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RICE UNIVERSITY STUDIES
Before proceeding, I might mention a working hypothesis on which
many of my arguments are based. The question will arise repeatedly,
“Why do living cells choose to accomplish ‘simple’ results in such com-
plicated ways?” One answer is that N billion years of evolution have
presumably optimized the internal structure of the cell as far as
mechanisms, rates, catalysts, and control are concerned. All we have
to do is discover how the cell does it, and then the fascinating part can
commence.
Another hypothesis, if it can be called that, I alluded to above. We are
not going to gain much insight by looking at individual reactions or even
reaction paths. There seems to be a “minimal set” of interrelated reac-
tions which will show the features of living systems. If we work with less
than this set, the behavior will literally be “dead” in the sense that the
system will not produce the characteristic bahavior we are looking for.
The reaction set I will describe later is hopefully, at least, a “minimal set,”
although this judgement is at best subjective. It is based on geometric as
well as mechanistic arguments with the final rationale dependent on the
assumption of evolutionary optimization which was just mentioned.
Before getting on with the algebra of the example reaction set, I need
to make some remarks about transport limitations and chemical kinetics
restrictions.
Time and Distance Scales in Determining Overall Rates
The “global” processes involved when a cell takes up nutrients, etc.,
take place on a distance scale of the order IO-4 cm in a “well-mixed”
culture. This overall process necessarily involves diffusive and membrane
transport steps in series with the eventual chemical reaction paths. The
example 1 have in mind is the ubiquitous E. Coli, assumed to be
metabolizing glucose.
The average E. Coli, during its twenty-minute half-life, takes glucose
through its membrane at about IO-'0 moles∕cm2-sec.If we allow a “rich”
driving force of 10~7 moles∕cm3operating over a distance equal to the cell
diameter, we arrive at a quasi-diffusion coefficient of order 10 ^7 cm-’/sec.
If the actual diffusivity of glucose is larger than this, which it should be,
then diffusion does not seriously limit the overall process. Of course,
there are systems which are external diffusion limited; I will choose to
ignore them.
This takes care of diffusion from the membrane outward. The only
argument which we can employ to justify discounting internal diffusion
as an absolutely controlling rate step is heuristic. Presumably the cell
has evolutionary control over internal processes, and will not let itself
be limited by factors it can change. There is in fact evidence that the
enzymes which catalyze a complete set of reactions are located in close