Entropy and Enzyme Catalysis

Practical Synthesis of Chiral α-Aminophosphonates with Weak Bonding Organocatalysis at ppm Loading

α-Aminophosphonic acids as an important class of bioisosteres of α-amino acids demonstrate various biologically important activities. We report here the development of a highly enantioselective isomerization of α-iminophosphonates enabled by an extraordinarily efficient organocatalyst. This organocatalyst afforded a total turnover number (TON) of 20,000-1,000,000 for a wide range of α-alkyl iminophosphonates. Even at a parts-per-million (ppm) loading, this catalyst achieved a complete reaction in greater than 93% enantiomeric excess (ee). Computational studies revealed that this small-molecule catalyst achieved enzyme-like efficiency via a network of weak bonding interactions that effectively preorganized the substrate and catalyst toward a transition-state-like complex. Considering the substrate tolerance, catalytic efficiency, and mechanism, this organocatalyst could be regarded as a small-molecule isomerase.

Enthalpies and entropies of hydration from Monte Carlo simulations

The changes in free energy, enthalpy, and entropy for transfer of a solute from the gas phase into solution are the fundamental thermodynamic quantities that characterize the solvation process. Owing to the development of methods based on free-energy perturbation theory, computation of free energies of solvation has become routine in conjunction with Monte Carlo (MC) statistical mechanics and molecular dynamics (MD) simulations. Computation of the enthalpy change and by inference the entropy change is more challenging. Two methods are considered in this work corresponding to direct averaging for the solvent and solution and to computing the temperature derivative of the free energy in the van't Hoff approach. The application is for neutral organic solutes in TIP4P water using long MC simulations to improve precision. Definitive results are also provided for pure TIP4P water. While the uncertainty in computed free energies of hydration is ca. 0.05 kcal mol-1, it is ca. 0.4 kcal mol-1 for the enthalpy changes from either van't Hoff plots or the direct method with sampling for 5 billion MC configurations. Partial molar volumes of hydration are also computed by the direct method; they agree well with experimental data with an average deviation of 3 cm3 mol-1. In addition, the results permit breakdown of the errors in the free energy changes from the OPLS-AA force field into their enthalpic and entropic components. The excess hydrophobicity of organic solutes is enthalpic in origin.

Perspectives on Computational Enzyme Modeling: From Mechanisms to Design and Drug Development

Understanding enzyme mechanisms is essential for unraveling the complex molecular machinery of life. In this review, we survey the field of computational enzymology, highlighting key principles governing enzyme mechanisms and discussing ongoing challenges and promising advances. Over the years, computer simulations have become indispensable in the study of enzyme mechanisms, with the integration of experimental and computational exploration now established as a holistic approach to gain deep insights into enzymatic catalysis. Numerous studies have demonstrated the power of computer simulations in characterizing reaction pathways, transition states, substrate selectivity, product distribution, and dynamic conformational changes for various enzymes. Nevertheless, significant challenges remain in investigating the mechanisms of complex multistep reactions, large-scale conformational changes, and allosteric regulation. Beyond mechanistic studies, computational enzyme modeling has emerged as an essential tool for computer-aided enzyme design and the rational discovery of covalent drugs for targeted therapies. Overall, enzyme design/engineering and covalent drug development can greatly benefit from our understanding of the detailed mechanisms of enzymes, such as protein dynamics, entropy contributions, and allostery, as revealed by computational studies. Such a convergence of different research approaches is expected to continue, creating synergies in enzyme research. This review, by outlining the ever-expanding field of enzyme research, aims to provide guidance for future research directions and facilitate new developments in this important and evolving field.

Iron Heme Enzyme-Catalyzed Cyclopropanations with Diazirines as Carbene Precursors: Computational Explorations of Diazirine Activation and Cyclopropanation Mechanism

The mechanism of cyclopropanations with diazirines as air-stable and user-friendly alternatives to commonly employed diazo compounds within iron heme enzyme-catalyzed carbene transfer reactions has been studied by means of density functional theory (DFT) calculations of model systems, quantum mechanics/molecular mechanics (QM/MM) calculations, and molecular dynamics (MD) simulations of the iron carbene and the cyclopropanation transition state in the enzyme active site. The reaction is initiated by a direct diazirine-diazo isomerization occurring in the active site of the enzyme. In contrast, an isomerization mechanism proceeding via the formation of a free carbene intermediate in lieu of a direct, one-step isomerization process was observed for model systems. Subsequent reaction with benzyl acrylate takes place through stepwise C-C bond formation via a diradical intermediate, delivering the cyclopropane product. The origin of the observed diastereo- and enantioselectivity in the enzyme was investigated through MD simulations, which indicate a preferred formation of the cis-cyclopropane by steric control.

Biochemical and in silico structural characterization of a cold-active arginase from the psychrophilic yeast, Glaciozyma antarctica PI12

Glaciozyma antarctica PI12 is a psychrophilic yeast isolated from Antarctica. In this work, we describe the heterologous production, biochemical properties and in silico structure analysis of an arginase from this yeast (GaArg). GaArg is a metalloenzyme that catalyses the hydrolysis of L-arginine to L-ornithine and urea. The cDNA of GaArg was reversed transcribed, cloned, expressed and purified as a recombinant protein in Escherichia coli. The purified protein was active against L-arginine as its substrate in a reaction at 20 °C, pH 9. At 10-35 °C and pH 7-9, the catalytic activity of the protein was still present around 50%. Mn2+, Ni2+, Co2+ and K+ were able to enhance the enzyme activity more than two-fold, while GaArg is most sensitive to SDS, EDTA and DTT. The predicted structure model of GaArg showed a very similar overall fold with other known arginases. GaArg possesses predominantly smaller and uncharged amino acids, fewer salt bridges, hydrogen bonds and hydrophobic interactions compared to the other counterparts. GaArg is the first reported arginase that is cold-active, facilitated by unique structural characteristics for its adaptation of catalytic functions at low-temperature environments. The structure and function of cold-active GaArg provide insights into the potentiality of new applications in various biotechnology and pharmaceutical industries.

Ultralight Ultrafast Enzymes

Inorganic materials depleted of heavy stable isotopes are known to deviate strongly in some physicochemical properties from their isotopically natural counterparts. Here we explored for the first time the effect of simultaneous depletion of the heavy carbon, hydrogen, oxygen and nitrogen isotopes on the bacterium E. coli and the enzymes expressed in it. Bacteria showed faster growth, with most proteins exhibiting higher thermal stability, while for recombinant enzymes expressed in depleted media, faster kinetics was discovered. At room temperature, luciferase, thioredoxin and dihydrofolate reductase and Pfu DNA polymerase showed up to a 250 % increase in activity compared to the native counterparts, with an additional ∼50 % increase at 10 °C. Diminished conformational and vibrational entropy is hypothesized to be the cause of the accelerated kinetics. Ultralight enzymes may find an application where extreme reaction rates are required.

Helping proteins come in from the cold: 5 burning questions about cold-active enzymes

Enzymes from psychrophilic (cold-loving) organisms have attracted considerable interest over the past decades for their potential in various low-temperature industrial processes. However, we still lack large-scale commercialization of their activities. Here, we review their properties, limitations and potential. Our review is structured around answers to 5 central questions: 1. How do cold-active enzymes achieve high catalytic rates at low temperatures? 2. How is protein flexibility connected to cold-activity? 3. What are the sequence-based and structural determinants for cold-activity? 4. How does the thermodynamic stability of psychrophilic enzymes reflect their cold-active capabilities? 5. How do we effectively identify novel cold-active enzymes, and can we apply them in an industrial context? We conclude that emerging screening technologies combined with big-data handling and analysis make it reasonable to expect a bright future for our understanding and exploitation of cold-active enzymes.

Entropy Confinement Promotes Hydrogenolysis Activity for Polyethylene Upcycling

Chemical upcycling that catalyzes waste plastics back to high-purity chemicals holds great promise in end-of-life plastics valorization. One of the main challenges in this process is the thermodynamic limitations imposed by the high intrinsic entropy of polymer chains, which makes their adsorption on catalysts unfavorable and the transition state unstable. Here, we overcome this challenge by inducing the catalytic reaction inside mesoporous channels, which possess a strong confined ability to polymer chains, allowing for stabilization of the transition state. This approach involves the synthesis of p-Ru/SBA catalysts, in which Ru nanoparticles are uniformly distributed within the channels of an SBA-15 support, using a precise impregnation method. The unique design of the p-Ru/SBA catalyst has demonstrated significant improvements in catalytic performance for the conversion of polyethylene into high-value liquid fuels, particularly diesel. The catalyst achieved a high solid conversion rate of 1106 g ⋅ gRu -1  ⋅ h-1 at 230 °C. Comparatively, this catalytic activity is 4.9 times higher than that of a control catalyst, Ru/SiO2 , and 14.0 times higher than that of a commercial catalyst, Ru/C, at 240 °C. This remarkable catalytic activity opens up immense opportunities for the chemical upcycling of waste plastics.

Theoretical study on the glycosidic C-C bond cleavage of 3''-oxo-puerarin

Puerarin, daidzein C-glucoside, was known to be biotransformed to daidzein by human intestinal bacteria, which is eventually converted to (S)-equol. The metabolic pathway of puerarin to daidzein by DgpABC of Dorea sp. PUE strain was reported as puerarin (1) → 3''-oxo-puerarin (2) → daidzein (3) + hexose enediolone (C). The second reaction is the cleavage of the glycosidic C-C bond, supposedly through the quinoid intermediate (4). In this work, the glycosidic C-C bond cleavage reaction of 3''-oxo-puerarin (2) was theoretically studied by means of DFT calculation to elucidate chemical reaction mechanism, along with biochemical energetics of puerarin metabolism. It was found that bioenergetics of puerarin metabolism is slightly endergonic by 4.99 kcal/mol, mainly due to the reaction step of hexose enediolone (C) to 3''-oxo-glucose (A). The result implied that there could be additional biochemical reactions for the metabolism of hexose enediolone (C) to overcome the thermodynamic energy barrier of 4.59 kcal/mol. The computational study focused on the C-C bond cleavage of 3''-oxo-puerarin (2) found that formation of the quinoid intermediate (4) was not accessible thermodynamically, rather the reaction was initiated by the deprotonation of 2''C-H proton of 3''-oxo-puerarin (2). The 2''C-dehydro-3''-oxo-puerarin (2a2C) anionic species produced hexose enediolone (C) and 8-dehydro-daidzein anion (3a8), and the latter quickly converted to daidzein through the daidzein anion (3a7). Our study also explains why the reverse reaction of C-glycoside formation from daidzein (3) and hexose enediolone (C) is not feasible.

A pH-responsive bi-MIL-88B MOF coated with folic acid-conjugated chitosan as a promising nanocarrier for targeted drug delivery of 5-Fluorouracil

Cancer has remained one of the leading causes of death worldwide, with a lack of effective treatment. The intrinsic shortcomings of conventional therapeutics regarding tumor specificity and non-specific toxicity prompt us to look for alternative therapeutics to mitigate these limitations. In this regard, we developed multifunctional bimetallic (FeCo) bi-MIL-88B-FC MOFs modified with folic acid-conjugated chitosan (FC) as drug delivery systems (DDS) for targeted delivery of 5-Fluorouracil (5-FU). The bi-MIL-88B nanocarriers were characterized through various techniques, including powder X-ray diffraction, scanning electron microscopy, energy-dispersive X-ray, thermogravimetric analysis, and Fourier transform infrared spectroscopy. Interestingly, 5-FU@bi-MIL-88B-FC showed slower release of 5-FU due to a gated effect phenomenon endowed by FC surface coating compared to un-modified 5-FU@bi-MIL-88B. The pH-responsive drug release was observed, with 58% of the loaded 5-FU released in cancer cells mimicking pH (5.2) compared to only 24.9% released under physiological pH (5.4). The in vitro cytotoxicity and cellular internalization experiments revealed the superiority of 5-FU@bi-MIL-88B-FC as a highly potent targeted DDS against folate receptor (FR) positive SW480 cancer cells. Moreover, due to the presence of Fe and Co in the structure, bi-MIL-88B exhibited peroxidase-like activity for chemodynamic therapy. Based on the results, 5-FU@bi-MIL-88B-FC could serve as promising candidate for smart DDS by sustained drug release and selective targeting.

Glycosylation increases active site rigidity leading to improved enzyme stability and turnover

Glycosylation is the most prevalent protein post-translational modification, with a quarter of glycosylated proteins having enzymatic properties. Yet, the full impact of glycosylation on the protein structure-function relationship, especially in enzymes, is still limited. Here, we show that glycosylation rigidifies the important commercial enzyme horseradish peroxidase (HRP), which in turn increases its turnover and stability. Circular dichroism spectroscopy revealed that glycosylation increased holo-HRP's thermal stability and promoted significant helical structure in the absence of haem (apo-HRP). Glycosylation also resulted in a 10-fold increase in enzymatic turnover towards o-phenylenediamine dihydrochloride when compared to its nonglycosylated form. Utilising a naturally occurring site-specific probe of active site flexibility (Trp117) in combination with red-edge excitation shift fluorescence spectroscopy, we found that glycosylation significantly rigidified the enzyme. In silico simulations confirmed that glycosylation largely decreased protein backbone flexibility, especially in regions close to the active site and the substrate access channel. Thus, our data show that glycosylation does not just have a passive effect on HRP stability but can exert long-range effects that mediate the 'native' enzyme's activity and stability through changes in inherent dynamics.

Enzyme Stability-Activity Trade-Off: New Insights from Protein Stability Weaknesses and Evolutionary Conservation

A general limitation of the use of enzymes in biotechnological processes under sometimes nonphysiological conditions is the complex interplay between two key quantities, enzyme activity and stability, where the increase of one is often associated with the decrease of the other. A precise stability-activity trade-off is necessary for the enzymes to be fully functional, but its weight in different protein regions and its dependence on environmental conditions is not yet elucidated. To advance this issue, we used the formalism that we have recently developed to effectively identify stability strength and weakness regions in protein structures and applied it to a large set of globular enzymes with known experimental structure and catalytic sites. Our analysis showed a striking oscillatory pattern of free energy compensation centered on the catalytic region. Indeed, catalytic residues are usually nonoptimal with respect to stability, but residues in the first shell around the catalytic site are, on the average, stability strengths and thus compensate for this lack of stability; residues in the second shell are weaker again, and so on. This trend is consistent across all enzyme families. It is accompanied by a similar, but less pronounced, pattern of residue conservation across evolution. In addition, we analyzed cold- and heat-adapted enzymes separately and highlighted different patterns of stability strengths and weaknesses, which provide insight into the longstanding problem of catalytic rate enhancement in cold environments. The successful comparison of our stability and conservation results with experimental fitness data, obtained by deep mutagenesis scanning, led us to propose criteria for improving catalytic activity while maintaining enzyme stability, a key goal in enzyme design.

Second-Shell Residues Contribute to Catalysis by Predominately Preorganizing the Apo State in PafA

Residues beyond the first coordination shell are often observed to make considerable cumulative contributions in enzymes. Due to typically indirect perturbations of multiple physicochemical properties of the active site, however, their individual and specific roles in enzyme catalysis and disease-causing mutations remain difficult to predict and understand at the molecular level. Here we analyze the contributions of several second-shell residues in phosphate-irrepressible alkaline phosphatase of flavobacterium (PafA), a representative system as one of the most efficient enzymes. By adopting a multifaceted approach that integrates quantum-mechanical/molecular-mechanical free energy computations, molecular-mechanical molecular dynamics simulations, and density functional theory cluster model calculations, we probe the rate-limiting phosphoryl transfer step and structural properties of all relevant enzyme states. In combination with available experimental data, our computational results show that mutations of the studied second-shell residues impact catalytic efficiency mainly by perturbation of the apo state and therefore substrate binding, while they do not affect the ground state or alter the nature of phosphoryl transfer transition state significantly. Several second-shell mutations also modulate the active site hydration level, which in turn influences the energetics of phosphoryl transfer. These mechanistic insights also help inform strategies that may improve the efficiency of enzyme design and engineering by going beyond the current focus on the first coordination shell.

Entropic control of the free-energy landscape of an archetypal biomolecular machine

Biomolecular machines are complex macromolecular assemblies that utilize thermal and chemical energy to perform essential, multistep, cellular processes. Despite possessing different architectures and functions, an essential feature of the mechanisms of action of all such machines is that they require dynamic rearrangements of structural components. Surprisingly, biomolecular machines generally possess only a limited set of such motions, suggesting that these dynamics must be repurposed to drive different mechanistic steps. Although ligands that interact with these machines are known to drive such repurposing, the physical and structural mechanisms through which ligands achieve this remain unknown. Using temperature-dependent, single-molecule measurements analyzed with a time-resolution-enhancing algorithm, here, we dissect the free-energy landscape of an archetypal biomolecular machine, the bacterial ribosome, to reveal how its dynamics are repurposed to drive distinct steps during ribosome-catalyzed protein synthesis. Specifically, we show that the free-energy landscape of the ribosome encompasses a network of allosterically coupled structural elements that coordinates the motions of these elements. Moreover, we reveal that ribosomal ligands which participate in disparate steps of the protein synthesis pathway repurpose this network by differentially modulating the structural flexibility of the ribosomal complex (i.e., the entropic component of the free-energy landscape). We propose that such ligand-dependent entropic control of free-energy landscapes has evolved as a general strategy through which ligands may regulate the functions of all biomolecular machines. Such entropic control is therefore an important driver in the evolution of naturally occurring biomolecular machines and a critical consideration for the design of synthetic molecular machines.

Unraveling Binding Mechanism and Stability of Urease Inhibitors: A QM/MM MD Study

Soil bacteria can produce urease, which catalyzes the hydrolysis of urea to ammonia (NH3) and carbamate. A variety of urease inhibitors have been proposed to reduce NH3 volatilization by interfering with the urease activity. We report a quantum mechanics/molecular mechanics molecular dynamics (QM/MM MD) study on the mechanism employed for the inhibition of urease by three representative competitive inhibitors; namely, acetohydroxamic acid (AHA), hydroxyurea (HU), and N-(n-butyl)phosphorictriamide (NBPTO). The possible connections between the structural and thermodynamical properties and the experimentally observed inhibition efficiency were evaluated and characterized. We demonstrate that the binding affinity decreases in the order NBPTO >> AHA > HU in terms of the computed activation and reaction free energies. This trend also indicates that NBPTO shows the highest inhibitory activity and the lowest IC50 value of 2.1 nM, followed by AHA (42 μM) and HU (100 μM). It was also found that the X=O moiety (X = carbon or phosphorous) plays a crucial role in the inhibitor binding process. These findings not only elucidate why the potent urease inhibitors are effective but also have implications for the design of new inhibitors.

Biochemical Insights into Imipenem Collateral Susceptibility Driven by ampC Mutations Conferring Ceftolozane/Tazobactam Resistance in Pseudomonas aeruginosa

Several Pseudomonas aeruginosa AmpC mutants have emerged that exhibit enhanced activity against ceftazidime and ceftolozane, while also evading inhibition by avibactam. Interestingly, P. aeruginosa strains harboring these AmpC mutations fortuitously exhibit enhanced carbapenem susceptibility. This acquired susceptibility was investigated by comparing the degradation of imipenem by wild-type and cephalosporin-resistant AmpC. We show that cephalosporin-resistant AmpC enzymes lose their efficacy for hydrolyzing imipenem and suggest that this may be due to their increased flexibility and dynamics relative to the wild type.

Accelerated Storage for Shelf-Life Prediction of Lyophiles: Temperature Dependence of Degradation of Amorphous Small Molecular Weight Drugs and Proteins

Prediction of lyophilized product shelf-life using accelerated stability data requires understanding the temperature dependence of the degradation rate. Despite the abundance of published studies on stability of freeze-dried formulations and other amorphous materials, there are no definitive conclusions on the type of pattern one can expect for the temperature dependence of degradation. This lack of consensus represents a significant gap which may impact development and regulatory acceptance of freeze-dried pharmaceuticals and biopharmaceuticals. Review of the literature demonstrates that the temperature dependence of degradation rate constants in lyophiles can be represented by the Arrhenius equation in most cases. In some instances there is a break in the Arrhenius plot around the glass transition temperature or a related characteristic temperature. The majority of the activation energies (E_a), which are reported for various degradation pathways in lyophiles, falls in the range of 8 to 25 kcal/mol. The degradation E_a values for lyophiles are compared with the E_a for relaxation processes and diffusion in glasses, as wells as solution chemical reactions. Collectively, analysis of the literature demonstrates that the Arrhenius equation represents a reasonable empirical tool for analysis, presentation, and extrapolation of stability data for lyophiles, provided that specific conditions are met.

Protein dynamics: The future is bright and complicated!

Biological life depends on motion, and this manifests itself in proteins that display motion over a formidable range of time scales spanning from femtoseconds vibrations of atoms at enzymatic transition states, all the way to slow domain motions occurring on micro to milliseconds. An outstanding challenge in contemporary biophysics and structural biology is a quantitative understanding of the linkages among protein structure, dynamics, and function. These linkages are becoming increasingly explorable due to conceptual and methodological advances. In this Perspective article, we will point toward future directions of the field of protein dynamics with an emphasis on enzymes. Research questions in the field are becoming increasingly complex such as the mechanistic understanding of high-order interaction networks in allosteric signal propagation through a protein matrix, or the connection between local and collective motions. In analogy to the solution to the "protein folding problem," we argue that the way forward to understanding these and other important questions lies in the successful integration of experiment and computation, while utilizing the present rapid expansion of sequence and structure space. Looking forward, the future is bright, and we are in a period where we are on the doorstep to, at least in part, comprehend the importance of dynamics for biological function.

Toward Reliable and Insightful Entropy Calculations on Flexible Molecules

The absolute entropy of a flexible molecule can be approximated by the sum of a rigid-rotor-harmonic-oscillator (RRHO) entropy and a Gibbs-Shannon entropy associated to the Boltzmann distribution for the occupation of the conformational energy levels. Herein, we show that such partitioning, which has received renewed interest, leads to accurate entropies of single molecules of increasing size provided that the conformational part is estimated by means of a set of discretization and expansion techniques that are able to capture the significant correlation effects among the torsional motions. To ensure a reliable entropy estimation, we rely on extensive sampling as that produced by classical molecular dynamics simulations on the microsecond time scale, which is currently affordable for small- and medium-sized molecules. According to test calculations, the gas-phase entropy of simple organic molecules is predicted with a mean unsigned error of 0.9 cal/(mol K) when the RRHO entropies are computed at the B3LYP-D3/cc-pVTZ level. Remarkably, the same protocol gives small errors [<1 cal/(mol K)] for the extremely flexible linear alkane molecules (C_nH_2n+2, n = 14, 16, and 18). Similarly, we obtain well-converged entropies for a more challenging test of drug molecules, which exhibit more pronounced correlation effects. We also perform equivalent entropy calculations on a 76 amino acid protein, ubiquitin, by taking advantage of the cutoff-dependent formulation of an expansion technique (correlation-consistent multibody local approximation, CC-MLA), which incorporates genuine correlation effects among the neighboring dihedral angles. Moreover, we show that insightful descriptors of the coupled torsional motions can be obtained with the CC-MLA approach.

Effects of Salinity and Temperature on the Flexibility and Function of a Polyextremophilic Enzyme

The polyextremophilic β-galactosidase enzyme of the haloarchaeon Halorubrum lacusprofundi functions in extremely cold and hypersaline conditions. To better understand the basis of polyextremophilic activity, the enzyme was studied using steady-state kinetics and molecular dynamics at temperatures ranging from 10 °C to 50 °C and salt concentrations from 1 M to 4 M KCl. Kinetic analysis showed that while catalytic efficiency (k_cat/K_m) improves with increasing temperature and salinity, K_m is reduced with decreasing temperatures and increasing salinity, consistent with improved substrate binding at low temperatures. In contrast, k_cat was similar from 2-4 M KCl across the temperature range, with the calculated enthalpic and entropic components indicating a threshold of 2 M KCl to lower the activation barrier for catalysis. With molecular dynamics simulations, the increase in per-residue root-mean-square fluctuation (RMSF) was observed with higher temperature and salinity, with trends like those seen with the catalytic efficiency, consistent with the enzyme's function being related to its flexibility. Domain A had the smallest change in flexibility across the conditions tested, suggesting the adaptation to extreme conditions occurs via regions distant to the active site and surface accessible residues. Increased flexibility was most apparent in the distal active sites, indicating their importance in conferring salinity and temperature-dependent effects.

Calculation of Heat Capacity Changes in Enzyme Catalysis and Ligand Binding

It has been suggested that heat capacity changes in enzyme catalysis may be the underlying reason for temperature optima that are not related to unfolding of the enzyme. If this were to be a common phenomenon, it would have major implications for our interpretation of enzyme kinetics. In most cases, the support for the possible existence of a nonzero (negative) activation heat capacity, however, only relies on fitting such a kinetic model to experimental data. It is therefore of fundamental interest to try to use computer simulations to address this issue. One way is simply to calculate the temperature dependence of the activation free energy and determine whether the relationship is linear or not. An alternative approach is to calculate the absolute heat capacities of the reactant and transition states from plain molecular dynamics simulations using either the temperature derivative or fluctuation formula for the enthalpy. Here, we examine these different approaches for a designer enzyme with a temperature optimum that is not caused by unfolding. Benchmark calculations for the heat capacity of liquid water are first carried out using different thermostats. It is shown that the derivative formula for the heat capacity is generally the most robust and insensitive to the thermostat used and its parameters. The enzyme calculations using this method give results in agreement with direct calculations of activation free energies and show no sign of a negative activation heat capacity. We also provide a simple scheme for the calculation of binding heat capacity changes, which is of clear interest in ligand design, and demonstrate it for substrate binding to the designer enzyme. Neither in that case do the simulations predict any negative heat capacity change.

Short-Range Diffusion Enables General Synthesis of Medium-Entropy Alloy Aerogels

Medium-entropy alloy aerogels (MEAAs) with the advantages of both multimetallic alloys and aerogels are promising new materials in catalytic applications. However, limited by the immiscible behavior of different metals, achieving single-phase MEAAs is still a grand challenge. Herein, a general strategy for preparing ultralight 3D porous MEAAs with the lowest density of 39.3 mg cm^-3 among the metal materials is reported, through combining auto-combustion and subsequent low-temperature reduction procedures. The homogenous mixing of precursors at the ionic level makes the short-range diffusion of metal atoms possible to drive the formation of single-phase MEAAs. As a proof of concept in catalysis, as-synthesized Ni₅₀ Co₁₅ Fe₃₀ Cu₅ MEAAs exhibit a high mass activity of 1.62 A mg^-1 and specific activity of 132.24 mA cm^-2 toward methanol oxidation reactions, much higher than those of the low-entropy counterparts. In situ Fourier transform infrared and NMR spectroscopies reveal that MEAAs can enable highly selective conversion of methanol to formate. Most importantly, a methanol-oxidation-assisted MEAAs-based water electrolyzer can achieve a low cell voltage of 1.476 V at 10 mA cm^-2 for making value-added formate at the anode and H₂ at the cathode, 173 mV lower than that of traditional alkaline water electrolyzers.

Quantum biology. π-π entanglement signatures in Protein-DNA interactions

DNA biological functions are carried out by individual proteins that interact with specific sequences along DNA to prime molecular processes required by cellular metabolism. Protein-DNA interactions include DNA replication, gene expression and its regulation, DNA repair, DNA restriction and modification by endonucleases, generally classified as enzymatic functions, or transcription factors functions. To find specific binding target sequences and finalize their activities, proteins must operate in symbiosis with cellular crowded environment identifying extremely small cognate sequences along the DNA chain, ranging from 15-20 bps for repressors to 4-6 bps for restriction enzymes in less than one second.

The Activation Parameters of a Cold-Adapted Short Chain Dehydrogenase Are Insensitive to Enzyme Oligomerization

The structural principles of enzyme cold adaptation are of fundamental interest both for understanding protein evolution and for biotechnological applications. It has become clear in recent years that structural flexibility plays a major role in tuning enzyme activity at low temperatures, which is reflected by characteristic changes in the thermodynamic activation parameters for psychrophilic enzymes, compared to those of mesophilic and thermophilic ones. Hence, increased flexibility of the enzyme surface has been shown to lead to a lower enthalpy and a more negative entropy of activation, which leads to higher activity in the cold. This immediately raises the question of how enzyme oligomerization affects the temperature dependence of catalysis. Here, we address this issue by computer simulations of the catalytic reaction of a cold-adapted bacterial short chain dehydrogenase in different oligomeric states. Reaction free energy profiles are calculated at different temperatures for the tetrameric, dimeric, and monomeric states of the enzyme, and activation parameters are obtained from the corresponding computational Arrhenius plots. The results show that the activation free energy, enthalpy, and entropy are remarkably insensitive to the oligomeric state, leading to the conclusion that assembly of the subunit interfaces does not compromise cold adaptation, even though the mobilities of interfacial residues are indeed affected.

Stereodivergent atom-transfer radical cyclization by engineered cytochromes P450

Naturally occurring enzymes can be a source of unnatural reactivity that can be molded by directed evolution to generate efficient biocatalysts with valuable activities. Owing to the lack of exploitable stereocontrol elements in synthetic systems, steering the absolute and relative stereochemistry of free-radical processes is notoriously difficult in asymmetric catalysis. Inspired by the innate redox properties of first-row transition-metal cofactors, we repurposed cytochromes P450 to catalyze stereoselective atom-transfer radical cyclization. A set of metalloenzymes was engineered to impose substantial stereocontrol over the radical addition step and the halogen rebound step in these unnatural processes, allowing enantio- and diastereodivergent radical catalysis. This evolvable metalloenzyme platform represents a promising solution to tame fleeting radical intermediates for asymmetric catalysis.

ThermoSlope: A Software for Determining Thermodynamic Parameters from Single Steady-State Experiments

The determination of the temperature dependence of enzyme catalysis has traditionally been a labourious undertaking. We have developed a new approach to the classical Arrhenius parameter estimation by fitting the change in velocity under a gradual change in temperature. The evaluation with a simulated dataset shows that the approach is valid. The approach is demonstrated as a useful tool by characterizing the Bacillus pumilus LipA enzyme. Our results for the lipase show that the enzyme is psychrotolerant, with an activation energy of 15.3 kcal/mol for the chromogenic substrate para-nitrophenyl butyrate. Our results demonstrate that this can produce equivalent curves to the traditional approach while requiring significantly less sample, labour and time. Our method is further validated by characterizing three α-amylases from different species and habitats. The experiments with the α-amylases show that the approach works over a wide range of temperatures and clearly differentiates between psychrophilic, mesophilic and thermophilic enzymes. The methodology is released as an open-source implementation in Python, available online or used locally. This method of determining the activation parameters can make studies of the temperature dependence of enzyme catalysis more widely adapted to understand how enzymes have evolved to function in extreme environments. Moreover, the thermodynamic parameters that are estimated serve as functional validations of the empirical valence bond calculations of enzyme catalysis.

Evolution of dynamical networks enhances catalysis in a designer enzyme

Activation heat capacity is emerging as a crucial factor in enzyme thermoadaptation, as shown by the non-Arrhenius behaviour of many natural enzymes. However, its physical origin and relationship to the evolution of catalytic activity remain uncertain. Here we show that directed evolution of a computationally designed Kemp eliminase reshapes protein dynamics, which gives rise to an activation heat capacity absent in the original design. These changes buttress transition-state stabilization. Extensive molecular dynamics simulations show that evolution results in the closure of solvent-exposed loops and a better packing of the active site. Remarkably, this gives rise to a correlated dynamical network that involves the transition state and large parts of the protein. This network tightens the transition-state ensemble, which induces a negative activation heat capacity and non-linearity in the activity-temperature dependence. Our results have implications for understanding enzyme evolution and suggest that selectively targeting the conformational dynamics of the transition-state ensemble by design and evolution will expedite the creation of novel enzymes.

Advances in optimizing enzyme electrostatic preorganization

Utilizing electric fields to catalyze chemical reactions is not a new idea, but in enzymology it undergoes a renaissance, inspired by Warhsel's concept of electrostatic preorganization. According to this concept, the source of the immense catalytic efficiency of enzymes is the intramolecular electric field that permanently favors the reaction transition state over the reactants. Within enzyme design, computational efforts have fallen short in designing enzymes with natural-like efficacy. The outcome could improve if long-range electrostatics (often omitted in current protocols) would be optimized. Here, we highlight the major developments in methods for analyzing and designing electric fields generated by the protein scaffolds, in order to both better understand how natural enzymes function, and aid artificial enzyme design.

Computer-aided understanding and engineering of enzymatic selectivity

Enzymes offering chemo-, regio-, and stereoselectivity enable the asymmetric synthesis of high-value chiral molecules. Unfortunately, the drawback that naturally occurring enzymes are often inefficient or have undesired selectivity toward non-native substrates hinders the broadening of biocatalytic applications. To match the demands of specific selectivity in asymmetric synthesis, biochemists have implemented various computer-aided strategies in understanding and engineering enzymatic selectivity, diversifying the available repository of artificial enzymes. Here, given that the entire asymmetric catalytic cycle, involving precise interactions within the active pocket and substrate transport in the enzyme channel, could affect the enzymatic efficiency and selectivity, we presented a comprehensive overview of the computer-aided workflow for enzymatic selectivity. This review includes a mechanistic understanding of enzymatic selectivity based on quantum mechanical calculations, rational design of enzymatic selectivity guided by enzyme-substrate interactions, and enzymatic selectivity regulation via enzyme channel engineering. Finally, we discussed the computational paradigm for designing enzyme selectivity in silico to facilitate the advancement of asymmetric biosynthesis.

Impact of dimensionality and confinement on reaction dynamics and thermodynamics within 1D and 2D nanostructures

Confinement has been shown to contribute to the dynamics of small molecules within nanoscale hydrophobic or hydrophilic cavities. Enclosure within a confined space can also influence energy transfer pathways, such as the enhancement of fluorescence over thermal relaxation. In this paper, the effect of confinement on the thermodynamic properties and reaction kinetics of small hydrophobic molecules confined in a soft polymeric template is detailed. A quasi-elastic neutron scattering experiment identified a substantial decrease in translational diffusion of pyrrole after solubilization within a hydrophobic cavity. This decrease in mobility is due to pyrrole's closer packing and increased density under confinement vs the bulk liquid. The decreased mobility and increased density explain the spontaneous polymerization reaction of pyrrole observed within the cavity. The precise characterization of the polymerization kinetics under confinement found that the reaction is independent of pyrrole concentration, consistent with the close packing density. Kinetic data also show that confinement dimensionality finds a thermodynamic expression in the transition state entropy. The dynamics and kinetics experiments reported here offer rare empirical insight into the important influence that cavity geometry places on the reactions they host.

Enthalpy-Entropy Compensation in Biomolecular Recognition: A Computational Perspective

This mini-review provides an overview of the enthalpy-entropy compensation phenomenon in the simulation of biomacromolecular recognition, with particular emphasis on ligand binding. We approach this complex phenomenon from the point of view of practical computational chemistry. Without providing a detailed description of the plethora of existing methodologies already reviewed in depth elsewhere, we present a series of examples to illustrate different approaches to interpret and predict compensation phenomena at an atomistic level, which is far from trivial to predict using canonical, classic textbook assumptions.

High-entropy materials for catalysis: A new frontier

Entropy plays a pivotal role in catalysis, and extensive research efforts have been directed to understanding the enthalpy-entropy relationship that defines the reaction pathways of molecular species. On the other side, surface of the catalysts, entropic effects have been rarely investigated because of the difficulty in deciphering the increased complexities in multicomponent systems. Recent advances in high-entropy materials (HEMs) have triggered broad interests in exploring entropy-stabilized systems for catalysis, where the enhanced configurational entropy affords a virtually unlimited scope for tailoring the structures and properties of HEMs. In this review, we summarize recent progress in the discovery and design of HEMs for catalysis. The correlation between compositional and structural engineering and optimization of the catalytic behaviors is highlighted for high-entropy alloys, oxides, and beyond. Tuning composition and configuration of HEMs introduces untapped opportunities for accessing better catalysts and resolving issues that are considered challenging in conventional, simple systems.

Kinetic effects of molecular clustering and solvation by extended networks in zeolite acid catalysis

Reactions catalyzed within porous inorganic and organic materials and at electrochemical interfaces commonly occur at high coverage and in condensed media, causing turnover rates to depend strongly on interfacial structure and composition, collectively referred to as "solvent effects". Transition state theory treatments define how solvation phenomena enter kinetic rate expressions, and identify two distinct types of solvent effects that originate from molecular clustering and from the solvation of such clusters by extended solvent networks. We review examples from the recent literature that investigate reactions within microporous zeolite catalysts to illustrate these concepts, and provide a critical appraisal of open questions in the field where future research can aid in developing new chemistry and catalyst design principles.

Biomolecular QM/MM Simulations: What Are Some of the "Burning Issues"?

QM/MM simulations have become an indispensable tool in many chemical and biochemical investigations. Considering the tremendous degree of success, including recognition by a 2013 Nobel Prize in Chemistry, are there still "burning challenges" in QM/MM methods, especially for biomolecular systems? In this short Perspective, we discuss several issues that we believe greatly impact the robustness and quantitative applicability of QM/MM simulations to many, if not all, biomolecules. We highlight these issues with observations and relevant advances from recent studies in our group and others in the field. Despite such limited scope, we hope the discussions are of general interest and will stimulate additional developments that help push the field forward in meaningful directions.

The high catalytic rate of the cold-active Vibrio alkaline phosphatase requires a hydrogen bonding network involving a large interface loop

The role of surface loops in mediating communication through residue networks is still a relatively poorly understood part in the study of cold adaptation of enzymes, especially in terms of their quaternary interactions. Alkaline phosphatase (AP) from the psychrophilic marine bacterium Vibrio splendidus (VAP) is characterized by an analogous large surface loop in each monomer, referred to as the large loop, that hovers over the active site of the other monomer. It presumably has a role in the high catalytic efficiency of VAP which accompanies its extremely low thermal stability. Here, we designed several different variants of VAP with the aim of removing intersubunit interactions at the dimer interface. Breaking the intersubunit contacts from one residue in particular (Arg336) reduced the temperature stability of the catalytically potent conformation and caused a 40% drop in catalytic rate. The high catalytic rates of enzymes from cold‐adapted organisms are often associated with increased dynamic flexibility. Comparison of the relative B‐factors of the R336L crystal structure to that of the wild‐type confirmed surface flexibility was increased in a loop on the opposite monomer, but not in the large loop. The increase in flexibility resulted in a reduced catalytic rate. The large loop increases the area of the interface between the subunits through its contacts and may facilitate an alternating structural cycle demanded by a half‐of‐sites reaction mechanism through stronger ties, as the dimer oscillates between high affinity (active) or low phosphoryl group affinity (inactive).

Unraveling the energetic significance of chemical events in enzyme catalysis via machine-learning based regression approach

The bacterial enzyme class of β-lactamases are involved in benzylpenicillin acylation reactions, which are currently being revisited using hybrid quantum mechanical molecular mechanical (QM/MM) chain-of-states pathway optimizations. Minimum energy pathways are sampled by reoptimizing pathway geometry under different representative protein environments obtained through constrained molecular dynamics simulations. Predictive potential energy surface models in the reaction space are trained with machine-learning regression techniques. Herein, using TEM-1/benzylpenicillin acylation reaction as the model system, we introduce two model-independent criteria for delineating the energetic contributions and correlations in the predicted reaction space. Both methods are demonstrated to effectively quantify the energetic contribution of each chemical process and identify the rate limiting step of enzymatic reaction with high degrees of freedom. The consistency of the current workflow is tested under seven levels of quantum chemistry theory and three non-linear machine-learning regression models. The proposed approaches are validated to provide qualitative compliance with experimental mutagenesis studies.

Comparison of Free-Energy Methods to Calculate the Barriers for the Nucleophilic Substitution of Alkyl Halides by Hydroxide

Calculating the free-energy barriers of liquid-phase chemical reactions with explicit solvent is a considerable challenge. Most studies use the energy and entropy of minimized single-point geometries of the reactants and transition state in implicit solvent using normal mode analysis (NMA). Explicit-solvent methods instead make use of the potential of mean force (PMF). Here, we propose a new energy-entropy (EE) method to calculate the Gibbs free energy of reactants and transition states in explicit solvent by combining quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations with multiscale cell correlation (MCC). We apply it to six nucleophilic substitution reactions of the hydroxide transfer to methyl and ethyl halides in water, where the halides are F, Cl, and Br. We compare EE-MCC Gibbs free energy barriers using two Hamiltonians, self-consistent charge density functional based tight-binding (SCC-DFTB) and B3LYP/6-31+G* density functional theory (DFT) with respective PMF values, EE-NMA values using B3LYP/6-31+G* and M06/6-31+G* DFT in implicit solvent and experimental values derived via transition state theory. The barriers using SCC-DFTB are found to agree well with the PMF and experiment and previous computational studies, being slightly higher but improving on the lower values obtained for the implicit solvent. Achieving convergence over many degrees of freedom remains a challenge for EE-MCC in explicit-solvent QM/MM systems, particularly for the more expensive B3LYP/6-31+G* and M06/6-31+G* DFT methods, but the insightful decomposition of entropy over all degrees of freedom should make EE-MCC a valuable tool for deepening the understanding of chemical reactions.

Temperature, Dynamics, and Enzyme-Catalyzed Reaction Rates

We review the adaptations of enzyme activity to different temperatures. Psychrophilic (cold-adapted) enzymes show significantly different activation parameters (lower activation enthalpies and entropies) from their mesophilic counterparts. Furthermore, there is increasing evidence that the temperature dependence of many enzyme-catalyzed reactions is more complex than is widely believed. Many enzymes show curvature in plots of activity versus temperature that is not accounted for by denaturation or unfolding. This is explained by macromolecular rate theory: A negative activation heat capacity for the rate-limiting chemical step leads directly to predictions of temperature optima; both entropy and enthalpy are temperature dependent. Fluctuations in the transition state ensemble are reduced compared to the ground state. We show how investigations combining experiment with molecular simulation are revealing fundamental details of enzyme thermoadaptation that are relevant for understanding aspects of enzyme evolution. Simulations can calculate relevant thermodynamic properties (such as activation enthalpies, entropies, and heat capacities) and reveal the molecular mechanisms underlying experimentally observed behavior.

Intertwined chemistry of hydroxyl hydrogen-bond donors, epoxides and isocyanates in the organocatalytic synthesis of oxazolidinones versus isocyanurates: rational catalytic investigation and mechanistic understanding

The efficiency and chemoselectivity of the cycloaddition of isocyanates to epoxides to afford oxazolidinones were investigated using hydroxyl hydrogen-bond donors as organocatalysts.

Towards Rational Computational Engineering of Psychrophilic Enzymes

Cold-adapted enzymes from psychrophilic species achieve their high catalytic efficiency at low temperature by a different partitioning of the activation free energy into its enthalpic and entropic components, compared to orthologous mesophilic enzymes. Their lower activation enthalpy, partly compensated by an increased entropic penalty, has been suggested to originate from changes in flexibility of the protein surface. Multiple sequence alignments of psychrophilic and mesophilic enzymes also show characteristic motifs located in surface loops of the protein. Here, we use computer simulations to examine the effects of a number of designed surface mutations of psychrophilic and mesophilic elastases on the temperature dependence of the catalyzed peptide cleavage reaction. For each of 14 mutant enzyme variants we report calculations of their thermodynamic activation parameters. The results show that substitution of psychrophilic loop residues into the mesophilic enzyme consistently changes both the activation parameters and loop flexibilities towards the former, and vice versa for opposite substitutions.

Emergence of a Negative Activation Heat Capacity during Evolution of a Designed Enzyme

Temperature influences the reaction kinetics and evolvability of all enzymes. To understand how evolution shapes the thermodynamic drivers of catalysis, we optimized the modest activity of a computationally designed enzyme for an elementary proton-transfer reaction by nearly 4 orders of magnitude over 9 rounds of mutagenesis and screening. As theorized for primordial enzymes, the catalytic effects of the original design were almost entirely enthalpic in origin, as were the rate enhancements achieved by laboratory evolution. However, the large reductions in ΔH^⧧ were partially offset by a decrease in TΔS^⧧ and unexpectedly accompanied by a negative activation heat capacity, signaling strong adaptation to the operating temperature. These findings echo reports of temperature-dependent activation parameters for highly evolved natural enzymes and are relevant to explanations of enzymatic catalysis and adaptation to changing thermal environments.

Thermodynamic View of Proton Activated Electron Transfer in the Reaction Center of Photosynthetic Bacteria

The temperature dependence of the sequential coupling of proton transfer to the second interquinone electron transfer is studied in the reaction center proteins of photosynthetic bacteria modified by different mutations and treatment by divalent cations. The Eyring plots of kinetics were evaluated by the Marcus theory of electron and proton transfer. In mutants of electron transfer limitation (including the wild type), the observed thermodynamic parameters had to be corrected for those of the fast proton pre-equilibrium. The electron transfer is nonadiabatic with transmission coefficient 6 × 10^-4, and the reorganization energy amounts to 1.2 eV. If the proton transfer is the rate limiting step, the reorganization energy and the works terms fall in the range of 200-500 meV, depending on the site of damage in the proton transfer chain. The product term is 100-150 meV larger than the reactant term. While the electron transfer mutants have a low free energy of activation (∼200 meV), the proton transfer variants show significantly elevated levels of the free energy barrier (∼500 meV). The second electron transfer in the bacterial reaction center can serve as a model system of coupled electron and proton transfer in other proteins or ion channels.

GTP Hydrolysis Without an Active Site Base: A Unifying Mechanism for Ras and Related GTPases

GTP hydrolysis is a biologically crucial reaction, being involved in regulating almost all cellular processes. As a result, the enzymes that catalyze this reaction are among the most important drug targets. Despite their vital importance and decades of substantial research effort, the fundamental mechanism of enzyme-catalyzed GTP hydrolysis by GTPases remains highly controversial. Specifically, how do these regulatory proteins hydrolyze GTP without an obvious general base in the active site to activate the water molecule for nucleophilic attack? To answer this question, we perform empirical valence bond simulations of GTPase-catalyzed GTP hydrolysis, comparing solvent- and substrate-assisted pathways in three distinct GTPases, Ras, Rab, and the G_αi subunit of a heterotrimeric G-protein, both in the presence and in the absence of the corresponding GTPase activating proteins. Our results demonstrate that a general base is not needed in the active site, as the preferred mechanism for GTP hydrolysis is a conserved solvent-assisted pathway. This pathway involves the rate-limiting nucleophilic attack of a water molecule, leading to a short-lived intermediate that tautomerizes to form H₂PO₄^- and GDP as the final products. Our fundamental biochemical insight into the enzymatic regulation of GTP hydrolysis not only resolves a decades-old mechanistic controversy but also has high relevance for drug discovery efforts. That is, revisiting the role of oncogenic mutants with respect to our mechanistic findings would pave the way for a new starting point to discover drugs for (so far) "undruggable" GTPases like Ras.