AutoMeKin2021: An open-source program for automated reaction discovery.

AutoMeKin2021 is an updated version of tsscds2018, a program for the automated discovery of reaction mechanisms (J. Comput. Chem. 2018, 39, 1922). This release features a number of new capabilities: rare-event molecular dynamics simulations to enhance reaction discovery, extension of the original search algorithm to study van der Waals complexes, use of chemical knowledge, a new search algorithm based on bond-order time series analysis, statistics of the chemical reaction networks, a web application to submit jobs, and other features. The source code, manual, installation instructions and the website link are available at: https://rxnkin.usc.es/index.php/AutoMeKin.

Nonadiabatic Kinetics in the Intermediate Coupling Regime: Comparing Molecular Dynamics to an Energy-Grained Master Equation.

We propose and test an extension of the energy-grained master equation (EGME) for treating nonadiabatic (NA) hopping between different potential energy surfaces, which enables us to model the competition between stepwise collisional relaxation and kinetic processes which transfer population between different electronic states of the same spin symmetry. By incorporating Zhu-Nakamura theory into the EGME, we are able to treat NA passages beyond the simple Landau-Zener approximation, along with the corresponding treatments of zero-point energy and tunneling probability. To evaluate the performance of this NA-EGME approach, we carried out detailed studies of the UV photodynamics of the volatile organic compound C6-hydroperoxy aldehyde (C6-HPALD) using on-the-fly ab initio molecular dynamics and trajectory surface hopping. For this multichromophore molecule, we show that the EGME is able to capture important aspects of the dynamics, including kinetic timescales, and diabatic trapping. Such an approach provides a promising and efficient strategy for treating the long-time dynamics of photoexcited molecules in regimes which are difficult to capture using atomistic on-the-fly molecular dynamics.

Exploring human-guided strategies for reaction network exploration: Interactive molecular dynamics in virtual reality as a tool for citizen scientists.

The emerging fields of citizen science and gamification reformulate scientific problems as games or puzzles to be solved. Through engaging the wider non-scientific community, significant breakthroughs may be made by analyzing citizen-gathered data. In parallel, recent advances in virtual reality (VR) technology are increasingly being used within a scientific context and the burgeoning field of interactive molecular dynamics in VR (iMD-VR) allows users to interact with dynamical chemistry simulations in real time. Here, we demonstrate the utility of iMD-VR as a medium for gamification of chemistry research tasks. An iMD-VR "game" was designed to encourage users to explore the reactivity of a particular chemical system, and a cohort of 18 participants was recruited to playtest this game as part of a user study. The reaction game encouraged users to experiment with making chemical reactions between a propyne molecule and an OH radical, and "molecular snapshots" from each game session were then compiled and used to map out reaction pathways. The reaction network generated by users was compared to existing literature networks demonstrating that users in VR capture almost all the important reaction pathways. Further comparisons between humans and an algorithmic method for guiding molecular dynamics show that through using citizen science to explore these kinds of chemical problems, new approaches and strategies start to emerge.

Interactive Molecular Dynamics in Virtual Reality Is an Effective Tool for Flexible Substrate and Inhibitor Docking to the SARS-CoV-2 Main Protease.

The main protease (Mpro) of the SARS-CoV-2 virus is one focus of drug development efforts for COVID-19. Here, we show that interactive molecular dynamics in virtual reality (iMD-VR) is a useful and effective tool for creating Mpro complexes. We make these tools and models freely available. iMD-VR provides an immersive environment in which users can interact with MD simulations and so build protein complexes in a physically rigorous and flexible way. Recently, we have demonstrated that iMD-VR is an effective method for interactive, flexible docking of small molecule drugs into their protein targets (Deeks et al. PLoS One 2020, 15, e0228461). Here, we apply this approach to both an Mpro inhibitor and an oligopeptide substrate, using experimentally determined crystal structures. For the oligopeptide, we test against a crystallographic structure of the original SARS Mpro. Docking with iMD-VR gives models in agreement with experimentally observed (crystal) structures. The docked structures are also tested in MD simulations and found to be stable. Different protocols for iMD-VR docking are explored, e.g., with and without restraints on protein backbone, and we provide recommendations for its use. We find that it is important for the user to focus on forming binding interactions, such as hydrogen bonds, and not to rely on using simple metrics (such as RMSD), in order to create realistic, stable complexes. We also test the use of apo (uncomplexed) crystal structures for docking and find that they can give good results. This is because of the flexibility and dynamic response allowed by the physically rigorous, atomically detailed simulation approach of iMD-VR. We make our models (and interactive simulations) freely available. The software framework that we use, Narupa, is open source, and uses commodity VR hardware, so these tools are readily accessible to the wider research community working on Mpro (and other COVID-19 targets). These should be widely useful in drug development, in education applications, e.g., on viral enzyme structure and function, and in scientific communication more generally.

Training atomic neural networks using fragment-based data generated in virtual reality.

The ability to understand and engineer molecular structures relies on having accurate descriptions of the energy as a function of atomic coordinates. Here, we outline a new paradigm for deriving energy functions of hyperdimensional molecular systems, which involves generating data for low-dimensional systems in virtual reality (VR) to then efficiently train atomic neural networks (ANNs). This generates high-quality data for specific areas of interest within the hyperdimensional space that characterizes a molecule's potential energy surface (PES). We demonstrate the utility of this approach by gathering data within VR to train ANNs on chemical reactions involving fewer than eight heavy atoms. This strategy enables us to predict the energies of much higher-dimensional systems, e.g., containing nearly 100 atoms. Training on datasets containing only 15k geometries, this approach generates mean absolute errors around 2 kcal mol-1. This represents one of the first times that an ANN-PES for a large reactive radical has been generated using such a small dataset. Our results suggest that VR enables the intelligent curation of high-quality data, which accelerates the learning process.

Training Neural Nets To Learn Reactive Potential Energy Surfaces Using Interactive Quantum Chemistry in Virtual Reality.

While the primary bottleneck to a number of computational workflows was not so long ago limited by processing power, the rise of machine learning technologies has resulted in an interesting paradigm shift, which places increasing value on issues related to data curation-that is, data size, quality, bias, format, and coverage. Increasingly, data-related issues are equally as important as the algorithmic methods used to process and learn from the data. Here we introduce an open-source graphics processing unit-accelerated neural network (NN) framework for learning reactive potential energy surfaces (PESs). To obtain training data for this NN framework, we investigate the use of real-time interactive ab initio molecular dynamics in virtual reality (iMD-VR) as a new data curation strategy that enables human users to rapidly sample geometries along reaction pathways. Focusing on hydrogen abstraction reactions of CN radical with isopentane, we compare the performance of NNs trained using iMD-VR data versus NNs trained using a more traditional method, namely, molecular dynamics (MD) constrained to sample a predefined grid of points along the hydrogen abstraction reaction coordinate. Both the NN trained using iMD-VR data and the NN trained using the constrained MD data reproduce important qualitative features of the reactive PESs, such as a low and early barrier to abstraction. Quantitative analysis shows that NN learning is sensitive to the data set used for training. Our results show that user-sampled structures obtained with the quantum chemical iMD-VR machinery enable excellent sampling in the vicinity of the minimum energy path (MEP). As a result, the NN trained on the iMD-VR data does very well predicting energies that are close to the MEP but less well predicting energies for "off-path" structures. The NN trained on the constrained MD data does better predicting high-energy off-path structures, given that it included a number of such structures in its training set.

Interactive molecular dynamics in virtual reality from quantum chemistry to drug binding: An open-source multi-person framework.

As molecular scientists have made progress in their ability to engineer nanoscale molecular structure, we face new challenges in our ability to engineer molecular dynamics (MD) and flexibility. Dynamics at the molecular scale differs from the familiar mechanics of everyday objects because it involves a complicated, highly correlated, and three-dimensional many-body dynamical choreography which is often nonintuitive even for highly trained researchers. We recently described how interactive molecular dynamics in virtual reality (iMD-VR) can help to meet this challenge, enabling researchers to manipulate real-time MD simulations of flexible structures in 3D. In this article, we outline various efforts to extend immersive technologies to the molecular sciences, and we introduce "Narupa," a flexible, open-source, multiperson iMD-VR software framework which enables groups of researchers to simultaneously cohabit real-time simulation environments to interactively visualize and manipulate the dynamics of molecular structures with atomic-level precision. We outline several application domains where iMD-VR is facilitating research, communication, and creative approaches within the molecular sciences, including training machines to learn potential energy functions, biomolecular conformational sampling, protein-ligand binding, reaction discovery using "on-the-fly" quantum chemistry, and transport dynamics in materials. We touch on iMD-VR's various cognitive and perceptual affordances and outline how these provide research insight for molecular systems. By synergistically combining human spatial reasoning and design insight with computational automation, technologies such as iMD-VR have the potential to improve our ability to understand, engineer, and communicate microscopic dynamical behavior, offering the potential to usher in a new paradigm for engineering molecules and nano-architectures.

A Simple "Boxed Molecular Kinetics" Approach To Accelerate Rare Events in the Stochastic Kinetic Master Equation.

The chemical master equation is a powerful theoretical tool for analyzing the kinetics of complex multiwell potential energy surfaces in a wide range of different domains of chemical kinetics spanning combustion, atmospheric chemistry, gas-surface chemistry, solution phase chemistry, and biochemistry. There are two well-established methodologies for solving the chemical master equation: a stochastic "kinetic Monte Carlo" approach and a matrix-based approach. In principle, the results yielded by both approaches are identical; the decision of which approach is better suited to a particular study depends on the details of the specific system under investigation. In this Article, we present a rigorous method for accelerating stochastic approaches by several orders of magnitude, along with a method for unbiasing the accelerated results to recover the "true" value. The approach we take in this paper is inspired by the so-called "boxed molecular dynamics" (BXD) method, which has previously only been applied to accelerate rare events in molecular dynamics simulations. Here we extend BXD to design a simple algorithmic strategy for accelerating rare events in stochastic kinetic simulations. Tests on a number of systems show that the results obtained using the BXD rare event strategy are in good agreement with unbiased results. To carry out these tests, we have implemented a kinetic Monte Carlo approach in MESMER, which is a cross-platform, open-source, and freely available master equation solver.

Characterising the evaporation kinetics of water and semi-volatile organic compounds from viscous multicomponent organic aerosol particles.

The physicochemical changes experienced by organic aerosol particles undergoing dehydration into the surrounding gas phase can be drastic, forcing rapid vitrification of the particle and suppressing internal diffusion. Until recently, experimental studies have concentrated on quantifying diffusional mixing of either water or non-volatile components, while relatively little attention has been paid to the role of semivolatile organic component (SVOC) diffusion and volatilisation in maintaining the equilibrium between the gas and particle phases. Here we present methods to simultaneously investigate diffusivities and volatilities in studies of evolving single ternary aerosol particle size and composition. Analysing particles of ternary composition must account for the multiple chemical species that volatilise in response to a step change in gas phase water activity. In addition, treatments of diffusion in multicomponent mixtures are necessary to represent evolving heterogeneities in particle composition. We find that the contributions to observed size behaviour from volatilisation of water and a SVOC can be decoupled and treated separately. Employing Fickian diffusion modelling, we extract the compositional dependence of the diffusion constant of water and compare the results to recently published parametrisations in binary aerosol particles. The treatment of ideality and activity in each case is discussed, with reference to use in multicomponent core shell models. Meanwhile, the evaporation of an SVOC into an unsaturated gas flow may be treated by Maxwell's equation, with slow diffusional transport manifesting as a suppression in the extracted vapour pressure.

Atomistic non-adiabatic dynamics of the LH2 complex with a GPU-accelerated ab initio exciton model.

We recently outlined an efficient multi-tiered parallel ab initio excitonic framework that utilizes time dependent density functional theory (TDDFT) to calculate ground and excited state energies and gradients of large supramolecular complexes in atomistic detail - enabling us to undertake non-adiabatic simulations which explicitly account for the coupled anharmonic vibrational motion of all the constituent atoms in a supramolecular system. Here we apply that framework to the 27 coupled bacterio-chlorophyll-a chromophores which make up the LH2 complex, using it to compute an on-the-fly nonadiabatic surface-hopping (SH) trajectory of electronically excited LH2. Part one of this article is focussed on calibrating our ab initio exciton Hamiltonian using two key parameters: a shift δ, which corrects for the error in TDDFT vertical excitation energies; and an effective dielectric constant ε, which describes the average screening of the transition-dipole coupling between chromophores. Using snapshots obtained from equilibrium molecular dynamics simulations (MD) of LH2, we tune the values of both δ and ε through fitting to the thermally broadened experimental absorption spectrum, giving a linear absorption spectrum that agrees reasonably well with experiment. In part two of this article, we construct a time-resolved picture of the coupled vibrational and excitation energy transfer (EET) dynamics in the sub-picosecond regime following photo-excitation. Assuming Franck-Condon excitation of a narrow eigenstate band centred at 800 nm, we use surface hopping to follow a single nonadiabatic dynamics trajectory within the full eigenstate manifold. Consistent with experimental data, this trajectory gives timescales for B800→B850 population transfer (τB800→B850) between 650-1050 fs, and B800 population decay (τ800→) between 10-50 fs. The dynamical picture that emerges is one of rapidly fluctuating LH2 eigenstates that are delocalized over multiple chromophores and undergo frequent crossing on a femtosecond timescale as a result of the atomic vibrations of the constituent chromophores. The eigenstate fluctuations arise from disorder that is driven by vibrational dynamics with multiple characteristic timescales. The scalability of our ab initio excitonic computational framework across massively parallel architectures opens up the possibility of addressing a wide range of questions, including how specific dynamical motions impact both the pathways and efficiency of electronic energy-transfer within large supramolecular systems.

Adaptive free energy sampling in multidimensional collective variable space using boxed molecular dynamics.

The past decade has seen the development of a new class of rare event methods in which molecular configuration space is divided into a set of boundaries/interfaces, and then short trajectories are run between boundaries. For all these methods, an important concern is how to generate boundaries. In this paper, we outline an algorithm for adaptively generating boundaries along a free energy surface in multi-dimensional collective variable (CV) space, building on the boxed molecular dynamics (BXD) rare event algorithm. BXD is a simple technique for accelerating the simulation of rare events and free energy sampling which has proven useful for calculating kinetics and free energy profiles in reactive and non-reactive molecular dynamics (MD) simulations across a range of systems, in both NVT and NVE ensembles. Two key developments outlined in this paper make it possible to automate BXD, and to adaptively map free energy and kinetics in complex systems. First, we have generalized BXD to multidimensional CV space. Using strategies from rigid-body dynamics, we have derived a simple and general velocity-reflection procedure that conserves energy for arbitrary collective variable definitions in multiple dimensions, and show that it is straightforward to apply BXD to sampling in multidimensional CV space so long as the Cartesian gradients ∇CV are available. Second, we have modified BXD to undertake on-the-fly statistical analysis during a trajectory, harnessing the information content latent in the dynamics to automatically determine boundary locations. Such automation not only makes BXD considerably easier to use; it also guarantees optimal boundaries, speeding up convergence. We have tested the multidimensional adaptive BXD procedure by calculating the potential of mean force for a chemical reaction recently investigated using both experimental and computational approaches - i.e., F + CD3CN → DF + D2CN in both the gas phase and a strongly coupled explicit CD3CN solvent. The results obtained using multidimensional adaptive BXD agree well with previously published experimental and computational results, providing good evidence for its reliability.

Unraveling the role of protein dynamics in dihydrofolate reductase catalysis.

Protein dynamics have controversially been proposed to be at the heart of enzyme catalysis, but identification and analysis of dynamical effects in enzyme-catalyzed reactions have proved very challenging. Here, we tackle this question by comparing an enzyme with its heavy ((15)N, (13)C, (2)H substituted) counterpart, providing a subtle probe of dynamics. The crucial hydride transfer step of the reaction (the chemical step) occurs more slowly in the heavy enzyme. A combination of experimental results, quantum mechanics/molecular mechanics simulations, and theoretical analyses identify the origins of the observed differences in reactivity. The generally slightly slower reaction in the heavy enzyme reflects differences in environmental coupling to the hydride transfer step. Importantly, the barrier and contribution of quantum tunneling are not affected, indicating no significant role for "promoting motions" in driving tunneling or modulating the barrier. The chemical step is slower in the heavy enzyme because protein motions coupled to the reaction coordinate are slower. The fact that the heavy enzyme is only slightly less active than its light counterpart shows that protein dynamics have a small, but measurable, effect on the chemical reaction rate.

Ab initio nonadiabatic dynamics of multichromophore complexes: a scalable graphical-processing-unit-accelerated exciton framework.

Conspectus Although advances in computer hardware and algorithms tuned for novel computer architectures are leading to significant increases in the size and time scale for molecular simulations, it remains true that new methods and algorithms will be needed to address some of the problems in complex chemical systems, such as electrochemistry, excitation energy transport, proton transport, and condensed phase reactivity. Ideally, these new methods would exploit the strengths of emerging architectures. Fragment based approaches for electronic structure theory decompose the problem of solving the electronic Schrodinger equation into a series of much smaller problems. Because each of these smaller problems is largely independent, this strategy is particularly well-suited to parallel architectures. It appears that the most significant advances in computer architectures will be toward increased parallelism, and therefore fragment-based approaches are an ideal match to these trends. When the computational effort involved scales with the third (or higher) power of the molecular size, there is a large benefit to fragment-based approaches even on serial architectures. This is the case for many of the well-known methods for solving the electronic structure theory problem, especially when wave function-based approaches including electron correlation are considered. A major issue in fragment-based approaches is determining or improving their accuracy. Since the Achilles' heel of any such method lies in the approximations used to stitch the smaller problems back together (i.e., in the treatment of the cross-fragment interactions), it can often be important to ensure that the size of the smaller problems is "large enough." Thus, there are two frontiers that need to be extended in order to enable molecular simulations for large systems and long times: the strongly coupled problem of medium sized molecules (100-500 atoms) and the more weakly coupled problem of decomposing ("fragmenting") a molecular system and then stitching it back together. In this Account, we address both of these problems, the first by using graphical processing units (GPUs) and electronic structure algorithms tuned for these architectures and the second by using an exciton model as a framework in which to stitch together the solutions of the smaller problems. The multitiered parallel framework outlined here is aimed at nonadiabatic dynamics simulations on large supramolecular multichromophoric complexes in full atomistic detail. In this framework, the lowest tier of parallelism involves GPU-accelerated electronic structure theory calculations, for which we summarize recent progress in parallelizing the computation and use of electron repulsion integrals (ERIs), which are the major computational bottleneck in both density functional theory (DFT) and time-dependent density functional theory (TDDFT). The topmost tier of parallelism relies on a distributed memory framework, in which we build an exciton model that couples chromophoric units. Combining these multiple levels of parallelism allows access to ground and excited state dynamics for large multichromophoric assemblies. The parallel excitonic framework is in good agreement with much more computationally demanding TDDFT calculations of the full assembly.

Prediction of enhanced solvent-induced enantioselectivity for a ring opening with a bifurcating reaction path.

Classical molecular dynamics simulations are reported for the deazetisation and ring opening of meso-2,3-difluoro-2,3-dimethyldiazocyclopropane in three solvents: CHCl3, CHFClBr and CH3CH(OH)CF3 (TFIPA). The achiral reactant leads to enantiomeric allene products, and the question addressed in the study is whether either of the chiral, enantiomerically pure solvents can induce significant enantiomeric excess in the products. The direct dynamics calculations use an empirical valence bond potential for the solute, with empirical parameters optimised against M06-2X/cc-pVTZ density functional results. The results reveal that the exothermic N2 loss and ring opening promote transient strong solvent-solute interactions within the first ∼100 fs of the reaction. Because of the bifurcating reaction path, these interactions occur at time when the "decision" about which enantiomer of the product to form has yet to be made (at least for many of the trajectories). Hence, it is possible in principle that the solvent could exert a larger-than-normal influence on the course of the reaction. In fact, the results reveal no such effect for CHFClBr but do predict that TFIPA should induce 15.2 ± 2.1% enantiomeric excess. This is roughly an order of magnitude larger than solvent-induced enantiomeric excesses found experimentally in reactions where the conversion of reactant(s) to enantiomeric products occur over separate transition states.

Non-equilibrium reaction and relaxation dynamics in a strongly interacting explicit solvent: F + CD3CN treated with a parallel multi-state EVB model.

We describe a parallelized linear-scaling computational framework developed to implement arbitrarily large multi-state empirical valence bond (MS-EVB) calculations within CHARMM and TINKER. Forces are obtained using the Hellmann-Feynman relationship, giving continuous gradients, and good energy conservation. Utilizing multi-dimensional Gaussian coupling elements fit to explicitly correlated coupled cluster theory, we built a 64-state MS-EVB model designed to study the F + CD3CN → DF + CD2CN reaction in CD3CN solvent (recently reported in Dunning et al. [Science 347(6221), 530 (2015)]). This approach allows us to build a reactive potential energy surface whose balanced accuracy and efficiency considerably surpass what we could achieve otherwise. We ran molecular dynamics simulations to examine a range of observables which follow in the wake of the reactive event: energy deposition in the nascent reaction products, vibrational relaxation rates of excited DF in CD3CN solvent, equilibrium power spectra of DF in CD3CN, and time dependent spectral shifts associated with relaxation of the nascent DF. Many of our results are in good agreement with time-resolved experimental observations, providing evidence for the accuracy of our MS-EVB framework in treating both the solute and solute/solvent interactions. The simulations provide additional insight into the dynamics at sub-picosecond time scales that are difficult to resolve experimentally. In particular, the simulations show that (immediately following deuterium abstraction) the nascent DF finds itself in a non-equilibrium regime in two different respects: (1) it is highly vibrationally excited, with ∼23 kcal mol(-1) localized in the stretch and (2) its post-reaction solvation environment, in which it is not yet hydrogen-bonded to CD3CN solvent molecules, is intermediate between the non-interacting gas-phase limit and the solution-phase equilibrium limit. Vibrational relaxation of the nascent DF results in a spectral blue shift, while relaxation of the post-reaction solvation environment results in a red shift. These two competing effects mean that the post-reaction relaxation profile is distinct from what is observed when Franck-Condon vibrational excitation of DF occurs within a microsolvation environment initially at equilibrium. Our conclusions, along with the theoretical and parallel software framework presented in this paper, should be more broadly applicable to a range of complex reactive systems.

Free energy along drug-protein binding pathways interactively sampled in virtual reality.

We describe a two-step approach for combining interactive molecular dynamics in virtual reality (iMD-VR) with free energy (FE) calculation to explore the dynamics of biological processes at the molecular level. We refer to this combined approach as iMD-VR-FE. Stage one involves using a state-of-the-art 'human-in-the-loop' iMD-VR framework to generate a diverse range of protein-ligand unbinding pathways, benefitting from the sophistication of human spatial and chemical intuition. Stage two involves using the iMD-VR-sampled pathways as initial guesses for defining a path-based reaction coordinate from which we can obtain a corresponding free energy profile using FE methods. To investigate the performance of the method, we apply iMD-VR-FE to investigate the unbinding of a benzamidine ligand from a trypsin protein. The binding free energy calculated using iMD-VR-FE is similar for each pathway, indicating internal consistency. Moreover, the resulting free energy profiles can distinguish energetic differences between pathways corresponding to various protein-ligand conformations (e.g., helping to identify pathways that are more favourable) and enable identification of metastable states along the pathways. The two-step iMD-VR-FE approach offers an intuitive way for researchers to test hypotheses for candidate pathways in biomolecular systems, quickly obtaining both qualitative and quantitative insight.

Interactive molecular dynamics in virtual reality for modelling materials and catalysts.

Interactive molecular dynamics simulation in virtual reality (iMD-VR) is emerging as a promising technique in molecular science. Here, we demonstrate its use in a range of fifteen applications in materials science and heterogeneous catalysis. In this work, the iMD-VR package Narupa is used with the MD package, DL_POLY [1]. We show how iMD-VR can be used to: (i) investigate the mechanism of lithium fast ion conduction by directing the formation of defects showing that vacancy transport is favoured over interstitialcy mechanisms, and (ii) guide a molecule through a zeolite pore to explore diffusion within zeolites, examining in detail the motion of methyl n-hexanoate in H-ZSM-5 zeolite and identifying bottlenecks restricting diffusion. iMD-VR allows users to manipulate these systems intuitively, to drive changes in them and observe the resulting changes in structure and dynamics. We make these simulations available, as a resource for both teaching and research. All simulation files, with videos, can be found online (https://doi.org/10.5281/zenodo.8252314) and are provided as open-source material.

Protein dynamics and enzyme catalysis: the ghost in the machine?

One of the most controversial questions in enzymology today is whether protein dynamics are significant in enzyme catalysis. A particular issue in these debates is the unusual temperature-dependence of some kinetic isotope effects for enzyme-catalysed reactions. In the present paper, we review our recent model [Glowacki, Harvey and Mulholland (2012) Nat. Chem. 4, 169-176] that is capable of reproducing intriguing temperature-dependences of enzyme reactions involving significant quantum tunnelling. This model relies on treating multiple conformations of the enzyme-substrate complex. The results show that direct 'driving' motions of proteins are not necessary to explain experimental observations, and show that enzyme reactivity can be understood and accounted for in the framework of transition state theory.