Recent years have seen tremendous effort in the development of approaches with which to obtain quantum mechanics/molecular mechanics (QM/MM) free energies for reactions in the condensed phase. Nevertheless, there remain significant challenges to address, particularly the high computational cost involved in performing proper configurational sampling and in particular in obtaining ab initio QM/MM (QM(ai)/MM) free energy surfaces. One increasingly popular approach that seems to offer an ideal way to progress in this direction is the elegant metadynamics (MTD) approach. However, in the current work we point out the subtle efficiency problems associated with this approach, and illustrate that we have at hand what is arguably a more powerful approach. More specifically, we demonstrate the effectiveness of an updated version of our original idea of using a classical reference potential for QM(ai)/MM calculations [J. Phys. Chem. B. 102 (1998), 2293)], which we refer to as “paradynamics” (PD). This approach is based on the use of an empirical valence bond (EVB) reference potential, which is already similar to the real ab initio potential. The reference potential is fitted to the ab initio potential by an iterative and, to a great degree, automated refinement procedure. The corresponding free energy profile is then constructed using the refined EVB potential, and the linear response approximation (LRA) is used to evaluate the QM(ai)/MM activation free energy barrier. The automated refinement of the EVB surface (and thus the reduction of the difference between the reference and ab initio potentials) is a key factor in accelerating the convergence of the LRA approach. We apply our PD approach to a test reaction, namely the SN2 reaction between chloride ion and methyl chloride, and demonstrate that, at present, this approach is far more powerful and cost effective than the metadynamics approach (at least in its current implementation). We also discuss the general features of the PD approach in terms of its ability to explore complex systems, and clarify that it is not a specialized approach limited to only accelerating QM(ai)/MM calculations with proper sampling, but rather, can be used in a wide variety of applications. In fact, we point out that the use of a reference (CG) potential coupled with its PD refinement, as well as our renormalization approach, both provide very general and powerful strategies that can be used very effectively to explore any property that has been studied by the MTD approach.

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.

The nature and mechanism of phosphate hydrolysis reactions are of great interest in view of the crucial role of these reactions in key biological processes. While it is becoming clearer that the ultimate way of resolving mechanistic controversies must involve reliable theoretical studies, it is not widely realized that such studies cannot be performed by using most existing automated ways and that only careful systematic mapping approach can lead to meaningful conclusions. The present work clarifies the above point by considering the hydrolysis of phosphate monoesters. The clarification starts by defining the actual issues that should be addressed in careful studies, and by highlighting the problems with studies that ignore the need for unique mechanistic definitions (e.g., works that confuse associative and dissociative pathways). We then focus on the analysis of the proton transfer (PT) pathways in phosphate hydrolysis and on recent suggestions that PT involves more than one water molecule. Here we point out that most of the studies that found a proton transfer through several water molecules have not involved a systematic search of the relevant reaction coordinates. This includes both energy minimization approaches as well as a recent metadynamics (MTD) simulation study. To illustrate the crucial need of exploring the potential surfaces reliably, rather than relying on automated approaches, we present here a very careful study of the free energy landscape along a 3D reaction coordinate (RC) exploring both the standard 2D RC, comprised of the attacking and leaving group reaction coordinates, as well as of the proton transfer (PT) coordinate. Our study points out that that QM/MM minimization or MTD studies, that concluded that the hydrolysis of phosphate monoesters involves a PT through several water molecules, have not explored the single water (1W) path (that involves a direct PT form the attacking water molecule to the phosphate oxygen). Furthermore, we identified the most likely reason for the difficulty in finding the 1W path by QM/MM minimization methods, as well as by the current MTD simulations. We also discuss the problems with current studies that challenge the phosphate as a base mechanism. Perhaps most importantly, we clarify and illustrate that crucial mechanistic problems with alternative pathways should not be explored by running black box search approaches.

Understanding the nature of the free energy surfaces for phosphate hydrolysis is a prerequisite for understanding the corresponding key chemical reactions in biology. Here the challenge has been to move to careful ab initio QM/MM (QM(ai)/MM) free energy calculations, where obtaining converging results is very demanding and computationally expensive. This work describes such calculations, focusing on the free energy surface for the hydrolysis of phosphate monoesters, paying a special attention to the comparison between the one water (1W) and two water (2W) paths for the proton transfer (PT) step. This issue has been explored before by energy minimization with implicit solvent models and by non-systematic QM/MM energy minimization, as well as by non-systematic free energy mapping. However, no study has provided the needed reliable 2D (3D) surfaces which are necessary for reaching concrete conclusions. Our study generated in a systematic way the 2D (3D) free energy maps for several relevant systems, comparing the results of QM(ai)/MM and QM(ai)/implicit solvent surfaces, and provides an advanced description of the relevant energetics. It is found that the 1W path for the hydrolysis of methyl diphosphate (MDP) trianion is 6–9 kcal/mol higher than the 2W path. This difference becomes slightly larger in the presence of Mg2+ ion, since this ion reduces the pKa of the conjugated acid form of the phosphate oxygen that accepts the proton. Interestingly, the BLYP approach (which has been used extensively in some studies) gives much smaller difference between the 1W and 2W activation barriers. At any rate, it is worth to point out that the 2W transition state for the PT is not much higher that the common plateau that serves as the starting point of both the 1W and 2W PT paths. Thus, the calculated catalytic effects of proteins based on the 2W PT mechanistic models are not expected to be different from the catalytic effects predicted using the 1W PT mechanistic models calibrated on the observed barriers in solution (as was done in all of our previous EVB studies).

Objectives The purpose of this article is to introduce an emerging field called 'Biopharmaceutical Informatics'. It describes how tools from Information technology and Molecular Biophysics can be adapted, developed and gainfully employed in discovery and development of biologic drugs. Key Findings The findings described here are based on literature surveys and the authors' collective experiences in the field of biologic drug product development. A strategic framework to forecast early the hurdles faced during drug product development is weaved together and elucidated using chemical degradation as an example. Efficiency of translating biologic drug discoveries into drug products can be significantly improved by combining learnings from experimental biophysical and analytical data on the drug candidates with molecular properties computed from their sequences and structures via molecular modeling and simulations. Summary Biopharmaceutical Informatics seeks to promote applications of computational tools towards discovery and development of biologic drugs. When fully implemented, industry-wide, it will enable rapid materials-free developability assessments of biologic drug candidates at early stages as well as streamline drug product development activities such as commercial scale production, purification, formulation, analytical characterization, safety and in vivo performance.