Maximum Entropy Production and Maximum Shannon Entropy as Germane Principles for the Evolution of Enzyme Kinetics

Is the catalytic activity of triosephosphate isomerase fully optimized? An investigation based on maximization of entropy production

“…Some of the examples used to disprove MaxEP are outside the range of the principle's applicability or even worse violate the second law corollary that EP must always be positive-definite [11]. Dewar [34,35] and Martyushev [10,11,30] pointed out the relevance of MaxEP as a physical principle in statistical physics [36], transport theory [37] and thermomechanics [38], while numerous other applications and supporting observations were found including geology [39], climatology [40], crystal growth [41], nanophysics [42], and biology [4,[12][13][14]43]. It is still an open question how general MaxEP is as a selection principle in irreversible thermodynamics [11] or even as a new paradigm for biological evolution-the survival of the likeliest [44]-providing muchneeded physical insight into the driving force for pre-biological and biological evolution.…”

“…It also leads to better similarity with measured kinetic constants. The applications of MaxEP to internal transitions [4,12,13] of cyclic enzyme kinetic schemes indicated that order of magnitude or better similarity with measured kinetic constants can be reached when these transitions are optimized, but optimization scenarios were not explored for different transitions between functional states, and corresponding entropy productions were not compared. In the present work, we used overall entropy production and a less-than-perfect agreement between optimized and experimental kinetic constants as a guide to which transition between functional states is the best candidate for additional optimization.…”

“…An alternative approach is to maximize entropy production for functionally important internal enzyme transitions [4,12] subject to appropriate constraints. The diffusion limit for ligands is the most important constraint.…”

“…We focused here only on calculating the entropy production without considering the distribution of state probabilities. In some cases, Shannon's information entropy associated with the enzyme state probabilities S ¼ − ∑ 4 i¼1 p i lnp i can also be maximized with respect to some or all forward kinetic constants [4,14]. Optimal kinetic constants found by information entropy maximization can then be compared to their optimal values found from the MaxEP application.…”

“…Since both biological evolution and the maintenance of macromolecules in an active cell are highly dissipative processes, it is natural to ask if some physical principle from the field of irreversible thermodynamics is relevant for life and its evolution [4]. Also, how we can judge if some enzymes have become fully evolved, as has been claimed [5,6]?…”