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A modeling and simulation approach to the study of metabolic control analysis

A modeling and simulation approach to the study of metabolic control analysis
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  See discussions, stats, and author profiles for this publication at: A Modeling and simulation approach to thestudy of metabolic control analysis  Article   in  Biochemistry and Molecular Biology Education · May 2002 DOI: 10.1002/bmb.2002.494030030060 CITATIONS 6 READS 36 3 authors:Some of the authors of this publication are also working on these related projects: Network theory applied to neuroimaging   View projectCarlos Rodríguez-CasoBrain Dynamics 47   PUBLICATIONS   664   CITATIONS   SEE PROFILE Francisca Sánchez-JiménezUniversity of Malaga 223   PUBLICATIONS   3,897   CITATIONS   SEE PROFILE Miguel Ángel MedinaUniversity of Malaga 275   PUBLICATIONS   4,359   CITATIONS   SEE PROFILE All content following this page was uploaded by Carlos Rodríguez-Caso on 13 October 2014. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the srcinal documentand are linked to publications on ResearchGate, letting you access and read them immediately.   Articles  A Modeling and Simulation Approach to the Study of MetabolicControl Analysis* Received for publication, February 8, 2002 Carlos Rodrı´guez-Caso, Francisca Sa´nchez-Jime´nez, and Miguel A ´ ngel Medina‡ From the Departamento de Biologı´a Molecular y Bioquı´mica, Facultad de Ciencias, Universidad de Ma´laga,E-29071 Ma´laga, Spain Metabolic control analysis has contributed to the rapid advance in our understanding of metabolic regu-lation. However, up to now this topic has not been covered properly in biochemistry courses. This workreports the development and implementation of a practical lesson on metabolic control analysis usingmodeling and simulation. Keywords : Metabolic control analysis, metabolic regulation, flux control coefficient, summation theorem. An understanding of metabolism is essential for theunderstanding of life. However, on many occasions stu-dents look on the study of metabolism as a boring task;they are almost reduced to learning a number of metabolicpathways by heart. On the other hand, the central role ofmetabolic regulation is not always stressed conveniently inbiochemistry courses. To study regulation requires aknowledge of changes of metabolites and enzymes withtime, that is, of kinetics. Traditionally, kinetics has beentaught in biochemistry courses in terms of enzyme steady-state kinetics. Obviously, this is a detailed study of thelocal properties of the individual enzymes [1]. However,control emerges as a systemic property of metabolic net-works [2], thus requiring a systemic approach to its study,including sensitivity analysis. Among the different theoriesbuilt to make this approach possible, metabolic controlanalysis (MCA) 1 has become a standard approach [3, 4].Despite the fact that MCA has contributed to the rapidadvance in our understanding of metabolic regulation atthe research level in recent years, paradoxically this topicis completely absent from most general biochemistry text-books, with the remarkable exception of the text by Voetand Voet [5]. Fortunately, some special books devoted tometabolic control [6, 7] and the inclusion of MCA in somerecent enzymology books [8, 9] are contributing to changethis situation.In our department, MCA has been included in the sylla-bus of a course devoted to metabolic biochemistry (for-merly called Metabolic Regulation) for 20 years. Our ownexperienceasteachersisthat,inasignificantproportionofstudents, the study of MCA induces what has been called“numerophobia” [10], as is the case for the study of en-zyme kinetics. In our experience, this is mainly because ofa “scenic panic” against the non-linear equations of MCA because of an insufficient mathematical background. This“numerophobia” frequently causes repulse and/or an in-adequate assimilation of the central concepts of MCA. Toavoid this problem, we think that a practical approachcould contribute to facilitate the assimilation of MCA. Sev-eral bench practical approaches to the study of MCA havebeen developed previously and applied successfully [11,12]. However, more than often the non-linear equations ofMCAhavenoanalyticalsolutions;modelingandsimulationcan be particularly useful here.Herein, we communicate our teaching experience in thedevelopment and implementation of a practical lesson onMCA using modeling and simulation. OBJECTIVES •  To promote an easy connection between enzymol-ogy and metabolism •  To build a model of a metabolic pathway from thekinetic parameters of the enzymes involved andsome data on the concentrations of substrates andmodulators •  To show clearly that there is a close relationshipbetween the local behavior of any enzyme and thesystemic responses of the metabolic pathways •  To get, by simulation, an easy, fast, and inexpensivemethod to obtain the required data to apply MCA theory •  To use concepts that are not always clearly assimi-lated by students •  To facilitate the learning of the different coefficientsand theorems of MCA  STRATEGY First, students are taught how to easily design a modelof a metabolic pathway from available kinetic parametersby using programs that allow such a design in an intuitive * This work was supported by funds from the Andalusian Gov-ernment (to the CVI-267 Group) and from the Spanish Ministry forScience and Technology.‡ To whom correspondence should be addressed. Tel.: 34-95-2137132; Fax: 34-95-2132000; E-mail: 1 The abbreviation used is: MCA, metabolic control analysis. © 2002 by The International Union of Biochemistry and Molecular Biology B IOCHEMISTRY AND  M OLECULAR  B IOLOGY  E DUCATION Printed in U.S.A.  Vol. 30, No. 3, pp. 169–171, 2002 This paper is available on line at  169  manner, without the need of intense computer knowledge.In a second stage, students are taught how to simulatethe model by changing the parameters required to applyMCA. Here, students have to identify accurately when asteady state is reached, a required condition to applyMCA.Finally, students obtain the numerical data required toapply MCA from the simulations. Several coefficients canbe calculated, and the different theorems of MCA can beverified. RESULTS AND DISCUSSION In our Metabolic Biochemistry course, we have devel-oped a practical protocol to be carried out in a 2 – 3-hsession in the computer laboratory. Students, grouped inpairs, were asked to study a virtual linear four-step path-way, with the last step being irreversible (Scheme 1). Theinitial values of parameters are given in Table I.The model was built and designed as a compartmentsystem by using the program STELLA (13). This is anintuitive program that allows the easy design of metabolicpathways in a graphical manner. Assuming Michaelianbehavior of all of the involved enzymes, functions relatingto the compartments were defined by using the Michaelis-Menten equation, the total velocity equation, and the Hal-dane relationship (9) (see Scheme 2). Starting with theinitial values given in Table I, the behavior of this modelsystem was simulated by using the program MADONNA (14). Once steady-state conditions were reached, numer-ical data were acquired to allow for the determination ofdifferent coefficients of MCA. In our practical session, wesuggested calculating flux control coefficients for all theenzymes. The values obtained by our students are shownin Table II. From these data, the summation theorem of fluxcontrol coefficients can be confirmed immediately. Se-quential simulations after changes in the external metab-olite (   X  1  ) over a couple orders of magnitude allowed cal-culating the response coefficient for X 1 . The valuesobtained by our students were in the range of 0.25 to 0.30.We have observed that, at least with the programs used, itis compulsory to use as many decimal values as possibleto obtain accurate results (otherwise, if we round values tothe second or third decimal value, the truncation errorincreases exponentially over the steps in the simulation,giving rise to final erroneous values). Although we have used Stella and Madonna, the proce-dure can be carried out using other programs. We recom-mend using GEPASY (15) because of its easy use, itspopularity, and because it can be downloaded free ofcharge from the World Wide Web.The approach described here can be used to model anykind of metabolic pathway, either real or virtual and linearor branched. This training is actually useful for a properassimilation of the concepts of MCA, as we have con-firmed with our students by a triple approach, which isdescribed as follows. T  ABLE  I Initial condition values for enzyme kinetics parameters and metabolite concentrations K M i Sj means the affinity constant of the enzyme  E  i  for the metabolite  S  j .Metabolites (   M  ) Activities (   M  min  1  ) EquilibriumconstantsK M for  E  1 (   M  ) K M for E 2 (   M  ) K M for E 3 (   M  ) K M for E 4 (   M  ) X 1  100 V 1  0.05  K  eq1  50  K  M  1  X  1 100 K M2S2 500 K M3S3 104 K M4S4 250S 2  0 V 2  100 K eq2  10  K  M  1 S 2 100 K M2S3 250 K M3S4 20S 3  0 V 3  250 K eq3  50S 4  0 V 4  100  K  eq4 T  ABLE  II Control flux coefficients for initial conditions Control flux coefficients are defined as  C E   i   J  J    J  E i    E i ,  with J being the flux through the metabolic pathway. The summation theorem of fluxcontrol coefficients states that  i  1 n C E i J  1.Enzyme 1 Enzyme 2 Enzyme 3 Enzyme 4 SummationControl flux coefficient(for initial conditions)0.32 0.07 0.15 0.52 1.06 S CHEME  1.  Virtual pathway consisting of four enzymes (   E  1 ,  E   2 , and  E   3  showing reversible kinetics and  E   4  being reversi-ble) and four metabolites (   X  1  is considered a parameter, and S  2 ,  S  3 , and  S  4  are variables). S CHEME  2.  Equations used in the model.  For enzymes 1 to 3,total velocity equations containing the Haldane relationship areconsidered; for enzyme 4 a simple Michaelis-Menten equation isconsidered. 170 BAMBED, Vol. 30, No. 3, pp. 169 – 171, 2002  1. According to our own records and notes on students ’ performance, the final degree of assimilation of MCA by those students who carried out the modeling andsimulation practical session was higher than that ofstudents in previous years who did not carry out thispractical session.2. Students had to solve numerical problems on MCA both before and after the practical session. Thescores obtained in the exercises carried out after thepractice were consistently higher than those ob-tained by the same students in those exercises car-ried out before the practical session.3. Taking into account the results obtained in a surveycompleted by students after training, the students feltthey had reached a better comprehension of MCA.Students agreed that the practical session indeedcontributed to clarifying their doubts.In conclusion, we are confident that this kind of ap-proach can facilitate to students the study and properassimilation of MCA, a systemic theory of control that wehope to be introduced in biochemistry teaching in a degreesimilar to the extension reached by metabolic regulation atresearch level. REFERENCES [1] J. Snoep, P. Mendes, H. Westerhoff (1999) Teaching metabolic con-trol analysis and kinetic modelling,  The Biochemist   21,  25 – 28.[2] D. A. Fell (1999) Traditional concepts of metabolic control misleadmore than enlighten,  The Biochemist   21,  13 – 16.[3] H. Kacser, J. A. Burns (1973) The control of flux,  Symp. Soc. Exp. Biol. 27,  65 – 104.[4] Fell, D. A. (1992) Metabolic control analysis: a survey of its theoreticaland experimental development,  Biochem. J.  286,  313 – 330.[5] D. Voet, J. G. Voet (1995) Biochemistry, 2nd ed., John Wiley & Sons,Inc., New York, pp. 470 – 476.[6] D. A. Fell (1997) Understanding the Control of Metabolism, PortlandPress, London.[7] R. Heinrich, S. Schuster (1996) The Regulation of Cellular Systems,Chapman & Hall, New York.[8] A. Cornish-Bowden (1995) Fundamentals of Enzyme Kinetics,Portland Press, London, pp. 239 – 270.[9] I. Nu ´  n  ˜  ez de Castro (2001) Enzimologı´a (in Spanish), Pira´mide, Madrid,pp. 309–348.[10] A. McDonald, K. Tipton (1999) Kinetics for the numerically chal-lenged,  The Biochemist   21,  18–23.[11] N. V. Torres, E. Mele´ndez-Hevia, J. M. Riolcimas (1988) A study of thedistribution of flux control coefficients in an  in vitro  metabolic system:a practical exercise,  Biochem. Educ.  16,  100–102.[12] P. Quant, M. Brand (1999) How to get your hands on a concept,  TheBiochemist   21,  29–33.[13] STELLA:[14] Madonna:[15] Gepasi Biochemical Kinetics Simulator: soft/gepasi.html. 171 View publication statsView publication stats
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