e.g., NaA) is the only substance penetrating the velocity constant will increase with increase of external pH value: if molecules of HA and the ions of a salt NaA. penetrate together the velocity constant may increase or decrease while the internal pH value rises. The initial rate See PDF for Equation (i.e., the rate when M(i) = 0 and A(i) = 0) falls off with increase of external pH value if HA alone is present and penetrates as molecules or as ions (or in both forms). But if a salt (e.g., NaA) penetrates the initial rate may in some cases decrease and then increase as the external pH value increases. At equilibrium the value of M(i) equals that of M(o) (no matter whether molecules alone penetrate, or ions alone, or both together). If the total external concentration (S(o) = M(o) + A(o)) be kept constant a decrease in the external pH value will increase the value of M(o) and make a corresponding increase in the rate of entrance and in the value at equilibrium no matter whether molecules alone penetrate, or ions alone, or both together. What is here said of weak acids holds with suitable modifications for weak bases and for amphoteric electrolytes and may also be applied to strong electrolytes.
Osterhout
W J
WJ
Laboratories of The Rockefeller Institute for Medical Research.