On 27 Jan 1998, Paul M. Schlosser wrote:
> Toni,
>> >I have a vague idea that heterogeneous kinetics look quite a bit
> >different from our regular solution-based kinetics. I've always
> >presumed heterogeneous kinetics would apply in the situation you
> >describe. Are you say they simply differ in the units? Or am I
> >missing something?
>> I did leave out one potentially significant factor: diffusional
> limitation. If you have a catalyst particle, where much of the
> catalyst is in pores in the particle, then the time it takes for the
> substrate to get in becomes important. Even with the catalyst or
> enzyme on an exposed surface, if the reaction rate is on the order
> of or faster than the rate of diffusion, the kinetics also change.
In this case the EFFECTIVE (observed) kinetic behavior will change not
necessarily because of a change in INTRINSIC properties of the enzyme
considered but primarily because of its special distibution, INHERENT to
its being confined to a restricted compartment, different than bulk
solution where the reactants concentration is calculated.
In this case, in the relatively concentrated enzyme phase, due to
fast catalysis there, the concentration of substrates and products at
steady state are lower and higher, respectively, in comparison
to these in bulk solution (where the substrates are added, and the
products are normally measured).
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). 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).
> In the case where diffusional resistance is negligable (e.g., the
> fluid medium is well mixed, all the catalyst/enzyme is "exposed",
> the rate of reaction is much slower than the rate of diffusion) the
> kinetics are basically the same.
Not necessarily. For small particles (e.g. mitochondria), this "well
mixed" exhalted state cannot easily be achieved, even with the fastest
magnetic stirrers.
A rather comprehensive treatment of modeling heterogeneous catalysis in a
coupled system (Ox Phos in mitochondria and hexokinase in solution) has
been published, where the intermediate ATP was measured either in solution
or at the surface of the membrane by native (soluble) or localized
luciferase [Aflalo, C. and L.A. Segel, Local probes and heterogeneous
catalysis: a case study of a mitochondria-luciferase-hexokinase coupled
system. J. Theor. Biol., 1992. 158: p. 67-108]. The experimental aspects
of that appear in [Aflalo, C., Localized firefly luciferase probes
ATP at the surface of mitochondria. J. Bioenerg. Biomemb., 1997. 29(6):
p. 549-559].
Diffusional restrictions were also reported in many other systems (e.g.
[Aflalo, C. and N. Shavit, Steady-state kinetics of photophosphorylation:
Limited access of nucleotides to the active site on the ATP synthetase.
FEBS Lett, 1983. 154: p. 175-179.
Aflalo, C. and N. Shavit, A new approach to the mechanism of photo-
phosphorylation: modulation of ATP synthetase activity by limited
diffusibility of nucleotides near the enzyme. Curr. Top. Cell. Regul.,
1984. 24: p. 435-445]).
> In fact, many of the cellular enzymes we treat as "in solution" are
> contained in membranes, but we can readily treat them with the same
> math.
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.
Only a combination of both provide useful information on the enzyme
function and regulation in situ.
Anyway both the mathematical treatment and the interpretation of bulk
measurements are not always so readily easy and unequivocal (which often
results in stochastic activity in this newsgroup...;-)
> -Paul
Sincerely,
Claude
Claude Aflalo ######################## Phones: Office 972-7-6472118 ####
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