  Yeast glycolysis is considered the prototype of dissipative biochemical
oscillators. In cellular conditions, under sinusoidal source of glucose, the
activity of glycolytic enzymes can display either periodic, quasiperiodic or
chaotic behavior.
  In order to quantify the functional connectivity for the glycolytic enzymes
in dissipative conditions we have analyzed different catalytic patterns using
the non-linear statistical tool of Transfer Entropy. The data were obtained by
means of a yeast glycolytic model formed by three delay differential equations
where the enzymatic speed functions of the irreversible stages have been
explicitly considered. These enzymatic activity functions were previously
modeled and tested experimentally by other different groups. In agreement with
experimental conditions, the studied time series corresponded to a
quasi-periodic route to chaos. The results of the analysis are three-fold:
first, 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. Second, the dynamical structure 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.

Quantitative Methods