1.2.2 Enzyme as Protein Catalyst and Its Kinetics
Essential unit of living organism is a cell and chemical reactions of its metabolic
system is catalyzed by specific enzymes synthesized by use of genetic information of
DNA. Chemical reaction mediated by enzymes is shown in following equations
where E, S ES and P denote enzyme, substrate, ES complex and product,
respectively.
E þ S
k À1
!
k þ1 ES !
k þ2 E þ P
Michaelis and Menten assume that E+S and ES are in equilibrium state and then
Michaelis constant K m becomes K m ¼
k À1
k þ1
[6].
Haldane assumes that concentration of ES complex is in stationary state and then
Michaelis constant is changed to K m ¼
k À1 þk þ2
k þ1
in this case [7].
1.2.3 Change of Free Energy in Chemical Reaction
Molecules in isolated system become finally equilibrium state by chemical reaction
among them. And the concentration of each molecule is determined by change of
Gibb’s free energy in the chemical reaction. In a case that reactants A and B make
product C, Gibb’s energy change is shown in reaction coordinate with activation
energy (Fig. 1.9). Ratio of product concentration to reactants concentration is
determined by equilibrium constant. Activation energy of chemical reaction is
reduced by specific enzyme mediating the reaction in a biological system of cell.
Rate of reaction is explained by transition state theory. Temperature dependency of
reaction rate, k is shown by following Arrhenius equation. k¼Ae
À
Ea
RT . A, E a , R and
T are frequency actor, activation energy, Gas constant and absolute temperature,
respectively. Eyring introduced activated complex as a transition state in his transient theory.
A þ B , AB
ð Þ∗ ! C
In this reaction mechanism, reaction rate v is shown by v¼k*[(AB) *]. When
equilibrium state between A+B and (AB) * is assumed, equilibrium constant K* is
shown by K*¼[(AB) *]/[A][B] and finally v¼k[A][B]¼k*K *[A][B].
△G*¼ÀRTlnK* and k¼k*exp(À△G/RT)¼k*exp(△S*/R)exp(À△H*/RT) shows
relationship between reaction rate, k and activation energy. The result means that
activation energy determines rate of chemical reaction.
1.2 Thermodynamics of Biological System
11
Essential unit of living organism is a cell and chemical reactions of its metabolic
system is catalyzed by specific enzymes synthesized by use of genetic information of
DNA. Chemical reaction mediated by enzymes is shown in following equations
where E, S ES and P denote enzyme, substrate, ES complex and product,
respectively.
E þ S
k À1
!
k þ1 ES !
k þ2 E þ P
Michaelis and Menten assume that E+S and ES are in equilibrium state and then
Michaelis constant K m becomes K m ¼
k À1
k þ1
[6].
Haldane assumes that concentration of ES complex is in stationary state and then
Michaelis constant is changed to K m ¼
k À1 þk þ2
k þ1
in this case [7].
1.2.3 Change of Free Energy in Chemical Reaction
Molecules in isolated system become finally equilibrium state by chemical reaction
among them. And the concentration of each molecule is determined by change of
Gibb’s free energy in the chemical reaction. In a case that reactants A and B make
product C, Gibb’s energy change is shown in reaction coordinate with activation
energy (Fig. 1.9). Ratio of product concentration to reactants concentration is
determined by equilibrium constant. Activation energy of chemical reaction is
reduced by specific enzyme mediating the reaction in a biological system of cell.
Rate of reaction is explained by transition state theory. Temperature dependency of
reaction rate, k is shown by following Arrhenius equation. k¼Ae
À
Ea
RT . A, E a , R and
T are frequency actor, activation energy, Gas constant and absolute temperature,
respectively. Eyring introduced activated complex as a transition state in his transient theory.
A þ B , AB
ð Þ∗ ! C
In this reaction mechanism, reaction rate v is shown by v¼k*[(AB) *]. When
equilibrium state between A+B and (AB) * is assumed, equilibrium constant K* is
shown by K*¼[(AB) *]/[A][B] and finally v¼k[A][B]¼k*K *[A][B].
△G*¼ÀRTlnK* and k¼k*exp(À△G/RT)¼k*exp(△S*/R)exp(À△H*/RT) shows
relationship between reaction rate, k and activation energy. The result means that
activation energy determines rate of chemical reaction.
1.2 Thermodynamics of Biological System
11