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entropy The quantitative measure of disor- the sinistralateral (s) or dextralateral (d) side
der, which in turn relates to the thermodynamic of the reaction equation for reaction r , X s|d,i
i
functions, temperature, and heat. is the number of reactants on the sinistralat-
eral and dextralateral sides, respectively (| used
enzyme A catalyst occurring naturally in a here as logical “or”), and k , k are the forward
i −i
biochemical system, or derived from or modeled and reverse rate constants, respectively. For the
upon a naturally occurring enzyme. Enzymes are entire system of reactions, K is
eq,R
a class of proteins made of polypeptide.
Comment: Until about 15 years ago all known
N
enzymes were proteins, but since then a number K eq,R = K eq,i .
of naturally occurring, catalytic RNAs have been i=1
discovered. This definition includes the products Comment: This definition sets up conditions
of laboratory manipulation as well as molecules
that allow one reasonably to approximate
found in nature.
thermodynamic activities by concentrations, and
reactant order by stoichiometries. It also
epimorphism A surjective morphism be-
assumes that experiments measuring the appar-
tween objects of a category. For example, an
ent equilibrium constant have been done by
epimorphism of vector spaces is a linear surjec-
measuring the constant at several different con-
tive map; an epimorphism of groups is a surjec-
centrations of reactants and extrapolating the
tive group homomorphism; an epimorphism of
results to zero concentration. Under these con-
manifolds is a surjective differentiable map. See
ditions, the equilibrium constant as used by
also bundle morphism.
biochemists comes reasonably close to the equi-
librium constant as defined in thermodynamics.
epitope Any part of a molecule that acts as
See also formal reaction equation.
an antigenic determinant. A macromolecule can
contain many different epitopes, each capable
equilibrium point (1) A point x is called
of stimulating production of a different specific 0
an equilibrium point, critical point,or singular
antibody.
point of a vector field X if X(x ) = 0. If F is
0
t
equations of motion The equations which the flow of X then F (x ) = x for all t.
0
0
t
select the evolution of a mechanical system, or (2) (of a dynamical system (M, X ) A point
more generally any system with only one inde- x ∈ M such that X(x) = 0. The constant curve
pendent variable. c (t) = x in an equilibrium point is an integral
x
See Hamilton principle and Euler-Lagrange curve.
equations.
equilibrium solution See coacervation.
equicontinuous Referring to a family F of
functions with the property that for every " > 0 equivalence classes See equivalence rela-
there exists a δ > 0 such that |f (x) − f (y)| <" tion.
whenever |x − y| < δ for all f ∈ F.
equivalencerelation ArelationR ={(a, b)
equilibrium constant For any reaction r i |a, b ∈ A} that is, a ∼ b ⇔ (a, b) ∈ R from A
that is at equilibrium and whose solutes are at to itself such that:
infinite dilution, r ∈ R (where R is a system of
i (i.) ∀a ∈ A, a ∼ a;
reactions), the equilibrium constant, K eq,i is
(ii.) ∀a, b ∈ A, a ∼ b ⇒ b ∼ a;
X d,i n i,d,j (iii.) ∀a, b, c ∈ A, a ∼ b, b ∼ c ⇒ a ∼ c.
x
j=1 j
K = = k /k ,
eq,i i −i
X s,i n i,s,j If ∼ is an equivalence relation, the equiva-
x
j=1 j
lence class of a ∈ A is the subset [a] ={b ∈
where x is the concentration of reactant x , A : b ∼ a}.If c ∈ A is not in the equivalence
j j
n i,s|d,j is the stoichiometry of that reactant on class of a (i.e., c ∈ [a] or equivalently a ∼ c)
© 2003 by CRC Press LLC
© 2003 by CRC Press LLC