Hattersley, J. G. (John G.), Pérez-Velázquez, J., Chappell, M. J. (Michael J.), Bearup, Daniel James, Roper, David I., Dowson, Christopher G., Bugg, Tim and Evans, N. D.. (2011) Indistinguishability and identifiability of kinetic models for the MurC reaction in peptidoglycan biosynthesis. Computer Methods and Programs in Biomedicine, Vol.104 (No.2). pp. 70-80. ISSN 01692607

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Abstract

An important question in Systems Biology is the design of experiments that enable discrimination between two (or more) competing chemical pathway models or biological mechanisms. In this paper analysis is performed between two different models describing the kinetic mechanism of a three-substrate three-product reaction, namely the MurC reaction in the cytoplasmic phase of peptidoglycan biosynthesis. One model involves ordered substrate binding and ordered release of the three products; the competing model also assumes ordered substrate binding, but with fast release of the three products. The two versions are shown to be distinguishable; however, if standard quasi steady-state assumptions are made distinguishability can not be determined. Once model structure uniqueness is ensured the experimenter must determine if it is possible to successfully recover rate constant values given the experiment observations, a process known as structural identifiability. Structural identifiability analysis is carried out for both models to determine which of the unknown reaction parameters can be determined uniquely, or otherwise, from the ideal system outputs. This structural analysis forms an integrated step towards the modelling of the full pathway of the cytoplasmic phase of peptidoglycan biosynthesis.

Item Type:	Journal Article
Subjects:	Q Science > QH Natural history > QH301 Biology
Divisions:	Faculty of Science > Life Sciences (2010- ) > Biological Sciences ( -2010) Faculty of Science > Chemistry Faculty of Science > Engineering Faculty of Science > Life Sciences (2010- )
Library of Congress Subject Headings (LCSH):	Peptidoglycans -- Synthesis -- Mathematical models, Systems biology -- Mathematical models, Experimental design
Journal or Publication Title:	Computer Methods and Programs in Biomedicine
Publisher:	Elsevier BV
ISSN:	01692607
Date:	2011
Volume:	Vol.104
Number:	No.2
Page Range:	pp. 70-80
Identification Number:	10.1016/j.cmpb.2010.07.009
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/E057535/1
Version or Related Resource:	This item was also submitted to the 7th IFAC Symposium on Modelling and Control in Biomedical Systems, Aalborg, Denmark, Aug 12 - 14, 2009.
References:	[1] Anderson, M. S., Eveland, S. S., Onishi, H. R., Pompliano, D. L., 1996. Kinetic mechanism of the Escherichia coli UDPMurNAc-Tripeptide D-Alanyl-D-alanine-adding enzyme: Use of a Glutathione S-Transferase Fusion. Biochemistry 35, 16264–16269. [2] Brown, E. D., Marquardt, J. L., Lee, J. P., Walsh, C. T., Anderson, K. S., Sep 1994. Detection and characterization of a phospholactoyl-enzyme adduct in the reaction catalyzed by udp-nacetylglucosamine enolpyruvoyl transferase, murz. Biochemistry 33 (35), 10638–10645. [3] Bellu, G., Saccomani, M., Audoly, S., D’Angiò, L., Oct 2007. Daisy: a new software tool to test global identifiability of biological and physiological systems. Computer Methods and Programs in Biomedicine 88 (1), 52–61. [4] Chappell, M. J., Godfrey, K. R., Vajda, S., Nov 1990. Global identifiability of the parameters of nonlinear systems with specified inputs: a comparison of methods. Math Biosci 102 (1), 41–73. [5] Cobelli, C., Salvan, A., 1977. Parameter estimation in a biological two compartment model– ii: a computer experimental study of the influence of the initial estimate in the parameter space,of some sampling protocols and of weighting factors. Mathematical Biosciences 37 (3-4), 267 – 274. [6] Franco, R., Gavaldà, M. T., Canela, E. I., Sep 1986. A computer program for enzyme kinetics that combines model discrimination, parameter refinement and sequential experimental design. Biochem J 238 (3), 855–862. [7] El Zoeiby, A., Sanschagrin, F., Havugimana, P. C., Garnier, A., Levesque, R. C., 2001. In vitro reconstruction of the biosynthetic pathway of peptidoglycan cytoplasmic precursor in Pseudomonas aeruginosa. FEMS Microbiol. Lett. 201, 229–235. [8] Emanuele, J. J., Jin, H., Yanchunas, J., Villafranca, J. J., 1997. Evaluation of the kinetic mechanism of Escherichia coli Uridine Diphosphate-N-acetylmuramate:L-Alanine Ligase. Biochemistry 36, 7264–7271. [9] Érdi, P., Tóth, J., 1989. Mathematical Models of Chemical Reactions. Princeton University Press. [10] Espenson, J. H., 1995. Chemical Kinetics and Reaction Mechanisms. McGraw-Hill, Singapore. [11] Evans, N., Hattersley, J., Hutchison, C., Hu, Y., Godfrey, K., Bradwell, A., Mead, G., Chappell, M., September 2006. Modelling of haemodialysis in limiting serum free light chains in patients with renal failure. In: D. Feng, O. Dubois, J. Z., Carson, E. (Eds.), Proceedings of the 6th IFAC Symposium on Modelling and Control in Biomedical Systems. Elsevier, Oxford, pp. 75–80. [12] Evans, N. D., Chapman, M. J., Chappell, M. J., Godfrey, K. R., 2002. Identifiability of uncontrolled nonlinear rational systems. Automatica 38, 1799–1805. [13] Evans, N. D., Chappell, M. J., Chapman, M. J., Godfrey, K. R., 2004. Structural indistinguishability between uncontrolled (autonomous) nonlinear analytic systems. Automatica 40, 1947–1953. [14] Fersht, A. R., 1999. Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding. Freeman, New York. [15] Fisher, F. M., 1959. Generalization of the rank and order conditions for identifiability. Econometrica 27 (3), 431–447. [16] Godfrey, K. R., Chapman, M. J., 1990. Identifiability and indistinguishability of linear compartmental models. Math. Comput. Simulat. 32, 273–295. [17] Godfrey, K. R., DiStefano III, J. J., 1987. Identifiability of model parameters. In: Walter, E. (Ed.), Identifiability of Parametric Models. Pergamon Press, Ch. 1, pp. 1–20. [18] Jacquez, J. A., Mar 1984. Red blood cell as glucose carrier: significance for placental and cerebral glucose transfer. Am J Physiol 246 (3 Pt 2), R289–R298. [19] Kholodenko, B. N., Bruggeman, F. J., Sauro, H. M., 2005. Mechanistic and modular approaches to modeling and inference of cellular regulatory networks. In: Alberghina, L., Westerhoff, H. (Eds.), Systems Biology: Definitions and Perspectives. Springer-Verlag. [20] Ljung, L., Glad, T., 1994. On global identifiability for arbitrary model parametrizations. Automatica 30, 265–276. [21] Marmor, S., Petersen, C. P., Reck, F., Yang, W., Gao, N., Fisher, S. L., 2001. Biochemical characterization of a phosphinate inhibitor of Escherichia coli MurC. Biochemistry 40, 12207– 12214. [22] Nölting, B., 1999. Protein Folding Kinetics: Biophysical Methods. Springer, Berlin. [23] Pohjanpalo, H., 1978. System identifiability based on the power series expansion of the solution. Math. Biosci. 41, 21–33. [24] Pohjanpalo, H., 1982. Identifiability of deterministic differential models in state space. research report no. 56. Tech. rep., Technical Research Centre of Finland, Espoo. [25] Saccomani, M., Audoly, S., Bellu, G., D’Angio, L., 2001. A new differential algebra algorithm to test identifiability of nonlinear systems with given initial conditions. IEEE Conference on Decision and Control 4, 3108–3113. [26] Saccomani, M. P., Audoly, S., D’Angio, L., 2003. Parameter identifiability of nonlinear systems: the role of initial conditions. Automatica 39, 619–632. [27] Sauer, U., Heinemann, M., Zamboni, N., 2007. GENETICS: Getting Closer to the Whole Picture. Science 316 (5824), 550–551. [28] Schnell, S., Chappell, M. J., Evans, N. D., Roussel, M. R., 2006. The mechanism distinguishability problem in biochemical kinetics: The single-enzyme, single-substrate reaction as a case study. Comptes Rendus Biologies 329, 51–61. [29] Segel, I. H., 1993. Enzyme Kinetics. Wiley Classics. [30] Snoep, J. L., Westerhoff, H. V., 2005. From isolation to integration, a systems biology approach for building the Silicon Cell. In: Alberghina, L., Westerhoff, H. (Eds.), Systems Biology: Definitions and Perspectives. Springer-Verlag. [31] Tunali, E. T., Tarn, T. J., 1987. New results for identifiability of nonlinear systems. IEEE T. Automat. Contr. 32, 146–154. [32] Vajda, S., Godfrey, K. R., Rabitz, R., 1989. Similarity transformation approach to identifiability analysis of nonlinear compartmental models. Math. Biosci. 93, 217–248. [33] Walsh, C., 2000. Molecular mechanisms that confer antibacterial drug resistance. Nature 406, 775–781. [34] Walter, E., 1982. Identifiability of State Space Models. Springer-Verlag.
URI:	http://wrap.warwick.ac.uk/id/eprint/40524

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