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HENRY EYRING, RICHARD P. BOYCE AND JOHN D. SPIKES
cessive free energy barriers. Examples are membrane permeability, diffusion-controlled processes, chain reactions, and nucleation. It is of interest, therefore, that Giddings and Eyring (19) have derived a general
solution for the steady state rate of such multi-barrier processes. Interesting results have been obtained treating diffusion (20), membrane
potentials (21), and heart action (22) using the method of reaction
rates.
The treatment also lends itself very nicely to the development of
irreversible thermodynamics. A temperature gradient modifies the absolute reaction rate equation by the appropriate substitution of temperature into the partition function for the normal and activated states.
When the free energy change is small the reaction rate treatment reduces to the standard irreversible thermodynamic formulation. The
absolute rate expression, however, continues to hold for large departures
from equilibrium in a range where the Onsager reciprocal relations
are no longer applicable.
3. Bioluminescence (22)
As a final application of absolute reaction rate theory to biological
phenomena we will consider the rate of bacterial luminescence.
The theoretical expression is readily derived if it is assumed that
the observed rate of an enzyme reaction at different temperatures is
governed primarily by (a) the activation energy of the catalytic reaction, and (b) an equilibrium between native and denatured forms of
the catalyst. For the present discussion a third important process, the
irreversible denaturation of the catalyst, will be omitted.
Let A w represent the native, active form of luciferase in equilibrium
with A d , the reversible denatured inactive form, and let A 0 equal the
total amount, A n -\- A d , under conditions where essentially none of the
enzyme undergoes irreversible destruction. We have
A n ^±A d
Thus,
[A d ]
K
and
[A d ] = KJAn]
(142)
Since A 0 = A n + A d , Eq. 142 in terms of total and active forms of
luciferase may be written
[A 0 ] = [A n ] + KUn]
HENRY EYRING, RICHARD P. BOYCE AND JOHN D. SPIKES
cessive free energy barriers. Examples are membrane permeability, diffusion-controlled processes, chain reactions, and nucleation. It is of interest, therefore, that Giddings and Eyring (19) have derived a general
solution for the steady state rate of such multi-barrier processes. Interesting results have been obtained treating diffusion (20), membrane
potentials (21), and heart action (22) using the method of reaction
rates.
The treatment also lends itself very nicely to the development of
irreversible thermodynamics. A temperature gradient modifies the absolute reaction rate equation by the appropriate substitution of temperature into the partition function for the normal and activated states.
When the free energy change is small the reaction rate treatment reduces to the standard irreversible thermodynamic formulation. The
absolute rate expression, however, continues to hold for large departures
from equilibrium in a range where the Onsager reciprocal relations
are no longer applicable.
3. Bioluminescence (22)
As a final application of absolute reaction rate theory to biological
phenomena we will consider the rate of bacterial luminescence.
The theoretical expression is readily derived if it is assumed that
the observed rate of an enzyme reaction at different temperatures is
governed primarily by (a) the activation energy of the catalytic reaction, and (b) an equilibrium between native and denatured forms of
the catalyst. For the present discussion a third important process, the
irreversible denaturation of the catalyst, will be omitted.
Let A w represent the native, active form of luciferase in equilibrium
with A d , the reversible denatured inactive form, and let A 0 equal the
total amount, A n -\- A d , under conditions where essentially none of the
enzyme undergoes irreversible destruction. We have
A n ^±A d
Thus,
[A d ]
K
and
[A d ] = KJAn]
(142)
Since A 0 = A n + A d , Eq. 142 in terms of total and active forms of
luciferase may be written
[A 0 ] = [A n ] + KUn]