Enzymatic reactions in cells and in certain types of biotechnological reactors operate as open thermodynamic systems with incoming and outgoing fluxes of matter. As a rule, such systems are often shifted far from thermodynamic equilibrium. While behaviour of systems operating in (or close to) equilibrium state is well understood, the behaviour of open non-equilibrium systems is much less clear. The maximum entropy production principle is a type of thermodynamic optimization, which states that open non-equilibrium systems spontaneously approach towards stationary state with maximal entropy production. It is also claimed that such a state is statistically most probable state of the system and thus characterised by the maximum in the Shannon information entropy. We investigated whether the most likely thermodynamic states of enzymatic reactions are indeed characterised by the maximal entropy production. For five different enzymes: Glucose Isomerase, three different types of b-Lactamases and Triose Phosphate Isomerase, we derived the entropy production and the Shannon information entropy as a function of enzyme rate constants. Under the conditions of mass and Gibbs free energy conservations the co-existence of well-defined global maxima in entropy production and Shannon information entropy is demonstrated, with respect to arbitrary chosen kinetic parameter. By the use of local stability analysis we demonstrate that co-existence of maxima in entropy production and information entropy might be a consequence of flexible enzymatic structure, which is required for fast transitions between different enzyme macromolecular states.

Financing: ARRS