Page 53 - Color_Atlas_of_Physiology_5th_Ed._-_A._Despopoulos_2003

!
Given the reaction called the activation energy (E a) : E a = P a – P e. It
– 1
A B + C, [1.25] is usually so large (! 50 kJ ! mol ) that only a
– 9
where A is the educt and B and C are the prod- tiny fraction (F ! 10 ) of the educt molecules
0
ucts, ∆G is converted to ∆G as follows: are able to provide it (! A, B). The energy
[B] + [C] levels of these individual educt molecules are
0
∆G ! ∆G + R ! T ! ln [1.26]
[A] incidentally higher than P e, which represents
or, at a temperature of 37 "C, the mean value for all educt molecules. The
∆G ! [B] + [C] ! [J ! mol ] size of fraction F is temperature-dependent
–1
0
∆G + 8.31 ! 310 ! 2.3 ! log
(! B). A 10 "C decrease or rise in temperature
Fundamentals and Cell Physiology (endergonic reaction), ∆G will be exergonic –1 reaction is 2 to 4. in evolution. Enzymes
[A]
lowers or raises F (and usually the reaction
[1.27]
rate) by a factor of 2 to 4, i.e. the Q 10 value of the
Assuming the ∆G of a reaction is + 20 kJ ! mol
0
Considering the high E a values of many non-
4
(# 0) if [B] ! [C] is 10 times smaller than A:
catalyzed reactions, the development of
–1
! –3.7 kJ!mol .
–4
∆G ! 20000+5925!log10
enzymes as biological catalysts was a very im-
[1.28]
step
portant
In this case, A is converted to B and C and reac-
enormously accelerate reaction rates by low-
ering the activation energy E a (! A). According
tion 1.25 proceeds to the right.
If [B] ! [C]/[A] = 4.2 $ 10 , ∆G will equal
– 4
to the Arrhenius equation, the rate constant k
– 1
–E a /(R ! T)
(no net reaction). This numeric ratio is called
to e
. For example, if a given enzyme re-
the equilibrium constant (K eq) of the reaction.
duces the E a of a unimolecular reaction from
126 to 63 kJ ! mol , the rate constant at 310 "K
1 zero and the reaction will come to equilibrium (s ) of a unimolecular reaction is proportional
0
K eq can be converted to ∆G and vice versa
– 1
using Equation 1.26: (37 "C) will rise by e – 63000/(8.31 ! 310) /e – 126000/(8.31 !
0
10
0 ! ∆G + R ! T ! lnK eq or 310) , i.e., by a factor of 4 ! 10 . The enzyme
0
∆G ! – R ! T ! lnK eq and [1.29] would therefore reduce the time required to
metabolize 50% of the starting materials (t /2)
1
K eq ! e –∆G"/(R ! T) . [1.30]
from, say, 10 years to 7 msec! The forward rate
– 1
– 4
Conversely, when [B] ! [C]/[A] % 4.2 $ 10 , ∆G of a reaction (mol ! L – 1 ! s ) is related to the
will be % 0, the net reaction will proceed back- product of the rate constant (s ) and the
– 1
– 1
wards, and A will arise from B and C. starting substrate concentration (mol ! L ).
∆G is therefore a measure of the direction of The second law of thermodynamics also im-
a reaction and of its distance from equilibrium. plies that a continuous loss of free energy oc-
Considering the concentration-dependency of curs as the total disorder or entropy (S) of a
∆G and assuming the reaction took place in an closed system increases. A living organism
open system (see below) where reaction prod- represents an open system which, by defini-
ucts are removed continuously, e.g., in sub- tion, can absorb energy-rich nutrients and dis-
sequent metabolic reactions, it follows that ∆G charge end products of metabolism. While the
would be a large negative value, and that the entropy of a closed system (organism + en-
reaction would persist without reaching equi- vironment) increases in the process, an open
librium. system (organism) can either maintain its en-
0
The magnitude of ∆G , which represents tropy level or reduce it using free enthalpy.
the difference between the energy levels This occurs, for example, when ion gradients
(chemical potentials) of the product P p and or hydraulic pressure differences are created
educt P e (! A), does not tell us anything about within the body. A closed system therefore has
the rate of the reaction. A reaction may be very a maximum entropy, is in a true state of chemi-
slow, even if ∆G # 0, because the reaction rate cal equilibrium, and can perform work only
0
also depends on the energy level (P a) needed once. An open system such as the body can
transiently to create the necessary transitional continuously perform work while producing
state. P a is higher than P e (! A). The additional only a minimum of entropy. A true state of
40 amount of energy required to reach this level is equilibrium is achieved in only a very few
Despopoulos, Color Atlas of Physiology © 2003 Thieme
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