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Biophys J, June 2002, p. 2833-2846, Vol. 82, No. 6
and
*Department of Chemistry, University of California, Davis,
California 95616 USA and Institute
of Problems of Chemical Physics, Russian Academy of Sciences,
142432 Chernogolovka, Moscow, Russia
Some proton pumps, such as cytochrome c
oxidase (CcO), translocate protons across biological
membranes at a rate that considerably exceeds the rate of proton
transport to the entrance of the proton-conducting channel via bulk
diffusion. This effect is usually ascribed to a proton-collecting
antenna surrounding the channel entrance. In this paper, we consider a
realistic phenomenological model of such an antenna. In our model, a
homogeneous membrane surface, which can mediate proton diffusion toward
the channel entrance, is populated with protolytic groups that are in
dynamic equilibrium with the solution. Equations that describe coupled
surface-bulk proton diffusion are derived and analyzed. A general
expression for the rate constant of proton transport via such a coupled
surface-bulk diffusion mechanism is obtained. A rigorous criterion is
formulated of when proton diffusion along the surface enhances the
transport. The enhancement factor is found to depend on the ratio of
the surface and bulk diffusional constants, pKa values of
surface protolytic groups, and their concentration. A capture radius
for a proton on the surface and an effective size of the antenna are found. The theory also predicts the effective distance that a proton
can migrate on the membrane surface between a source (such as CcO) and
a sink (such as ATP synthase) without fully equilibrating with the
bulk. In pure aqueous solutions, protons can travel over long distances
(microns). In buffered solutions, the travel distance is much shorter
(nanometers); still the enhancement effect of the surface diffusion on
the proton flow to a target on the surface can be tens to hundreds at
physiological buffer concentrations. These results are discussed in a
general context of chemiosmotic theory.
Biophys J, June 2002, p. 2833-2846, Vol. 82, No. 6
© 2002 by the Biophysical Society 0006-3495/02/06/2833/14 $2.00
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