On the faithfulness of molecular mechanics representations of proteins towards quantum-mechanical energy surfaces

Axial H-Bonding Solvent Controls Inhomogeneous Spectral Broadening, While Peripheral H-Bonding Solvent Controls Vibronic Broadening: Cresyl Violet in Methanol

The dynamics of the nuclei of both a chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both force field and ab initio molecular dynamics trajectories along with the inclusion of only certain solvent molecules in the excited-state calculations, we determine that the methanol molecules axial to the chromophore are responsible for the majority of inhomogeneous broadening, with a single methanol molecule that forms an axial hydrogen bond dominating the response. The strong peripheral hydrogen bonds do not contribute to spectral broadening, as they are very stable throughout the dynamics and do not lead to increased energy-gap fluctuations. We also find that treating the strong peripheral hydrogen bonds as molecular mechanical point charges during the molecular dynamics simulation underestimates the vibronic coupling. Including these peripheral hydrogen bonding methanol molecules in the quantum-mechanical region in a geometry optimization increases the vibronic coupling, suggesting that a more advanced treatment of these strongly interacting solvent molecules during the molecular dynamics trajectory may be necessary to capture the full vibronic spectral broadening.

Toward a general neural network force field for protein simulations: Refining the intramolecular interaction in protein

Molecular dynamics (MD) is an extremely powerful, highly effective, and widely used approach to understanding the nature of chemical processes in atomic details for proteins. The accuracy of results from MD simulations is highly dependent on force fields. Currently, molecular mechanical (MM) force fields are mainly utilized in MD simulations because of their low computational cost. Quantum mechanical (QM) calculation has high accuracy, but it is exceedingly time consuming for protein simulations. Machine learning (ML) provides the capability for generating accurate potential at the QM level without increasing much computational effort for specific systems that can be studied at the QM level. However, the construction of general machine learned force fields, needed for broad applications and large and complex systems, is still challenging. Here, general and transferable neural network (NN) force fields based on CHARMM force fields, named CHARMM-NN, are constructed for proteins by training NN models on 27 fragments partitioned from the residue-based systematic molecular fragmentation (rSMF) method. The NN for each fragment is based on atom types and uses new input features that are similar to MM inputs, including bonds, angles, dihedrals, and non-bonded terms, which enhance the compatibility of CHARMM-NN to MM MD and enable the implementation of CHARMM-NN force fields in different MD programs. While the main part of the energy of the protein is based on rSMF and NN, the nonbonded interactions between the fragments and with water are taken from the CHARMM force field through mechanical embedding. The validations of the method for dipeptides on geometric data, relative potential energies, and structural reorganization energies demonstrate that the CHARMM-NN local minima on the potential energy surface are very accurate approximations to QM, showing the success of CHARMM-NN for bonded interactions. However, the MD simulations on peptides and proteins indicate that more accurate methods to represent protein-water interactions in fragments and non-bonded interactions between fragments should be considered in the future improvement of CHARMM-NN, which can increase the accuracy of approximation beyond the current mechanical embedding QM/MM level.

Benefits of hybrid QM/MM over traditional classical mechanics in pharmaceutical systems

Hybrid quantum mechanics/molecular mechanics (QM/MM) is one of the most reliable approaches for accurately modeling and studying the complex pharmaceutical discovery system. Classical mechanics has significantly accelerated the drug discovery process in the past decade. However, the current challenge is the large pool of false positives, which require extensive validation. Hybrid QM/MM is an effective solution for accurately studying ligand binding, structural mechanisms, free energy evaluation, and spectroscopic characterization. This article highlights the methodological details relevant to cost-effective hybrid QM/MM methods. This approach, combined with traditional pharmacoinformatics methods, could be a reliable strategy to balance the cost and accuracy of the calculations.

Transferable Classical Force Field for Pure and Mixed Metal Halide Perovskites Parameterized from First-Principles

Many key features in photovoltaic perovskites occur in relatively long time scales and involve mixed compositions. This requires realistic but also numerically simple models. In this work we present a transferable classical force field to describe the mixed hybrid perovskite MA_xFA_1-xPb(Br_yI_1-y)₃ for variable composition (∀x, y ∈ [0, 1]). The model includes Lennard-Jones and Buckingham potentials to describe the interactions between the atoms of the inorganic lattice and the organic molecule, and the AMBER model to describe intramolecular atomic interactions. Most of the parameters of the force field have been obtained by means of a genetic algorithm previously developed to parametrize the CsPb(Br_xI_1-x)₃ perovskite (Balestra et al. J. Mater. Chem. A. 2020, DOI: 10.1039/d0ta03200j). The algorithm finds the best parameter set that simultaneously fits the DFT energies obtained for several crystalline structures with moderate degrees of distortion with respect to the equilibrium configuration. The resulting model reproduces correctly the XRD patterns, the expansion of the lattice upon I/Br substitution, and the thermal expansion coefficients. We use the model to run classical molecular dynamics simulations with up to 8600 atoms and simulation times of up to 40 ns. From the simulations we have extracted the ion diffusion coefficient of the pure and mixed perovskites, presenting for the first time these values obtained by a fully dynamical method using a transferable model fitted to first-principles calculations. The values here reported can be considered as the theoretical upper limit, that is, without grain boundaries or other defects, for ion migration dynamics induced by halide vacancies in photovoltaic perovskite devices under operational conditions.

Accurate Quantum-Mechanically Derived Force-Fields through a Fragment-Based Approach: Balancing Specificity and Transferability in the Prediction of Self-Assembly in Soft Matter

The wide range of time/length scales covered by self-assembly in soft matter makes molecular dynamics (MD) the ideal candidate for simulating such a supramolecular phenomenon at an atomistic level. However, the reliability of MD outcomes heavily relies on the accuracy of the adopted force-field (FF). The spontaneous re-ordering in liquid crystalline materials stands as a clear example of such collective self-assembling processes, driven by a subtle and delicate balance between supramolecular interactions and single-molecule flexibility. General-purpose transferable FFs often dramatically fail to reproduce such complex phenomena, for example, the error on the transition temperatures being larger than 100 K. Conversely, quantum-mechanically derived force-fields (QMD-FFs), specifically tailored for the target system, were recently shown (J. Phys. Chem. Lett.2022,13, 243) to allow for the required accuracy as they not only well reproduced transition temperatures but also yielded a quantitative agreement with the experiment on a wealth of structural, dynamic, and thermodynamic properties. The main drawback of this strategy stands in the computational burden connected to the numerous quantum mechanical (QM) calculations usually required for a target-specific parameterization, which has undoubtedly hampered the routine application of QMD-FFs. In this work, we propose a fragment-based strategy to extend the applicability of QMD-FFs, in which the amount of QM calculations is significantly reduced, being a single-molecule-optimized geometry and its Hessian matrix the only QM information required. To validate this route, a new FF is assembled for a large mesogen, exploiting the parameters obtained for two smaller liquid crystalline molecules, in this and previous work. Lengthy MD simulations are carried out with the new transferred QMD-FF, observing again a spontaneous re-orientation in the correct range of temperatures, with good agreement with the available experimental measures. The present results strongly suggest that a partial transfer of QMD-FF parameters can be invoked without a significant loss of accuracy, thus paving the way to exploit the method's intrinsic predictive capabilities in the simulation of novel soft materials.

Complexes of Alkaline and Ammonium Cations with Dopamine and Eumelanin Precursors: Dissecting the Role of Noncovalent Cation-π and Cation-Lone Pair (σ-Type) Interactions

Cation-π interactions and their possible competition with other noncovalent interactions (NCI) might play a key role in both dopamine- and eumelanin-based bioinspired materials. In this contribution, to unravel the delicate interplay between cation-π interactions and other possible competing forces, the configurational space of noncovalent complexes formed by dopamine or eumelanin precursors (o-benzoquinone, DHI and a semiquinone dimer) and three different cations (Na⁺, K⁺, and NH₄⁺) is sampled by means of accurate ab initio calculations. To this end, we resort to the mp2^mod method, recently validated by us for benzene-, phenol-, and catechol-cation complexes, whose computational convenience allows for an extensive exploration of the cation-molecule interaction energy surface, by sampling a total of more than 10⁴ arrangements. The mp2^mod interaction energy landscapes reveal that, besides the expected cation-π driven arrangements, for all considered molecule-cation pairs the most stable complexes are found when the cation lies within the plane containing the six-membered ring, thus maximizing the σ-type interaction with the oxygen's lone pairs. Due to the loss of aromaticity, the σ-type/cation-π strength ratio is remarkably large in o-benzoquinone, where cation-π complexes seem unlikely to be formed. The above features are shared among all considered cations but are significantly larger when considering the smaller Na⁺. Besides delivering a deeper insight onto the NCI network established by the considered precursors in the presence of ions, the present results can serve as a reference database to validate or refine lower level methods, as, for instance, the force fields employed in classical simulations.

Integration of Experimental Data and Use of Automated Fitting Methods in Developing Protein Force Fields

The development of accurate protein force fields has been the cornerstone of molecular simulations for the past 50 years. During this period, many lessons have been learned regarding the use of experimental target data and parameter fitting procedures. Here, we review recent advances in protein force field development. We discuss the recent emergence of polarizable force fields and the role of electronic polarization and areas in which additive force fields fall short. The use of automated fitting methods and the inclusion of additional experimental solution data during parametrization is discussed as a means to highlight possible routes to improve the accuracy of force fields even further.

Predicting Spontaneous Orientational Self-Assembly: In Silico Design of Materials with Quantum Mechanically Derived Force Fields

De novo design of self-assembled materials hinges upon our ability to relate macroscopic properties to individual building blocks, thus characterizing in such supramolecular architectures a wide range of observables at varied time/length scales. This work demonstrates that quantum mechanical derived force fields (QMD-FFs) do satisfy this requisite and, most importantly, do so in a predictive manner. To this end, a specific FF, built solely based on the knowledge of the target molecular structure, is employed to reproduce the spontaneous transition to an ordered liquid crystal phase. The simulations deliver a multiscale portrait of such self-assembly processes, where conformational changes within the individual building blocks are intertwined with a 200 ns ensemble reorganization. The extensive characterization provided not only is in quantitative agreement with the experiment but also connects the time/length scales at which it was performed. Realizing QMD-FF predictive power and unmatched accuracy stands as an important leap forward for the bottom-up design of advanced supramolecular materials.

Does the inclusion of electronic polarisability lead to a better modelling of peptide aggregation?

Simulating the process of amyloid aggregation with atomic detail is a challenging task for various reasons. One of them is that it is difficult to parametrise a force field such that all protein states ranging from the folded through the unfolded to the aggregated state are represented with the same level of accuracy. Here, we test whether the consideration of electronic polarisability improves the description of the different states of Aβ_16–22. Surprisingly, the CHARMM Drude polarisable force field is found to perform worse than its unpolarisable counterpart CHARMM36m. Sources for this failure of the Drude model are discussed.

Simulating the process of amyloid aggregation is a hard task. We test whether the inclusion of electronic polarisability as done in CHARMM-Drude improves the modelling of Aβ_16–22 aggregation and find it does not. Reasons for the failure are given.

Automated Parameterization of Quantum Mechanically Derived Force Fields for Soft Materials and Complex Fluids: Development and Validation

The reliability of molecular dynamics (MD) simulations in predicting macroscopic properties of complex fluids and soft materials, such as liquid crystals, colloidal suspensions, or polymers, relies on the accuracy of the adopted force field (FF). We present an automated protocol to derive specific and accurate FFs, fully based on ab initio quantum mechanical (QM) data. The integration of the Joyce and Picky procedures, recently proposed by our group to provide an accurate description of simple liquids, is here extended to larger molecules, capable of exhibiting more complex fluid phases. While the standard Joyce protocol is employed to parameterize the intramolecular FF term, a new automated procedure is here proposed to handle the computational cost of the QM calculations required for the parameterization of the intermolecular FF term. The latter is thus obtained by integrating the old Picky procedure with a fragmentation reconstruction method (FRM) that allows for a reliable, yet computationally feasible sampling of the intermolecular energy surface at the QM level. The whole FF parameterization protocol is tested on a benchmark liquid crystal, and the performances of the resulting quantum mechanically derived (QMD) FF were compared with those delivered by a general-purpose, transferable one, and by the third, "hybrid" FF, where only the bonded terms were refined against QM data. Lengthy atomistic MD simulations are carried out with each FF on extended 5CB systems in both isotropic and nematic phases, eventually validating the proposed protocol by comparing the resulting macroscopic properties with other computational models and with experiments. The QMD-FF yields the best performances, reproducing both phases in the correct range of temperatures and well describing their structure, dynamics, and thermodynamic properties, thus providing a clear protocol that may be explored to predict such properties on other complex fluids or soft materials.