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

Theoretical Improvements in Enzyme Efficiency Associated with Noisy Rate Constants and Increased Dissipation

Previous studies have revealed the extraordinarily large catalytic efficiency of some enzymes. High catalytic proficiency is an essential accomplishment of biological evolution. Natural selection led to the increased turnover number, kcat, and enzyme efficiency, kcat/KM, of uni-uni enzymes, which convert a single substrate into a single product. We added or multiplied random noise with chosen rate constants to explore the correlation between dissipation and catalytic efficiency for ten enzymes: beta-galactosidase, glucose isomerase, β-lactamases from three bacterial strains, ketosteroid isomerase, triosephosphate isomerase, and carbonic anhydrase I, II, and T200H. Our results highlight the role of biological evolution in accelerating thermodynamic evolution. The catalytic performance of these enzymes is proportional to overall entropy production-the main parameter from irreversible thermodynamics. That parameter is also proportional to the evolutionary distance of β-lactamases PC1, RTEM, and Lac-1 when natural or artificial evolution produces the optimal or maximal possible catalytic efficiency. De novo enzyme design and attempts to speed up the rate-limiting catalytic steps may profit from the described connection between kinetics and thermodynamics.

Self-Organization of Enzyme-Catalyzed Reactions Studied by the Maximum Entropy Production Principle

The self-organization of open reaction systems is closely related to specific mechanisms that allow the export of internally generated entropy from systems to their environment. According to the second law of thermodynamics, systems with effective entropy export to the environment are better internally organized. Therefore, they are in thermodynamic states with low entropy. In this context, we study how self-organization in enzymatic reactions depends on their kinetic reaction mechanisms. Enzymatic reactions in an open system are considered to operate in a non-equilibrium steady state, which is achieved by satisfying the principle of maximum entropy production (MEPP). The latter is a general theoretical framework for our theoretical analysis. Detailed theoretical studies and comparisons of the linear irreversible kinetic schemes of an enzyme reaction in two and three states are performed. In both cases, in the optimal and statistically most probable thermodynamic steady state, a diffusion-limited flux is predicted by MEPP. Several thermodynamic quantities and enzymatic kinetic parameters, such as the entropy production rate, the Shannon information entropy, reaction stability, sensitivity, and specificity constants, are predicted. Our results show that the optimal enzyme performance may strongly depend on the number of reaction steps when linear reaction mechanisms are considered. Simple reaction mechanisms with a smaller number of intermediate reaction steps could be better organized internally and could allow fast and stable catalysis. These could be features of the evolutionary mechanisms of highly specialized enzymes.

Maximum Entropy Production Theorem for Transitions between Enzyme Functional States and Its Applications

Transitions between enzyme functional states are often connected to conformational changes involving electron or proton transport and directional movements of a group of atoms. These microscopic fluxes, resulting in entropy production, are driven by non-equilibrium concentrations of substrates and products. Maximal entropy production exists for any chosen transition, but such a maximal transitional entropy production (MTEP) requirement does not ensure an increase of total entropy production, nor an increase in catalytic performance. We examine when total entropy production increases, together with an increase in the performance of an enzyme or bioenergetic system. The applications of the MTEP theorem for transitions between functional states are described for the triosephosphate isomerase, ATP synthase, for β-lactamases, and for the photochemical cycle of bacteriorhodopsin. The rate-limiting steps can be easily identified as those which are the most efficient in dissipating free-energy gradients and in performing catalysis. The last step in the catalytic cycle is usually associated with the highest free-energy dissipation involving proton nanocurents. This recovery rate-limiting step can be optimized for higher efficiency by using corresponding MTEP requirements. We conclude that biological evolution, leading to increased optimal catalytic efficiency, also accelerated the thermodynamic evolution, the synergistic relationship we named the evolution-coupling hypothesis.

The maximum entropy production requirement for proton transfers enhances catalytic efficiency for β-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 β-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 β-lactamases is similarly high. These results may have implications in particular for latent potential of β-lactamases to evolve further and in general for selection of optimized enzymes through natural or directed evolution.