It's more interesting. If you assume (correctly) that the enzymes are NOT
homogeneously distributed, A and B are small molecules and free, and E is
an enzyme in the membrane, E is effectively immobile on the timescale of
most common interest, but A and B can get to it one of 2 ways: by 3D
diffusion from bulk to surface where they hit it 'directly', or by 3D
diffusion to the "large" overall target surface followed by 2D diffusion
ALONG the surface. It was first shown, in a slightly obscure but
nonetheless classic paper (277 citations in the ISI database) by G. Adam &
M. Delbrück (1968), in Structural Chemistry & Molecular Biology, ed.
A.Rich, pp. [not to hand but cited properly in my 1979 BBA review 549,
55-99] that the 2D route tends to win hands down. (There are many implicit
assumptions about unstirred layers &c that could be looked at in more
detail.)
Hans & I also discussed some of these issues apropos microcompartmentation
of membrane energy coupling in e.g. Westerhoff, H.V., Kell, D.B., Kamp, F.
& van Dam, K. (1988) The membranes involved in proton-mediated free-energy
transduction: thermodynamic implications of their physical structure. In:
Microcompartmentation (D.P. Jones, ed.) CRC Press, Boca Raton, pp. 115-154.
Douglas.
(Prof.) Douglas B. Kell, Cledwyn Building,
Institute of Biological Sciences, University of Wales,
Aberystwyth SY23 3DD
Tel: +44 1970 622334 Fax: +44 1970 622354
dbk at aber.ac.ukhttp://gepasi.dbs.aber.ac.uk/home.htm
