Advances in optimizing enzyme electrostatic preorganization

Multiobjective Evolutionary Strategy for Improving Semiempirical Hamiltonians in the Study of Enzymatic Reactions at the QM/MM Level of Theory

Quantum mechanics/molecular mechanics (QM/MM) simulations are crucial for understanding enzymatic reactions, but their accuracy depends heavily on the quantum-mechanical method used. Semiempirical methods offer computational efficiency but often struggle with accuracy in complex systems. This work presents a novel multiobjective evolutionary strategy for optimizing semiempirical Hamiltonians, specifically designed to enhance their performance in enzymatic QM/MM simulations while remaining broadly applicable to condensed-phase systems. Our methodology combines automated parameter optimization, targeting ab initio or density functional theory (DFT)-reference potential energy surfaces, atomic charges, and gradients, with comprehensive validation through minimum free energy path (MFEP) calculations. To demonstrate its effectiveness, we applied our approach to improve the GFN2-xTB Hamiltonian using two enzymatic systems that involve hydride transfer reactions where the activation energy barrier is severely underestimated: Crotonyl-CoA carboxylase/reductase (CCR) and dihydrofolate reductase (DHFR). The optimized parameters showed significant improvements in reproducing potential and free energy surfaces, closely matching higher-level DFT calculations. Through an efficient two-stage optimization process, we first developed parameters for CCR using reaction path data, then refined these parameters for DHFR by incorporating a targeted set of additional training geometries. This strategic approach minimized the computational cost while achieving accurate descriptions of both systems, as validated through QM/MM simulations using the Adaptive String Method (ASM). Our method represents an efficient approach for optimizing semiempirical methods to study larger systems and longer time scales, with potential applications in enzymatic reaction mechanism studies, drug design, and enzyme engineering.

Preorganized Electric Fields in Voltage-Gated Sodium Channels

Enzymes are reported to catalyze reactions by generating electric fields that promote the evolution of the reaction in the active site. Although seldom used outside enzymatic catalysis, electrostatic preorganization theory and language of electric fields can be generalized to other biological macromolecules. Herein, we performed molecular dynamics simulations of human Nav1.5, Nav1.6, and Nav1.7 with the atomic multipole optmimized energetics for biomolecular applications  polarizable force field. We show that in the absence of an external potential, charged and uncharged residues generate strong electric fields that assist in Na+ motion in the pore. This work emphasizes the importance of charge-dipole interactions in modulating Na+ dynamics, in addition to charge-charge interactions, the focus of a majority of previous studies. Finally, we find that residues share a high level of mutual information through electric fields that can enable the optimization of allosteric pathways.

PyCPET─Computing Heterogeneous 3D Protein Electric Fields and Their Dynamics

Electrostatic preorganization is an exciting mode to understand the catalytic function of enzymes, yet limited tools exist to computationally analyze it. In particular, no methods exist to interpret the geometry, dynamics, and fundamental components of 3D electric fields, E⃗(r), in protein active sites. To address this, we present PyCPET (Python Computation of Electric Field Topologies), a comprehensive, open-source toolbox to analyze E⃗(r) in enzymes. We designed it around computational efficiency and user friendliness with both CPU- and GPU-accelerated codes. Our aim is to provide a set of functions for rich, descriptive analysis of enzyme systems including dynamics, benchmarking, distribution of streamlines analysis in 3D E⃗(r), computation of point E⃗(r), principal component analysis, and 3D E⃗(r) visualization. Finally, we demonstrate its versatility by exploring the nature of electrostatic preorganization and dynamics in three cases: Cytochrome C, Co-substituted Liver Alcohol Dehydrogenase, and HIV Protease. These test systems, along with previous work, establish PyCPET as an essential toolkit for the in-depth analysis and visualization of electric fields in enzymes, unlocking new avenues for understanding electrostatic contributions to enzyme catalysis.

Methods for Theoretical Treatment of Local Fields in Proteins and Enzymes

Electric fields generated by protein scaffolds are crucial in enzymatic catalysis. This review surveys theoretical approaches for detecting, analyzing, and comparing electric fields, electrostatic potentials, and their effects on the charge density within enzyme active sites. Pioneering methods like the empirical valence bond approach rely on evaluating ionic and covalent resonance forms influenced by the field. Strategies employing polarizable force fields also facilitate field detection. The vibrational Stark effect connects computational simulations to experimental Stark spectroscopy, enabling direct comparisons. We highlight how protein dynamics induce fluctuations in local fields, influencing enzyme activity. Recent techniques assess electric fields throughout the active site volume rather than only at specific bonds, and machine learning helps relate these global fields to reactivity. Quantum theory of atoms in molecules captures the entire electron density landscape, providing a chemically intuitive perspective on field-driven catalysis. Overall, these methodologies show protein-generated fields are highly dynamic and heterogeneous, and understanding both aspects is critical for elucidating enzyme mechanisms. This holistic view empowers rational enzyme engineering by tuning electric fields, promising new avenues in drug design, biocatalysis, and industrial applications. Future directions include incorporating electric fields as explicit design targets to enhance catalytic performance and biochemical functionalities.

Spatially Regulated Electrical Forces for Biological Catalysis

It is now well-recognized that biological catalysis depends crucially on spatially regulated electrical forces for optimal efficiency. Several examples of the mechanisms underpinning this will be covered, as will the experimental evidence that oriented electrical fields can enhance specific chemical reactions.

Organophosphate Hydrolysis by a Designed Metalloenzyme: Impact of Mutations Explained

The efficient design of novel enzymes has been attainable only by a combination of theoretical approaches and experimental refinement, suggesting inadequate performance of de novo design protocols. Based on the analysis of the evolutionary trajectory of a designed organophosphate hydrolase, this work aimed at developing and validating the improved theoretical models describing the catalytic activity of five enzyme variants (including wild-type as well as theoretically derived and experimentally refined enzymes) performing the hydrolysis of diethyl 7-hydroxycoumarinyl phosphate. The following aspects possibly important for enzyme design were addressed: the level of theory sufficient for a reliable description of enzyme-reactant interactions, the issue of ground state (GS) destabilization versus transition state (TS) stabilization, and the derivation of the proper side chain rotamers of amino acid residues. For enzyme variants analyzed herein, differential transition state stabilization (DTSS, i.e., preferential TS binding by an enzyme over the GS binding) calculated with a non-empirical model of the interaction energy (i.e., multipole electrostatic plus approximate dispersion terms, MED) displayed a superior performance in ranking the enzyme catalytic activity. The MED DTSS-based systematic rotamer refinement performed with an efficient scanning procedure and accounting for long-range interaction energy terms is an important step capable of unlocking the full potential impact of the given residue that could be otherwise overlooked with a conventional static approach featuring optimization to the nearby minimum. While TS stabilization is the main factor contributing to the increased catalytic activity of the de novo-designed variant studied in this work, directed evolution refinement appears to impact the catalytic activity of another enzyme variant analyzed herein via GS destabilization.

Electric Fields in Polymeric Systems

Polymer-based electronic devices are limited by slow transport and recombination of newly separated charges. Built-in electric fields, which arise from compositional gradients, are known to improve charge separation, directional charge transport, and to reduce recombination. Yet, the optimization of these fields through the rational design of polymeric materials is not prevalent. Indeed, polymers are disordered and generate nonuniform electric fields that are hard to measure, and therefore, hard to optimize. Here, we review work focusing on the intentional optimization of electric fields in polymeric systems with applications to catalysis, energy conversion, and storage. This includes chemical tuning of constituent monomers, linkers, morphology, etc. that result in stronger molecular dipoles, polarizability or crystallinity. We also review techniques to characterize electric fields in polymers and emerging processing strategies based on electric fields. These studies demonstrate the benefits of optimizing electric fields in polymers. However, rational design is often restricted to the molecular scale, deriving new pendants on, or linkers between, monomers. This does not always translate in strong electric fields at the polymer level, because they strongly depend on the monomer orientation. A better control of the morphology and monomer-to-polymer scaling relationship is therefore crucial to enhance electric fields in polymeric materials.

Catalytic mechanism, computational design, and crystal structure of a highly specific and efficient benzoylecgonine hydrolase

Enzyme therapy for cocaine detoxification should break down both cocaine and its primary toxic metabolite, benzoylecgonine (BZE), which is also the main form of cocaine contaminant in the environment. An ideal BZE-metabolizing enzyme (BZEase) is expected to be highly efficient and selective in BZE hydrolysis. Here, BZEase4 was engineered from bacterial cocaine esterase (CocE) by our reactant state-based enzyme design theories (RED), which has a 34,977-fold improved substrate discrimination between BZE and the neurotransmitter acetylcholine (ACh), compared with wild-type CocE. Under the physiological concentrations of BZE and ACh, the reaction velocity of BZEase4 against BZE is 2.25 × 106-fold higher than it against ACh, suggesting BZEase4 has extremely high substrate selectivity for BZE over ACh to minimize the potential cholinergic side-effects. This study provides additional evidence supporting the further development of BZEase4 toward a promising therapeutic for cocaine overdose, a potentially effective and eco-friendly enzymatic method for BZE degradation in the environment.

XMECP: Reaching State-of-the-Art MECP Optimization in Multiscale Complex Systems

The Python-based program, XMECP, is developed for realizing robust, efficient, and state-of-the-art minimum energy crossing point (MECP) optimization in multiscale complex systems. This article introduces the basic capabilities of the XMECP program by theoretically investigating the MECP mechanism of several example systems including (1) the photosensitization mechanism of benzophenone, (2) photoinduced proton-coupled electron transfer in the cytosine-guanine base pair in DNA, (3) the spin-flip process in oxygen activation catalyzed by an iron-containing 2-oxoglutarate-dependent oxygenase (Fe/2OGX), and (4) the photochemical pathway of flavoprotein adjusted by the intensity of an external electric field. MECPs related to multistate reaction and multistate reactivity in large-scale complex biochemical systems can be well-treated by workflows suggested by the XMECP program. The branching plane updating the MECP optimization algorithm is strongly recommended as it provides derivative coupling vector (DCV) with explicit calculation and can equivalently evaluate contributions from non-QM residues to DCV, which can be nonadiabatic coupling or spin-orbit coupling in different cases. In the discussed QM/MM examples, we also found that the influence on the QM region by DCV can occur through noncovalent interactions and decay with distance. In the example of DNA base pairs, the nonadiabatic coupling occurs across the π-π stacking structure formed in the double-helix system. In contrast to general intuition, in the example of Fe/2OGX, the central ferrous and oxygen part contribute little to the spin-orbit coupling; however, a nearby arginine residue, which is treated by molecular mechanics in the QM/MM method, contributes significantly via two hydrogen bonds formed with α-ketoglutarate (α-KG). This indicates that the arginine residue plays a significant role in oxygen activation, driving the initial triplet state toward the productive quintet state, which is more than the previous knowledge that the arginine residue can bind α-KG at the reaction site by hydrogen bonds.

Designed Local Electric Fields-Promising Tools for Enzyme Engineering

Designing efficient catalysts is one of the ultimate goals of chemists. In this Perspective, we discuss how local electric fields (LEFs) can be exploited to improve the catalytic performance of supramolecular catalysts, such as enzymes. More specifically, this Perspective starts by laying out the fundamentals of how local electric fields affect chemical reactivity and review the computational tools available to study electric fields in various settings. Subsequently, the advances made so far in optimizing enzymatic electric fields through targeted mutations are discussed critically and concisely. The Perspective ends with an outlook on some anticipated evolutions of the field in the near future. Among others, we offer some pointers on how the recent data science/machine learning revolution, engulfing all science disciplines, could potentially provide robust and principled tools to facilitate rapid inference of electric field effects, as well as the translation between optimal electrostatic environments and corresponding chemical modifications.

Free Energy Profile Decomposition Analysis for QM/MM Simulations of Enzymatic Reactions

In enzyme mechanistic studies and mutant design, it is highly desirable to know the individual residue contributions to the reaction free energy and barrier. In this work, we show that such free energy contributions from each residue can be readily obtained by postprocessing ab initio quantum mechanical molecular mechanical (ai-QM/MM) free energy simulation trajectories. Specifically, through a mean force integration along the minimum free energy pathway, one can obtain the electrostatic, polarization, and van der Waals contributions from each residue to the free energy barrier. Separately, a similar analysis procedure allows us to assess the contribution from different collective variables along the reaction coordinate. The chorismate mutase reaction is used to demonstrate the utilization of these two trajectory analysis tools.

From random to rational: improving enzyme design through electric fields, second coordination sphere interactions, and conformational dynamics

Enzymes are versatile and efficient biological catalysts that drive numerous cellular processes, motivating the development of enzyme design approaches to tailor catalysts for diverse applications. In this perspective, we investigate the unique properties of natural, evolved, and designed enzymes, recognizing their strengths and shortcomings. We highlight the challenges and limitations of current enzyme design protocols, with a particular focus on their limited consideration of long-range electrostatic and dynamic effects. We then delve deeper into the impact of the protein environment on enzyme catalysis and explore the roles of preorganized electric fields, second coordination sphere interactions, and protein dynamics for enzyme function. Furthermore, we present several case studies illustrating successful enzyme-design efforts incorporating enzyme strategies mentioned above to achieve improved catalytic properties. Finally, we envision the future of enzyme design research, spotlighting the challenges yet to be overcome and the synergy of intrinsic electric fields, second coordination sphere interactions, and conformational dynamics to push the state-of-the-art boundaries.

Preorganized Internal Electric Field Promotes a Double-Displacement Mechanism for the Adenine Excision Reaction by Adenine DNA Glycosylase

Adenine DNA glycosylase (MutY) is a monofunctional glycosylase, removing adenines (A) misinserted opposite 8-oxo-7,8-dihydroguanine (OG), a common product of oxidative damage to DNA. Through multiscale calculations, we decipher a detailed adenine excision mechanism of MutY that is consistent with all available experimental data, involving an initial protonation step and two nucleophilic displacement steps. During the first displacement step, N-glycosidic bond cleavage is accompanied by the attack of the carboxylate group of residue Asp144 at the anomeric carbon (C1'), forming a covalent glycosyl-enzyme intermediate to stabilize the fleeting oxocarbenium ion. After departure of the excised base, water nucleophiles can be recruited to displace Asp144, completing the catalytic cycle with retention of stereochemistry at the C1' position. The two displacement reactions are found to mostly involve the movement of the oxocarbenium ion, occurring with large charge reorganization and thus sensitive to the internal electric field (IEF) exerted by the polar protein environment. Intriguingly, we find that the negatively charged carboxylate group is a good nucleophile for the oxocarbenium ion, yet an unactivated water molecule is not, and that the electric field catalysis strategy is used by the enzyme to enable its unique double-displacement reaction mechanism. A strong IEF, pointing toward 5' direction of the substrate sugar ring, greatly facilitates the second displacement reaction at the expense of elevating the barrier of the first one, thereby allowing both reactions to occur. These findings not only increase our understanding of the strategies used by DNA glycosylases to repair DNA lesions, but also have important implications for how internal/external electric field can be applied to modulate chemical reactions.

Evaluating the Transition State Stabilization/Destabilization Effects of the Electric Fields from Scaffold Residues by a QM/MM Approach

The protein scaffolds of enzymes not only provide structural support for the catalytic center but also exert preorganized electric fields for electrostatic catalysis. In recent years, uniform oriented external electric fields (OEEFs) have been widely applied to enzymatic reactions to mimic the electrostatic effects of the environment. However, the electric fields exerted by individual residues in proteins may be quite heterogeneous across the active site, with varying directions and strengths at different positions of the active site. Here, we propose a QM/MM-based approach to evaluate the effects of the electric fields exerted by individual residues in the protein scaffold. In particular, the heterogeneity of the residue electric fields and the effect of the native protein environment can be properly accounted for by this QM/MM approach. A case study of the O-O heterolysis reaction in the catalytic cycle of TyrH shows that (1) for scaffold residues that are relatively far from the active site, the heterogeneity of the residue electric field in the active site is not very significant and the electrostatic stabilization/destabilization due to each residue can be well approximated with the interaction energy between a uniform electric field and the QM region dipole; (2) for scaffold residues near the active site, the residue electric fields can be highly heterogeneous along the breaking O-O bond. In such a case, approximating the residue electric fields as uniform fields may misrepresent the overall electrostatic effect of the residue. The present QM/MM approach can be applied to evaluate the residues' electrostatic impact on enzymatic reactions, which also can be useful in computational optimization of electric fields to boost the enzyme catalysis.

Protein Dynamics and Enzymatic Catalysis

This Perspective presents a review of our work and that of others in the highly controversial topic of the coupling of protein dynamics to reaction in enzymes. We have been involved in studying this topic for many years. Thus, this perspective will naturally present our own views, but it also is designed to present an overview of the variety of viewpoints of this topic, both experimental and theoretical. This is obviously a large and contentious topic.

Intrinsic Dynamics of the ClpXP Proteolytic Machine Using Elastic Network Models

ClpXP complex is an ATP-dependent mitochondrial matrix protease that binds, unfolds, translocates, and subsequently degrades specific protein substrates. Its mechanisms of operation are still being debated, and several have been proposed, including the sequential translocation of two residues (SC/2R), six residues (SC/6R), and even long-pass probabilistic models. Therefore, it has been suggested to employ biophysical-computational approaches that can determine the kinetics and thermodynamics of the translocation. In this sense, and based on the apparent inconsistency between structural and functional studies, we propose to apply biophysical approaches based on elastic network models (ENM) to study the intrinsic dynamics of the theoretically most probable hydrolysis mechanism. The proposed models ENM suggest that the ClpP region is decisive for the stabilization of the ClpXP complex, contributing to the flexibility of the residues adjacent to the pore, favoring the increase in pore size and, therefore, with the energy of interaction of its residues with a larger portion of the substrate. It is predicted that the complex may undergo a stable configurational change once assembled and that the deformability of the system once assembled is oriented, to increase the rigidity of the domains of each region (ClpP and ClpX) and to gain flexibility of the pore. Our predictions could suggest under the conditions of this study the mechanism of the interaction of the system, of which the substrate passes through the unfolding of the pore in parallel with a folding of the bottleneck. The variations in the distance calculated by molecular dynamics could allow the passage of a substrate with a size equivalent to ∼3 residues. The theoretical behavior of the pore and the stability and energy of binding to the substrate based on ENM models suggest that in this system, there are thermodynamic, structural, and configurational conditions that allow a possible translocation mechanism that is not strictly sequential.

Geometry of Charge Density as a Reporter on the Role of the Protein Scaffold in Enzymatic Catalysis: Electrostatic Preorganization and Beyond

Enzymes host active sites inside protein macromolecules, which have diverse, often incredibly complex, and atom-expensive structures. It is an outstanding question what the role of these expensive scaffolds might be in enzymatic catalysis. Answering this question is essential to both enzymology and the design of artificial enzymes with proficiencies that will match those of the best natural enzymes. Protein rigidifying the active site, contrasted with the dynamics and vibrational motion promoting the reaction, as well as long-range electrostatics (also known as electrostatic preorganization) were all proposed as central contributions of the scaffold to the catalysis. Here, we show that all these effects inevitably produce changes in the quantum mechanical electron density in the active site, which in turn defines the reactivity. The phenomena are therefore fundamentally inseparable. The geometry of the electron density-a scalar field characterized by a number of mathematical features such as critical points-is a rigorous and convenient descriptor of enzymatic catalysis and a reporter on the role of the protein. We show how this geometry can be analyzed, linked to the reaction barriers, and report in particular on intramolecular electric fields in enzymes. We illustrate these tools on the studies of electrostatic preorganization in several representative enzyme classes, both natural and artificial. We highlight the forward-looking aspects of the approach.

Automated Variable Electric-Field DFT Application for Evaluation of Optimally Oriented Electric Fields on Chemical Reactivity

Recent theoretical work and experiments at molecular junctions have provided a strong conceptualization for the effects of oriented electric fields (OEFs) on organic reactions. Depending on the axis of application, OEFs can increase (or decrease) the reaction rate or distinguish between isomeric pathways. Despite the conceptual elegance of OEFs, which may be applied externally or induced locally, as tools for catalyzing organic reactions, implementation in synthetically relevant systems has been hampered by inefficiencies in evaluating reaction sensitivity to field effects. Herein, we describe the development of the Automated Variable Electric-Field DFT Application (A.V.E.D.A.) for streamlined evaluation of a reaction's susceptibility to OEFs. This open-source software was designed to be accessible for nonexpert users of computational and programming tools. Following initiation by a single command (and with no subsequent intervention) the Linux workflow manages a series of density functional theory calculations and mathematical manipulations to optimize local-minimum and transition-state structures in oriented electric fields of increasing magnitude. The resulting molecular and reaction dipole moments, field-perturbed geometries, and net effective activation energies are compiled for user interpretation. Ten representative pericyclic reactions that showcase the development and evaluation of A.V.E.D.A. are described.

Bond Bundle Analysis of Ketosteroid Isomerase

Bond bundle analysis is used to investigate enzymatic catalysis in the ketosteroid isomerase (KSI) active site. We identify the unique bonding regions in five KSI systems, including those exposed to applied oriented electric fields and those with amino acid mutations, and calculate the precise redistribution of electron density and other regional properties that accompanies either enhancement or inhibition of KSI catalytic activity. We find that catalytic enhancement results from promoting both inter- and intra-molecular electron density redistribution, between bond bundles and bond wedges within the KSI-docked substrate molecule, in the forward direction of the catalyzed reaction. Though the redistribution applies to both types of perturbed systems and is thus suggestive of a general catalytic role, we observe that bond properties (e.g., volume vs energy vs electron count) can respond independently and disproportionately depending on the type of perturbation. We conclude that the resulting catalytic enhancement/inhibition proceeds via different mechanisms, where some bond properties are utilized more by one type of perturbation than the other. Additionally, we find that the correlations between bond wedge properties and catalyzed reaction barrier energies are additive to predict those of bond bundles and atomic basins, providing a rigorous grounding for connecting changes in local charge density to resulting shifts in reaction barrier energy.

Insights into the importance of WPD-loop sequence for activity and structure in protein tyrosine phosphatases

Protein tyrosine phosphatases (PTPs) possess a conserved mobile catalytic loop, the WPD-loop, which brings an aspartic acid into the active site where it acts as an acid/base catalyst. Prior experimental and computational studies, focused on the human enzyme PTP1B and the PTP from Yersinia pestis, YopH, suggested that loop conformational dynamics are important in regulating both catalysis and evolvability. We have generated a chimeric protein in which the WPD-loop of YopH is transposed into PTP1B, and eight chimeras that systematically restored the loop sequence back to native PTP1B. Of these, four chimeras were soluble and were subjected to detailed biochemical and structural characterization, and a computational analysis of their WPD-loop dynamics. The chimeras maintain backbone structural integrity, with somewhat slower rates than either wild-type parent, and show differences in the pH dependency of catalysis, and changes in the effect of Mg2+. The chimeric proteins' WPD-loops differ significantly in their relative stability and rigidity. The time required for interconversion, coupled with electrostatic effects revealed by simulations, likely accounts for the activity differences between chimeras, and relative to the native enzymes. Our results further the understanding of connections between enzyme activity and the dynamics of catalytically important groups, particularly the effects of non-catalytic residues on key conformational equilibria.

Influence of an Oriented External Electric Field on the Mechanism of Double Proton Transfer between Pyrazole and Guanidine: from an Asynchronous Plateau Transition State to a Synchronous or Stepwise Mechanism

The double proton transfer (DPT) reaction between pyrazole and guanidine, a concerted reaction but strongly asynchronous and presenting a "plateau transition region", has been theoretically reinvestigated in the presence of an external uniform electric field. First, we computed the reaction path by DFT and proposed a very detailed description of the constitutive electronic events, based on the ELF topology and the bond evolution theory. Then, we studied the effect of an oriented external electric field (OEEF) on the reaction mechanism, for an OEEF oriented along the proton transfer axis. We observe that in one direction, the DPT reaction can be transformed into a stepwise reaction, going through a stabilized single proton transferred intermediate. Contrarily, the two proton transfers occur simultaneously when the electric field is applied in the opposite direction. In the latter case, the order in which the two protons are transferred in the same elementary step can even be reversed if the OEEF is intense enough. Finally, it has been shown that the evolution of the double proton transfer reaction in the presence of an electric field could be quantitatively anticipated by analyzing the ELF value at the bifurcation point between V(A, H) proton donor and V(B) proton acceptor of the double hydrogen bonded complex in the entrance channel.

Structural dynamics support electrostatic interactions in the active site of Adenylate Kinase

Electrostatic preorganization as well as structural and dynamic heterogeneity are often used to rationalize the remarkable catalytic efficiency of enzymes. However, they are often presented as incompatible because the generation of permanent electrostatic effects implies that the protein structure remains rigid. Here, we use a metric, electric fields, that can treat electrostatic contributions and dynamics effects on equal footing, for a unique perspective on enzymatic catalysis. We find that the residues that contribute the most to electrostatic interactions with the substrate in the active site of Adenylate Kinase (our working example) are also the most flexible residues. Further, entropy-tuning mutations raise flexibility at the picosecond timescale where more conformations can be visited on short time periods, thereby softening the sharp heterogeneity normally visible at the microsecond timescale.