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mesosphere That region of the atmosphere Comment: Once equilibrium is attained, any
which lies above the stratopause (about 4752 reaction will continue in both directions, shifting
km) and below the mesopause (about 8090 km) the reaction away from and back toward equilib-
and in which temperature decreases with increas- rium from instant to instant, but by infinitesi-
ing height; this is the region in which the lowest mally small changes. See also dextralateral,
temperatures of the atmosphere occur. direction, dynamic equilibrium, formal reaction
equation, product, rate constant, reversibility,
metabolite A molecule which participates sinistralateral, and substrate.
noncatalytically in metabolism and is not an inor-
ganic ion or element. migration (1) The (usually intramolecular)
Comment: This seems a bit circular, because transfer of an atom or group during the course of
it depends on being able to recognize what a molecular rearrangement.
metabolism is. Metabolites tend to be relatively (2)The movement of a bond to a new position,
small (usually less than 1000 daltons molecu- within the same molecular entity, is known as
lar weight) and structurally simple. They can be “bond migration.”
monomers or polymers (for example, fatty acids), Allylic rearrangements, e.g.,
but are not usually considered to be macro-
RCH = CHCH X −→ RCCHCH = CH 2
2
molecules or their smaller polymers (oligonu- |
X
cleotides, peptides). As should be obvious, the
notion of a metabolite is rather elastic. exemplify both types of migration.
metric A metric on a set M is a map d : minimal biochemical network The min-
M × M → R satisfying for all x, y, z ∈ M, imal biochemical network is the network
(i.) d(x, y) ≥ 0, equal 0 iff x = y, positive N ({v ,v ,v }, {e(s, v ,v ),
B 0 m,1 m,2 r,1 m,1 r,1
definiteness,
e(d, v m,2 ,v )}, ∅, {l m,1 ,l m,2 ,l }).
r,1
r,1
(ii.) d(x, y) = d(y, x), symmetry,
(iii.) d(x, z) ≤ d(x, y) + d(y, z), triangle Comment: This is a network of a single spon-
inequality. taneous reaction, without any known parameters
but for which the identities of the reactants (but
A metric space is a pair (M, d). not their stoichiometry, a parameter of the edges)
are known.
metric space See metric.
minimal element (of a partially ordered set
Michaelis-Menten kinetics The mathemat- [A, ]) An element m ∈ A such that there is
ical model for enzyme kinetics based on the law no element a ∈ A except a = m such that m a.
of mass action. The resulting equations are non- See ordering and minimum.
linear. However, due to the peculiar nature of
the enzymatic reaction in which the concentra- minimal surface equation Let U ⊂ R n
tion of the enzyme is usually significantly greater open and u : U × R → R. The minimal surface
than that of the substrate, the system of nonlinear equation for u is
ordinary differential equations can be treated by
Du
singular perturbation. This treatment gives the div = 0,
2 1/2
(1 +|Du| )
steady-state approximation well known in bio-
chemical literature. where Du = D u = (u ,...,u ) denotes the
x x 1 x n
gradient of u with respect to the spatial variable
microscopic reversibility The continuous x = (x ,...,x ).
1
n
reaction of sinistralateral and dextralateral sets
of coreactants, such that no net change in the minimum (of a partially ordered set [A, ])
concentrations of coreactants occurs over meas- An element m ∈ A such that ∀a ∈ A, a m.
urable time. See ordering.

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