Thermodynamics of Transport Across Membranes

Like other processes, the Gibbs free energy change determines the direction in which a transport process occurs. The free energy change associated with movement of compound(s) across a biological membrane is a function of 1) the relative concentration of the material on both sides of the membrane, 2) the change in charge brought about by the movement of ionic compound(s) across the membrane, and 3) other energy releasing processes coupled to the transfer, such as hydrolysis of ATP. The Gibbs free energy for a transfer process of compound C from outside the membrane to inside the membrane is given by

> G = RTln(C in/C out) + G',

where G' depends on the particular transport process as follows:

> G' = 0 for a diffusion-based process;

> G' = ZF for processes where net charge differences occur. F is the Faraday constant (96.5 kJ/mol/V), is the membrane potential in volts, and Z is the charge of the ion; and

> G' = G process for processes coupled to the transport.

When G for a transport is negative, movement of the compound(s) is favored in the direction for which it was calculated. If the G is positive, movement is favored in the reverse direction. When G = 0, net movement is favored in neither direction. Note that at equilibrium for a diffusion-based process, G = 0, so C in = C out. Thus, a diffusion-based process results in equal concentrations of the transported molecule inside and out.

These three scenarios (differences in concentration and charge, as well as the input of chemical energy) provide forces to transport molecules across membranes and are all used in biology.

The first diffusion-based process is called a passive process, because it employs no additional input of energy (G' = 0) and cannot move substances against a concentration gradient (from low to high concentration). All movement of molecules in diffusion-based processes is with the gradient (from high to low concentrations).

The processes that use energy from changes in potential or from energetically favorable chemical processes are called active transport processes. They can move substances against a concentration gradient using the additional contribution from G' which is not available in diffusion-driven processes. Students should be aware that both of these mechanisms can also be used to oppose transfer as well. Hence, electrical differences across a membrane may oppose a transfer instead of favor it and formation of ATP from ADP + Pi may be too energetically unfavorable of a barrier to allow a transfer to occur.

See also: Transport Mechanisms, Resting Potential, Free Energy and Useful Work (from Chapter 3), Free Energy and Concentration (from Chapter 3)