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<h1 class="top">Computer Simulation and Drug Design</h1>
<p class="header">This page contains the full text of the following chapter: Athel Cornish-Bowden and Robert Eisenthal (2000) <q>Computer Simulation as a Tool for
Studying Metabolism and Drug Design</q>, pp. 165–172 in <a href="kluwer.htm"><cite>Technological and Medical Implications of Metabolic Control Analysis</cite></a>
(ed. Athel Cornish-Bowden and María Luz Cárdenas), Kluwer Academic Publishers,
Dordrecht, The Netherlands
<h2 class="framed">
<a name="1"></a>1 Introduction
</h2>
<div class="sidebar-wide">
<p class="in-sidebar">1. <a href="#1">Introduction</a>
<p class="in-sidebar">2. <a href="#2">Use of inhibitors as pesticides</a>
<p class="in-sidebar">2.1 <a href="#2">Depressing fluxes</a>
<p class="in-sidebar">2.2 <a href="#22">Increasing metabolite concentrations</a>
<p class="in-sidebar">3. <a href="#3">Usefulness of metabolic simulation</a>
<p class="in-sidebar">3.1 <a href="#3">Do the results go beyond what is qualitatively obvious?</a>
<p class="in-sidebar">3.2 <a href="#32">Are they of any practical significance?</a>
<p class="in-sidebar">3.3 <a href="#33">Can they be trusted?</a>
<p class="in-sidebar">4. <a href="#4">Conclusion</a>
</div>
<p>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.
<div class="sidebar-medium">
<p class="ref-in-sidebar">Bakker, B. M., Michels, P. A. M., Opperdoes, F. R. & Westerhoff, H. V. (1997)
Glycolysis in bloodstream form <i>Trypanosoma brucei</i> can be understood in terms of the kinetics of the glycolytic enzymes,
<cite><acronym title="Journal of Biological Chemistry">J. Biol. Chem.</acronym></cite>
<strong>272,</strong> 3207–3215
<p class="ref-in-sidebar">Garfinkel, D. & Hess, B. (1964) Metabolic control mechanisms. vii. A detailed computer model of the glycolytic pathway in ascites cells,
<cite><acronym title="Journal of Biological Chemistry">J. Biol. Chem.</acronym></cite>
<strong>239,</strong> 971–983
<p class="ref-in-sidebar">Mendes, P. (1993) Gepasi: a software package for modelling the dynamics, steady states and control of biochemical and other systems,
<cite><acronym title="Computer Applications in the Biosciences">Comp. Appl. Biosci.</acronym></cite>
<strong>9,</strong> 563–571
<p class="ref-in-sidebar">Sauro, H. M. (1993) SCAMP: a general-purpose simulator and metabolic control analysis program,
<cite><acronym title="Computer Applications in the Biosciences">Comp. Appl. Biosci.</acronym></cite>
<strong>9,</strong> 441–450
</div>
<p>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 <a href="kluwer.htm#ch16">Chapter 16</a> 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
<i>Trypanosoma brucei,</i> 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 <cite><acronym title="et alii (= and others)">et al.</acronym></cite> (1997) to construct
and validate a computer model of trypanosomal glycolysis. If we add to this the fact that <i><acronym title="Trypanosoma brucei">T. brucei</acronym></i> 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.
<p>In this chapter, therefore, we use glycolysis in <i><acronym title="Trypanosoma brucei">T. brucei</acronym></i> as a system to examine three questions
about computer simulation:
<ol>
<li>Can it lead to conclusions that would not be (qualitatively) obvious to any biochemist just from visual inspection of the metabolic pathway?
<li>If conclusions that are not obvious can be generated, are these of any practical importance, for example do they have any implications about which strategies
for drug design are likely to work?
<li>Can such conclusions be trusted, i.e. is there any independent reason to believe that the predictions that one could make from a computer model are valid?
</ol>
<div class="centred"><h4><a name="f1"></a><img src="images/eise31.gif" width="482" height="478" alt="Metabolic scheme"></h4></div>
<p class="legend"><strong>Fig. 1.</strong> Schematic representation of glycolysis in <i>Trypanosoma brucei.</i> 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
<a href="kluwer.htm#ch17">Chapter 17</a> 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.
<div class="sidebar-medium">
<p class="ref-in-sidebar">Eisenthal, R. & Cornish-Bowden, A. (1998) Prospects for antiparasitic drugs. The case of <i>Trypanosoma brucei,</i> the causative agent of African sleeping sickness,
<cite><acronym title="Journal of Biological Chemistry">J. Biol. Chem.</acronym></cite>
<strong>273,</strong> 5500–5505
</div>
<p>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.
<h2 class="framed">
<a name="2"></a>2 Use of inhibitors as pesticides
<br><small>2.1 Depressing fluxes</small>
</h2>
<p>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 <i>in vitro,</i> when reactant concentrations are typically held constant by the experimenter, but quite another matter to
obtain correspondingly effective inhibition <i>in vivo.</i> Quite apart from the well understood problem of delivering the inhibitor to the target enzyme
<i>in vivo,</i> 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 <i>in vivo.</i>
<p>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 <a href="kluwer.htm#ch17">Chapter 17</a> of this book Bakker
and colleagues discuss a different case that is particularly relevant to <i><acronym title="Trypanosoma brucei">T. brucei</acronym>,</i> and we shall return
to this later.
<h3 class="framed">
<a name="22"></a>2.2 Increasing metabolite concentrations
</h3>
<div class="sidebar-medium">
<p class="ref-in-sidebar">Boocock, M. R. & Coggins, J. R. (1983) Kinetics of inhibition of 5 - enolpyruvylshikimate - 3 - phosphate synthase
by glyphosate,
<cite><acronym title=" FEBS (Federation of European Biochemical Societies) Letters">FEBS Lett.</acronym></cite>
<strong>154,</strong> 127–133
<p class="ref-in-sidebar">Cornish-Bowden, A. (1986) Why is uncompetitive inhibition so rare?
<cite><acronym title=" FEBS (Federation of European Biochemical Societies) Letters">FEBS Lett.</acronym></cite>
<strong>203,</strong> 3–6
</div>
<p>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
<i>in vitro</i> 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 <a href="#2">Section 2.1</a>), 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).
<h2 class="framed">
<a name="3"></a>3 Usefulness of metabolic simulation
<br><small>3.1 Do the results go beyond what is qualitatively obvious?</small>
</h2>
<div class="sidebar-medium">
<p class="ref-in-sidebar">Bakker, B. M., Michels, P. A. M., Opperdoes, F. R. & Westerhoff, H. V. (1997)
Glycolysis in bloodstream form <i>Trypanosoma brucei</i> can be understood in terms of the kinetics of the glycolytic enzymes,
<cite><acronym title="Journal of Biological Chemistry">J. Biol. Chem.</acronym></cite>
<strong>272,</strong> 3207–3215
<p class="ref-in-sidebar">Eisenthal, R. & Cornish-Bowden, A. (1998) Prospects for antiparasitic drugs. The case of <i>Trypanosoma brucei,</i> the causative agent of African sleeping sickness,
<cite><acronym title="Journal of Biological Chemistry">J. Biol. Chem.</acronym></cite>
<strong>273,</strong> 5500–5505
<p class="ref-in-sidebar">Mendes, P. (1993) Gepasi: a software package for modelling the dynamics, steady states and control of biochemical and other systems,
<cite><acronym title="Computer Applications in the Biosciences">Comp. Appl. Biosci.</acronym></cite>
<strong>9,</strong> 563–571
<p class="ref-in-sidebar">Sauro, H. M. (1993) SCAMP: a general-purpose simulator and metabolic control analysis program,
<cite><acronym title="Computer Applications in the Biosciences">Comp. Appl. Biosci.</acronym></cite>
<strong>9,</strong> 441–450
</div>
<p>When Bakker <cite><acronym title="et alii (= and others)">et al.</acronym></cite> (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
<cite><acronym title="et alii (= and others)">et al.</acronym></cite> (1997) that the four relationships existed we did not supply
this information to Gepasi.
<p>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 <acronym title="Oxidized nicotinamide adenine dinucleotide">NAD<sup>+</sup></acronym> +
<acronym title="Reduced nicotinamide adenine dinucleotide">NADH</acronym> pool in the glycosome), but even with the pathway presented anonymously as
in <a href="#f1">Fig. 1</a> these three can be recognized very quickly. A computer program is certainly not necessary for this.
<p>The fourth relationship, involving all those metabolites represented in <a href="#f1">Fig. 1</a> by black squares, is very different from the first three:
it is complicated even to express as an algebraic equation (see Bakker <cite><acronym title="et alii (= and others)">et al.</acronym>,</cite>
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).
<p>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.
<h3 class="framed">
<a name="32"></a>3.2 Are they of any practical significance?
</h3>
<p>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 <i>in vivo</i> is that when substrate concentrations can adjust to the inhibition it can easily be overcome,
as discussed in <a href="#2">Section 2.1</a>. 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 <a href="kluwer.htm#ch17">Chapter 17</a>, an inhibitor that competes with
<acronym title="Oxidized nicotinamide adenine dinucleotide">NAD<sup>+</sup></acronym> for glyceraldehyde-3-phosphate dehydrogenase can be very effective at
inhibiting the glycolytic flux in <i><acronym title="Trypanosoma brucei">T. brucei</acronym></i> because the concentration of
<acronym title="Oxidized nicotinamide adenine dinucleotide">NAD<sup>+</sup></acronym> 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.
<div class="sidebar-medium">
<p class="ref-in-sidebar">Eisenthal, R. & Cornish-Bowden, A. (1998) Prospects for antiparasitic drugs. The case of <i>Trypanosoma brucei,</i> the causative agent of African sleeping sickness,
<cite><acronym title="Journal of Biological Chemistry">J. Biol. Chem.</acronym></cite>
<strong>273,</strong> 5500–5505
</div>
<p>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 <a href="#f1">Fig. 1</a> 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 <acronym title="Oxidized nicotinamide adenine dinucleotide">NAD<sup>+</sup></acronym> and NADH involved in more obvious relationships, one
realizes that there are extremely few metabolites in the cytosol, glycosome or mitochondrion of <i><acronym title="Trypanosoma brucei">T. brucei</acronym></i> 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.
<h3 class="framed">
<a name="33"></a>3.3 Can they be trusted?
</h3>
<p>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.
<p>In their original simulation of glycolysis in <i><acronym title="Trypanosoma brucei">T. brucei</acronym></i> Bakker
<cite><acronym title="et alii (= and others)">et al.</acronym></cite> (1997) assumed that under anaerobic conditions glycerol kinase followed
the rate equation obtained from measurements <i>in vitro,</i> 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 <a href="#f1">Fig. 1</a>.) 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 <cite><acronym title="et alii (= and others)">et al.</acronym></cite> (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.
<div class="centred"><h4><img src="images/eise32.gif" width="450" height="361" alt="Graph of efflux ratio as a function of oxygen concentration"></h4></div>
<p class="legend"><strong>Fig. 2</strong> 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.
<div class="sidebar-wide">
<p class="ref-in-sidebar">Bakker, B. M., Michels, P. A. M., Opperdoes, F. R. & Westerhoff, H. V. (1997)
Glycolysis in bloodstream form <i>Trypanosoma brucei</i> can be understood in terms of the kinetics of the glycolytic enzymes,
<cite><acronym title="Journal of Biological Chemistry">J. Biol. Chem.</acronym></cite>
<strong>272,</strong> 3207–3215
<p class="ref-in-sidebar">Eisenthal, R. & Cornish-Bowden, A. (1998) Prospects for antiparasitic drugs. The case of <i>Trypanosoma brucei,</i> the causative agent of African sleeping sickness,
<cite><acronym title="Journal of Biological Chemistry">J. Biol. Chem.</acronym></cite>
<strong>273,</strong> 5500–5505
<p class="ref-in-sidebar"><a name="reis85"></a>Eisenthal, R. & Panes, A. (1985) The aerobic/anaerobic transition of glucose metabolism in <i>Trypanosoma brucei,</i>
<cite><acronym title=" FEBS (Federation of European Biochemical Societies) Letters">FEBS Lett.</acronym></cite>
<strong>181,</strong> 23–27; corrigendum
<cite><acronym title=" FEBS (Federation of European Biochemical Societies) Letters">FEBS Lett.</acronym></cite>
<strong>190,</strong> 18 (1985)
</div>
<p>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 <a href="kluwer.htm#ch4">Chapter 4</a> of this book. Even though the model of
Bakker <cite><acronym title="et alii (= and others)">et al.</acronym></cite> (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.
<h2 class="framed">
<a name="4"></a>4 Conclusion
</h2>
<p>The results that we have presented, together with those of Bakker and colleagues (<a href="kluwer.htm#ch17">Chapter 17</a>) 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.
<p class="acknowledgements">This work was supported by the Alliance programme for collaboration between France and the United Kingdom under the auspices of
<em>l’Agence pour l’Accueil des Personnalités Etrangères</em> and the British Council.
<div class="sidebar-tail">
<p class="in-tail">
Page created on 27 February 2000<br>
Last update: 22 December 2008<br>
Last significant update: 28 October 2008<br>
<em>Comments to <a href="mailto:acornish@ifr88.cnrs-mrs.fr">Athel Cornish-Bowden</a></em><br>
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