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MCA 99NATO Advanced Research WorkshoponTechnological and Medical Implications of
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Metabolic Control Design: implications and applicationsLuis AcerenzaSección Biofísica, Facultad de Ciencias, Igua 4225, Montevideo 11400, Uruguay In a metabolic system, the values of the control coefficients are determined by the values of the parameters of the component enzyme-catalysed reactions. One important result of Metabolic Control Analysis is that this relationship can be split in two parts: control coefficients as a function of elasticities and elasticities as a function of parameters. Metabolic Control Design (MCD) addresses the "inverse" problem. Starting from given values of the control coefficients, we ask what elasticities and, in turn, rate laws and parameter values are needed to obtain such a control profile. Two types of sensitivity constraints restrict the types of control patterns that it is possible to design: structural and kinetic. The structural constraints are the well-known conservation and summation relationships and follow from the stoichiometry of the network. The kinetic constraints result from the existence of restrictions in the values of the elasticities and therefore depend on the type of rate law associated to each step. Owing to the structural and kinetic constraints the control coefficients are not all independent. The dependent control coefficients can be calculated from the values of the independent control coefficients by algebraic manipulation of the equations representing the constraints. The fraction of independent control coefficients can be used as an indicator of how constrained is metabolic control. Using experimental information available we have shown that for an organism such as E. coli only a small fraction of the control coefficients are independent, the kinetic constraints being the main cause of the low value obtained for this fraction. MCD has been used to design metabolic systems, such as monocyclic cascades, that show high sensitivity of response. Its application renders the necessary conditions that the parameters have to fulfil in order to show this property. The advantage of the MCD procedure is that all possible solutions that show the desired property can be obtained in a systematic way. According to MCD, the design of particular metabolic responses imposes restrictions on the kinetic properties of the component enzymes. In addition, these properties could also be conditioned by the operation of optimization processes, such as the maximization of a flux. To account for the simultaneous action of these two effects, we have combined MCD with optimization methods. The resulting procedure, which we have called Optimal-MCD, renders a metabolic scheme that shows the "appropriate" values of "relevant" control coefficients and the optimum value of a "target" quantity. One consequence of this procedure is that the optimization of a flux may result in different metabolic structures depending on the values that we impose to the control coefficients.
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Theory and practice of determining control coefficients or Exploring the sea by swimming in the poolChristoph GierschInstitut für Botanik, University of Technology Darmstadt, Schnittspahnstr. 3-5, D-64287 Darmstadt, Germany For several years it has been known that control coefficients can be measured by modulating the activity of a reaction by a known amount or, alternatively, by determining the elasticities via multiple modulation. The former method is simple but applies only to the determination of flux control coefficients. The alternative approach, determining control coefficients via elasticities, is more general. It has the advantage that the magnitude of the modulation brought about by a modulator has not to be known. Moreover, to determine all elasticities of a pathway, not all reactions have to be modulated. This allows one to account for experimental constraints (e. g., for which reactions are there specific modulators?) in selecting the reactions that are to be modulated, provided only that these reactions are independent of each other. Recent work from this group revealed that the essence of dependent/independent reactions can be described by means of certain separability properties of the concentration control coefficient matrix C The matrix SP, whose elements are the changes in metabolite concentrations with the amount of a modulator, has the same separability properties as matrix C . For a given pathway, the separability structure of matrix C (or SP) summarizes essential pathway characteristics by providing the complete information on (i) the dependence/independence of modulations, on (ii) whether ratios of control coefficients are identical, and on (iii) the monovalent functional units. For simple pathways, the separability structure of C can be obtained without using any algebra. Compared with the theoretical issue, the experimental side of determining control coefficients is far less developed, and the recent progress in the theoretical analysis only underlines the weakness of the experimental side. There are reasons to believe that we cannot expect much progress here: First, the biological system has to be maintained at one and the same steady state over a certain period of time (at least several days, more likely weeks) for the experimentator to be able to do all the required measurements. Second, because the home of metabolic control analysis is the space of derivatives, the individual measurement has to quantify the small change with respect to the preceding and following measurements. This requires an exactness that is hard to meet. Some of the problems can be (and have been) circumvented by designing special experimental situations, but compared to the full richness of life this is like exploring the sea by observing the events that may happen in a pool. My personal view is that it is only fair to say that metabolic control analysis describes relations among quantities that cannot be measured for any real biological system. So why should we go on to (claim to) use metabolic control analysis as an experimental tool? Where are better tools? |
Predicting the structural design of metabolic pathways: an evolutionary approachReinhart HeinrichTheoretical Biophysics, Institute of Biology, Humboldt-University Berlin, Invalidenstrasse 42, D-10115 Berlin, Germany Metabolic systems are characterised by two different types of experimental data. These are (a) the fluxes and metabolite concentrations which may vary in a rather short time scale and (b) the stoichiometric properties and kinetic parameters of the reactions which are generally fixed during the lifetime of a cell or are changing rather slowly. Traditionally, the mathematical analysis (simulation models, metabolic control analysis) focuses on the prediction of the steady state or time dependent behaviour of the system variables (a) as functions of the system parameters (b). However, a deeper understanding of the relationship between structure and function of metabolic pathways necessitates also the explanation of the their structural design which was fixed during evolution. It seems to be promising to start from the hypothesis that mutation and selection have driven the metabolic systems toward states characterised by certain optimum properties. In the present communication it is analysed whether important structural characteristics of enzymatic reaction systems can be understood on the basis of flux optimisation. Optimisation of the reaction rates of single enzymes shows that a high catalytic power of enzymes is only achieved for certain values of the kinetic parameters. Depending on the catalytic mechanism and on the concentrations of the external reactants we are able to predict optimal parameter values which may be checked by experimental data. The theory predicts also optimal ratios between substrate concentrations and the corresponding Michaelis constants. Taking into account that the total cellular pool of proteins is limited optimisation of multienzyme systems may be viewed as a competition of the different reactions or of different metabolic branches for enzyme resources. Optimisation leads to special distributions of enzyme concentrations as well as of flux control. The optimal flux control coefficients are generally characterised by lower standard deviations compared to those in reference states with uniform distribution of enzymes. Taking into account kinetic and thermodynamic principles the optimisation of fluxes of ATP-producing pathways leads to pathways whose stoichiometric properties reflect very well the structural design of glycolysis. This concerns, in particular, the number and location of ATP consuming as well as of ATP-producing reactions. A thorough theoretical analysis is presented which considers a broad class of stoichiometrically feasible designs and where optimisation is performed on the basis of evolutionary algorithms. A typical outcome of the optimisation is the sequence: AAUUpaUPPaUPaa (A/a: ATP-consuming/producing reaction, U: uncoupled reactions, P/p: uptake/release of inorganic phosphate). It is shown how the optimal reaction sequences depend on the time constants of the participating reactions as well as on the total concentration of cofactors.
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Steps towards the analysis of large biochemical systemsToni KazicInstitute for Biomedical Computing, Box 8036, Washington University, 700 South Euclid Ave., St. Louis, MO 63110, USA In improving our understanding of cells and organisms as physiological, biochemical, and genetic systems, one has two basic choices: to study portions of the whole, or to study the whole (or very large portions of it). Both approaches are essential, but the first is obviously far more advanced. For some time now we have been working on methods to model extremely large systems of biochemical reactions. For example, many use the metaphor of "network" when thinking of systems of genes, molecules, and reactions. It is biochemically and dynamically apt, and when carefully defined offers a number of important techniques for analysis and modeling. As researchers turn their attention to the cellular network's function and integration at "higher levels" — a definition of functional genomics in the broader sense — it is important to ask how these complex networks are organized and how they behave and evolve. This requires both data on and analytical methods for thousands of reactions and their participating molecular species. I shall present a brief summary of our methods for scalably representing information on biochemical function in databases in ways which support a wide variety of computations; give a status report on efforts to mitigate the problems of data entry and maintenance; sketch our progress in developing analytical methods; and illustrate some preliminary applications of these methods to the study of a sample large network. |
Combined NMR experimental and computer-simulation study of 2,3-BPG metabolism in human erythrocytesPhilip W. Kuchel and Peter J. MulquineyDepartment of Biochemistry, University of Sydney, NSW 2006, Australia 2,3-Bisphosphoglycerate (2,3-BPG) plays an important role in human erythrocytes by regulating their oxygen transport. Its concentration is elevated above normal values in clinical and environmental conditions such as in anaemia, congenital heart disease, and at high altitudes. 2,3-BPG is an allosteric effector of haemoglobin (Hb) and by binding preferentially to the deoxygenated form it decreases the apparent affinity for O2. While the interaction between 2,3-BPG and Hb has been known for over 30 years [1, 2] the precise mechanism(s) by which 2,3-BPG metabolism is regulated is still the subject of debate. 2,3-BPG is synthesised in the Rapoport-Luebering shunt that entails the flux of 1,3-bisphosphoglycerate to 2,3-BPG, thus bypassing the phosphoglycerate kinase reaction. Carbon atoms pass back to the glycolytic pathway when 2,3-BPG is hydrolysed to 3-phosphoglycerate. When studying the control of this shunt it is difficult to accurately measure the true flux into and out of it. When isotopic tracer methods are used flux is overestimated due to the exchange of phosphorus-atom TlabelU in the phosphoglycerate mutase reaction. In response to this and other technical problems, a combined approach of mathematical modelling and NMR spectroscopy was used to investigate the regulation and control of 2,3-BPG metabolism. The combined approach involved developing a very detailed mathematical model of the enzyme-catalysed reactions of the main metabolic processes of the human erythrocyte. Through an interative loop of experimental and simulation analysis, values of kinetic parameters of the model were refined to yield close conformity between the predictions of the model and the TrealU NMR data. Metabolic control analysis was implemented in the computer program thus enabling the control and regulatory properties of 2,3-BPG metabolism to be studied. The changes in 2,3-BPG metabolism that occur in different environmental and disease states can now be understood in terms of the details of the metabolite-enzyme interactions that occur inside the cell.
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Computational approaches to the study of biochemical pathways and metabolic controlPedro MendesNational Center for Genome Resources, 1800 A Old Pecos Trail, Santa Fe, New Mexico 87505, USA Since its first development in the early 1970s, metabolic control analysis (MCA) has become the method of choice to study control and regulation of metabolic pathways. MCA also promised to be useful for rational optimisation of metabolic fluxes. However, this latter application of MCA in biotechnology is limited by the approach's inability to predict the effect of large changes in metabolic parameters. A complement to MCA studies is the use of computer simulation of metabolic models. Although this approach has the disadvantage of requiring more information about the system than does MCA, the payoff is that it is easy to predict the behaviour of systems after large changes in parameter values. There are several software packages available for this purpose and a number of them allow one to map the dependence of the model (e.g. a flux of interest) in its parameters easily. Such a parameter space scan is feasible for a small number of parameters but is impractical for large models as computational time grows exponentially with the number of parameters scanned. An alternative is to use nonlinear optimization methods to search for appropriate maxima or minima of metabolic properties of interest. The current version of the simulation package Gepasi is able to carry out such guided searches with a series of diverse optimization methods. These can also be used to assist in the model building process at the level of parameter estimation. The computer application of (combined) nonlinear optimization, simulation and MCA to biotechnological problems will be further discussed. For more than a decade now molecular biologists have been cataloguing gene and protein sequences in computer databases. These are easy to search and allow a large number of scientists to access each other's data in convenient formats. Unfortunately for a long time the same could not be said about biochemists. However this is now changing: a number of metabolic databases have been recently become public. At the NCGR we are currently developing a plant secondary metabolism database, PlaSMA. One of the aims in the design schema of PlaSMA is that it can equally be used for metabolic data of any other organism. I will discuss how metabolic databases can be integrated with simulation and optimization software to enhance both the study of metabolic control and design in metabolic engineering. |
An integrated approach to the analysis of the control and regulation of cellular systemsJohann M. Rohwer and Jan-Hendrik S. HofmeyrDepartment of Biochemistry, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa Historically, biochemistry has been a descriptive science concerned with the identification and characterisation of (sub-)cellular components. As more and more of these components became known, the focus of attention shifted from the components themselves to their interactions and interplay in the functioning of the living cell as a whole. However, such a description was typically limited to the effect of a certain property of a component on the whole system (e.g., the presence of allosteric feed-back inhibition in an enzyme on the regulation of a whole metabolic pathway). With the advent of systemic approaches like control analysis, it became evident that the systemic behaviour of a living cell (or a part thereof, even of a single metabolic pathway) cannot be described adequately by considering properties of a few `key' components. All of them contribute to the global behaviour in one way or another: one of the main tenets of control analysis tells us that `enzymes share the control of a flux', another that many elasticities contribute to the value of a specific control coefficient. Whilst this is a very important realisation (and the gospel has not yet reached general acceptance amongst the biochemical community), control analysis has the definite shortcoming that the coefficients are defined around (and only valid for) a reference steady state. Extrapolation of the control coefficients to a more distant steady state is generally impossible (although some approximations are available) - a fact that is often used by the `refuseniks' to disregard or even discredit the `controlniks'. In this contribution we argue for an integrated approach, combining control analysis with experimental work and kinetic modelling (numerical simulation). The latter two approaches are indeed valid for a whole series of steady states. We show that experimental results can aid in the construction of a kinetic model, that this model can be used to compute the coefficients of control analysis, that the model can simulate conditions which have not yet been tested experimentally and thus direct the planning of future experiments, and that the results of these new experiments can be used for the refining of the kinetic model. Such an iterative `integrated approach' can lead to many novel insights into how the living cell works, as will be exemplified by studies on the bacterial phosphotransferase system, anaerobic energy metabolism in yeast and sucrose metabolism in sugar cane. |
Recent developments in metabolic pathway analysis and their potential implications for biotechnology and medicineStefan SchusterMax Delbrück Center for Molecular Medicine, Dept. of Bioinformatics, D-13092 Berlin-Buch, Germany The complete sequencing of several genomes has opened a new era in biology. Amongst various other novel opportunities in research due to this achievement, there is now the possibility to delineate the metabolic maps for several organisms by "inverse genetics," that is, by inferring the function of enzymes from the genes encoding them. To perform this in a rational way, the mathematical analysis of network structures is a valuable tool. Methods for the computer-aided synthesis of biochemical pathways (Seressiotis & Bailey, 1988; Mavrovouniotis et al., 1990) have been developed. A related approach is based on the concept of elementary flux modes (Schuster & Hilgetag, 1994). These methods allow one to test whether sets of enzymes form a coherent pathway allowing mass balancing for each intermediate and complying with the directionality of reactions given by thermodynamic constraints. Importantly, pathway analysis (as well as flux-balance analysis) can be performed without the knowledge of kinetic parameters. A potential field of application of elementary-modes analysis in medicine is the study of enzyme deficiencies. In rational metabolic engineering, this method can help to predict the effects of the insertion or deletion of enzymes. In particular, it can be used to detect pathways with a maximum stoichiometric yield (Schuster et al., 1999). Alternatively, the problem of maximizing yield can be solved by linear programming (e.g. Fell & Small, 1986; Savinell & Palsson, 1992), provided that the substrate consumption rate or product formation rate can be appropriately normalized. A comparison of the two approaches is given. It is shown that in the case where normalization is problematic (e.g. in the presence of alternative substrates), the approach based on elementary modes provides more information.
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Time-dependent or steady-state control of metabolic systems?Stefan SzedlacsekDepartment of Enzymology, Institute of Biochemistry, Spl. Independentei 296, Bucuresti 77700, Romania Metabolic control theory was originally developed for metabolic systems assumed to be at steady state. Thus, it was accepted that changes of enzyme concentration cause modifications of the fluxes and metabolite concentrations so that the steady state is continuously maintained. In fact, changing the concentration of an enzyme generally implies the setting up of a non-steady state. Consequently, the system will enter in a transient, time-dependent state until a new steady state is established. There are two main directions to deal with the control of the time-dependent metabolic systems. One of them is concerned with the transition time — a term introduced by Easterby (1981) to reflect the time required to reach the new stationary state. A second direction (Acerenza et al., 1989) extended the definitions of the control and elasticity coefficients to time-dependent systems. A new type of coefficient, named time coefficient was defined and introduced in order to characterize the change of a given variable — flux or metabolite concentration — as a response to a relative increase of the time. Formally, time-dependent treatment in metabolic control analysis implies additional difficulties. The time dependence of the system variables make the mathematical formalism more complicated; sometimes it is impossible to derive analytical expressions, where the analogous expressions for the steady-state has been already derived. In particular situations, for instance in case of metabolic systems with relatively short transition time, the steady-state analysis may create a preliminary image of the behaviour of the given metabolic system. However, the time-dependent analysis may reveal unexpected features of the system under consideration. Thus, a metabolic system that displays, according to the steady-state analysis, a high responsiveness to an external effector, could be in fact a "slow-answering" system. In addition, the non-steady-state treatment has the advantage that it provides also information concerning the steady-state behaviour as a limit situation of the time dependence. To illustrate these findings, a simple metabolic system under the control of an external effector is considered. As a conclusion, it can be stated that the steady-state analysis cannot be a priori taken as reflecting the reality. Only together with the time-dependent approach it can offer a more realistic image of the behaviour of the metabolic system.
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