= Membrane transport
{wiki}
<Membrane transport> is the passage of substances across a <cell membrane>. For the small <solutes> considered here, distinguish the available route from its driving force: a <lipid bilayer>, <ion channel>, or <carrier protein> determines how passage can occur, while differences in <chemical potential> and <membrane potential> determine which direction is energetically downhill. A large driving force cannot make an unavailable route conduct. See https://www.ncbi.nlm.nih.gov/books/NBK26815/[Alberts et al.: principles of membrane transport].
For an ideal dilute <chemical solution> at uniform <temperature> and <pressure>, with the same reference molar <chemical potential> on both sides, the molar <electrochemical potential> change for transferring a <solute> from compartment A to B is
$$
\Delta\widetilde\mu_{\mathrm{A}\to\mathrm{B}}=RT\ln\!\left(\frac{c_{\mathrm B}}{c_{\mathrm A}}\right)+zF(V_{\mathrm B}-V_{\mathrm A}).
$$
Here $c_{\mathrm A},c_{\mathrm B}$ are <concentrations>, $T$ is absolute <temperature>, $R$ is the <molar gas constant>, $z$ is signed <ion> charge number, $F$ is the <Faraday constant>, and $V_{\mathrm B}-V_{\mathrm A}$ is the <electric potential> difference. The <natural logarithm> contains a dimensionless ratio. The electrical term vanishes for an uncharged <solute>. More generally, use <thermodynamic activities> in place of the ideal <concentration> ratio. This combines the ideal-solution <chemical potential> difference with electrical <energy> per mole; see https://goldbook.iupac.org/terms/view/E01945[IUPAC Gold Book: electrochemical potential]. For a <biological cell>, taking B inside and A outside makes the voltage term use the existing <membrane potential> convention.
\Image[/membrane-transport-gradients.png]
{title=<Passive transport> and <active transport> for a stipulated <concentration> difference}
{description=Ten illustrative neutral <solute> tracers are split 8:2 between equal fixed-<volume> compartments. The lower sketches compare conceptual <free energy> profiles for <passive transport> and the <solute> part of <active transport>. Heights are unscaled and are not experimental barriers; the lower-right curve excludes the driving process, so it is not a full coupled-cycle <free energy> profile.}
Back to article page
