Finding the transition state without initial guess: The growing string method for Newton trajectory to isomerization and enantiomerization reaction of alanine dipeptide and poly(15)alanine

Machine Learning to Predict Diels-Alder Reaction Barriers from the Reactant State Electron Density

Reaction barriers are key to our understanding of chemical reactivity and catalysis. Certain reactions are so seminal in chemistry that countless variants, with or without catalysts, have been studied, and their barriers have been computed or measured experimentally. This wealth of data represents a perfect opportunity to leverage machine learning models, which could quickly predict barriers without explicit calculations or measurement. Here, we show that the topological descriptors of the quantum mechanical charge density in the reactant state constitute a set that is both rigorous and continuous and can be used effectively for the prediction of reaction barrier energies to a high degree of accuracy. We demonstrate this on the Diels-Alder reaction, highly important in biology and medicinal chemistry, and as such, studied extensively. This reaction exhibits a range of barriers as large as 270 kJ/mol. While we trained our single-objective supervised (labeled) regression algorithms on simpler Diels-Alder reactions in solution, they predict reaction barriers also in significantly more complicated contexts, such a Diels-Alder reaction catalyzed by an artificial enzyme and its evolved variants, in agreement with experimental changes in k_cat. We expect this tool to apply broadly to a variety of reactions in solution or in the presence of a catalyst, for screening and circumventing heavily involved computations or experiments.

Interplay between the Gentlest Ascent Dynamics Method and Conjugate Directions to Locate Transition States

An algorithm to locate transition states on a potential energy surface (PES) is proposed and described. The technique is based on the GAD method where the gradient of the PES is projected into a given direction and also perpendicular to it. In the proposed method, named GAD-CD, the projection is not only applied to the gradient but also to the Hessian matrix. Then, the resulting Hessian matrix is block diagonal. The direction is updated according to the GAD method. Furthermore, to ensure stability and to avoid a high computational cost, a trust region technique is incorporated and the Hessian matrix is updated at each iteration. The performance of the algorithm in comparison with the standard ascent dynamics is discussed for a simple two dimensional model PES. Its efficiency for describing the reaction mechanisms involving small and medium size molecular systems is demonstrated for five molecular systems of interest.

Quantum chemical approaches to [NiFe] hydrogenase

The mechanism by which [NiFe] hydrogenase catalyses the oxidation of molecular hydrogen is a significant yet challenging topic in bioinorganic chemistry. With far-reaching applications in renewable energy and carbon mitigation, significant effort has been invested in the study of these complexes. In particular, computational approaches offer a unique perspective on how this enzyme functions at an electronic and atomistic level. In this article, we discuss state-of-the art quantum chemical methods and how they have helped deepen our comprehension of [NiFe] hydrogenase. We outline the key strategies that can be used to compute the (i) geometry, (ii) electronic structure, (iii) thermodynamics and (iv) kinetic properties associated with the enzymatic activity of [NiFe] hydrogenase and other bioinorganic complexes.

Methods for Efficiently and Accurately Computing Quantum Mechanical Free Energies for Enzyme Catalysis

Enzyme activity is inherently linked to free energies of transition states, ligand binding, protonation/deprotonation, etc.; these free energies, and thus enzyme function, can be affected by residue mutations, allosterically induced conformational changes, and much more. Therefore, being able to predict free energies associated with enzymatic processes is critical to understanding and predicting their function. Free energy simulation (FES) has historically been a computational challenge as it requires both the accurate description of inter- and intramolecular interactions and adequate sampling of all relevant conformational degrees of freedom. The hybrid quantum mechanical molecular mechanical (QM/MM) framework is the current tool of choice when accurate computations of macromolecular systems are essential. Unfortunately, robust and efficient approaches that employ the high levels of computational theory needed to accurately describe many reactive processes (ie, ab initio, DFT), while also including explicit solvation effects and accounting for extensive conformational sampling are essentially nonexistent. In this chapter, we will give a brief overview of two recently developed methods that mitigate several major challenges associated with QM/MM FES: the QM non-Boltzmann Bennett's acceptance ratio method and the QM nonequilibrium work method. We will also describe usage of these methods to calculate free energies associated with (1) relative properties and (2) along reaction paths, using simple test cases with relevance to enzymes examples.

Efficiently computing pathway free energies: New approaches based on chain-of-replica and Non-Boltzmann Bennett reweighting schemes

BACKGROUND

Accurately modeling condensed phase processes is one of computation's most difficult challenges. Include the possibility that conformational dynamics may be coupled to chemical reactions, where multiscale (i.e., QM/MM) methods are needed, and this task becomes even more daunting.

METHODS

Free energy simulations (i.e., molecular dynamics), multiscale modeling, and reweighting schemes.

RESULTS

Herein, we present two new approaches for mitigating the aforementioned challenges. The first is a new chain-of-replica method (off-path simulations, OPS) for computing potentials of mean force (PMFs) along an easily defined reaction coordinate. This development is coupled with a new distributed, highly-parallel replica framework (REPDstr) within the CHARMM package. Validation of these new schemes is carried out on two processes that undergo conformational changes. First is the simple torsional rotation of butane, while a much more challenging glycosidic rotation (in vacuo and solvated) is the second. Additionally, a new approach that greatly improves (i.e., possibly an order of magnitude) the efficiency of computing QM/MM PMFs is introduced and compared to standard schemes. Our efforts are grounded in the recently developed method for efficiently computing QM-based free energies (i.e., QM-Non-Boltzmann Bennett, QM-NBB). Again, we validate this new technique by computing the QM/MM PMF of butane's torsional rotation.

CONCLUSIONS

The OPS-REPDstr method is a promising new approach that overcomes many limitations of standard pathway simulations in CHARMM. The combination of QM-NBB with pathway techniques is very promising as it offers significant advantages over current procedures.

GENERAL SIGNIFICANCE

Efficiently computing potentials of mean force is a major, unresolved, area of interest. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Comparison of Three Chain-of-States Methods: Nudged Elastic Band and Replica Path with Restraints or Constraints

Chain-of-state methods are becoming important tools in studying the chemical reaction mechanisms, especially for biomacromolecules. In this article, three chain-of-state methods, nudged elastic band (NEB) method and the replica path method with restraints or constraints, were tested and compared using three model systems with various sizes and at different levels of theory: alanine dipeptide isomerization, β-alanine intramolecular condensation, and the matrix metalloproteinase 2 inhibition mechanism. The levels of theory used to describe the three model systems include molecular mechanics (MM), quantum mechanics (QM), and combined quantum mechanics and molecular mechanics (QM/MM). All three methods could correctly determine a reaction path with reasonable estimation of reaction barriers in most cases. The RMSD measurement with additional weighting schemes provides practically infinite choices of reaction coordinates to describe the reaction progress. These findings demonstrate that the chain-of-state methods are powerful tools when being used carefully to generate a plausible reaction mechanism with full pathway for complex systems at an affordable computational cost.

THE GROWING STRING METHOD FOR FLOWS OF NEWTON TRAJECTORIES BY A SECOND-ORDER METHOD

The reaction path is an important concept of theoretical chemistry. We use a definition with a reduced gradient (see Quapp et al., Theor Chem Acc100:285, 1998), also named Newton trajectory (NT). To follow a reaction path, we design a numerical scheme for a method for finding a transition state between reactant and product on the potential energy surface: the growing string (GS) method. We extend the method (see W. Quapp, J Chem Phys122:174106, 2005) by a second-order scheme for the corrector step, which includes the use of the Hessian matrix. A dramatic performance enhancement for the exactness to follow the NTs, and a dramatic reduction of the number of corrector steps are to report. Hence, we can calculate flows of NTs. The method works in nonredundant internal coordinates. The corresponding metric to work with is curvilinear. The GS calculation is interfaced with the GamessUS package (we have provided this algorithm on ). Examples for applications are the HCN isomerization pathway and NTs for the isomerization C7ax ↔ C5 of alanine dipeptide.

UV resonance Raman investigation of the conformations and lowest energy allowed electronic excited states of tri- and tetraalanine: charge transfer transitions

UV resonance Raman excitation profiles and Raman depolarization ratios were measured for trialanine and tetraalanine between 198 and 210 nm. Excitation within the pi --> pi* electronic transitions of the peptide bond results in UVRR spectra dominated by amide peptide bond vibrations. In addition to the resonance enhancement of the normal amide vibrations, we find enhancement of the symmetric terminal COO(-) vibration. The Ala(3) UVRR AmIII(3) band frequencies indicate that poly-proline II and 2.5(1) helix conformations and type II turns are present in solution. We also find that the conformation of the interior peptide bond of Ala(4) is predominantly poly-proline-II-like. The Raman excitation profiles of both Ala(3) and Ala(4) reveal a charge transfer electronic transition at 202 nm, where electron transfer occurs from the terminal nonbonding carboxylate orbital to the adjacent peptide bond pi* orbital. Raman depolarization ratio measurements support this assignment. An additional electronic transition is found in Ala(4) at 206 nm.

A spline for your saddle

Pinpointing extrema on a multidimensional hypersurface is an important generic problem with a broad scope of application in statistical mechanics, biophysics, chemical reaction dynamics, and quantum chemistry. Local minima of the hypersurface correspond to metastable structures and are usually the most important points to look for. They are relatively easy to find using standard minimizing algorithms. A considerably more difficult task is the location of saddle points. The saddle points most sought for are those which form the lowest barriers between given minima and are usually required for determining rates of rare events. We formulate a path functional minimum principle for the saddle point. We then develop a cubic spline method for applying this principle and locating the saddle point(s) separating two local minima on a potential hypersurface. A quasi-Newton algorithm is used for minimization. The algorithm does not involve second derivatives of the hypersurface and the number of potential gradients evaluated is usually less than 10% of the number of potential evaluations. We demonstrate the performance of the method on several standard examples and on a concerted exchange mechanism for self-diffusion in diamond. Finally, we show that the method may be used for solving large constrained minimization problems which are relevant for self-consistent field iterations in large systems.

Helix forming tendency of valine substituted poly-alanine: a molecular dynamics investigation

In this study, classical molecular dynamics simulations have been carried out on the valine (guest) substituted poly alanine (host) using the host-guest peptide approach to understand the role of valine in the formation and stabilization of helix. Valine has been substituted in the host peptide starting from N terminal to C terminal. Various structural parameters have been obtained from the molecular dynamics simulation to understand the tolerance of helical motif to valine. Depending on the position of valine in the host peptide, it stabilizes (or destabilizes) the formation of the helical structure. The substitution of valine in the poly alanine at some positions has no effect on the helix formation (deformation). It is interesting to observe the coexistence of 3 10 and alpha-helix in the peptides due to the dynamical nature of the hydrogen bonding interaction and sterical interactions.