Resilience of the topological phases to frustration.

Recently it was highlighted that one-dimensional antiferromagnetic spin models with frustrated boundary conditions, i.e. periodic boundary conditions in a ring with an odd number of elements, may show very peculiar behavior. Indeed the presence of frustrated boundary conditions can destroy the local magnetic orders presented by the models when different boundary conditions are taken into account and induce novel phase transitions. Motivated by these results, we analyze the effects of the introduction of frustrated boundary conditions on several models supporting (symmetry protected) topological orders, and compare our results with the ones obtained with different boundary conditions. None of the topological order phases analyzed are altered by this change. This observation leads naturally to the conjecture that topological phases of one-dimensional systems are in general not affected by topological frustration.

The maximum entropy production requirement for proton transfers enhances catalytic efficiency for ß-lactamases.

Movement of charges during enzyme catalytic cycle may be due to conformational changes, or to fast electron or proton transfer, or to both events. In each case, entropy production can be calculated using Terrel L. Hill's method, if relevant microscopic rate constants are known. When ranked by their evolutionary distance from putative common ancestor, three ß-lactamases considered in this study show correspondingly increased catalytic constant, catalytic efficiency, and overall entropy production. The acylation and deacylation steps with concomitant proton shuttles are the most important contributors to overall entropy production. The maximal entropy production requirement for the ES↔EP or EP↔E + P step leads to optimal rate constants, performance parameters, and entropy production values, which are close to those extracted from experiments and also rank in accordance with evolutionary distances. Concurrent maximization of entropy productions for both proton transfer steps revealed that evolvability potential of different ß-lactamases is similarly high. These results may have implications in particular for latent potential of ß-lactamases to evolve further and in general for selection of optimized enzymes through natural or directed evolution.

Enzyme kinetics and the maximum entropy production principle.

A general proof is derived that entropy production can be maximized with respect to rate constants in any enzymatic transition. This result is used to test the assumption that biological evolution of enzyme is accompanied with an increase of entropy production in its internal transitions and that such increase can serve to quantify the progress of enzyme evolution. The state of maximum entropy production would correspond to fully evolved enzyme. As an example the internal transition ES↔EP in a generalized reversible Michaelis-Menten three state scheme is analyzed. A good agreement is found among experimentally determined values of the forward rate constant in internal transitions ES→EP for three types of ß-Lactamase enzymes and their optimal values predicted by the maximum entropy production principle, which agrees with earlier observations that ß-Lactamase enzymes are nearly fully evolved. The optimization of rate constants as the consequence of basic physical principle, which is the subject of this paper, is a completely different concept from a) net metabolic flux maximization or b) entropy production minimization (in the static head state), both also proposed to be tightly connected to biological evolution.