Experimental Test of the Pulse Perturbation Method for Determining Causal Connectivities of Chemical Species in a Reaction Network

60 DETERMINATION OF COMPLEX REACTION MECHANISMS

Fig. 6.3 Relative variations of several concentrations after a pulse of G6P. (From [1].)

(slightly higher), G3P, 3PG, and F6P (slightly lower). These small differences were within errors of measurement and are therefore not significant. In this experiment the measurements of F1,6BP are reliable. The intercepts of successive curves, in order of amplitudes, support the same propagation order as that of the maximum relative concentration: the relaxation curve of DHAP crosses that of F1,6BP before G3P and 3PG intercept DHAP.

The responses to a pulse of DHAP are plotted in fig. 6.5. The maximum response is that of F1,6BP. The maximum of the perturbed species DHAP is next in amplitude followed by G3P and 3PG. G6P and F6P have within experimental error no response. In contrast to the ordering of the amplitudes, the maximum of the DHAP deviation occurs in time before that of the maximum of the F1,6BP deviation. A pulse of G3P brings a response only from DHAP. There are no responses from a pulse of 3PG.

In recording the responses from a pulse of NADH we plot absolute concentrations versus. time (fig. 6.6), since there are positive and negative responses. G3P shows a significant positive response, the remainder are negative. The ordering of extremes in time is: F1,6BP, G3P, G6P, and 3PG.

Fig. 6.4 Relative variations of several concentrations after a pulse of F1,6BP. (From [1].)

Fig. 6.5 Relative variations of several concentrations after a pulse of DHAP. (From [1].)

Now we come to an interpretation of these experimental results. The measurements are of limited precision but adequate for a useful analysis. In this analysis we made a point of sequestering ourselves as much as possible from prior available information in order to establish a severe test of the pulse method. In fact, we first assigned random numbers to the chemical species, and then repeated the analysis with the known names of the species. The conclusions were not different and hence for ease of presentation we use the chemical names. We could not detect GAP and 1,3-bisphosphoglycerate. Further, we assumed DHAP and GAP to be in rapidly established equilibrium, which we confirmed by experiment. The ratio of DHAP to GAP was found to be close to the equilibrium constant of the isomerization, 0.045. The equilibrium is way on the side of DHAP, and therefore the concentration of GAP is quite small and not measurable. A number of features of the reaction pathway can be deduced from the experiments with a pulse of G6P. Strong propagation to F6P suggests that this species follows G6P; F6P is the first species to respond to the pulse. The pulse of G6P propagates next to DHAP, which follows F6P in the pathway.

The most damped responses to a pulse of G6P were those of 3PG and G3P; these two species may therefore follow DHAP or they may participate in one or more irreversible reactions preceding G6P. We shall see that we can distinguish between these

Fig. 6.6 Absolute variations of several concentrations after a pulse of NADH. The dotted line is the sum of variations of F1,6BP, G3P, and 3PG. (From [1].)

62 DETERMINATION OF COMPLEX REACTION MECHANISMS

two possibilities. Pulses of F1,6BP (fig. 6.4) showed that it must be an intermediate between F6P and DHAP. DHAP displayed the strongest response to these pulses, whereas propagation to G6P and F6P is small. This result suggests that an irreversible reaction occurs between F6P and F1,6BP. Pulses of DHAP resolve further issues. The response of F1,6BP is strong and quick and the amplitude of its maximum is larger than that of DHAP. This suggests that the stoichiometry of the transition from F1,6BP to DHAP is not 1:1, that these two species are connected by fast reactions, and that the equilibrium constant, with F1,6BP as reactant, must be low (reported values are 0.069 mM). The maximum relative deviation of F1,6BP is approximately twice that of DHAP, and we conclude that two molecules of DHAP are formed from one molecule of F1,6BP, as one would conclude from a knowledge of the molecules and conservation of mass. (Compare with the example in fig. 5.7, the reaction 2X2 → X3, and eq. (5.17).) G3P and 3PG respond similarly, with low intensity. If these two species were located before G6P, then their responses to a DHAP pulse should not be detectable; remember that propagation of G6P pulses to DHAP is strong. The concentrations of G6P and F6P vary hardly at all, indicating again that irreversible reactions must be present. Since the response of F1,6BP to DHAP is strong, such irreversible reactions must precede F1,6BP, in agreement with the F1,6BP pulse results.

3PG does not respond to a pulse of G3P and vice versa. These species could be separated by slow and/or irreversible reactions, but this hypothesis is not compatible with experiments in which the responses of these two species are similar, for example fig. 6.5. Thus these two species have a common precursor, but neither is a precursor of the other. Hence a bifurcation of the reaction chain into two branches must occur and one species is on one branch and the other species on the other branch. There is no response of any species to a pulse of 3PG, which shows that it is a terminal species produced by either several or irreversible reactions, as these two possibilities would prevent the pulse from propagating upstream. A slight response of DHAP is obtained from a pulse of G3P, which indicates that these two species are connected by few and reversible reactions.

Additional evidence for two branches in this reaction system is obtained from experiments with pulses of NADH (fig. 6.6). The deviation in G3P is positive but that of 3PG negative. We can explain that by assuming that NADH is an activator or a substrate in the branch with G3P and an inhibitor or product in the branch with 3PG. The sum of the deviations of F1,6BP, G3P, and 3PG is close to zero (see the dotted line in fig. 6.6), which we interpret as follows: NADH elicits an overall activation on the two branches leading to 3PG and G3P which increases the sum of the concentrations of these two species. The concentration of the common precursor decreases by the same amount. DHAP follows F1,6BP and therefore DHAP is that precursor. However, the response of DHAP to a pulse of NADH was too small to measure; variations in DHAP propagate quickly to F1,6BP, and hence this species shows a negative deviation. F1,6BP and DHAP are close to equilibrium.

From all these deductions the connectivities of chemical species and a reaction pathway can be inferred (fig. 6.7). G6P is transformed into F6P, with some reversibility in that step. F6P in turn is transformed irreversibly into F1,6BP, which subsequently produces two molecules of DHAP in a fast reaction that is close to equilibrium. At this point in the reaction pathway a bifurcation occurs into two branches, one leading to G3P the other to 3PG. NADH is involved as effector or substrate on the branch producing G3P, and as an inhibitor or substrate on the branch producing 3PG. From the

Fig. 6.7 Proposed reaction scheme based on experiments. Dashed lines with circles indicate that activation (+) or inhibition (−) maybe effected by a metabolite either as a substrate or as a product, or as an effector. PEP, phosphoenolpyruvate. (From [1].)

determined connectivities of the reaction pathway in fig. 6.7 and the known chemistry of the individual species, much of the reaction mechanism can be established. From other experiments we determined that phosphoenolpyruvate (PEP) is an inhibitor of the enzyme PFK, which catalyzes the reaction of F6P to F1,6BP.

We see that the pulse method described in the previous chapter and applied in experiments in this chapter yields causal reaction connectivities, reaction pathways, and reaction mechanisms. The global structure of the reaction network is obtained by piecing together local connectivities. The number of species to be measured depends on the system, but not necessarily all species require pulsing. The concentrations of the species need to be measured in time, but since only the location and amplitude of the maximum response of a species to a pulse is required, only a modest number of measurements are needed. Frequently reaction orders and sometimes rate coefficients also become available.

For the application of the pulse method to an unknown reaction system we would of course use all information available, which we resisted in this test example. The pulse method does not require the pulsing of each reactant species. We did not perturb F6P but showed its connectivities from pulses of G6P and F1,6BP. Further, we did not measure NADH (although it is easy to do so spectroscopically), but pulses of this species showed its connectivities in the reaction system. Reactions that are fast compared with others may be difficult to detect because responses of more than one species may occur