Sender: <yaneer at necsi.org> (Yaneer Bar-Yam)
To: complex-science
Date: Wed, 07 Nov 2001 22:29:11 -0500
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From: Sungchul Ji <sji at eohsi.rutgers.edu>
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Subject: Induced-fit vs. the generalized Franck-Condon principle
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       The X-ray structures of enzyme substrate complexes have
established the fact that the shape of the active site of an enzyme is
complementary to that of its substrate.  This complementary fit between
enzymes and their substrates seems consistent with both of the following

theories:

    1)  The lock-and-key model of Emil Fischer proposed in 1890,
according to which the shape of the active site of an enzyme is already
complementary to that of its substrate, so that the substrate can bind
to the active site without any appreciable conformational changes, just
like a key fitting into a lock.  It may be convenience to refer to such
a
conformation of the active site of an enzyme as the 'Fischer
conformation'.

    2)  The induced-fit model proposed by Daniel E. Koshland, Jr. in
1958, according to which the shape of the active site of an enzyme is
induced to undergo marked conformational changes upon binding a
substrate [see Figures 8-13 and -14 in L. Stryer's "Biochemistry",
Fourth Edition, W. H. Freeman, New York,  1995, p. 191].  Let us refer
to the conformation of the active site of an enzyme before binding its
substrate as the 'Koshland conformation'.

    Stryer, in his book cited above, gives the reader the impression
that,
because "the shapes of the active sites of many enzymes are markedly
modified by the binding of substrates" as revealed by X-ray data, the
induced-fit model of Koshland is favored over the lock-and-key model of
Fischer.

    Although Stryer's conclusion may turn out to be true, at least for
some enzymes, there is an alternative way of accounting for the
substrate binding-correlated conformational changes of the active site
of enzymes that is suggested by the so-called generalized Franck-Condon
principle.  This principle states that, when a physicochemical process
results from coupling two partial processes, one fast and the other slow

by a factor of about 100 or more, the slow process must precede the fast

one [Ann. N. Y. Acad. Sci. 227: 419-437 (1974); BioSystems 54:
107-130 (2000)].  To present this alternative view, it is necessary to
use some symbols defined as follows:

Koshland confromation or form  = E/Koshalnd/ . . . . (1)

where E stands for enzyme and /.../ indicates a subscript.

Fischer conformation or form =  E/Fischer/      . . . . . (2)


    Using these notations, we can represent the net conformational
change accompanying substrate binding as follows:

        E/Koshland/  +  S  <----->    S.E/Fischer/  . . . . (3)

where S is the substrate and S.E is the enzyme-substrate complex.

    Clearly, the volume of the active site in the Koshland conformation
is significantly greater than the volume of the active site in the
Fischer conformation, i.e., after binding its substrate.   There are
three possible mechanisms that can account for the binding reaction
depicted in (1):

    1)  The Fischer mechanism:

           E/Fischer/   +    S   <---->    S.E/Fischer/  . . . . .(4)

where the conformation of the active site of an enzyme remains more or
less constant through out the binding process.

    2)  The induced-fit mechanism:

        E/Koshland/  +   S  <--->   S.E/Koshland/  . . . . . . (5)
        S.E/Koshland/         <--->   S.E/Fischer/   . . . . . . . (6)

where the conformational transition of the active site
from the Koshland form to the Fischer form, Process (6),
FOLLOWS (or is INDUCED by) the binding of the substrate
to the active site, Process (5).

   3)  The Franck-Condon mechanism:

        E/Koshland/         <--->   E/Fischer/       . . . . . . . . .
(7)
        E/Fischer/  +   S   <--->   S.E/Fischer/    . . . . . . . . .
(8)

This mechanism assumes that the conformational change of the
active site of an enzyme from the Koshland form to the Fischer form,
Process (7), PRECEDES the binding of the substrate to the active
site, Process (8).

    I predict that the Franck-Condon mechanism will prevail whenever the

rate of the conformational change is much slower (by a factor of about
100 or more) than the rate of substrate binding to the active site of
the enzyme.  If conformational changes accompanying substrate binding
are extensive, involving the number of atoms far greater than the number

of atoms of the substrate in question, it is highly likely that the
Koshland to Fischer conformational transition of the active site of an
enzyme will be much slower than the diffusion rate of the substrate to
its binding site and hence the Franck-Condon mechanism will prevail.

    It seems eminently conceivable that these potential mechanisms
of enzyme-substrate interactions can be tested experimentally, using
ultrafast spectroscopic and X-ray techniques now available.

    The generalized Franck-Condon principle, a derivative of the
Born-Oppenhimer approximation in quantum mechanics, has been
used to formulate molecular mechanisms of enzymic catalysis,
redox reaction-driven proton pumping, muscle contraction, and
redox reaction-driven ATP synthesis [Ann. N. Y. Acad. Sci. 227:
211-226 (1974); In "Structure and Function of Biomembranes
(K. Yagi, ed.), Japan Scientific Societies Press, Tokyo, 1979,
pp. 25-37].  As indicated in another post on this list, the
'binding-change mechanism of ATP synthesis' in mitochondria
proposed by P. D. Boyer is consistent with (and hence can
be can be reformulated using) the Franck-Condon principle.
I sincerely doubt that the induced-fit theory can be applied to
such a wide range of energy-coupled processes.

    Finally, it may be pointed out that, if the Franck-Condon
mechanism turns out to be valid, both the lock-and-key theory of
Fischer and the induced-fit theory of Koshland must be accorded
an equal validity (or invalidity, depending on your taste).
    Any comments or criticisms will be welcome.

    With all the best.

    Sung

    _________________________________________
    Sungchul Ji, Ph.D.
    Department of Pharmacology and Toxicology
    Rutgers University
    Piscataway, N.J. 08855