18
HENRY EYRING, RICHARD P. BOYCE AND JOHN D. SPIKES
and matter are entering, reacting, and leaving the cell at the same rate.
This too is a time-independent state. Furthermore it more closely approximates the conditions existing in biological systems. Let us consider
such a system composed of molecules and ions. These particles may
exist in various energy states depending upon whether they are free or
have formed chemical combinations. Let Ni represent the number of
particles in a particular energy state i. In general the collisions, chemical
reactions, and movement in force fields cause the individual elements
to change energy states, and Ni may or may not change. We may express this idea in the form
dt
Li\dt
dt )
u;
3
where dTji/dt denotes the number of elements entering state i from
state / per unit time and dTij/dt denotes the number of elements leaving state i for state / per unit time. That is the change in state i is just
the number of particles entering from all other states minus the number
leaving it for any other state. If the right side of the equation does not
vanish, Ni is a function of time and we have a nonstationary state. If
the right side vanishes, Ni is not a function of time. If this is true for
every i, the system is in a steady state. If this is true for every value of
i and /, then
dTdT·
dt
dt
W
and the right side of the equation vanishes. But note that this is a much
more restrictive imposition and corresponds to an equilibrium state. As
an example consider a cell in which there are i components which may
diffuse into or out of the cell. Then
dN
= \(***i) - (
άΝ
'<) 1 + \(^±) - (
dN
'<) 1
L\ dt /chem
\ dt /chemj
[_\ dt /difiF
\ dt /diffj
=
L WT/chem
+
WT/diff J ~ L WT/chem
+
\"^T/diff J
^
where
Ti = the net rate of production of the ith component,
Pi = the net rate of consumption of the ith component,
( -Y1 1
= the rate of production of the ith component by
chemical reaction,
HENRY EYRING, RICHARD P. BOYCE AND JOHN D. SPIKES
and matter are entering, reacting, and leaving the cell at the same rate.
This too is a time-independent state. Furthermore it more closely approximates the conditions existing in biological systems. Let us consider
such a system composed of molecules and ions. These particles may
exist in various energy states depending upon whether they are free or
have formed chemical combinations. Let Ni represent the number of
particles in a particular energy state i. In general the collisions, chemical
reactions, and movement in force fields cause the individual elements
to change energy states, and Ni may or may not change. We may express this idea in the form
dt
Li\dt
dt )
u;
3
where dTji/dt denotes the number of elements entering state i from
state / per unit time and dTij/dt denotes the number of elements leaving state i for state / per unit time. That is the change in state i is just
the number of particles entering from all other states minus the number
leaving it for any other state. If the right side of the equation does not
vanish, Ni is a function of time and we have a nonstationary state. If
the right side vanishes, Ni is not a function of time. If this is true for
every i, the system is in a steady state. If this is true for every value of
i and /, then
dTdT·
dt
dt
W
and the right side of the equation vanishes. But note that this is a much
more restrictive imposition and corresponds to an equilibrium state. As
an example consider a cell in which there are i components which may
diffuse into or out of the cell. Then
dN
= \(***i) - (
άΝ
'<) 1 + \(^±) - (
dN
'<) 1
L\ dt /chem
\ dt /chemj
[_\ dt /difiF
\ dt /diffj
=
L WT/chem
+
WT/diff J ~ L WT/chem
+
\"^T/diff J
^
where
Ti = the net rate of production of the ith component,
Pi = the net rate of consumption of the ith component,
( -Y1 1
= the rate of production of the ith component by
chemical reaction,