Metabolic control and its analysis

Additional relationships between elasticities and control coefficients

Authors


  • Symbols. ɛij, elasticity of step i with respect to substance j; Cij, flux control coefficient of enzyme j on the flux measured at step i; vi, rate of enzyme i; [x], absolute magnitude of x

Correspondence to D. A. Fell, Department of Biology, Oxford Polytechnic, Headington, Oxford, England OX3 OBP

Abstract

Existing theorems from the analysis of metabolic control have been taken and embedded in a simple matrix algebra procedure for calculating the flux control coefficients of enzymes (formerly known as sensitivities) in a metabolic pathway from their kinetic properties (their elasticities). New theorems governing the flux control coefficients of branched pathways and substrate cycles have been derived to allow the procedure to be applied to complex pathway configurations. Modifications to the elasticity terms used in the equations have been theoretically justified so that the method remains valid for pathways with conserved metabolites (for example, the adenine nucleotide pool or the intermediates of a catalytic cycle such as the tricarboxylic acid cycle) or with pools of metabolites kept very near to equilibrium by very rapid reactions.

The matrix equations generated using these theorems and relationships may be solved algebraically or numerically. Algebraic solutions have been used to determine the factors responsible for the degree of amplification of flux control coefficients by substrate cycles and to show that it is possible to derive expressions for the elasticities of a group of enzymes.

Abbreviations
Gra P

glyceraldehyde 3-phosphate

Grn P

dihydroxyacetone phosphate

Enzymes
 

Adenylate kinase (EC 2.7.4.3)

 

triosephosphate isomerase (EC 5.3.1.1)

Ancillary