Entner-Doudoroff glycolysis pathway as quadratic-cubic mixed autocatalytic network: A kinetic assay

Concentration oscillations are ubiquitous phenomenon in biochemical systems. The present paper considers the simple nonlinear chemical feedback model for standard glycolytic route with prototype autocatalytic steps. Quadratic S + P reversible arrow 2P. Cubic S + 2P reversible arrow 3P. We couple these steps to get the mixed quadratic-cubic model but remarkable array of complex behavior and oscillatory patterns as expected on coupling is surprisingly missing. The observation is in conformity with natural glycolytic alternatives like the Entner-Doudoroff (ED), and phosphoketolase pathways found in Archaea - Thermoproteustenax and other prokaryotes. The fundamental and the practical implications of our findings are thoroughly discussed with pilot calculations and numerical simulations supported via non-linear dynamic analysis. A basic kinetic scheme is suggested for natural glycolytic alternative, ED pathway with its comparison and contrast to other standard routes for glucose metabolism. A key outcome of the study is the phenomenon of oscillator death for the coupled network. A discussion on the thermodynamic aspect of entropy production rate for the model networks are also presented for a comparison.