The thermostatics and thermodynamics of cotransport

The thermostatics of cotransport are reviewed. A static-head equilibrium state across a cotransport system, without leaks, is thought to occur when the electrochemical potential of the driven solute, B prevents net flow of the driving solute, A. For a symport this gives the relationship (formula: see text) Where n is the stoichiometric coefficient, namely the number of moles of A transported per mole of B. (2) If either a symporter with a 2:1 stoichiometric coefficient and a 1:1 symporter, or alternatively, a 1:1 symporter and a 1:1 antiporter are placed in a series membrane array, then the predicted static-head equilibrium across the entire array conflicts with the zeroth law of thermodynamics. (3) There are two major reasons for this failure of cotransport theory; these are: (A) the thermostatic relationships derived shown in Point 1 are based on the assumption that the cotransport process takes place within a closed system. However, the membrane and the external reservoirs are open to the cotransported ligands. It follows that A and B in the external reservoirs can vary independently of the changes within the cotransport process. As no chemical reaction between A and B occurs in the external solutions, reactions within the membrane phase do not affect the equilibrium between the transported ligands in the open reservoirs. (B) It is assumed that the law of mass action can be applied to the cotransport chemical reactions within the membrane phase, without any allowance for the fact that these reactions occur within a 'small thermodynamic system'. Any proper analysis of the chemical potential of the transported intermediate must consider the effects of lower order ligand-carrier forms, which coexist and compete for space with the higher order cotransported forms on the binding matrix. If account is taken of this necessity, then a simple extension of the work of Hill and Kedem (1966) J. Theor. Biol. 10, 399-441 shows that: (a) the static-head equilibrium state cannot exist; (b) the stoichiometry of cotransport, whether symport, or antiport, does not affect the static-head distribution of cotransported ligands; (c) the hypothetical net charge of the transported ligand-carrier complex does not affect static-head equilibrium; (d) the only equilibrium state where there is zero net flow of both driving and driven transported ligand is at true equilibrium when the ligands are uniformly distributed across the membrane. (4) It is deduced that cotransport is not entirely an affinity-driven, but is partially an entropy-driven process.(ABSTRACT TRUNCATED AT 400 WORDS)