Random effects and variances as a synthesis of nonlinear regression analyses of mitochondrial electron transport

Abstract

SUMMARY This cross-disciplinary paper develops random effects and variances methods, especially for small samples within effects, and applies them to mitochondrial enzyme kinetics. A new force flux kinetic model is introduced for the alternative oxidase of plant mitochondria, the results of 42 experiments are published and the force flux function is fitted by nonlinear regression for each experiment. The results of the regression analyses are synthesized by a random effects model specifying random nonlinear regression coefficients and random variances within experiments distributed in an inverse gamma distribution. The paper shows how random nonlinear regression coefficients analysis can summarize the results of a long series of similar biological experiments and sharpen the analysis of the results of each. A large data set often consists of a family of components each of which can be fitted with the same model. There is a within-component variation for each compo- nent and random effects variation between components. The interpretation of the data requires not only regression analysis of each component but also a subsequent synthesis of the results of such analysis into an overall summary, achieved by specifying random regression coefficients and random error variances. In the example which follows, the individual samples are so small that random variances are specified and contracted predictors of them are computed which are more accurate than the individual estimates. They are required for weights in the analysis. The residual maximum likelihood estimates of the random effects variance matrices are sometimes singular. A Lagrange multiplier method is introduced to compute them. The strength of the integrated analysis comes, however, at the price of a complex set of decisions as to how the different components of the computation are to be fitted together. The paper shows how this is done by a flow diagram for the computations, as well as describing each individual component.