This work presents the review of the results obtained during last years on the mathematical modeling of glycolytic dynamics under influx1,2,3 and temperature4,5 control. They are motivated by an extensive set of experimental findings obtained by the Biophysics Group of Magdeburg University (Germany) during 2002-2009 and tested using these data.
We base our study on the Selkov model (with certain modifications), which takes into account the key step the glycolytic reaction cascade governed by phosphofructokinase. The introduced control via an inhomogeneous influx of substrate into the yeast extract allows to reproduce and explain recent experimentally detected phenomena of phase reversal for the traveling waves in a chemical reactor. As well, we discuss new biochemical three-dimensional reaction-diffusion model, where spatio-temporal oscillatory dynamics originates due to the boundary conditions instead of reaction terms in a classic sense.
Finally, we reproduce in a model the key features observed in the experiments with temperature regulation introducing the temperature-dependent autocatalytic coefficient and analyzing its influence on the chemical reaction dynamics in local and coupled glycolytic systems.
These results highlight new unexpected phenomena of such basic biochemical system as glycolysis and provide new opportunities in their utilization in biophysical experiments (e.g. diffusivity determination for dense media).