Quantitative analysis of the effective functional structure in yeast glycolysis.

The understanding of the effective functionality that governs the enzymatic self-organized processes in cellular conditions is a crucial topic in the post-genomic era. In recent studies, Transfer Entropy has been proposed as a rigorous, robust and self-consistent method for the causal quantification of the functional information flow among nonlinear processes. Here, in order to quantify the functional connectivity for the glycolytic enzymes in dissipative conditions we have analyzed different catalytic patterns using the technique of Transfer Entropy. The data were obtained by means of a yeast glycolytic model formed by three delay differential equations where the enzymatic rate equations of the irreversible stages have been explicitly considered. These enzymatic activity functions were previously modeled and tested experimentally by other different groups. The results show the emergence of a new kind of dynamical functional structure, characterized by changing connectivity flows and a metabolic invariant that constrains the activity of the irreversible enzymes. In addition to the classical topological structure characterized by the specific location of enzymes, substrates, products and feedback-regulatory metabolites, an effective functional structure emerges in the modeled glycolytic system, which is dynamical and characterized by notable variations of the functional interactions. The dynamical structure also exhibits a metabolic invariant which constrains the functional attributes of the enzymes. Finally, in accordance with the classical biochemical studies, our numerical analysis reveals in a quantitative manner that the enzyme phosphofructokinase is the key-core of the metabolic system, behaving for all conditions as the main source of the effective causal flows in yeast glycolysis.