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Both equations for d[C]/dt are of the form Comment:As defined here, the biochemical reac-
tion corresponds to that for an elementary chem-
d[C] r[A][OH ] ical reaction. The nice correspondence among
−
= (3)
−
dt 1 + s[OH ] molecularity, stoichiometry, and order is a direct
consequence of the restriction to elementary
where r and s are constants (sometimes called
reactions. In practice, the (partial) order is sim-
“coefficients in the rate equation”). The equa-
ply that exponent for a molecular species in a
tions are identical in their dependence on con-
kinetic equation that fully accounts for the pro-
centrations and do not distinguish whether OH −
duction or consumption of that species, the over-
catalyzes the formation of B, and necessarily also
all order being the sum of the partial orders for
its reversion to A, or is involved in its further
all species. Thus until a reaction is established to
transformation to C. The two schemes are there-
be elementary, one cannot assume that the expo-
fore kinetically equivalent under conditions to
nents will be the stoichiometries. If the concen-
which the stated provisos apply.
tration of a reactant is so large compared to the
othersastobe“effectivelyinfinite,” thenthereac-
kinetic motif A kinetic sequence and asso- tion becomes zeroth order for that reactant.
ciated constants, represented as a set of balanced
reactions and their parameters, conserved over kinetic proofreading A mathematical
different molecules, reactions, or combinations model based on the kinetics of transcription
thereof. (from DNA to RNA) or translation (from RNA
Comment: One of several different appli- to protein) which explains how an extremely
cations of graph theory to biochemistry is to high accuracy is achieved in these biological
represent such kinetic motifs. Notice there is processes in the presence of thermal noise. The
no constraint on the number of species in the key idea is that these biological processes utilize
reaction equation. The definition may later be free energy in order to obtain high fidelity (cf.
expanded to include noninitial studies. The J.J. Hopfield, Proc. Natl. Acad. Sci. U.S.A., 71,
words used to characterize qualitatively enzyme 4135, 1974).
kinetics (ping-pong, ordered) are useful but
incomplete. In practice, recognition of the values Kolmogorov equation Let U ⊂ R open
n
of the constants will clearly be within tolerances and u : U × R → R. The Kolmogorov equation
to minimize experimental variation. See also for u is
chemical, dynamical, functional, mechanistic,
n n
phylogenetic, regulatory, thermodynamic, and ij i
u − a u − b u = 0.
t
topological motives. x i x j x i
i,j=1 i=1
kinetic order The kinetic order of a bio- Korteweg-deVries (KdV) equation Let
n
chemical reaction is the sum of the molecular- U ⊂ R open and u : U × R → R. The
ities of the reaction. A reaction is said to be of Korteweg-deVries (KdV) equation is the shallow
nth order in a reactant (partial order) if the stoi- water wave equation
chiometryofthatreactantinthereactionequation
is n. u + uu + u xxx = 0 .
x
t

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