The name is absent

a single “overall” reaction. First we assume the catalyst modification
steps are at equilibrium. Then we write reversible rate equations for each
primary step; we employ the steady state hypothesis along with the
conservation of enzyme i, to eliminate the intermediate unknowns; and
finally, we write the resulting rate in terms of reactant-product concentra-
tions and the pseudo-constants.

For the redox reaction in which ATP is produced, a similar process
will yield f* and b* which depend upon the concentrations of ADP,
phosphate, and ATP. The functionality will be such that the rate will
approach zero if either phosphate or ADP concentration vanishes.

Beginning in Figure 6 1 have faced the problem of determinancy in

ASSUME (O₁)_tOXYGEN, AND (R₁)₁WATER ARE FIXED INPUT PARAMETERS

EQUATIONS                    UNKNOWN INTERMEDIATES, ETC.

r= f∙∣ (Oj)(Rj₊∣)-b_j (0j₊∣)(R_j)   6    Oj  i = 2,....7       6

Oj +R∣ = Tj I =2....7      6 Rj i= 2,....7       6

r                                     I

TF                       13

Noteiinthesteady state, r= 5 r, where r is the rate of use

OF T₀ IN KREBS CYCLE

fig.6-Determinacy in the electron transport

PATHWAY

the reaction set. The facts to recall when counting unknowns and equa-
tions are that 1) the total amount of any O_i — R_i pair, namely T_i, is fixed;
2) the f*andb_i*contain only theθ_i and R₁ and constants, i. e., the unknown
catalyst concentrations have been eliminated; a similar process yields
a similar situation for the f_i and b₁ in the Krebs cycle which we see in
Figure 7; 3) the overall rate of the electron transport pathway is five
times the rate of the Krebs cycle “rotation,” because of stoichiometry;
and 4) O_x and R_x are unknowns in both the Krebs and redox systems.

We see that there is an excess in unknowns of 1. That is, if we set I₀
(fuel), O₁ (oxygen), and R₁ (water) compositions, the system is still
underdetermined by one. The difficulty stems from the cyclic structure
of the Krebs system, and is characteristic of cyclic stoichiometric
schemes. One of the intermediates (in the simplest case) I₂-I₉ must be
set in the steady state by an additional restriction. I have shown this
simplest case in Figure 8, with I₈ (Malic acid) picked as the base inter-
mediate for no good reason.

<<   5   6   7   8   9   10   >>

More intriguing information