Free‐Energy Transport across Membranes

Cells expend a large amount of their free energy currency keeping the appropriate environment inside the cell. Thus, for example, Ca 2+is present intracellularly at < 10 ‐7 M, while extracellular Ca 2+ is present in millimolar (10 ‐3 M) concentrations, that is, 10,000‐fold higher. The free energy difference due to the difference in [Ca 2+], sometimes termed its chemical potential, can be calculated. The difference of the ΔG°’ values when Ca 2+ is at the same concentration (1M) on each side of a membrane is, of course, zero, so the free energy is given by:


Converting from natural to base 10 logarithms, and substituting values for the gas constant, and a standard temperature of 25° C. (298° K.):


 


This expression means that the influx of Ca 2+ into a cell is highly exergonic. If a channel is opened into a cell to allow Ca 2+ across the membrane, it will flood into the cell. In muscle cells, this influx of Ca 2+ is the signal for contraction. Cells, especially muscle cells, have a Ca 2+ active transport system, which transports two Ca 2+ ions out of the cell for every ATP hydrolyzed. The ΔG°’ of ATP hydrolysis is enough to do transport only a single ion. Because, however, the ATP/ADP ratio is kept very high during active metabolic conditions, the concentration gradient of higher [Ca 2+] outside the cell is maintained.