Algorithms for the derivation of Flux and Concentration Control Coefficients

Abstract

A computer program is described that derives the Flux and Concentration Control Coefficients for linear and branched metabolic pathways. The program prompts the user to enter a concise description of the metabolic pathway. From this description, the program constructs the appropriate equations in matrix form. The algorithm employed to obtain the symbolic determinants is described, and this algorithm also provides a convenient method for manual derivation of the Control Coefficients. The computer-based method will accommodate unlimited feed-forward and feed-backward loops and a maximum of two branches from each metabolite on the main pathway. The utility of the method is illustrated with a linear path with feed-forward and feed-backward loops, and with a substrate cycle as an example of a path with two branches.

Metabolic control analysis: a survey of its theoretical and experimental development

“…The search for more accessible ways to determine the relationships between control coefficients and elasticities has led to graphical or diagrammatic methods [178][179][180][181] and the use of analogies from electrical circuits [182]. As happened in enzyme kinetics, the use of computers to generate and solve the equations is being developed [183,184,185].…”

A computer program for the algebraic determination of control coefficients in Metabolic Control Analysis

“…Not surprisingly, a number of microcomputer-based methods have been described for applying Metabolic Control Analysis, of which MetaCon is one of the latest. Examples include SCAMP (Sauro and Fell, 1991), MetaModel (Cornish-Bowden and Hofmeyr, 1991), CONTROL (Letellier et al, 1991) and a program developed by Schulz (1991).…”

“…The program written and described by Schulz (1991) is the most similar to MetaCon in that it produces symbolic expressions for control coefficients. However, it is currently limited to a linear pathway, which can have branches arising from that pathway, and does not have any facility for analysing pathways with conserved cycles.…”

Advances in Metabolic Control Analysis

“…We will not discuss these ad hoc relationships here, since a general approach will be discussed shortly. The calculation of the control coefficients from the elasticity coefficients has been made systematic using matrix representations (Bohnensack, 1985;Fell and Sauro, 1985;Sauro et al, 1987;Barrett, 1989;Cascante et al, 1989a,b;Small and Fell, 1989;Schultz, 1991). A few other approaches have also been developed to facilitate the calculation of control coefficients from the t-elasticities (Hofmeyr, 1989;Sen, 1991).…”