A new paradigm for electrostatic catalysis of radical reactions in vitamin B12 enzymes

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.

Machine-Learning Prediction of Protein Function from the Portrait of Its Intramolecular Electric Field

We introduce a machine learning framework designed to predict enzyme functionality directly from the heterogeneous electric fields inherent to protein active sites. We apply this method to a curated data set of heme-iron oxidoreductases, spanning three enzyme classes: monooxygenases, peroxidases, and catalases. Conventional analysis, focused on simplistic, point electric fields along the Fe-O bond, is shown to be inadequate for accurate activity prediction. Our model demonstrates that the enzyme's heterogeneous 3-D electric field, alone, can accurately predict its function, without relying on additional protein-specific information. Through feature selection, we uncover key electric field components that not only validate previous studies but also underscore the crucial role of multiple components beyond the traditionally emphasized electric field along the Fe-O bond in heme enzymes. Furthermore, by integrating protein dynamics, principal component analysis, clustering, and QM/MM calculations, we reveal that while dynamic complexities in protein structures can obscure predictions, the model still retains its accuracy. This research significantly advances our understanding of how protein scaffolds possess signature electric fields tailored to their functions at the active site. Moreover, it presents a novel electrostatics-based tool to harness these signature electric fields for predicting enzyme function.

Non-Aufbau electronic structure in radical enzymes and control of the highly reactive intermediates

Radicals are highly reactive, short-lived chemical species that normally react indiscriminately with biological materials, and yet, nature has evolved thousands of enzymes that employ radicals to catalyze thermodynamically challenging chemistry. How these enzymes harness highly reactive radical intermediates to steer the catalysis to the correct outcome is a topic of intense investigation. Here, the results of detailed QM/MM calculations on archetype radical B12-enzymes are presented that provide new insights into how these enzymes control the reactivity of radicals within their active sites. The catalytic cycle in B12-enzymes is initiated through the formation of the 5'-deoxyadenosyl (Ado˙) moiety, a primary carbon-centred radical, which must migrate up to 8 Å to reach the target substrate to engage in the next step of the catalytic process, a hydrogen atom abstraction. Our calculations reveal that Ado˙ within the protein environment exhibits an unusual non-Aufbau electronic structure in which the singly occupied molecular orbital is lower in energy than the doubly occupied orbitals, an uncommon phenomenon known as SOMO-HOMO inversion (SHI). We find that the magnitude of SHI in the initially formed Ado˙ is larger compared to when the Ado˙ is near the intended substrate, leading to the former being relatively less reactive. The modulation of the SHI originates from Coulombic interactions of a quantum nature between a negative charge on a conserved glutamate residue and the spin on the Ado˙. Our findings support a novel hypothesis that these enzymes utilize this quantum Coulombic effect as a means of maintaining exquisite control over the chemistry of highly reactive radical intermediates in enzyme active sites.

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.

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.

The inorganic chemistry of the cobalt corrinoids - an update

The inorganic chemistry of the cobalt corrinoids, derivatives of vitamin B₁₂, is reviewed, with particular emphasis on equilibrium constants for, and kinetics of, their axial ligand substitution reactions. The role the corrin ligand plays in controlling and modifying the properties of the metal ion is emphasised. Other aspects of the chemistry of these compounds, including their structure, corrinoid complexes with metals other than cobalt, the redox chemistry of the cobalt corrinoids and their chemical redox reactions, and their photochemistry are discussed. Their role as catalysts in non-biological reactions and aspects of their organometallic chemistry are briefly mentioned. Particular mention is made of the role that computational methods - and especially DFT calculations - have played in developing our understanding of the inorganic chemistry of these compounds. A brief overview of the biological chemistry of the B₁₂-dependent enzymes is also given for the reader's convenience.

If It Is Hard, It Is Worth Doing: Engineering Radical Enzymes from Anaerobes

With a pressing need for sustainable chemistries, radical enzymes from anaerobes offer a shortcut for many chemical transformations and deliver highly sought-after functionalizations such as late-stage C-H functionalization, C-C bond formation, and carbon-skeleton rearrangements, among others. The challenges in handling these oxygen-sensitive enzymes are reflected in their limited industrial exploitation, despite what they may deliver. With an influx of structures and mechanistic understanding, the scope for designed radical enzymes to deliver wanted processes becomes ever closer. Combined with new advances in computational methods and workflows for these complex systems, the outlook for an increased use of radical enzymes in future processes is exciting.

Computational investigations of B12-dependent enzymatic reactions

Nature employs two biologically active forms of vitamin B₁₂, adenosylcobalamin (or coenzyme B₁₂) and methylcobalamin, as cofactors in molecular transformations both in bacteria and mammals. Computational chemistry, guided by experimental data, has been used to explore fundamental characteristics of these enzymatic reactions. In particular, the quantum mechanics/molecular mechanics (QM/MM) method has proven to be a powerful tool in elucidating important characteristics of B₁₂-dependent enzymatic reactions. Herein, we will present a brief tutorial in conducting QM/MM calculations for B₁₂ enzymatic reactions. We will summarize recent contributions that target the use of QM/MM calculations in both photochemical and enzymatic reactions including AdoCbl-dependent ethanolamine ammonia lyase, glutamate mutase, and photoreceptor CarH.

Electronic structure studies of free and enzyme-bound B12 species by magnetic circular dichroism and complementary spectroscopic techniques

Electronic absorption (Abs) and circular dichroism (CD) spectroscopic techniques have been used successfully for over half a century in studies of free and enzyme-bound B₁₂ species. More recently, magnetic circular dichroism (MCD) spectroscopy and other complementary techniques have provided an increasingly detailed understanding of the electronic structure of cobalamins. While CD spectroscopy measures the difference in the absorption of left- and right-circularly polarized light, MCD spectroscopy adds the application of a magnetic field parallel to the direction of light propagation. Transitions that are formally forbidden according to the Abs and CD selection rules, such as ligand field (or d→d) transitions, can gain MCD intensity through spin-orbit coupling. As such, MCD spectroscopy provides a uniquely sensitive probe of the different binding modes, Co oxidation states, and axial ligand environments of B₁₂ species in enzyme active sites, and thus the distinct reactivities displayed by these species. This chapter summarizes representative MCD studies of free and enzyme-bound B₁₂ species, including those present in adenosyltransferases, isomerases, and reductive dehalogenases. Complementary spectroscopic and computational data are also presented and discussed where appropriate.

Pairing structural reconstruction with catalytic competence to evaluate the mechanisms of key enzymes in the folate-mediated one-carbon pathway

Mammalian metabolism comprises a series of interlinking pathways that include two major cycles: the folate and methionine cycles. The folate-mediated metabolic cycle uses several oxidation states of tetrahydrofolate to carry activated one-carbon units to be readily used and interconverted within the cell. They are required for nucleotide synthesis, methylation and metabolism, and particularly for proliferation of cancer cells. Based on the latest progress in genome-wide CRISPR loss-of-function viability screening of 789 cell lines, we focus on the most cancer-dependent enzymes in this pathway, especially those that are hyperactivated in cancer, to provide new insight into the chemical basis for cancer drug development. Since the complete 3D structure of several of these enzymes of the one-carbon pathway in their active form are not available, we used homology modelling integrated with the interpretation of the reaction mechanism. In addition, have reconstructed the most likely scenario for the reactions taking place paired with their catalytic competence that provides a testable framework for this pathway.

Resolution and characterization of contributions of select protein and coupled solvent configurational fluctuations to radical rearrangement catalysis in coenzyme B12-dependent ethanolamine ammonia-lyase

Coenzyme B12 (adenosylcobalamin) -dependent ethanolamine ammonia-lyase (EAL) is the signature enzyme in ethanolamine utilization metabolism associated with microbiome homeostasis and disease conditions in the human gut. The enzyme conducts a complex choreography of bond-making/bond-breaking steps that rearrange substrate to products through a radical mechanism, with themes common to other coenzyme B12-dependent and radical enzymes. The methods presented are targeted to test the hypothesis that particular, select protein and coupled solvent configurational fluctuations contribute to enzyme function. The general approach is to correlate enzyme function with an introduced perturbation that alters the properties (for example, degree of concertedness, or collectiveness) of protein and coupled solvent dynamics. Methods for sample preparation and low-temperature kinetic measurements by using temperature-step reaction initiation and time-resolved, full-spectrum electron paramagnetic resonance spectroscopy are detailed. A framework for interpretation of results obtained in ensemble systems under conditions of statistical equilibrium within the reacting, globally unstable state is presented. The temperature-dependence of the first-order rate constants for decay of the cryotrapped paramagnetic substrate radical state in EAL, through the chemical step of radical rearrangement, displays a piecewise-continuous Arrhenius dependence from 203 to 295K, punctuated by a kinetic bifurcation over 219-220K. The results reveal the obligatory contribution of a class of select collective protein and coupled solvent fluctuations to the interconversion of two resolved, sequential configurational substates, on the decay time scale. The select class of collective fluctuations also contributes to the chemical step. The methods and analysis are generally applicable to other coenzyme B12-dependent and related radical enzymes.

Through-Space Electrostatic Interactions Surpass Classical Through-Bond Electronic Effects in Enhancing CO2 Reduction Performance of Iron Porphyrins

In his pioneering work to unravel the catalytic power of enzymes, Warshel has pertinently validated that electrostatic interactions play a major role in the activation of substrates. Implementing such chemical artifice in molecular catalysts may help improve their catalytic properties. In this study, a series of tetra-, di-, and mono-substituted iron porphyrins with cationic imidazolium groups were designed. Their presence in the second coordination sphere helped stabilize the [Fe-CO₂ ] intermediate through electrostatic interactions. It was found herein that the electrocatalytic overpotential is a function of the number of embarked imidazolium. Importantly, a gain of six orders of magnitude in turnover frequencies was observed going from a tetra- to a mono-substituted catalyst. Furthermore, the comparative study showed that catalytic performances trend of through-space electrostatic interaction, a first topological effect reported for iron porphyrins, outperforms the classical through-structure electronic effect.

Mechanism of Rate Acceleration of Radical C-C Bond Formation Reaction by a Radical SAM GTP 3',8-Cyclase

While the number of characterized radical S-adenosyl-l-methionine (SAM) enzymes is increasing, the roles of these enzymes in radical catalysis remain largely ambiguous. In radical SAM enzymes, the slow radical initiation step kinetically masks the subsequent steps, making it impossible to study the kinetics of radical chemistry. Due to this kinetic masking, it is unknown whether the subsequent radical reactions require rate acceleration by the enzyme active site. Here, we report the first evidence that a radical SAM enzyme MoaA accelerates the radical-mediated C-C bond formation. MoaA catalyzes an unprecedented 3',8-cyclization of GTP into 3',8-cyclo-7,8-dihydro-GTP (3',8-cH₂GTP) during the molybdenum cofactor (Moco) biosynthesis. Through a series of EPR and biochemical characterizations, we found that MoaA catalyzes a shunt pathway in which an on-pathway intermediate, GTP C-3' radical, abstracts H-4' atom from (4'R)-5'-deoxyadenosine (5'-dA) to transiently generate 5'-deoxyadenos-4'-yl radical (5'-dA-C4'^•) that is subsequently reduced stereospecifically to yield (4'S)-5'-dA. Detailed kinetic characterization of the shunt and the main pathways provided the comprehensive view of MoaA kinetics and determined the rate of the on-pathway 3',8-cyclization step as 2.7 ± 0.7 s^-1. Together with DFT calculations, this observation suggested that the 3',8-cyclization by MoaA is accelerated by 6-9 orders of magnitude. Further experimental and theoretical characterizations suggested that the rate acceleration is achieved mainly by constraining the triphosphate and guanine base positions while leaving the ribose flexible, and a transition state stabilization through H-bond and electrostatic interactions with the positively charged R17 residue. This is the first evidence for rate acceleration of radical reactions by a radical SAM enzyme and provides insights into the mechanism by which radical SAM enzymes accelerate radical chemistry.

Modeling the Reactions Catalyzed by Coenzyme B12 Dependent Enzymes: Accuracy and Cost-Quality Balance

The reactions catalyzed by coenzyme B₁₂ dependent enzymes are formally initiated by the homolytic cleavage of a carbon-cobalt bond and a subsequent or concerted H-atom-transfer reaction. A reasonable model chemistry for describing those reactions should, therefore, account for an accurate description of both reactions. The inherent limitation due to the necessary system size renders the coenzyme B₁₂ system a suitable candidate for DFT or hybrid QM/MM methods; however, the accurate description of both homolytic Co-C cleavage and H-atom-transfer reactions within this framework is challenging and can lead to controversial results with varying accuracy. We present an assessment study of 16 common density functionals applied to prototypical model systems for both reactions. H-abstraction reactions were modeled on the basis of four reference reactions designed to resemble a broad range of coenzyme B₁₂ reactions. The Co-C cleavage reaction is treated by an ONIOM(QM/MM) setup that is in excellent agreement with solution-phase experimental data and is as accurate as full DFT calculations on the complete model system. We find that the meta-GGAs TPSS-D3 and M06L-D3 and the meta-hybrid M06-D3 give the best overall performance with MUEs for both types of reactions below 10 kJ mol^-1. Our recommended model chemistry allows for a fast and accurate description of coenzyme B₁₂ chemistry that is readily applicable to study the reactions in an enzymatic framework.

Efficient methylation of C2 in l-tryptophan by the cobalamin-dependent radical S-adenosylmethionine methylase TsrM requires an unmodified N1 amine

TsrM catalyzes the methylation of C2 in l-tryptophan (Trp). This reaction is the first step in the biosynthesis of the quinaldic acid moiety of the thiopeptide antibiotic thiostrepton, which exhibits potent activity against Gram-positive pathogens. TsrM is a member of the radical S-adenosylmethionine (SAM) superfamily of enzymes, but it does not catalyze the formation of 5'-deoxyadenosin-5'-yl or any other SAM-derived radical. In addition to a [4Fe-4S] cluster, TsrM contains a cobalamin cofactor that serves as an intermediate methyl carrier in its reaction. However, how this cofactor donates a methyl moiety to the Trp substrate is unknown. Here, we showed that the unmodified N1 position of Trp is important for turnover and that 1-thia-Trp and 1-oxa-Trp serve as competitive inhibitors. We also showed that β-cyclopropyl-Trp undergoes C2 methylation in the absence of cyclopropyl ring opening, disfavoring mechanisms that involve unpaired electron density at C3 of the indole ring. Moreover, we showed that all other indole-substituted analogs of Trp undergo methylation at varying but measurable rates and that the analog 7-aza-Trp, which is expected to temper the nucleophilicity of C2 in Trp, is a very poor substrate. Last, no formation of cob(II)alamin or substrate radicals was observed during the reaction with Trp or any molecule within a tested panel of Trp analogs. In summary, our results are most consistent with a mechanism that involves two polar nucleophilic displacements, the second of which requires deprotonation of the indole nitrogen in Trp during its attack on methylcobalamin.

Radical Reaction Control in the AdoMet Radical Enzyme CDG Synthase (QueE): Consolidate, Destabilize, Accelerate

Controlling radical intermediates and thus catalysing and directing complex radical reactions is a central feature of S-adensosylmethionine (SAM)-dependent radical enzymes. We report ab initio and DFT calculations highlighting the specific influence of ion complexation, including Mg2+ , identified as a key catalytic component on radical stability and reaction control in 7-carboxy-7-deazaguanine synthase (QueE). Radical stabilisation energies (RSEs) of key intermediates and radical clock-like model systems of the enzyme-catalysed rearrangement of 6-carboxytetrahydropterin (CPH4), reveals a directing role of Mg2+ in destabilising both the substrate-derived radical and corresponding side reactions, with the effect that the experimentally-observed rearrangement becomes dominant over possible alternatives. Importantly, this is achieved with minimal disruption of the thermodynamics of the substrate itself, affording a novel mechanism for an enzyme to both maintain binding potential and accelerate the rearrangement step. Other mono and divalent ions were probed with only dicationic species achieving the necessary radical conformation to facilitate the reaction.

Structural Basis for Substrate Specificity in Adenosylcobalamin-dependent Isobutyryl-CoA Mutase and Related Acyl-CoA Mutases

Acyl-CoA mutases are a growing class of adenosylcobalamin-dependent radical enzymes that perform challenging carbon skeleton rearrangements in primary and secondary metabolism. Members of this class of enzymes must precisely control substrate positioning to prevent oxidative interception of radical intermediates during catalysis. Our understanding of substrate specificity and catalysis in acyl-CoA mutases, however, is incomplete. Here, we present crystal structures of IcmF, a natural fusion protein variant of isobutyryl-CoA mutase, in complex with the adenosylcobalamin cofactor and four different acyl-CoA substrates. These structures demonstrate how the active site is designed to accommodate the aliphatic acyl chains of each substrate. The structures suggest that a conformational change of the 5'-deoxyadenosyl group from C2'-endo to C3'-endo could contribute to initiation of catalysis. Furthermore, detailed bioinformatic analyses guided by our structural findings identify critical determinants of acyl-CoA mutase substrate specificity and predict new acyl-CoA mutase-catalyzed reactions. These results expand our understanding of the substrate specificity and the catalytic scope of acyl-CoA mutases and could benefit engineering efforts for biotechnological applications ranging from production of biofuels and commercial products to hydrocarbon remediation.

The entropic contributions in vitamin B12 enzymes still reflect the electrostatic paradigm

The catalytic power of enzymes containing coenzyme B12 has been, in some respects, the "last bastion" for the strain hypothesis. Our previous study of this system established by a careful sampling that the major part of the catalytic effect is due to the electrostatic interaction between the ribose of the ado group and the protein and that the strain contribution is very small. This finding has not been sufficiently appreciated due to misunderstandings of the power of the empirical valence bond (EVB) calculations and the need of sufficient sampling. Furthermore, some interesting new experiments point toward entropic effects as the source of the catalytic power, casting doubt on the validity of the electrostatic idea, at least, in the case of B12 enzymes. Here, we focus on the observation of the entropic effects and on analyzing their origin. We clarify that our EVB approach evaluates free energies rather than enthalpies and demonstrate by using the restraint release (RR) approach that the observed entropic contribution to the activation barrier is of electrostatic origin. Our study illustrates the power of the RR approach by evaluating the entropic contributions to catalysis and provides further support to our paradigm for the origin of the catalytic power of B12 enzymes. Overall, our study provides major support to our electrostatic preorganization idea and also highlights the basic requirements from ab initio quantum mechanics/molecular mechanics calculations of activation free energies of enzymatic reactions.

Glutamate 338 is an electrostatic facilitator of C-Co bond breakage in a dynamic/electrostatic model of catalysis by ornithine aminomutase

How cobalamin-dependent enzymes promote C–Co homolysis to initiate radical catalysis has been debated extensively. For the pyridoxal 5′-phosphate and cobalamin-dependent enzymes lysine 5,6-aminomutase and ornithine 4,5-aminomutase (OAM), large-scale re-orientation of the cobalamin-binding domain linked to C–Co bond breakage has been proposed. In these models, substrate binding triggers dynamic sampling of the B₁₂-binding Rossmann domain to achieve a catalytically competent ‘closed’ conformational state. In ‘closed’ conformations of OAM, Glu338 is thought to facilitate C–Co bond breakage by close association with the cobalamin adenosyl group. We investigated this using stopped-flow continuous-wave photolysis, viscosity dependence kinetic measurements, and electron paramagnetic resonance spectroscopy of a series of Glu338 variants. We found that substrate-induced C–Co bond homolysis is compromised in Glu388 variant forms of OAM, although photolysis of the C–Co bond is not affected by the identity of residue 338. Electrostatic interactions of Glu338 with the 5′-deoxyadenosyl group of B₁₂ potentiate C–Co bond homolysis in ‘closed’ conformations only; these conformations are unlocked by substrate binding. Our studies extend earlier models that identified a requirement for large-scale motion of the cobalamin domain. Our findings indicate that large-scale motion is required to pre-organize the active site by enabling transient formation of ‘closed’ conformations of OAM. In ‘closed’ conformations, Glu338 interacts with the 5′-deoxyadenosyl group of cobalamin. This interaction is required to potentiate C–Co homolysis, and is a crucial component of the approximately 10¹² rate enhancement achieved by cobalamin-dependent enzymes for C–Co bond homolysis.

Mathematical and computational modeling in biology at multiple scales

A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms. The use of maximum entropy as an inference tool in the fields of biology and drug discovery is discussed. Mathematical and computational methods and models in the areas of epidemiology, cell physiology and cancer are surveyed. The technique of molecular dynamics is covered, with special attention to force fields for protein simulations and methods for the calculation of solvation free energies. The utility of quantum mechanical methods in biophysical and biochemical modeling is explored. The field of computational enzymology is examined.

Challenges in computational studies of enzyme structure, function and dynamics

In this review we give an overview of the field of Computational enzymology. We start by describing the birth of the field, with emphasis on the work of the 2013 chemistry Nobel Laureates. We then present key features of the state-of-the-art in the field, showing what theory, accompanied by experiments, has taught us so far about enzymes. We also briefly describe computational methods, such as quantum mechanics-molecular mechanics approaches, reaction coordinate treatment, and free energy simulation approaches. We finalize by discussing open questions and challenges.

Co-C dissociation of adenosylcobalamin (coenzyme B12): role of dispersion, induction effects, solvent polarity, and relativistic and thermal corrections

Quantum-chemical cluster modeling is challenged in the limit of large, soft systems by the effects of dispersion and solvent, and well as other physical interactions. Adenosylcobalamin (AdoCbl, coenzyme B12), as one of the most complex cofactors in life, constitutes such a challenge. The cleavage of its unique organometallic Co-C bond has inspired multiple studies of this cofactor. This paper reports the fully relaxed potential energy surface of Co-C cleavage of AdoCbl, including for the first time all side-chain interactions with the dissociating Ado group. Various methods and corrections for dispersion, relativistic effects, solvent polarity, basis set superposition error, and thermal and vibrational effects were investigated, totaling more than 550 single-point energies for the large model. The results show immense variability depending on method, including solvation, functional type, and dispersion, challenging the conceived accuracy of methods used for such systems. In particular, B3LYP-D3 seems to severely underestimate the Co-C bond strength, consistent with previous results, and BP86 remains accurate for cobalamins when dispersion interactions are accounted for.

How does the protein environment optimize the thermodynamics of thiol sulfenylation? Insights from model systems to QM/MM calculations on human 2-Cys peroxiredoxin

Protein thiol/sulfenic acid oxidation potentials provide a tool to select specific oxidation agents, but are experimentally difficult to obtain. Here, insights into the thiol sulfenylation thermodynamics are obtained from model calculations on small systems and from a quantum mechanics/molecular mechanics (QM/MM) analysis on human 2-Cys peroxiredoxin thioredoxin peroxidase B (Tpx-B). To study thiol sulfenylation in Tpx-B, our recently developed computational method to determine reduction potentials relatively compared to a reference system and based on reaction energies reduction potential from electronic energies is updated. Tpx-B forms a sulfenic acid (R-SO(-)) on one of its active site cysteines during reactive oxygen scavenging. The observed effect of the conserved active site residues is consistent with the observed hydrogen bond interactions in the QM/MM optimized Tpx-B structures and with free energy calculations on small model systems. The ligand effect could be linked to the complexation energies of ligand L with CH3S(-) and CH3SO(-). Compared to QM only calculations on Tpx-B's active site, the QM/MM calculations give an improved understanding of sulfenylation thermodynamics by showing that other residues from the protein environment other than the active site residues can play an important role.

Role of active site residues in promoting cobalt-carbon bond homolysis in adenosylcobalamin-dependent mutases revealed through experiment and computation

Adenosylcobalamin (AdoCbl) serves as a source of reactive free radicals that are generated by homolytic scission of the coenzyme's cobalt-carbon bond. AdoCbl-dependent enzymes accelerate AdoCbl homolysis by ∼10(12)-fold, but the mechanism by which this is accomplished remains unclear. We have combined experimental and computational approaches to gain molecular-level insight into this process for glutamate mutase. Two residues, glutamate 330 and lysine 326, form hydrogen bonds with the adenosyl group of the coenzyme. A series of mutations that impair the enzyme's ability to catalyze coenzyme homolysis and tritium exchange with the substrate by 2-4 orders of magnitude were introduced at these positions. These mutations, together with the wild-type enzyme, were also characterized in silico by molecular dynamics simulations of the enzyme-AdoCbl-substrate complex with AdoCbl modeled in the associated (Co-C bond formed) or dissociated [adenosyl radical with cob(II)alamin] state. The simulations reveal that the number of hydrogen bonds between the adenosyl group and the protein side chains increases in the homolytically dissociated state, with respect to the associated state, for both the wild-type and mutant enzymes. The mutations also cause a progressive increase in the mean distance between the 5'-carbon of the adenosyl radical and the abstractable hydrogen of the substrate. Interestingly, the distance between the 5'-carbon and substrate hydrogen, determined computationally, was found to inversely correlate with the log k for tritium exchange (r = 0.93) determined experimentally. Taken together, these results point to a dual role for these residues: they both stabilize the homolytic state through electrostatic interactions between the protein and the dissociated coenzyme and correctly position the adenosyl radical to facilitate the abstraction of hydrogen from the substrate.

Entropic origin of cobalt-carbon bond cleavage catalysis in adenosylcobalamin-dependent ethanolamine ammonia-lyase

Adenosylcobalamin-dependent enzymes accelerate the cleavage of the cobalt-carbon (Co-C) bond of the bound coenzyme by >10(10)-fold. The cleavage-generated 5'-deoxyadenosyl radical initiates the catalytic cycle by abstracting a hydrogen atom from substrate. Kinetic coupling of the Co-C bond cleavage and hydrogen-atom-transfer steps at ambient temperatures has interfered with past experimental attempts to directly address the factors that govern Co-C bond cleavage catalysis. Here, we use time-resolved, full-spectrum electron paramagnetic resonance spectroscopy, with temperature-step reaction initiation, starting from the enzyme-coenzyme-substrate ternary complex and (2)H-labeled substrate, to study radical pair generation in ethanolamine ammonia-lyase from Salmonella typhimurium at 234-248 K in a dimethylsulfoxide/water cryosolvent system. The monoexponential kinetics of formation of the (2)H- and (1)H-substituted substrate radicals are the same, indicating that Co-C bond cleavage rate-limits radical pair formation. Analysis of the kinetics by using a linear, three-state model allows extraction of the microscopic rate constant for Co-C bond cleavage. Eyring analysis reveals that the activation enthalpy for Co-C bond cleavage is 32 ± 1 kcal/mol, which is the same as for the cleavage reaction in solution. The origin of Co-C bond cleavage catalysis in the enzyme is, therefore, the large, favorable activation entropy of 61 ± 6 cal/(mol·K) (relative to 7 ± 1 cal/(mol·K) in solution). This represents a paradigm shift from traditional, enthalpy-based mechanisms that have been proposed for Co-C bond-breaking in B12 enzymes. The catalysis is proposed to arise from an increase in protein configurational entropy along the reaction coordinate.

Radical use of Rossmann and TIM barrel architectures for controlling coenzyme B12 chemistry

The ability of enzymes to harness free-radical chemistry allows for some of the most amazing transformations in nature, including reduction of ribonucleotides and carbon skeleton rearrangements. Enzyme cofactors involved in this chemistry can be large and complex, such as adenosylcobalamin (coenzyme B(12)), simpler, such as S-adenosylmethionine and an iron-sulfur cluster (i.e., poor man's B(12)), or very small, such as one nonheme iron atom coordinated by protein ligands. Although the chemistry catalyzed by these enzyme-bound cofactors is unparalleled, it does come at a price. The enzyme must be able to control these radical reactions, preventing unwanted chemistry and protecting the enzyme active site from damage. Here, we consider a set of radical folds: the (β/α)(8) or TIM barrel, combined with a Rossmann domain for coenzyme B(12)-dependent chemistry. Using specific enzyme examples, we consider how nature employs the common TIM barrel fold and its Rossmann domain partner for radical-based chemistry.

Mutagenesis of a conserved glutamate reveals the contribution of electrostatic energy to adenosylcobalamin co-C bond homolysis in ornithine 4,5-aminomutase and methylmalonyl-CoA mutase

Binding of substrate to ornithine 4,5-aminomutase (OAM) and methylmalonyl-CoA mutase (MCM) leads to the formation of an electrostatic interaction between a conserved glutamate side chain and the adenosyl ribose of the adenosylcobalamin (AdoCbl) cofactor. The contribution of this residue (Glu338 in OAM from Clostridium sticklandii and Glu392 in human MCM) to AdoCbl Co-C bond labilization and catalysis was evaluated by substituting the residue with a glutamine, aspartate, or alanine. The OAM variants, E338Q, E338D, and E338A, showed 90-, 380-, and 670-fold reductions in catalytic turnover and 20-, 60-, and 220-fold reductions in k(cat)/K(m), respectively. Likewise, the MCM variants, E392Q, E392D, and E392A, showed 16-, 330-, and 12-fold reductions in k(cat), respectively. Binding of substrate to OAM is unaffected by the single-amino acid mutation as stopped-flow absorbance spectroscopy showed that the rates of external aldimine formation in the OAM variants were similar to that of the native enzyme. The decrease in the level of catalysis is instead linked to impaired Co-C bond rupture, as UV-visible spectroscopy did not show detectable AdoCbl homolysis upon binding of the physiological substrate, d-ornithine. AdoCbl homolysis was also not detected in the MCM mutants, as it was for the native enzyme. We conclude from these results that a gradual weakening of the electrostatic energy between the protein and the ribose leads to a progressive increase in the activation energy barrier for Co-C bond homolysis, thereby pointing to a key role for the conserved polar glutamate residue in controlling the initial generation of radical species.

Computational enzymology

Techniques for modelling enzyme-catalyzed reaction mechanisms are making increasingly important contributions to biochemistry. They can address fundamental questions in enzyme catalysis and have the potential to contribute to practical applications such as drug development.

Electrostatic origin of the catalytic effect of a supramolecular host catalyst

The development of enzyme mimetic catalysts as well as the analysis of the catalytic effects of such catalysts has been a major challenge for synthetic chemists. One of the impressive examples of artificial catalysts has been the development of a highly charged host compound that provides a significant acceleration to the hydrolysis of orthoformates and other systems. However, the origin of the catalytic effect has not been quantified, and its origin remains somewhat unclear. The understanding of the corresponding supramolecular catalysis has thus become a major challenge, both in terms of computational modeling and in terms of the analysis of the corresponding acid-catalyzed reaction. Here we present a computer simulation study and kinetic analyses that reproduce the experimentally observed catalytic effect, establishing that this effect is due to electrostatic stabilization of the positively charged transition state (relative to the uncharged bound complex). Our study illustrates the crucial need for careful analysis of the complex kinetics of the catalytic effect and the host system, as well as the need for computational modeling in analyzing the catalytic effect and in the potential design of better catalysts. Finally, our finding of the large stabilization of the bound H(3)O(+) points out the very low "local pH" inside the host system even when the solvent is kept at a high pH.

Computational protein engineering: bridging the gap between rational design and laboratory evolution

Enzymes are tremendously proficient catalysts, which can be used as extracellular catalysts for a whole host of processes, from chemical synthesis to the generation of novel biofuels. For them to be more amenable to the needs of biotechnology, however, it is often necessary to be able to manipulate their physico-chemical properties in an efficient and streamlined manner, and, ideally, to be able to train them to catalyze completely new reactions. Recent years have seen an explosion of interest in different approaches to achieve this, both in the laboratory, and in silico. There remains, however, a gap between current approaches to computational enzyme design, which have primarily focused on the early stages of the design process, and laboratory evolution, which is an extremely powerful tool for enzyme redesign, but will always be limited by the vastness of sequence space combined with the low frequency for desirable mutations. This review discusses different approaches towards computational enzyme design and demonstrates how combining newly developed screening approaches that can rapidly predict potential mutation “hotspots” with approaches that can quantitatively and reliably dissect the catalytic step can bridge the gap that currently exists between computational enzyme design and laboratory evolution studies.

Exploring, refining, and validating the paradynamics QM/MM sampling

The performance of the paradynamics (PD) reference potential approach in QM/MM calculations is examined. It is also clarified that, in contrast to some possible misunderstandings, this approach provides a rigorous strategy for QM/MM free energy calculations. In particular, the PD approach provides a gradual and controlled way of improving the evaluation of the free energy perturbation associated with moving from the EVB reference potential to the target QM/MM surface. This is achieved by moving from the linear response approximation to the full free energy perturbation approach in evaluating the free energy changes. We also present a systematic way of improving the reference potential by using Gaussian-based correction potentials along a reaction coordinate. In parallel, we review other recent adaptations of the reference potential approach, emphasizing and demonstrating the advantage of using the EVB potential as a reference potential, relative to semiempirical QM/MM molecular orbital potentials. We also compare the PD results to those obtained by direct calculations of the potentials of the mean force (PMF). Additionally, we propose a way of accelerating the PMF calculations by using Gaussian-based negative potentials along the reaction coordinate (which are also used in the PD refinement). Finally, we discuss performance of the PD and the metadynamics approaches in ab initio QM/MM calculations and emphasize the advantage of using the PD approach.

Adenosylcobalamin enzymes: theory and experiment begin to converge

Adenosylcobalamin (coenzyme B(12)) serves as the cofactor for a group of enzymes that catalyze unusual rearrangement or elimination reactions. The role of the cofactor as the initiator of reactive free radicals needed for these reactions is well established. Less clear is how these enzymes activate the coenzyme towards homolysis and control the radicals once generated. The availability of high resolution X-ray structures combined with detailed kinetic and spectroscopic analyses have allowed several adenosylcobalamin enzymes to be computationally modeled in some detail. Computer simulations have generally obtained good agreement with experimental data and provided valuable insight into the mechanisms of these unusual reactions. Importantly, atomistic modeling of the enzymes has allowed the role of specific interactions between protein, substrate and coenzyme to be explored, leading to mechanistic predictions that can now be tested experimentally. This article is part of a Special Issue entitled: Radical SAM enzymes and Radical Enzymology.

Direct hydride shift mechanism and stereoselectivity of P450nor confirmed by QM/MM calculations

Nitric oxide reductase (P450(nor)) found in Fusarium oxysporum catalyzes the reduction of nitric oxide to N(2)O in a multistep process. The reducing agent, NADH, is bound in the distal pocket of the enzyme, and direct hydride transfer occurs from NADH to the nitric oxide bound heme enzyme, forming intermediate I. Here we studied the possibility of hydride transfer from NADH to both the nitrogen and oxygen of the heme-bound nitric oxide, using quantum chemical and combined quantum mechanics/molecular mechanics (QM/MM) calculations, on two different protein models, representing both possible stereochemistries, a syn- and an anti-NADH arrangement. All calculations clearly favor hydride transfer to the nitrogen of nitric oxide, and the QM-only barrier and kinetic isotope effects are good agreement with the experimental values of intermediate I formation. We obtained higher barriers in the QM/MM calculations for both pathways, but hydride transfer to the nitrogen of nitric oxide is still clearly favored. The barriers obtained for the syn, Pro-R conformation of NADH are lower and show significantly less variation than the barriers obtained in the case of anti conformation. The effect of basis set and wide range of functionals on the obtained results are also discussed.

Investigating the intermediates in the reaction of ribonucleoside triphosphate reductase from Lactobacillus leichmannii: An application of HF EPR-RFQ technology

In this investigation high-frequency electron paramagnetic resonance spectroscopy (HFEPR) in conjunction with innovative rapid freeze-quench (RFQ) technology is employed to study the exchange-coupled thiyl radical-cob(II)alamin system in ribonucleotide reductase from a prokaryote Lactobacillus leichmannii. The size of the exchange coupling (Jex) and the values of the thiyl radical g tensor are refined, while confirming the previously determined (Gerfen et al. (1996) [20]) distance between the paramagnets. Conclusions relevant to ribonucleotide reductase catalysis and the architecture of the active site are presented. A key part of this work has been the development of a unique RFQ apparatus for the preparation of millisecond quench time RFQ samples which can be packed into small (0.5 mm ID) sample tubes used for CW and pulsed HFEPR--lack of this ability has heretofore precluded such studies. The technology is compatible with a broad range of spectroscopic techniques and can be readily adopted by other laboratories.

Does compound I vary significantly between isoforms of cytochrome P450?

The cytochrome P450 (CYP) enzymes are important in many areas, including pharmaceutical development. Subtle changes in the electronic structure of the active species, Compound I, have been postulated previously to account partly for the experimentally observed differences in reactivity between isoforms. Current predictive models of CYP metabolism typically assume an identical Compound I in all isoforms. Here we present a method to calculate the electronic structure and to estimate the Fe-O bond enthalpy of Compound I, and apply it to several human and bacterial CYP isoforms. Conformational flexibility is accounted for by sampling large numbers of structures from molecular dynamics simulations, which are subsequently optimized with density functional theory (B3LYP) based quantum mechanics/molecular mechanics. The observed differences in Compound I between human isoforms are small: They are generally smaller than the spread of values obtained for the same isoform starting from different initial structures. Hence, it is unlikely that the variation in activity between human isoforms is due to differences in the electronic structure of Compound I. A larger difference in electronic structure is observed between the human isoforms and P450(cam) and may be explained by the slightly different hydrogen-bonding environment surrounding the cysteinyl sulfur. The presence of substrate in the active site of all isoforms studied appears to cause a slight decrease in the Fe-O bond enthalpy, apparently due to displacement of water out of the active site, suggesting that Compound I is less stable in the presence of substrate.