KINETICS ON THE MICROBIAL SCALE
49
|
Z = "ACTIVATED" |
COUPLING ENZYME | |
|
( I ) |
R∣t∙∣ + z = |
(ZR)iti |
|
(2) |
Oi +(ZR)itl = |
∣Z0∣it∣ + Ri |
|
(3) |
∣zo∣itl+ p = |
IZPi + oitl |
(4) ∣ZP} * ADP = Z t ATP + H2O
FIG. 4- A POSSIBLE MECHANISM FOR PHOSPHATE
FIXATION IN THE ELECTRON TRANSPORT
PATHWAY
algebra of the kinetic relations. Clearly we are going to end up with a
large number of parameters “to be determined" in the expressions we
will derive, simply because of the large number of reactions and elemen-
tary steps. The usual objective of “fitting the data to the theory” and
evaluating the constants is obviously out of the question. The best we
hope for is a set of equations which we can subject to certain tests.
These will necessarily be of the plausibility type, i. e., can we find a set
of physically meaningful parameters such that the mathematical system
is a reasonable model of the living system.
In Figure 5 I outline the procedure for obtaining the rate equation for
ALL SYMBOLS NOW REPRESENT CONCENTRATIONS
(THE K,∙j ARE EQUILIBRIUM CONSTANTS)
<f∣>i ∙^{'⅛0lΦij- b⅛(o*⅛)
THE fij ARE FORWARD
rate constantsithe
b*j ARE REVERSE RATE
CONSTANTS
*(J0b∣i.∣l ∙ E°. (CONSTANT 1
,Rl,∣ ANOTHE CONSTANTS kij , 11∣ , Ц,, E°
(2) (rt)i .∑(fij(θJ)ijiRitl - bijRi (Jθ)ijit∣)
(⅞)j .∑uj(Jo)ijitl - bij(J)ij oitl I
AT STEADY STATE: (rι)i∙(⅞)∣∙ ( Γj )∣
CONSERVATION OF ENZYME i :(Ej) ♦ ),j ♦ •••
(3) r . f* (OiXRld) - b* (OjdXRi)
WHERE f*,b*∣ ARE FUNCTIONS OF (Aj).(O∣). R∣ .O1
FIG.5-RATE EQUATIONS ANO ALGEBRA FOR TYPICAL STEP IN A PATHWAY