Correlation Metric Construction: Theory of Statistical Construction of Reaction Mechanisms

Abstract

In chapter 5, we studied the responses of chemical species in a reaction system to pulse perturbations and showed the deduction of direct, causal connectivities by chemical reactions—the reaction pathway—and the reaction mechanism from such measurements. The causal connectivites give the information on how the chemical species are connected by chemical reactions. In this chapter we turn to another source of information about chemical species in a reaction system, that of correlations among the species. Correlations of concentrations are measures of the statistical dependence of the concentration of one species on that of one or more of the other species in the system. Such correlations can be determined from measurements of time series of concentrations collected around a stationary state (nonequilibrium or equilibrium). We shall show that from concentration correlations it is possible to construct a skeletal diagram of the reaction system that gives a graphical measure of strong control and regulatory structure in reaction networks, gives some information on connectivity, leads to information on the reaction pathway and mechanism, and may simplify the analysis of such networks by identifying possible, nearly separable subsystems. We begin with the demonstration and explanation of this approach by analyzing some abstract reaction models. In chapter 8 we show the utility of this “correlation metric construction” (CMC) with application to time-series measurements on a part of glycolysis, and in chapter 13 on an extensive genome study. Consider a chemical system as shown in fig. 7.1. Mechanisms of this type are common in biochemical networks. For example, the subnetwork of fig. 7.1 containing S3 to S5 is based on a simple model of fructose interconversion in glycolysis and the subnetwork composed of S6 to S7 is similar to the phosphorylation/dephosphorylation cycles found in cyclic cascades. As an aside, this mechanism performs the function of a biochemical NAND gate, another example of a chemical computational function (see chapter 4).