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We investigate the relations between the enzyme kinetic flexibility, the rate of entropy production, and the Shannon information entropy in a steady-state enzyme reaction. All these quantities are maximized with respect to enzyme rate constants. We show that the steady-state, which is characterized by the most flexible enzymatic transitions between the enzyme conformational states, coincides with the global maxima of the Shannon information entropy and the rate of entropy production. This steady-state of an enzyme is referred to as globally optimal. This theoretical approach is then used for the analysis of the kinetic and the thermodynamic performance of the enzyme triose-phosphate isomerase. The analysis reveals that there exist well-defined maxima of the kinetic flexibility, the rate of entropy production, and the Shannon information entropy with respect to any arbitrarily chosen rate constant of the enzyme and that these maxima, calculated from the measured kinetic rate constants for the triose-phosphate isomerase are lower, however of the same order of magnitude, as the maxima of the globally optimal state of the enzyme. This suggests that the triose-phosphate isomerase could be a well, but not fully evolved enzyme, as it was previously claimed. Herein presented theoretical investigations also provide clear evidence that the flexibility of enzymatic transitions between the enzyme conformational states is a requirement for the maximal Shannon information entropy and the maximal rate of entropy production.

The origin of translation is critical for understanding the evolution of life, including the origins of life. The canonical genetic code is one of the most dominant aspects of life on this planet, while the origin of heredity is one of the key evolutionary transitions in living world. Why the translation apparatus evolved is one of the enduring mysteries of molecular biology. Assuming the hypothesis, that during the emergence of life evolution had to first involve autocatalytic systems which only subsequently acquired the capacity of genetic heredity, we propose and discuss possible mechanisms, basic aspects of the emergence and subsequent molecular evolution of translation and ribosomes, as well as enzymes as we know them today. It is possible, in this sense, to view the ribosome as a digital-to-analogue information converter. The proposed mechanism is based on the abilities and tendencies of short RNA and polypeptides to fold and to catalyse biochemical reactions. The proposed mechanism is in concordance with the hypothesis of a possible chemical co-evolution of RNA and proteins in the origin of the genetic code or even more generally at the early evolution of life on Earth. The possible abundance and availability of monomers at prebiotic conditions are considered in the mechanism. The hypothesis that early polypeptides were folding on the RNA scaffold is also considered and mutualism in molecular evolutionary development of RNA and peptides is favoured.

We demonstrate that the maximum entropy production principle (MEPP) serves as a physical selection principle for the description of the most probable non-equilibrium steady states in simple enzymatic reactions. A theoretical approach is developed, which enables maximization of the density of entropy production with respect to the enzyme rate constants for the enzyme reaction in a steady state. Mass and Gibbs free energy conservations are considered as optimization constraints. In such a way computed optimal enzyme rate constants in a steady state yield also the most uniform probability distribution of the enzyme states. This accounts for the maximal Shannon information entropy. By means of the stability analysis it is also demonstrated that maximal density of entropy production in that enzyme reaction requires flexible enzyme structure, which enables rapid transitions between different enzyme states. These results are supported by an example, in which density of entropy production and Shannon information entropy are numerically maximized for the enzyme Glucose Isomerase.

Explaining the emergence of life is perhaps central and the most challenging question in modern science. Within this area of research, the emergence and evolution of the genetic code is supposed to be a critical transition in the evolution of modern organisms. The canonical genetic code is one of the most dominant aspects of life on this planet, and thus studying its origin is critical to understanding the evolution of life, including life’s emergence. In this sense it is possible to view the ribosome as a digital-to-analogue information converter. Why the translation apparatus evolved, is one of the enduring mysteries of molecular biology. Assuming the hypothesis that during the emergence of life evolution had to first involve autocatalytic systems, which only subsequently acquired the capacity of genetic heredity, in the present article we discuss some aspects and causes of the possible emergence of digital, discrete information arising from analogue information realized in the intra- and inter-molecular interactions throughout molecular evolution. How such reverse translation was achieved at a molecular level is still unclear. The results of such debates and investigations might shift current biological paradigms and might also have a momentous significance for modern philosophy in understanding our place in the universe.

A procedure for maximization of the density of entropy production in a single stationary two-step enzyme reaction is developed. Under the constraints of mass conservation, fixed equilibrium constant of a reaction and fixed products of forward and backward enzyme rate constants the existence of maximum in the density of entropy production is demonstrated. In the state with maximal density of entropy production the optimal enzyme rate constants, the stationary concentrations of the substrate and the product, the stationary product yield as well as the stationary reaction flux are calculated. The test, whether these calculated values of the reaction parameters are consistent with their corresponding measured values, is performed for the enzyme Glucose Isomerase. It is found that calculated and measured rate constants agree within an order of magnitude, whereas the calculated reaction flux and the product yield differ from their corresponding measured values for less than 20 % and 5 %, respectively. This indicates that the enzyme Glucose Isomerase, considered in a non-equilibrium stationary state, as found in experiments using the continuous stirred tank reactors, possibly operates close to the state with the maximum in the density of entropy production.