Coefficientsof skewness (gl)of all distributions were determined. The differences between the 'me' values of the control coefficients and the modes of the.
294s BiochemicalSociety Transactions (1995) 23
Error and bias in control coefficients calculated from elasticities SIMON THOMAS and DAVID A. FELL School of Biological and Molecular Sciences, Oxford Brookes University, Gipsy Lane, OXFORD,OX3 OBP. The connectivity, summation and branch-point theorems are central features of Metabolic Control Analysis, that enable the calculation of control coefficients from quantities such as elasticity coefficients (elasticities),metabolite concentrationsand pathway fluxes. The mamx method combines these theorems, enabling calculation of the flux control, concentration control and branchpoint distribution control coefficients bj means of a single matrix equation [ 1,2]. Consider the simple case of the determination of the flux and concentration control coefficients of a linear pathway, using the summation and connectivity theorems. The normal experimental approach would be to make replicate measurements of each of the elasticities, calculate their means, and use the means to calculate the control coefficients using, for example, the matrix method. However, the experimentallydetermined means will be uncertain, and repeated determinations of these means will give rise to a distribution of values around the 'true' value of each elasticity. Corresponding to the uncertainties in the elasticities there will be correspondingdistributions in the values of the control coefficients. The actual value of a control coefficient calculated from a set of experimentally determined elasticities will represent just one value from the distribution. Therefore, the most likely result of the experiment is given, by definition, by the mode of the control cocfficient distribution. Because of the non-linearity of the matrix method equations, skewed dismbutions of control coefficients will arise, even from normally distributed elasticities. Consequently. the mode of the distribution will not coincide with the true value of the control coefficient, and there is an inherent inaccuracy in the determination of the control coefficients by this method. We have investigated whether this error and bias is siflicant We used computer simulation of experimental results, for a hypothetical two-step linear pathway, in which steps 1 and 2 convert an initial substrate to a final product via intermediate metabolite S. A set of random normal deviates [3] was used to simulate the effect of experimental error on the determination of the s s true value of the pathway's two elasticities (el and €2, using the usual notation). Near-normal dismbutions of the two elasticities were generated, each containing 480 points, simulating the spread of possible experimental results if each of the elasticities had been determined with an SEM corresponding to 10%of its value. The corresponding distributions of the two flux control (d and d)and coefficients were the two concentration control (Cs and determined, by taking pairs of values, one from each of the two elasticity distributions,and calculating the comespondingvalues of the conaol coefficients.The distributions were checked for sixteen S combinations of elasticity values (all combinationsof El = -01, -0.5, -1, - 1 0 &: = 0.1,0.5, 1, 10). Coefficientsof skewness (gl)of all distributions were determined. The differences between the 'me' values of the control coefficients and the modes of the corresponding fnquency dismbutions were also calculated, and expressed as percentages of the true values. The procedure was repeated simulating an SEM of 20%.
6)
Table 1.
