Page 61 -

Table 1 Some Examples of Functional Motives
Type An Example
Biochemical Methyl transfer reaction
Thermodynamic Reaction r has G = G , reaction r i+1 has

i
i
G = G i+1 , G > 0, G i+1 < 0, |G i+1 | > |G |

i
i
Chemical Aldol condensation
Mechanistic Phosphoenzyme intermediate
Kinetic Non-allosteric sequential enzyme
Dynamical Connected reactions exhibiting birythmicity
Topological Reactions and compounds forming a cycle of length
n,4 ≤ n ≤ 7, with at least one reaction requiring
an additional compound not a member of the cycle
Regulatory Rate increased upon binding of ligand
Phylogenetic Mammalian phosphoglycerate mutases

Comment: Types of motif and some examples futile cycle A cycle of alternating com-
can be found in Table 1 below. See also bio- pound and reactive conjunction nodes which,
chemical, chemical, dynamical, kinetic, mecha- stoichiometrically, regenerates all compounds
nistic, phylogenetic, regulatory, thermodynamic, in the cycle and consumes more nucleotide
and topological motives. or coenzyme molecules than it produces.
Comment: The biochemical connotation of
functor (1) A function between categories. the word is strongly dependent on the notion
(2) An operator denoting the relation satisfied of futility. A disproportionately large energy
by a tuple’s arguments. or substituent consumption for no apparent syn-
Comment: Where the functor, also called an thetic or catabolic change. It also depends on
operator in some contexts, is written is largely a stoichiometry. Clearly for futility to occur, all
matter of convention. Some operators are written “nonenergetic” molecules which enter the cycle
as prefixes (e.g., derivatives, logical predicates); must remain in it. Thus if some proportion are
others are infix operators, such as the common diverted out of the cycle to other fates, so that
arithmetic ones; and still others are postfix oper- the stoichiometry condition is broken, the cycle
ators, such as exponentiation. Consider the equa- will decay and energy or substituent consump-
tion x = y + a. This equation uses two binary tion will decline.
operators, = and +, seen more easily by writing The quotation marks of “nonenergetic” are
the operations as relations = (+(y, a), x). meant to warn of elastic biological language.
Every molecule has the intrinsic energy of its
fundamental theorem of algebra Every
chemical bonds, so strictly speaking no molecule
polynomial of degree n ≥ 1 with complex coef-
is nonenergetic. But in a biochemical context,
ficients has at least one root in the complex num-
certain bonds of certain molecules such as ATP
bers C.
and NADH are broken in many reactions to yield
particularly convenient amounts of energy for the
fundamental theorem of calculus Let f be
reaction or a substituent group for transfer to
continuous (hence integrable) on [a, b] and let F
another molecule. Compounds used as energy
be an antiderivative of f (i.e., F (x) = f(x)),

or substituent sources are regenerated by many
then
b other reactions. The net result is that energy
f(x)dx = F(b) − F(a). or substituent groups (or both) are transferred
a
among molecules by these “energetic” or “cur-
fusion (in biotechnology) The amalgama- rency” metabolites.
tion of two distinct cells or macromolecules into
a single integrated unit.

© 2003 by CRC Press LLC