This page contains the full text of the following chapter: Athel Cornish-Bowden and Robert Eisenthal (2000) Computer Simulation as a Tool for
Studying Metabolism and Drug Design
, pp. 165–172 in Technological and Medical Implications of Metabolic Control Analysis
(ed. Athel Cornish-Bowden and María Luz Cárdenas), Kluwer Academic Publishers,
Dordrecht, The Netherlands
Computer simulation has a long history as a tool for the study of metabolism, starting with the pioneering work of Garfinkel & Hess (1964), but it has still to realize its full potential. The early programs were designed by experts for experts to use, they made heavy demands on computer resources, and they depended on large amounts of experimental kinetic information about the component enzymes that was available only in very small part, forcing the user to guess the values of many parameters. There have also sometimes been suggestions that the conclusions that come from computer simulation are either obvious from inspection of the metabolic pathway, or else of no practical usefulness. Even when these pitfalls have been avoided it has not always been clear how far the results from the computer correspond with reality and hence how far they can be trusted.
Most of these criticisms can be set aside in the present context. Modern programs such as Gepasi (Mendes, 1993) and SCAMP (Sauro, 1993) are easy to use, run on universally available equipment, and powerful enough to handle most of the problems likely to interest the metabolic simulator. (These programs are discussed from a general point of view in Chapter 16 in this book.) The problem of obtaining adequate kinetic data, however, still exists for many systems, as it is unfortunately rare for kinetic equations to be available for most of the enzymes in a pathway, and even rarer for these equations to be based on measurements made under reversible conditions in the presence of all substrates, products and other relevant metabolites. Thanks to the efforts of Opperdoes and colleagues over a long period, there now exists an important exception to this generalization, as high-quality data are now available for most of the enzymes of glycolysis in the bloodstream form of Trypanosoma brucei, including all of those likely to be influential in controlling glycolytic flux in this organism. Not only do the equations refer to measurements made under reversible conditions (in most cases), but nearly all were made in the same laboratory under comparable conditions. The availability of the body of kinetic information allowed Bakker et al. (1997) to construct and validate a computer model of trypanosomal glycolysis. If we add to this the fact that T. brucei is the agent responsible for African sleeping sickness, a disease of major medical and economic importance, it becomes clear that it offers an ideal opportunity for exploring the potential value of computer simulation as a means of arriving at a better understanding of metabolism and hence a more rational approach to drug design.
In this chapter, therefore, we use glycolysis in T. brucei as a system to examine three questions about computer simulation:
Fig. 1. Schematic representation of glycolysis in Trypanosoma brucei. Metabolites are represented by squares, and each set of squares connected by grey lines represents a single pool of a metabolite that participates in more than one process (e.g. ATP in the glycosome participates in the reactions of hexokinase, phosphofructokinase, pyruvate kinase and myokinase). All of the stoicheiometric information that would be available to a computer program is thus shown explicitly in the Figure. A less anonymous representation of the pathway is given as Fig. 1 of Chapter 17 by Bakker and colleagues, but note that they illustrate a later version of the model that is not identical in all respects with the one shown here.
We shall try to show that all three of these questions can be answered in the affirmative. The details of our simulations of this system may be found elsewhere (Eisenthal & Cornish-Bowden, 1998); here we are concerned with the general aspects. To focus attention on these the system is shown in a highly schematic way in Fig. 1, and before examining it in any specific way it may be useful to ask whether it is obvious from inspection which metabolites are involved in stoicheiometric relationships that might prevent their concentrations from varying freely, and second whether it is obvious which of the various processes shown would make the most promising target for action of an inhibitor intended to kill the organism. Readers who consider the answers to both questions to be indeed obvious may find the remainder of this chapter redundant.
There are two distinct ways in which inhibitors can be used to interfere with the metabolism of an undesirable organism. The more obvious is to decrease a metabolic flux to the point where the organism is no longer viable. In many cases this is likely to have disappointing results: it is easy to design a substrate analogue that inhibits an enzyme in vitro, when reactant concentrations are typically held constant by the experimenter, but quite another matter to obtain correspondingly effective inhibition in vivo. Quite apart from the well understood problem of delivering the inhibitor to the target enzyme in vivo, there is an equally important problem that is commonly ignored. Substrate analogues normally act as competitive inhibitors (if they do not act as competing substrates) and competition works both ways: anything that can compete with a substrates is something that the substrate can compete with. What this means that unless the substrate concentration is constrained to remain constant by independent considerations a modest increase is sufficient to overcome the effects of a competitive inhibitor completely. For example, if the substrate concentration in the absence of inhibition is equal to the Michaelis constant of the enzyme that consumes it, then doubling this concentration is sufficient to nullify all effects of a competitive inhibitor present at a concentration equal to its inhibition constant. At lower concentrations of inhibitor correspondingly lower increases in substrate concentration suffice. The converse is also true, of course, but that is less important, because very high concentrations of substrate analogues are not easy to achieve in vivo.
If the substrate concentration is independently constrained then competitive inhibition cannot be nullified so easily, and there are some circumstances where this will be true. For example, if the substrate in question is a metabolite like glucose that is maintained at a high and constant concentration by regulatory mechanisms, then it is not likely to change much in the presence of a competitive inhibitor. In Chapter 17 of this book Bakker and colleagues discuss a different case that is particularly relevant to T. brucei, and we shall return to this later.
The less obvious effect of an inhibitor is to increase the substrate concentration in conditions of constant rate. As it is extremely rare for experiments in vitro to be done at constant rate, the concentrations normally being fixed by the experimenter in such experiments, this effect is given little attention, but it can be of profound importance, being responsible, for example, for the enormous commercial success of the herbicide Roundup, which produces several hundredfold increases in the shikimate concentration in the cells of treated plants. However, just as the increase in substrate concentration needed to nullify the effect of a competitive inhibitor is typically small (see Section 2.1), the effect that such an inhibitor has on the concentration of the substrate at constant rate is correspondingly small. By contrast, inhibition with a significant uncompetitive component may generate enormous effects on substrate concentrations at constant rate (Cornish-Bowden, 1986), and it is not surprising, therefore, to find that Roundup is indeed an uncompetitive inhibitor of an enzyme in the shikimate pathway (Boocock & Coggins, 1983).
When Bakker et al. (1997) first studied the trypanosome model the stoicheiometric analysis made by the program Scamp (Sauro, 1993) reported the existence of four distinct conservation relationships between the metabolite concentrations. When we subsequently implemented the model in a different program, Gepasi (Mendes, 1993), it identified the same four relationships. This can be regarded as independent confirmation because although we were aware from the paper of Bakker et al. (1997) that the four relationships existed we did not supply this information to Gepasi.
Three of the four relationships are indeed obvious from general biochemical principles (the total adenine nucleotide pool inside the cytosol is conserved, as well as the separate adenine nucleotide pool and the NAD+ + NADH pool in the glycosome), but even with the pathway presented anonymously as in Fig. 1 these three can be recognized very quickly. A computer program is certainly not necessary for this.
The fourth relationship, involving all those metabolites represented in Fig. 1 by black squares, is very different from the first three: it is complicated even to express as an algebraic equation (see Bakker et al., 1997 or Eisenthal & Cornish-Bowden, 1998), and once it is known it remains far from straightforward to rationalize it. (It links that part of the pool of phosphate groups in the glycosome, together with dihydroxyacetone phosphate and glycerol 3-phosphate in the cytosol, that is not accounted for by entry of inorganic phosphate and exit of 3-phosphoglycerate).
It seems fair to conclude that the identification of the fourth stoicheiometric constraint establishes that computer analysis can supply information about the structure of a pathway that is not obvious from inspection or from general biochemical principles. However, it does not establish that the knowledge gained in this way has any practical importance. This question we shall now examine.
Stoicheiometric analysis can easily be mistaken for the most academic and mathematical of topics in metabolism, but in reality it has profound practical implications. The reason why competitive inhibitors are often ineffective in vivo is that when substrate concentrations can adjust to the inhibition it can easily be overcome, as discussed in Section 2.1. However, this argument does not apply if the substrate of the inhibited enzyme forms part of a conservation system, because its concentration cannot then vary freely. As Bakker and colleagues discuss in Chapter 17, an inhibitor that competes with NAD+ for glyceraldehyde-3-phosphate dehydrogenase can be very effective at inhibiting the glycolytic flux in T. brucei because the concentration of NAD+ cannot change very much in response. They were right to point out, therefore, that we previously overlooked this aspect of conservation relationships, and this weakens our argument (Eisenthal & Cornish-Bowden, 1998) that using inhibitors to depress the glycolytic flux is unlikely to be a useful strategy for combatting the parasite. On the other hand it strengthens the main argument that we want to advance here, namely that far from being an academic topic stoicheiometric analysis is an essential component of metabolic investigation. It is perhaps worth pointing out also that enormous inhibitor concentrations were needed for obtaining the significant effects on flux from inhibiting glyceraldehyde-3-phosphate dehydrogenase and phosphoglycerate kinase that Bakker and colleagues report: an inhibitor concentration 100 times the inhibition constant may be achievable with very careful design of the inhibitor but it is hardly realistic for the substrate analogues that compose most of the known competitive inhibitors.
Stoicheiometric considerations are even more important if the objective of inhibition is to raise a metabolite concentration to toxic levels, as in the case of Roundup. At first sight there are many enzymes or transport processes in Fig. 1 that could serve as the target of an uncompetitive inhibitor intended to raise the substrate concentration. On closer inspection, however, once one considers both the metabolites involved in the fourth stoicheiometric relationship (the black squares), and the others such as NAD+ and NADH involved in more obvious relationships, one realizes that there are extremely few metabolites in the cytosol, glycosome or mitochondrion of T. brucei that have concentrations that can vary freely. Of these several (glucose, inorganic phosphate and glycerol) are rendered unsuitable by additional considerations that we shall not discuss here, and pyruvate is left as the unique candidate for a metabolite whose concentration might be raised to toxic levels. We have discussed this in more detail elsewhere (Eisenthal & Cornish-Bowden, 1998); the point here is that without the stoicheiometric information one would be unlikely to place the pyruvate transporter very high on the list of potential drug targets.
Of course, none of this will be taken seriously by experimenters who do not trust the results of computer simulation, and given the large amount of kinetic information that needs to be included in a model, not all of it based on reliable measurements (some of it often based on no measurements at all), the mistrust is not without foundation. We need to show, therefore, that a computer model can accurately reproduce known behaviour.
In their original simulation of glycolysis in T. brucei Bakker et al. (1997) assumed that under anaerobic conditions glycerol kinase followed the rate equation obtained from measurements in vitro, but they assumed that it had no activity under aerobic conditions, as this was the only way to ensure a zero efflux of glycerol under aerobic conditions. (Glycerol efflux is represented by the left-hand arrow at the bottom of Fig. 1.) However, as we had experimental reason to believe that glycerol efflux does occur in aerobic conditions, we did not assume this discontinuity in the properties of glycerol kinase but instead examined how well the model could account for the measured ratio of glycerol and pyruvate effluxes during the transition from anaerobic to aerobic conditions (Eisenthal & Panes, 1985). The result (Fig. 2) is that the model predicts the observed behaviour with virtually best-fit precision. In other words the model of Bakker et al. (1997) can accurately account for observations that were not taken into account when it was constructed. We believe that this result gives good reason to believe the other predictions that the model makes, most of which have not yet been tested experimentally.
Fig. 2 The transition from anaerobic to aerobic conditions. The points show experimental measurements by Eisenthal & Panes (1985) of the ratio of glycerol and pyruvate effluxes as a function of oxygen concentration. The curve is not a best fit to these points but shows the behaviour calculated independently from the computer model. In the original version of this Figure (Fig. 2 of Eisenthal & Cornish-Bowden, 1998) the measurements continue up to about 0.23 mM.
Some caution remains necessary, of course, as one must distinguish between genuine predictions made before experiments are done and calculations made afterwards, whether independently or not, an important distinction emphasized by Bailey in Chapter 4 of this book. Even though the model of Bakker et al. (1997) was developed without taking the data of Eisenthal & Panes (1985) into account it is unlikely that we should have reported the comparison with the same enthusiasm if the agreement had proved to be poor.
The results that we have presented, together with those of Bakker and colleagues (Chapter 17) indicate that in ideal conditions computer simulation is capable of providing information that is qualitatively different from what may appear obvious from inspection, is of potential practical value for the design of new pharmaceuticals, and is reliable. Most systems of practical importance lack the extensive body of excellent experimental data that were needed for constructing the trypanosome model, and thus are much further from ideal conditions than those considered here. However, this will certainly improve in the future, and we may therefore expect computer simulation to become an essential tool for achieving success in drug development and other biotechnological applications.
This work was supported by the Alliance programme for collaboration between France and the United Kingdom under the auspices of l’Agence pour l’Accueil des Personnalités Etrangères and the British Council.
