>Now since the localized enzyme "senses" LOCAL substrate concentration,
>it behaves accordingly (slower rate at steady state, not only due to
>relatively lower substrate but sometimes to higher product
>concentrations, as well different pH, ionic strength or cofactor
>concentrations occuring locally).
In chemical engineering the ratio:
actual rate
------------------------------------------------------
rate that would occur without mass transfer resistance
is referred to as an effectiveness factor. It is (by definition) less
than one, since there will always be some resistance. But it can be very
close to one.
>When bulk measurements are plotted
>against the concentration of reactants added to solution, the kinetic
>behavior of the enzyme looks different than that observed for the same
>solubilized enzyme (homogeneous catalysis).
This may also be due to the fact that being in a membrane holds the enzyme
in a particular orientation--so that a collision with a substrate molecule
is more likely to result in binding--and/or changes in enzyme conformation
due to being (mostly) in a lipid vs. an aqueous environment (protection
against denaturation included). One can easily estimate the diffusivity
of small molecules and compare this to the actual rate of the reaction
(along with an appropriate diffusional distance, like the diameter of a
cell) to see if diffusion is playing much of a role.
Tortuosity of the path required for a substrate molecule to reach the
enzyme adds to diffusional resistance.
>This may apply to EFFECTIVE behaviors which would yield EFFECTIVE kinetic
>parameters. The latter may represent only a vague estimate of the
>INTRINSIC parameters of the enzyme which are relevant to its mechanism.
I.e, the effectiveness factor is lumped in with the kinetics.
But the original question asked if you needed to use different equations
(i.e., if the rate becomes independent of [enzyme]). Given some of the
factors mentioned above (especially conformational changes), I suggest
that it is very difficult to measure an enzyme's intrinsic properties (in
the environment of the membrane), though the references given by Claude
show that it can be done.
More often, one is stuck with fitting effective parameters to data which
include whatever diffusional resistance exists. Which brings us back to
the question: what equation should be used? I'd still suggest using the
same equation as for bulk solution as a first attempt, and only turning
to more complex analyses which include diffusional resistance if that
fails.
At the other extreme, the rate can be almost entirely diffusion-limited
(and hence independent of [enzyme]) which may be the case in Peter
Kuzmic's citation. But I don't think that is common.
-Paul
