Manchester Home Snapshots of Systems - Metabolic Control Analysis
and Biotechnology in the Post-Genomic Era





1,* & 1,2Pedro Mendes

1Institute of Biological Sciences, Cledwyn Building, University of Wales, Aberystwyth SY23 3DD, UK
2 Present address: National Center for Genome Resources, 1800-A Old Pecos Trail, Santa Fe, New Mexico 87505, U.S.A.
*Corresponding author: phone +44 161 2004492 fax +44 161 2004556, email
http://dbk.ch.umist.ac.uk/

Summary | Introduction | Assumptions in MCA | All cells are not the same | Not all organisms are the same | Moiety conservation and flux enhancement | Modelling at the right scale | Critique of top-down methods | Proton-coupled electron transport-linked phosphorylation | Large changes and MCA | The not-very Universal Method | Multi-site modulation | Active learning | Acknowledgements | References


  Summary

We provide, as requested, a personal and critical survey of some of the major limitations of the principles and applications of metabolic control analysis, with special reference to the enhancement of fluxes of biotechnological interest.

  • Experimental methods of single-cell analysis such as flow cytometry show that the implicit assumption that we study and model ensembles of identical cells is completely untenable, and that cellular heterogeneity is much greater than we normally assume.

  • A feature of the post-genomic era is the recognition that many more genes exist, and are expressed, than we had ever recognised, and that methods are being developed for the quantitative asssessment of this. Even if the individual flux-control coefficients of these gene products were each very small their enormous number means that over-simplified analyses that ignore them are very likely to lead to erroneous analyses of the true structure and organisation of a metabolic system of interest.

  • Even the assumption that the components of moiety-conserved cycles do not change their total concentrations during an experiment ignores a demonstrably large impact of this on the control structure. In the absence of compartmentation or channelling, such cycles also serve to connect segments of metabolism usually considered rather distant from each other.

  • Simplified (‘top-down’) methods in which the system structure is assumed a priori will not work for complex systems where the combinatorial explosion of possible interactions requires much more sophisticated methods for system identification.

  • Dual-inhibitor titrations can reveal direct kinetic interactions between individual catalytic activities in appropriate cases.

  • No example exists in which one can extrapolate the conventional control coefficients to provide reliable predictions about the behaviour of metabolic systems subjected to ‘large’ changes in parameters.

  • A "Universal Method" proposed for this (i) does not work when it is the end product itself which feeds back to inhibit its own production (as is usually the case in any high-yielding fermentation), and (ii) the method works even in principle only for systems in which there are no interactions between pathways, such as those involving conserved moieties such as adenine and pyridine nucleotide couples.

Metabolic contol analysis and functional genomics share the same agenda, in that they seek to relate the presence and activities of individual genes and gene products to cellular biochemistry and physiology. They can be considered to differ, however, in a philosophical sense since the former is essentially deductive in character (and as practised) while the latter is of necessity inductive, at least initially, because so many ORFs are of unknown function. Inductive methods of machine learning should prove of value in unravelling their properties.


Snapshots of Systems - Metabolic Control Analysis
and Biotechnology in the Post-Genomic Era

"So the first requirement will be for a theoretical framework in which to embed all the detailed knowledge we have accumulated, to allow us to compute outcomes of the complex interactions and to start to understand the dynamics of the system. The second will be to make parallel measurements of the behaviour of many components during the execution by the cell of an integrated action in order to test whether the theory is right. Is there some other approach? If I knew it I would be doing it, and not writing about the problem."

Sydney Brenner, 1997, in Loose Ends publ. Current Biology, London, p.73


 

Holism and reductionism, and MCA’s view of the operations of complex biochemical systems

Following its original formulation in 1973 (Heinrich & Rapoport, 1973; Heinrich & Rapoport, 1974; Kacser & Burns, 1973) as a means of understanding the contribution of the individual steps of a biochemical pathway to the values of flux and metabolite concentrations observed, some 13 years were to pass before we first surveyed (Kell & Westerhoff, 1986a; Kell & Westerhoff, 1986b) how the formalism, tools and terms of metabolic control analysis might usefully be applied to such systems in a biotechnological context. Since another such tridecennium has now elapsed, it is timely to take stock of progress, to recognise that the take-up of these methods among biotechnologists has been less than widespread, and (as requested by the Editor) to give a personal and critical review of successes, failures, problems and prospects for the use of MCA in biotechnology. In what follows, it is taken that the reader has a good working knowledge of the essential principles of MCA, as summarised for instance in (Cornish-Bowden & Cárdenas, 1990; Fell, 1992; Fell, 1996; Heinrich & Schuster, 1996; Kell et al., 1989; Kell & Westerhoff, 1986a; Ovádi, 1995) and on the Internet at http://dbk.ch.umist.ac.uk/mca_home.htm and in links therefrom. In addition, we shall concentrate on unicellular systems, implicitly those most commonly exploited to make products of biotechnological interest.

Perhaps the chief intellectual benefits of MCA have been the recognition (i) that in the steady state of a (linear) pathway where all steps are proceeding at the same rate it is nevertheless appropriate to recognise that each contributes quantitatively to the control of flux, in a manner which (for small or infinitesimal changes) can be summed to unity, (ii) that the flux-control coefficients so determined are consequently necessarily small, and (iii) that the activities of many steps must be changed simultaneously if fluxes are to be enhanced substantially. MCA thus constituted a bridge between the rather reductionistic view then prevalent (that we can understand a systems by looking at its component parts in isolation, without considering the interactions between them - see (Kell & Welch, 1991; Mendes et al., 1995)) and the holistic one (which in extremum - and in practice for many real, nonlinear, coherent, self-organising systems (Kell & Hitchens, 1983) - would hold that the whole is so much more than the sum of its parts that it is essentially pointless to consider the individual parts in isolation at all (Ho, 1998)).

Coupled to these aperçus has been the recognition that computer simulation can be a powerful tool in solving the forward problem of metabolism: given the parameters of the system (usually the external metabolite and effector concentrations and the kinetic properties of the enzymes) one can solve the relevant differential equations and predict the time course and - if such exist - the steady-state values of flux and metabolite concentrations. Software such as the program gepasi produced in aberystwyth by one of us (Mendes, 1993; Mendes, 1997; Mendes & Kell, 1998a, b) has been designed for (and indeed by) biologists (and successfully hides the mathematical details from the typical user), and given a simulation of a pathway it is easy to extract the ‘MCA properties’ such as flux- and concentration-control coefficients by numerical simulation of the effects of small changes in parameter values or analytically by differentiating the rate equations to acquire the elasticities and inverting the elasticity matrix so obtained (Fell, 1996; Fell & Sauro, 1985; Mendes, 1993; Reder, 1988; Westerhoff & Kell, 1987). The metabolic control anaysis of a system is thus normally ‘merely’ a snapshot of a typically rather restricted subset of the cellular biochemistry actually taking place in time and space.


 

Assumptions in MCA, implicit and explicit

With its concentration on small or infinitesimal changes, a domain where for (spatially) homogeneous systems its analysis is both exact and complete, MCA necessarily represents an approximation to a more complex reality, and this begs the question of how adequate this approximation is. In view of the recognition that it is but a subset of a full simulation of whatever system it is desired to simulate, it is probably unsupportable. Some other common assumptions of MCA (and its usual implementations) which will be explored later are summarised in Table 1. They include the implicit view that all cells in a suspension are the same, that it is possible to lump together large segments of metabolism without losing important knowledge of the behaviour of the overall system, and that there are ‘universal’ methods which can permit the rational optimisation of metabolic fluxes in systems of arbitrarily complex organisation.

Table 1. Some explicit and implicit assumptions of modern MCA, and some inadequacies of its usual implementations in a biotechnological context.
Assumption / Misapplication Comments / Consequences
All cells are the same Heterogeneity is very much greater than normally assumed, and this can be determined experimentally using single-cell analyses
Simple models are adequate Genome sequencing has uncovered the fact that we know the function of fewer than half of their genes, and there is evidence that almost all contribute to fitness even in laboratory conditions. Much more of metabolism is relevant to a flux than is normally recognised.
The Universal Method permits a rational approach to the optimisation of flux in any metabolic system It doesn’t work if (i) the end-product feeds back to inhibit its own synthesis, whetehr kinetically or by mass action, and/or (ii) there are interactions between pathway branches involving moiety-conserved cycles.
The coefficients of MCA determined using large changes are not too badly different from those obtained via very small parameter changes Nonlinearities, unknown interactions and the overall complexity of biological systems mean that deviation indices are reasonably small only in simple systems.


 

All cells in an axenic culture are not the same; microbial differentiation

Whilst it is rather obvious that the phenotypes of all cells in a differentiated organism are not the same (so much so that there is no such thing as a biochemically "normal" individual (Williams, 1956)), it is implicit in a standard MCA analysis that they are; in other words we tend to treat the system under study as an ensemble in the thermodynamic sense (Welch & Kell, 1986; Westerhoff & van Dam, 1987). In fact, the essence of the problem (Kell et al., 1991) is that one is trying, typically, to correlate a rate of change (v) of a certain variable with respect to the value of a certain parameter or property (p), but a correlation may be expected between the mean values and only if v is kinetically of first order with respect to p. This is completely unrealistic even for the axenic microbial cultures that are the focus of this review, and with the availability of techniques such as flow cytometry (Davey & Kell, 1996; Kell et al., 1991) it becomes possible to determine the heterogeneity of cellular properties directly. In one example of our own (Kaprelyants & Kell, 1992), the extent to which chemostat-grown (and thus as near as one can get to genuinely steady-state cultures of) Micrococcus luteus cells could take up the membrane energisation probe rhodamine 123 varied by more than 1000-fold under conditions in which uptake was fully uncoupler-sensitive and neither efflux pumps nor lack of membrane permeability were an issue. The unwanted consequence of the failure to take culture heterogeneity into account (in terms of being led to erroneous conclusions about causality and mechanism) reaches its apotheosis in the study of microbial viability/culturability (Kell et al., 1998). Such an analysis ignoring heterogeneity will also tend to mask intercellular interactions (Fuqua et al., 1996; Kell et al., 1995) such as those in which culturable cells secrete a factor necessary for the resuscitation and growth of non-growing cells of the same organism (Kaprelyants & Kell, 1993; Kaprelyants et al., 1994; Kaprelyants et al., 1999; Mukamolova et al., 1998).


 

Not all organisms are the same...

So far as the typical textbook of biochemistry is concerned, cells are inevitably taken to be essentially similar, with a great majority of their broad activities (and the ‘housekeeping’ genes which code for them) being common throughout biology (at least at the level of prokaryote, eukaryote and archaean). Specific features such as photsynthesis or nitrogen fixation are seen merely as occasional adjuncts. Our attempts to simulate metabolism seem to rely implicitly on this, and it is perhaps assumed that models have a validity beyond the sytem for which they are constructed. However, as we enter the post-genomic era, two major facts have become evident; (i) many or most ORFs code for products of unknown function (Blattner et al., 1997; Bork et al., 1998; Cole et al., 1998; Goffeau et al., 1996; Hinton, 1997; Oliver, 1996) with many being conserved but most comparatively unique (Koonin & Galperin, 1997), and (ii) large-scale, genome-wide comparisons of orthologous genes point up the prevalence of horizontal gene transfer (Forterre, 1997a; Forterre, 1997b; Koonin et al., 1997; Rivera et al., 1998) and the consequent inadequacy of gradualist views of evolution. (Note however that these analyses are to date restricted to the very small fraction (Amann et al., 1995) of cultured microbes, and that many close relative of existing taxa remain to be cultured (Kaprelyants et al., 1999; Kell et al., 1998; McVeigh et al., 1996).) Consequently, we now recognise that many more genes contribute to fitness than had previously been considered.

The major approaches to functional genomics currently being undertaken involve the systematic knocking out of individual genes seriatim; where this is being done, e.g. in S. cerevisiae (Dujon, 1998; Oliver & Baganz, 1998; Oliver et al., 1998; Teusink et al., 1998), it is found that only some 15% are ‘essential’, and the question arises as to the role of the others - do they have a very high contribution to fitness under a restricted set of conditions met only occasionally and never in the laboratory, or do they all provide a marginal contribution to fitness? At least as judged by the fact that they are both transcribed under laboratory conditions in rich media and can be shown to contribute to fitness in sensitive growth rate tests (Eisen et al., 1998; Smith et al., 1995; Smith et al., 1996; Thatcher et al., 1998), one is led to attach significance to the latter view. The mental picture which emerges then is that whilst there may be core or major blocks of primary metabolism which are important, the contribution of the rest of the cellular activities which are normally neglected is likely to be just as great or greater. Although they may be individually small they are collectively numerous (the totals of genes in E. coli, baker’s yeast and Streptomyces coelicolor A3(2) are some 4000, 6000 and 8000 respectively), and while fewer will contribute to a flux than to the overall fitness as correctly judged (Kell, 1987; Westerhoff et al., 1983) by growth rate, the emerging paradigm is of a much greater complexity and sophistication of unicellular controls than we had heretofore recognised. One example of an important (and probably excessive) simplification in common usage is that the total values of pyridine nucleotides in cellular compartments are not of particular significance.


 

Moiety conservation and flux enhancement

One aspect of metabolism that has received little attention for the purposes of flux maximisation is the existence of moiety-conserved cycles (Reich & Sel'kov, 1981). These are ubiquitous in metabolism and a few of them (e.g. NAD/NADH and ATP/ADP) act as major links between various parts of metabolism. Whilst affecting the poise of these cofactor couples can be most useful in metabolic engineering (Lopez de Felipe et al., 1998) the flux through a pathway, as seen within the MCA formalism (Hofmeyr et al., 1986), is also controlled by the total amount of conserved moieties. We have observed by computer simulation that the flux of several model pathways responds to the total amount of conserved moiety according to a bell-shaped curve. This suggests that there is an optimal amount of cofactor for a given pathway flux (and that compartmenation of pathways would be necessary to optimise them separately), otherwise the flux will be somewhat limited by the availability of the conserved moiety. To manipulate the total amount of the moiety we will thus need to target the pathways of their biosynthesis and degradation. Alternatively we could as well manipulate the number and/or affinity of moiety binding sites which modulate the amount of available (i.e. free) total moiety. The existence of large numbers of NAD binding sites may indeed be a cellular mechanism for the rapid adjustments of the available total amount of NAD (rather than a slower adjustment by increased/decreased biosynthesis). Fig. 1 depicts such a bell-shaped relation between the total amount of the moiety and the flux for a simple branched pathway in which other parameters are held constant.

Figure 1. Dependence of entry steady-state flux on the total amount of conserved moiety in a model branched pathway. The pathway simulated is shown in the inset, the arrows representing the positive direction of flux. All reactions are fully reversible, all kinetic and equilibrium constants are unity, [A] = 10, [C] = [D] = 1 such that the overall disequilibrium ratio is 0.1 on both branches.


 

On modelling at the right scale

We have traditionally treated our systems relatively simply, due in part to the difficulty of measuring everything. With the emergence of measurements of the proteome (Anderson & Anderson, 1998; Wilkins et al., 1997), the transcriptome (de Saizieu et al., 1998; DeRisi et al., 1997; schena et al., 1996; Spellman et al., 1998; Velculescu et al., 1997; Wodicka et al., 1997) and the metabolome (Oliver & Baganz, 1998; Oliver et al., 1998) we now have the ability to carry out hundreds of measurements on macromolecular and metabolic variables simultaneously. The outcomes of the pioneering studies are in many cases given in the form of lists of expression ratios for the hundreds of genes of interest, which are hard to interpret - the appropriate scale for easy understanding is not a life-sized model (Eisen et al., 1998). Treating related segments of metabolism as ‘blocks’ is one solution (Kell et al., 1989), sometimes referred to as top-down analysis (Brand, 1996; Brand, 1998; Brown et al., 1990) and is being exploited in functional genomics as the FANCY method (Oliver & Baganz, 1998; Teusink et al., 1998), but this approach fails to give a true account of the system of interest under a number of circumstances.


 

A critique of ‘top-down’ methods in which segments of metabolism are treated as one

In the early literature of MCA (Kacser & Burns, 1973) it was already proposed that one could group sequential enzymes and treat them as one unit for the purposes of control analysis. This is possible due to the summation theorem (Kacser & Burns, 1973) and the fact that the elasticity concept can be applied to groups of reactions (Kacser, 1983). Brown et al. (Brown et al., 1990) took this one step further and formally proposed the ‘top-down’ method for determining control coefficients. In this method one builds two groups of metabolic steps around (upstream and downstream of) one single intermediate metabolite. Provided that this central intermediate metabolite is the only kinetic link between the two groups of steps then one can determine the elasticites of the two groups towards that metabolite with just two single-modulation experiments. Group control coefficients can then be calculated using the connectivity and summation theorems (the assumption therefore being that no other interactions - such as feedback loops or metabolic channelling (Agius & Sherratt, 1997; Mendes et al., 1995; Ovádi, 1995) - exist between the two groups). The control coefficients thus obtained for the two groups of steps could reveal which of them has more control, e.g. as in (Simpson et al. 1998; Stephanopoulos & Simpson, 1997), where knowledge of this can allow one to vary the control structure of a pathway to improve fluxes of biotechnological interest (Simpson et al., 1995).

An attractive application of this method would be to apply it repeatedly by subdividing each group into smaller groups. This would result in the determination of the complete control structure of the pathway, each time with more resolution (hence the ‘top-down’ name). Although elegant in conception, this method is effectively impossible in practice, due to the requirement of grouping steps such that there is only one kinetic link (via the intermediate metabolite) between them. Ainscow and Brand have recently extended the method (Ainscow & Brand, 1995) such that it can be applied to the case when the groups of steps are connected by more than one metabolite. Nevertheless, for the method to work as intended one must be absolutely sure that all the kinetic links between the groups of steps are known and included in the analysis explicitly (or are unaffected by the modulations performed (Ainscow & Brand, 1998a)). Thus, one can never be sure that the coefficients determined by this method are correct as there could be extra kinetic interactions between the two groups of steps other than the ones taken into consideration. The classical method of direct determination of control coefficients by perturbation of enzyme activities is immune from this problem and so could (and should) be used to confirm the results with the top-down method - but this rather defeats the purpose of using it in the first place! (Recently, Kholodenko and colleagues have presented a combination of top-down MCA and the perturbation method which they refer to as ‘Metabolic Design Analysis’ (Kholodenko et al., 1998).) But there are extra problems when one wants to use this method in general: (i) there are several known (and certainly many more unknown) feedback loops in metabolism and (ii) many reactions include cosubstrates such as NAD/NADH or ATP/ADP which form kinetic links between steps normally considered distant. Both these reduce the number of metabolites that can be effectively used in the top-down approach to separate groups of steps. As such the method is not amenable, in general, to a true ‘top-down’ approach of measuring all control coefficients. The problems are greatly compounded by the propagation of errors and bias contingent on the measurement of elasticities (Schlosser et al., 1993; Thomas & Fell, 1995) and control coefficients (Ehlde & Zacchi, 1996; Small, 1993), and such errors may not be normally distributed (Ainscow & Brand, 1998b). We therefore find that the (correct) application of the top-down method to large, complex biosystems may be rather limited in practice, and above all dangerous if results are not validated by an independent method.

Note that this is not a critique of simplification per se, since in many cases the intrinsic dimensonality of the major blocks of a complex system of interest may well be comparatively small and the level of understanding that we require, and indeed good precision in our models (Broadhurst et al., 1997; Kell & Sonnleitner, 1995; Shaw et al., 1997), is more easily attained with small models than with large ones. But this is something that we find out afterwards, when measurements of many variables have been made and evaluated (Eisen et al., 1998), not something to build in beforehand!


 

Proton-coupled electron transport-linked phosphorylation - an example of a chanelled system, assessed using dual-inhibitor titrations

A consequence of lumping reactions together in the macroscopic way typified by the top-down approach is that it is assumed that their intermediates are delocalised. One of the major areas of interest of this laboratory has been in the problem of channelling, most recently in terms of intermediary metabolites (Mendes et al.,1992 , 1995, 1996) but more classically in terms of the problem of whether the energetic intermediates of electron transport-linked phosphorylation are delocalised or not (Kell, 1979; Kell, 1988; Kell & Westerhoff, 1990). The basic idea is as follows. In the classical chemiosmotic coupling model (Mitchell, 1966; Nicholls & Ferguson, 1992), electron transport generates a transmembrane proton gradient which, due to the rapid diffusion rates of protons in aqueous media, leads to a delocalised protonmotive force Dp consisting of a membrane potential Dy and a pH gradient zDpH which is consequently avaiable to all ATP synthase enzymes in the organelle in whose membrane the pmf-generators are embedded. Uncouplers act by dissipating the pmf as heat. (In addition, the pmf can in principle feed back to inhibit electron transport via ‘slip’ or be dissipated ‘naturally’ to heat via a pmf-dependent ‘leak slip’ which does not differ formally from the imperfect coupling naturally present.) This is depicted in Fig 2.
Figure 2. The classical chemiosmotic coupling paradigm for electron transport-linked phosphorylation.
The consequence is that the rate of phosphylation Jp depends only and monotonically on Dp, typically according (when assessed experimentally by acid-bath-type experiments) to a sigmoidal function of the pmf, i.e.:

Jp = [ATP-synthase] . f(Dp) (Eq. 1)

In a typical dual-inhibitor titration using an uncoupler and an ATP synthase inhibitor, we first study the effect of uncoupler on Jp, with results similar to those in Fig 3 (open circles). We then inhibit half of the ATP synthases using a tight-binding (or better covalent) inhibitor such that Jp falls to one half of its original value (Fig 3). The effect of the uncoupler titration that must be predicted from the delocalised chemiosmotic type of uncoupling model is similar to that given by the closed triangles in Fig 3, since the pmf canot be made smaller by this treatment and it is probably slightly larger due to the smaller drain on it - the shape of the curve is the same but the rate at any level of uncoupler (and putatively pmf) is just one half of the control. Similarly, the amount of uncoupler needed to achieve full uncoupling is the same. Unfortunately for this view, the experimental curve is quite different: lowering the initial Jp to one-half of its original value with the ATP synthase inhibitor decreases by one half the amunt of uncoupler necessary to achieve full uncoupling. No delocalised coupling model can account for this type of behaviour in uncoupler/energy transfer inhibitor titrations (Herweijer et al.,1986; Hitchens & Kell, 1983a; Hitchens & Kell, 1983b; Kell, 1988; Kell, 1992; Westerhoff & Kell, 1988), and indeed none has made a serious attempt to do so.
Figure 3. Theoretical and experimental traces from dual uncoupler/energy transfer inhibitor titrations.


 

Between the Bud and the Rose: Large Changes and Metabolic Control Analysis

As is well-known, and is mentioned above, the theorems of classical MCA work only for parameter changes which are small (and in principle infintesimal). However, it is to be assumed (and see below) that substantial increases in flux towards metabolites of biotechnological interest require large changes in at least some of the parameters such as enzyme concentrations (and the same is true for the phenotypic manifestation of disease states when a sufficient (‘theshold’) loss in enzymatic function is induced (Durrieu et al., 1997; Letellier et al., 1998; Mazat et al., 1997, 1998)). Small and Kacser tackled the problem of exactly how great an inaccuracy in estimating control coefficients via large changes in parameters might be involved. They first introduced the idea of a deviation index as the relative change in a metabolic variable such as a flux to a large change in a parameter (Small & Kacser, 1993a), and showed that for unbranched chains of enzymes with linear kinetics there was a direct relationship between deviation indices and flux-control coefficients. They also pointed out that combined changes of the activity of individual enzymes will produce a more-than-additive response (and see below). The behaviour of branched and non-linear pathways was more complex (Small & Kacser, 1993b), and though it was stated that many metabolic systems behave in practice as quasi-linear systems, the differences between the actual and predicted amplification factors were often quite great. Indeed, a detailed study by R. Schuster & Holzhütter (Schuster & Holzhutter, 1995) of erythrocyte properties resulting from large-scale alterations in enzymatic activities concluded that no existing extrapolation method using the conventional control coefficients was able to provide reliable predictions.


 

The not-very Universal Method

It is worth noting that, as proven in the summation theorem of Metabolic Control Analysis (e.g. Cornish-Bowden et al., 1995; Fell, 1996; Heinrich & Rapoport, 1974; Heinrich & Schuster, 1996; Kacser & Burns, 1973; Kell & Westerhoff, 1986a), changes in the concentrations of individual enzymes tend to have little effect on particular metabolic fluxes (nor, indeed, on the gross phenotype under most laboratory conditions (Thatcher et al., 1998)). However, in part because of the so-called connectivities of MCA, changes in individual enzyme concentrations can and do have substantial effects on metabolite concentrations, even when the changes in flux are negligible (Mendes et al., 1995; Mendes et al., 1996). It is therefore very reasonable that attempts to increase metabolic fluxes by increasing the concentrations of metabolic enzymes may lead to substantial increases in metabolite levels, and that these may either prove cytotoxic or at least necessarily lead to the diversion of flux to pathways other than that desired. It would therefore be desirable (if it were indeed possible) to seek to modulate fluxes by changing enzyme activities in a manner that managed to preserve the steady-state levels of metabolites. Thus Kacser and Acerenza (Kacser & Acerenza, 1993) introduced the so-called Universal Method that purported to have this effect and to be ‘entirely general’. In the Universal Method, it is recognised that in any pathway leading to the output of interest, the activities of whose enzymes one would wish to increase, there will be branch points leading to other parts of metabolism which should not be perturbed. Because of the conservation of mass, the fluxes down each branch point following a change in flux are related both to the changes in flux before and after the branchpoint in the ‘main’ pathway and to the ratio r of enzyme activities before and after the change in flux. For unimolecular reactions, there is a unique value of r for each such reaction at which the fluxes down the branches remain unchanged.

However, this method has two major failings: (i) it does not work when it is the end product itself which feeds back to inhibit its own production (and this is usually the case in any high-yielding fermentation, for both thermodynamic and kinetic reasons), and (ii) the method works in principle only for systems in which there are no interactions between pathways, such as those involving conserved moieties such as adenine and pyridine nucleotide couples. Since any system of interest is likely intimately to involve cofactors of this type, it seems that the Universal Method as presented is unlikely to prove of substantive utility, nor seems to have done so to date.


 

Multi-site modulation

Whilst the Universal Method cannnot work as advertised, it does draw attention to the need - whatever the effects on the rest of metabolism - for multisite modulations to be performed if there is to be a substantial increase in flux, and this is now widely recognised (Cornish-Bowden, 1995; Cornish-Bowden et al., 1995; Fell, 1998; Fell & Thomas, 1995; Niederberger et al., 1992; Thomas & Fell, 1998). This does not contradict any of the insights of MCA, and in fact it can be shown both by analysis and simulation (Small & Kacser, 1993a, 1993b) that this result is to be expected: as soon as the step with higher control becomes faster (as happens with overexpression) the control shifts to other steps in the pathway. It is now evident that for any strategy to be successful in increasing the flux of a pathway substantially there is a requirement for the manipulation of several steps. This was clearly demonstrated experimentally by Niederberger and colleagues in their classical study (Niederberger et al., 1992) and has been discussed at some length by Fell and Thomas (Fell, 1998; Fell & Thomas, 1995; Thomas & Fell, 1998). In a recent conference it was evident that the metabolic engineering community (both research and industry) is converging to this conclusion, and it is now largely accepted that to increase flux one should manipulate at least two metabolic steps (Mendes & Kell, 1997). Removing the fluxes to unproductive pathways is likely to be much more significant for mature fermentations than seeking solely to stimulate the flux through the desired one per se (Holms, 1996; Holms et al., 1991).


 

Active learning and a post-Baconian approach to science in the post-genomic era

The commonest conventional method of experimental science, generally referred to as ‘the scientific method’, involves the preparation of an experimental system in a specified state and the manipulation of, preferably, a single parameter, whereupon one observes the time-evolution of the values of one or more variables compared to that of a control in which the ‘triggering’ manipulation is not performed. The parameter may then be moved to different set points. Each of those variables might also be controlled at a fixed level, i.e. as a parameter, and comparable experiments performed. If the system is comparatively simple and well behaved (e.g. asymptotically stable, and not chaotic as in (Davey et al., 1996)) it is usually possible to determine the form and parameterisation of the equations relating the parameters and the variables and the time evolution of the system by mathematical fitting procedures (Mendes & Kell, 1998a), leading to what is usually considered an "understanding" of the system. However, this is true only for simple systems, and one may put forward the views that (i) this kind of deductive reasoning is that usually practised in the MCA community, (ii) the functional genomics agenda (Bork et al., 1998; Hieter & Boguski, 1997; Hinton, 1997; Kell, 1998; Oliver, 1996) is likely to be much better attacked under current conditions via an inductive type of approach.

Indeed, we consider that complex systems cannot be treated to best advantage (Westerhoff & Kell, 1996) in this more classical, deductive way. First of all, there are far too many variables and potential parameters for an exhaustive set of experiments to be performed, and those parameter sets producing ‘desirable’ outcomes may be few and far between. (For n parameters which might adopt m values the number of combinations is obviously mn, and even if m is only a miserable 2 for n=100, 2100 ~ 1031, and the lifetime of the Universe is ‘only’ some 1017s.) The inevitable conclusion for the study of complex systems is that we we must vary many (or at least several) parameters at a time and use the methods of multivariate statistics and machine learning to deconvolute the data so obtained to extract those features most relevant to the operation of the system. Then, because of the high dimensionality of the system and problem, we must iterate this process further (somewhat in the way in which we traditionally need to provide rounds of mutation and selection in fermentation development programmes (Crueger & Crueger, 1989)). Indeed, our own approach in recent years to the understanding of complex cellular systems has been to exploit spectroscopic methods such as pyrolysis mass spectrometry (Broadhurst et al., 1997; Gilbert et al., 1997; Goodacre & Kell, 1996; Goodacre et al., 1993, 1994a, 1994b, 1996a; Taylor et al., 1998), ft-ir (Goodacre et al., 1996b, 1998a; Oliver et al., 1998; Winson et al., 1997, 1998), and dispersive Raman (Goodacre et al., 1998b) in which hundreds of variables are measured simultaneously, and to couple these measurements with advanced chemometric and related analyses based on the methods of artificial intelligence, machine learning and evolutionary computing (Bäck et al., 1997; Michie et al., 1994; Rich & Knight, 1991; Weiss & Kulikowski, 1991).

Although the above described the overall structure of a single experiment, scientific research of course proceeds by a process of experimental hypothesis testing (e.g. Oldroyd, 1986), and it is appropriate to end by outlining one way of computer-assisted knowledge acquisition with which we think important progress might be made. This process is an active approach, which in fact differs markedly from the passive nature of most ‘scientific discovery’ systems (Langley et al., 1987), which either receive data all at once in a single batch, or have no choice over the next example (Raju & Cooney, 1998), and suffer from the problem that most of the observables have little bearing on the overall outcome (Blum & Langley, 1997) and for the purposes of this analysis amount to ‘noise’. The study of systems that can choose the next experiment is known as ‘active learning’. There are two computational tasks in active learning: formation of hypotheses that are consistent with known background knowledge and experimental results, and selection of the best experiment (or set of experiments) to discriminate between hypotheses. It should be noted that experiment selection in active learning is not to be confused with the traditional statistical study of experimental design, where the difference is between deciding which question to ask next (active learning) versus ensuring that a set of experiments can answer a question (traditional experimental design).

To conclude, it seems reasonable that active learning approaches can lead us efficiently to means for asking and answering the right kinds of question at the right kind of complexity in the post-genomic era.


  Publications

Acknowledgments

We thank Ross King and Steve Oliver for useful discussions, and the BBSRC for financial support.


  Publications

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Westerhoff, H. V. & Kell, D. B. (1987). Matrix method for determining the steps most rate-limiting to metabolic fluxes in biotechnological processes. Biotechnol. Bioeng. 30, 101-107.

Westerhoff, H. V. & Kell, D. B. (1988). A control theoretical analysis of inhibitor titrations of metabolic channelling. Comments Mol. Cell. Biophys. 5, 57-107.

Westerhoff, H. V. & Kell, D. B. (1996). What BioTechnologists knew all along...? J. Theoret. Biol. 182, 411-420. [abstract]

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Winson, M. K., Goodacre, R., Timmins, É. M., Jones, A., Alsberg, B. K., Woodward, A. M., Rowland, J. J. & Kell, D. B. (1997). Diffuse reflectance absorbance spectroscopy taking in chemometrics (DRASTIC). A hyperspectral FT-IR-based approach to rapid screening for metabolite overproduction. Anal. Chim. Acta 348, 273-282. [abstract]

Winson, M. K., Todd, M., Rudd, B. A. M., Jones, A., Alsberg, B. K., Woodward, A. M., Goodacre, R., Rowland, J. J. & Kell, D. B. (1998). A DRASTIC (Diffuse Reflectance Absorbance Spectroscopy Taking in Chemometrics) approach for the rapid analysis of microbial fermentation products: quantification of aristeromycin and neplanocin A in Streptomyces citricolor broths. In New frontiers in screening for microbial biocatalysts (ed. K. Kieslich, C. P. van der Beek, J. A. M. de Bont and W. J. J. van den Tweel), pp. 185-191. Elsevier, Amsterdam.

Wodicka, L., Dong, H. L., Mittmann, M., Ho, M. H. & Lockhart, D. J. (1997). Genome-wide expression monitoring in Saccharomyces cerevisiae. Nature Biotechnol. 15, 1359-1367. [abstract]


Copyright © 1999 Douglas B. Kell and Pedro Mendes, All rights reserved.

Last update: 19 February 2004


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