Foreword

Arieh Warshel

Department of Chemistry, University of Southern California, Los Angeles, USA

The EVB Approach as a Powerful Tool for Simulating Chemical and Biological Processes

The search for reliable yet practical approach for modeling reactions in condensed phases and enzymes led to the inception of the empirical valence bond (EVB) approach around 1980. The idea for this approach emerged from the realization that the use of molecular orbitals (MO) based hybrid quantum mechanical/molecular mechanical (QM/MM) approaches faces major problems when it comes to obtaining the proper asymptotic energetics for the autodissociation of water,[1] while the corresponding valence bond (VB) representation provides an excellent way of imposing the correct physics on the system. This idea was initially formulated in 1980,[2] using a simplified Langevin dipoles solvent model, which led to the need for a conceptual description of the response of the solvent to the different VB states. A much more rigorous coupling to the solvent was introduced in 1988,[3] with an all-atom molecular dynamics treatment that included the free energy functional as well as a rigorous non-equilibrium solvation treatment. The main remaining fundamental problem therefore was the validation of the reasonable (but ad hoc) assumption about the transferability of the off-diagonal elements (that couple different resonance structures) between different phases; for example between vacuum to aqueous solution or an enzyme active site. This assumption has been numerically validated by means of constrained density functional theory (CDFT) studies.[4] Overall, it appears that despite its seemingly oversimplified features, the EVB approach provides a very valid theoretical QM/MM framework that incorporates the environment in arguably the most physically meaningful way. Furthermore, the EVB approach can be systematically improved by the paradynamics approach,[5] and by constraining it to reproduce experimental results in reference systems (while moving to other systems). The power of EVB is largely due to its "simple" orthogonal diabatic representation, as well as the assumption that the off-diagonal elements of the EVB Hamiltonian do not change significantly upon transfer of the reacting system from one phase to another.

Overall, therefore, despite unjustified criticism (see e.g., ref. [6]), the EVB approach has became widely used with an increasing recognition of its potential as a very powerful way of simulating chemical processes in different environments. This book includes chapters that consider different features of the EVB and its successful applications to complex chemical and biological problems. The different chapters presented in this book are briefly considered below.

In Chapter 1, Nagy and Meuwly describe reactive force field-based approaches for studies of bond breaking/making chemical reactions, including the EVB, ARMD, and MS-ARMD methods.

Particular emphasis is put on enabling investigations of the dynamics of such reactions. In this respect, we note that the EVB approach is arguably still the most powerful approach for studying the dynamics of reactions in the condensed phase, due to the consistent incorporation of the effect of solvent, which facilitates, among other special features, the consistent exploration of nonequilibrium solvation effects.

In Chapter 2, Duarte et al. provide a historical overview of the use of both MO and VB methods in the context of (bio)molecular modeling, introducing the basic theoretical aspects of both approaches. Particular emphasis is put on the EVB approach, following the overall theme of this book. This chapter exemplified the power of the EVB approach for studying challenging chemical processes in both the condensed phase and in enzymes. It concludes with an overview of further opportunities for utilizing the EVB framework, in combination with other approaches, for the study of enzymatic reactions.

In Chapter 3, Nikolay Plotnikov describes the paradynamics (PD) approach, showing how we can conveniently move from the EVB approach to high level ab initio surfaces. This method provides a very powerful way of obtaining the free energy surface for ab initio potentials, since the EVB presents an ideal reference potential for the ab initio surfaces.

In Chapter 4, Harvey et al. discuss the use of the EVB approach to exploring reaction dynamics in the gas and condensed phases. This chapter considers some of the relevant background and practical applications. The authors also discuss the ability of the EVB to explore short timescale dynamical effects, and discuss some applications, chosen to highlight the power of the method.

In considering the use of EVB in modeling dynamical effects, it is useful to add that the ability to explore not just short but also long timescale dynamical effects is particularly important in exploring the proposal that special "dynamical" effects play a major role in enzyme catalysis (e.g., refs. [7, 8]), which has become quite popular in recent years (e.g., refs. [9-11]). However, a significant part of this popularity is a reflection of confusion with regards to the nature of dynamical effects. Combining the EVB approach with coarse-grained (CG) modeling allows one to explore the dynamical proposal that has been discussed in great length in several recent reviews.[12-14] These reviews (and related works) have shown that enzyme catalysis is not due to dynamical effects, regardless of the definition used. In this respect we note that the recently developed approach[15] has allowed us to use a CG model to simulate effective millisecond trajectories in the conformational and chemical coordinates, establishing that the conformational kinetic energy is fully randomized before it can be transfer to the chemical coordinate.[15] Thus it had been determined that dynamical effects cannot be used to accelerate enzymatic reactions. It is also useful to note that the EVB approach is arguably the most effective approach for long timescale all atom simulations as it allows for the exploration of dynamical effect on quite long situation timescales with reasonable computational power.

In Chapter 5, Thaunay et al. describe the combination of the EVB approach with the AMOEBA polarizable force field, and demonstrate the performance of the resulting model in reproducing experimentally observed spectra. In this respect, we note that the EVB has originally been formulated with a polarizable force field considering both the induced dipoles of the solute and solvent.[2]

In Chapter 6, Avital Shurki describes the applications of the EVB approach in studies of biological reactions. It is pointed out that the convenient and reliable calibration of the EVB approach provides a great advantage relative to other QM/MM approaches in terms of elucidating catalytic effects. Furthermore, the simplicity of the potential energy surface enables highly efficient sampling, which is important when particularly large systems or averages over considerably large conformational ensembles are of interest. Additionally, the EVB approach also provides simple definition of the reaction coordinate, which includes all the system's degrees of freedom. Finally, the method benefits from the valence bond character of the wavefunction, which includes easily accessible chemical insight. The review discusses the different capabilities of the method while highlighting the advantages of the method over other standard (MO based) QM/MM approaches.

In Chapter 7, Fuxreiter and Mones discuss the potential of the EVB approach in enzyme design, emphasizing in particular the use of the reorganization energy as a screening tool for predicting catalytic effects of enzymes. The ability to design effective enzymes presents one of the most fundamental challenges in biotechnology, and such ability would provide convincing manifestations of a general understanding of the origin of enzyme catalysis. A recent study[16] explored the reliability of different simulation approaches in terms of their ability to rank different possible active-site constructs. This study demonstrated that the EVB approach is a practical and reliable quantitative tool in the final stages of computer aided-enzyme design, while other approaches were found to be comparatively less accurate, and mainly useful for the qualitative screening of ionized residues. The most obvious problem arises from the fact that current design approaches (e.g., refs. [17-19]) are not based on modeling the chemical process in the enzyme active site. In fact, some approaches (e.g., ref. [20]) use gas phase or small model cluster calculations, which then estimate the interaction between the enzyme and the transition state model, rather than the transition state binding free energy (or the relevant activation free energy). However, accurate ranking of the different options for enzyme design cannot be accomplished by approaches that cannot capture the electrostatic preorganization effect. Clearly, the ability of the EVB model to act as a quantitative tool in the final stages of computer-aided enzyme design is a major step towards the design of enzymes whose catalytic power is closer to native enzymes than the current generation of designer enzymes. It should be noted, however, that despite the temptation to use reorganization energies in the screening process there are many cases[16] when it is essential to invest the additional computational time and to evaluate the full EVB free energy surfaces to obtain the relevant...