DIFFERENTIAL EQUATIONS
Abbreviations are listed in
the page of components. You
can also check the description of
the rate equations
for all enzymes.
REACTIONS IN EQUILIBRIUM
The reactions catalyzed by triose phosphate isomerase and adenylate
kinase are considered to be in equilibrium, with the following
equilibrium constants:
|
(1) |
|
(2) |
Their numerical values are listed in
the page of parameters.
CONSERVATION RELATIONSHIPS
Two conservation relationships hold:
|
(3) |
|
(4) |
POOL OF TRIOSES
The equilibrium constant of triose phosphate isomerase,
eq. (1),
can be used to eliminate one variable, by defining the
pool [GAP]+[DHAP].
The individual differential equations for DHAP and GAP are
|
|
(5) |
and
|
|
(6) |
so the differential equation for the pool is:
|
|
(7) |
Using the equilibrium constant,
eq. (1),
eqs. (5)
and (6)
can be rewritten as
eqs. (13.5)
and (13.9).
CONCENTRATIONS OF THE ADENYLATE SYSTEM
The concentrations of adenylates can be calculated, for a given ratio
|
|
(8) |
from the conservation
eq. (4)
and the equilibrium constant of adenylate kinase,
eq. (2).
After some algebraic manipulation, they result:
|
|
(9) |
|
|
(10) |
|
|
(11) |
DIFFERENTIAL EQUATIONS OF THE MODEL
The response of the system,
|
|
(12) |
is calculated by integrating the following
set of equations:
|
|
(13.1) |
|
|
(13.2) |
|
|
(13.3) |
|
|
(13.4) |
|
|
(13.5) |
|
|
(13.6) |
|
|
(13.7) |
|
|
(13.8) |
|
|
(13.9) |
|
|
(13.10) |
|
