Binding structures of tri-N-acetyl-β-glucosamine in hen egg white lysozyme using molecular dynamics with a polarizable force field

Harnessing Deep Learning for Optimization of Lennard-Jones Parameters for the Polarizable Classical Drude Oscillator Force Field

The outcomes of computational chemistry and biology research, including drug design, are significantly influenced by the underlying force field (FF) used in molecular simulations. While improved FF accuracy may be achieved via inclusion of explicit treatment of electronic polarization, such an extension must be accompanied by optimization of van der Waals (vdW) interactions, in the context of the Lennard-Jones (LJ) formalism in the present study. This is particularly challenging due to the extensive nature of chemical space combined with the correlated nature of LJ parameters. To address this challenge, a deep learning (DL)-based parametrization framework is developed, allowing for sampling of wide ranges of LJ parameters targeting experimental condensed phase thermodynamic properties. The present work utilizes this framework to develop the LJ parameters for atoms associated with four distinct groups covering 10 different atom types. Final parameter selection was facilitated by quantum mechanical data on rare-gas interactions with the training set molecules. The chosen parameters were then validated through experimental hydration free energies and condensed phase thermodynamic properties of validation set molecules to confirm transferability. The ultimate outcome of utilizing this framework is a set of LJ parameters in the context of the polarizable Drude FF, which demonstrated improvement in the reproduction of both experimental pure solvent and crystal properties and hydration free energies of the molecules compared to the additive CHARMM General FF (CGenFF) including the ability of the Drude FF to accurately reproduce both experimental pure solvent properties and hydration free energies. The study also shows how correlations between difference in the reproduction of condensed phase data between model compounds may be used to direct the selection of new atom types and training set molecules during FF development.

CHARMM-GUI Drude prepper for molecular dynamics simulation using the classical Drude polarizable force field

Explicit treatment of electronic polarizability in empirical force fields (FFs) represents an extension over a traditional additive or pairwise FF and provides a more realistic model of the variations in electronic structure in condensed phase, macromolecular simulations. To facilitate utilization of the polarizable FF based on the classical Drude oscillator model, Drude Prepper has been developed in CHARMM-GUI. Drude Prepper ingests additive CHARMM protein structures file (PSF) and pre-equilibrated coordinates in CHARMM, PDB, or NAMD format, from which the molecular components of the system are identified. These include all residues and patches connecting those residues along with water, ions, and other solute molecules. This information is then used to construct the Drude FF-based PSF using molecular generation capabilities in CHARMM, followed by minimization and equilibration. In addition, inputs are generated for molecular dynamics (MD) simulations using CHARMM, GROMACS, NAMD, and OpenMM. Validation of the Drude Prepper protocol and inputs is performed through conversion and MD simulations of various heterogeneous systems that include proteins, nucleic acids, lipids, polysaccharides, and atomic ions using the aforementioned simulation packages. Stable simulations are obtained in all studied systems, including 5 μs simulation of ubiquitin, verifying the integrity of the generated Drude PSFs. In addition, the ability of the Drude FF to model variations in electronic structure is shown through dipole moment analysis in selected systems. The capabilities and availability of Drude Prepper in CHARMM-GUI is anticipated to greatly facilitate the application of the Drude FF to a range of condensed phase, macromolecular systems.

Drude Polarizable Force Field Parametrization of Carboxylate and N-Acetyl Amine Carbohydrate Derivatives

In this work, we report the development of Drude polarizable force field parameters for the carboxylate and N-acetyl amine derivatives, extending the functionality of the existing Drude polarizable carbohydrate force field. The force field parameters have been developed in a hierarchical manner, reproducing the quantum mechanical gas-phase properties of small model compounds representing the key functional group in the carbohydrate derivatives, including optimization of the electrostatic and bonded parameters. The optimized parameters were then used to generate the models for carboxylate and N-acetyl amine carbohydrate derivatives. The transferred parameters were further tested and optimized to reproduce crystal geometries and J-coupling data from nuclear magnetic resonance experiments. The parameter development resulted in the incorporation of d-glucuronate, l-iduronate, N-acetyl-d-glucosamine (GlcNAc), and N-acetyl-d-galactosamine (GalNAc) sugars into the Drude polarizable force field. The parameters developed in this study were then applied to study the conformational properties of glycosaminoglycan polymer hyaluronan, composed of d-glucuronate and N-acetyl-d-glucosamine, in aqueous solution. Upon comparing the results from the additive and polarizable simulations, it was found that the inclusion of polarization improved the description of the electrostatic interactions observed in hyaluronan, resulting in enhanced conformational flexibility. The developed Drude polarizable force field parameters in conjunction with the remainder of the Drude polarizable force field parameters can be used for future studies involving carbohydrates and their conjugates in complex, heterogeneous systems.

Refined Empirical Force Field to Model Protein-Self-Assembled Monolayer Interactions Based on AMBER14 and GAFF

Understanding protein interaction with material surfaces is important for the development of nanotechnological devices. The structures and dynamics of proteins can be studied via molecular dynamics (MD) if the protein-surface interactions can be accurately modeled. To answer this question, we computed the adsorption free energies of peptides (representing eleven different amino acids) on a hydrophobic self-assembled monolayer (CH₃-SAM) and compared them to the benchmark experimental data set. Our result revealed that existing biomolecular force fields, GAFF and AMBER ff14sb, cannot reproduce the experimental peptide adsorption free energies by Wei and Latour (Langmuir, 2009, 25, 5637-5646). To obtain the improved force fields, we systematically tuned the Lennard-Jones parameters of selected amino acid sidechains and the functional group of SAM with repeated metadynamics and umbrella sampling simulations. The final parameter set has yielded a significant improvement in the free energy values with R = 0.83 and MSE = 0.65 kcal/mol. We applied the refined force field to predict the initial adsorption orientation of lysozyme on CH₃-SAM. Two major orientations-face-down and face-up-were predicted. Our analysis on the protein structure, solvent accessible surface area, and binding of native ligand NAG₃ suggested that lysozyme in the face-up orientation can remain active after initial adsorption. However, because of its weaker affinity (ΔΔG = 7.86 kcal/mol) for the ligand, the bioactivity of the protein is expected to reduce. Our work facilitates the use of MD for the study of protein-SAM systems. The refined force field compatible with GROMACS is available at https://cbbio.cis.um.edu.mo/software/SAMFF .

Force Fields for Small Molecules

Molecular dynamics (MD) simulations have been widely applied to computer-aided drug design (CADD). While MD has been used in a variety of applications such as free energy perturbation and long-time simulations, the accuracy of the results from those methods depends strongly on the force field used. Force fields for small molecules are crucial, as they not only serve as building blocks for developing force fields for larger biomolecules but also act as model compounds that will be transferred to ligands used in CADD. Currently, a wide range of small molecule force fields based on additive or nonpolarizable models have been developed. While these nonpolarizable force fields can produce reasonable estimations of physical properties and have shown success in a variety of systems, there is still room for improvements due to inherent limitations in these models including the lack of an electronic polarization response. For this reason, incorporating polarization effects into the energy function underlying a force field is believed to be an important step forward, giving rise to the development of polarizable force fields. Recent simulations of biological systems have indicated that polarizable force fields are able to provide a better physical representation of intermolecular interactions and, in many cases, better agreement with experimental properties than nonpolarizable, additive force fields. Therefore, this chapter focuses on the development of small molecule force fields with emphasis on polarizable models. It begins with a brief introduction on the importance of small molecule force fields and their evolution from additive to polarizable force fields. Emphasis is placed on the additive CHARMM General Force Field and the polarizable force field based on the classical Drude oscillator. The theory for the Drude polarizable force field and results for small molecules are presented showing their improvements over the additive model. The potential importance of polarization for their application in a wide range of biological systems including CADD is then discussed.

Inhibition of lysozyme's polymerization activity using a polymer structural mimic

Hen egg white lysozyme (HEWL) is a green catalyst capable of polymerizing the formation of 2-ethynylpyridine. 1,3-di(2-pyridyl)propane (DPP) is a mimic of the polymer repeating unit and a polymerization inhibitor. DPP's interaction with HEWL reveals structural insight into the mechanism of polymerization.

Protein-Ligand Dissociation Simulated by Parallel Cascade Selection Molecular Dynamics

We investigated the dissociation process of tri-N-acetyl-d-glucosamine from hen egg white lysozyme using parallel cascade selection molecular dynamics (PaCS-MD), which comprises cycles of multiple unbiased MD simulations using a selection of MD snapshots as the initial structures for the next cycle. Dissociation was significantly accelerated by PaCS-MD, in which the probability of rare event occurrence toward dissociation was enhanced by the selection and rerandomization of the initial velocities. Although this complex was stable during 1 μs of conventional MD, PaCS-MD easily induced dissociation within 10⁰-10¹ ns. We found that velocity rerandomization enhances the dissociation of triNAG from the bound state, whereas diffusion plays a more important role in the unbound state. We calculated the dissociation free energy by analyzing all PaCS-MD trajectories using the Markov state model (MSM), compared the results to those obtained by combinations of PaCS-MD and umbrella sampling (US), steered MD (SMD) and US, and SMD and the Jarzynski equality, and experimentally determined binding free energy. PaCS-MD/MSM yielded results most comparable to the experimentally determined binding free energy, independent of simulation parameter variations, and also gave the lowest standard errors.

Lysozyme-catalyzed formation of a conjugated polyacetylene

Hen egg white lysozyme catalyzes the polymerization of 2-ethynylpyridine in water as the singular protein catalyst. This marks the first time a protein has been observed generating conjugated polymers from alkynes.

Structural, Functional and Phylogenetic Analysis of Sperm Lysozyme-Like Proteins

Sperm lysozyme-like proteins belonging to c-type lysozyme family evolved in multiple forms. Lysozyme-like proteins, viz., LYZL2, LYZL3 or SLLP1, LYZL4, LYZL5 and LYZL6 are expressed in the testis of mammals. Not all members of LYZL family have been uniformly and unambiguously identified in the genome and proteome of mammals. Some studies suggested a role of SLLP1 and LYZL4 in fertilization; however, the function of other LYZL proteins is unknown. We identified all known forms of LYZL proteins in buffalo sperm by LC-MS/MS. Cloning and sequence analysis of the Lyzl cDNA showed 38-50% identity at amino acid level among the buffalo LYZL paralogs, complete conservation of eight cysteines and other signature sequences of c-type lysozyme family. Catalytic residues in SLLP1, LYZL4 and LYZL5 have undergone replacement. The substrate binding residues showed significant variation in LYZL proteins. Residues at sites 62, 101, 114 in LYZL4; 101 in SLLP1; 37, 62, and 101 in LYZL6 were more variable among diverse species. Sites 63 and 108 occupied by tryptophan were least tolerant to variation. Site 37 also showed lower tolerance to substitution in SLLP1, LYZL4 and LYZL5, but more variable in non-testicular lysozymes. Models of LYZL proteins were created by homology modeling and the substrate binding pockets were analyzed in term of binding energies and contacting residues of LYZL proteins with tri-N-acetylglucosamine (NAG)3 in the A-B-C and B-C-D binding mode. Except LYZL6, LYZL proteins did not show significant difference in binding energies in comparison to hen egg white lysozyme in the A-B-C mode. (NAG)3 binding energy in the B-C-D mode was higher by 1.3-2.2 kcal/mol than in A-B-C mode. Structural analysis indicated that (NAG)3 was involved in making more extensive interactions including hydrogen bonding with LYZL proteins in B-C-D mode than in A-B-C mode. Despite large sequence divergence among themselves and with respect to c-type lysozymes, substrate binding residues as well as hydrogen bonding network between (NAG)3 and proteins were mostly conserved. LYZL5 in buffalo and other mammalian species contained additional 10-12 amino acid sequence at c-terminal that matched with ankyrin repeat domain-containing protein 27. Phylogenetic analysis indicated LYZL2 to be most ancient among all the LYZL proteins and that the evolution of LYZL proteins occurred through several gene duplications preceding the speciation of mammals from other vertebrates as distant as reptiles and amphibians.

An Empirical Polarizable Force Field Based on the Classical Drude Oscillator Model: Development History and Recent Applications

Molecular mechanics force fields that explicitly account for induced polarization represent the next generation of physical models for molecular dynamics simulations. Several methods exist for modeling induced polarization, and here we review the classical Drude oscillator model, in which electronic degrees of freedom are modeled by charged particles attached to the nuclei of their core atoms by harmonic springs. We describe the latest developments in Drude force field parametrization and application, primarily in the last 15 years. Emphasis is placed on the Drude-2013 polarizable force field for proteins, DNA, lipids, and carbohydrates. We discuss its parametrization protocol, development history, and recent simulations of biologically interesting systems, highlighting specific studies in which induced polarization plays a critical role in reproducing experimental observables and understanding physical behavior. As the Drude oscillator model is computationally tractable and available in a wide range of simulation packages, it is anticipated that use of these more complex physical models will lead to new and important discoveries of the physical forces driving a range of chemical and biological phenomena.

Can we treat ab initio atomic charges and bond orders as conformation-independent electronic structure descriptors?

It is shown that atomic charges and bond orders of 2′-deoxycytidine depend on the molecule conformation.

CHARMM Drude Polarizable Force Field for Aldopentofuranoses and Methyl-aldopentofuranosides

An empirical all-atom CHARMM polarizable force filed for aldopentofuranoses and methyl-aldopentofuranosides based on the classical Drude oscillator is presented. A single electrostatic model is developed for eight different diastereoisomers of aldopentofuranoses by optimizing the existing electrostatic and bonded parameters as transferred from ethers, alcohols, and hexopyranoses to reproduce quantum mechanical (QM) dipole moments, furanose-water interaction energies and conformational energies. Optimization of selected electrostatic and dihedral parameters was performed to generate a model for methyl-aldopentofuranosides. Accuracy of the model was tested by reproducing experimental data for crystal intramolecular geometries and lattice unit cell parameters, aqueous phase densities, and ring pucker and exocyclic rotamer populations as obtained from NMR experiments. In most cases the model is found to reproduce both QM data and experimental observables in an excellent manner, whereas for the remainder the level of agreement is in the satisfactory regimen. In aqueous phase simulations the monosaccharides have significantly enhanced dipoles as compared to the gas phase. The final model from this study is transferrable for future studies on carbohydrates and can be used with the existing CHARMM Drude polarizable force field for biomolecules.

Recent Advances in Polarizable Force Fields for Macromolecules: Microsecond Simulations of Proteins Using the Classical Drude Oscillator Model

In this Perspective, we summarize recent efforts to include the explicit treatment of induced electronic polarization in biomolecular force fields. Methods used to treat polarizability, including the induced dipole, fluctuating charge, and classical Drude oscillator models, are presented, including recent advances in force fields using those methods. This is followed by recent results obtained with the Drude model, including microsecond molecular dynamics (MD) simulations of multiple proteins in explicit solvent. Results show significant variability of backbone and side-chain dipole moments as a function of environment, including significant changes during individual simulations. Dipole moments of water in the vicinity of the proteins reveal small but systematic changes, with the direction of the changes dependent on the environment. Analyses of the full proteins show that the polarizable Drude model leads to larger values of the dielectric constant of the protein interior, especially in the case of hydrophobic regions. These results indicate that the inclusion of explicit electronic polarizability leads to significant differences in the physical forces affecting the structure and dynamics of proteins, which can be investigated in a computationally tractable fashion in the context of the Drude model.

Polarizable empirical force field for hexopyranose monosaccharides based on the classical Drude oscillator

A polarizable empirical force field based on the classical Drude oscillator is presented for the hexopyranose form of selected monosaccharides. Parameter optimization targeted quantum mechanical (QM) dipole moments, solute-water interaction energies, vibrational frequencies, and conformational energies. Validation of the model was based on experimental data on crystals, densities of aqueous-sugar solutions, diffusion constants of glucose, and rotational preferences of the exocylic hydroxymethyl of d-glucose and d-galactose in aqueous solution as well as additional QM data. Notably, the final model involves a single electrostatic model for all sixteen diastereomers of the monosaccharides, indicating the transferability of the polarizable model. The presented parameters are anticipated to lay the foundation for a comprehensive polarizable force field for saccharides that will be compatible with the polarizable Drude parameters for lipids and proteins, allowing for simulations of glycolipids and glycoproteins.

Force Field for Peptides and Proteins based on the Classical Drude Oscillator

Presented is a polarizable force field based on a classical Drude oscillator framework, currently implemented in the programs CHARMM and NAMD, for modeling and molecular dynamics (MD) simulation studies of peptides and proteins. Building upon parameters for model compounds representative of the functional groups in proteins, the development of the force field focused on the optimization of the parameters for the polypeptide backbone and the connectivity between the backbone and side chains. Optimization of the backbone electrostatic parameters targeted quantum mechanical conformational energies, interactions with water, molecular dipole moments and polarizabilities and experimental condensed phase data for short polypeptides such as (Ala)₅. Additional optimization of the backbone φ, ψ conformational preferences included adjustments of the tabulated two-dimensional spline function through the CMAP term. Validation of the model included simulations of a collection of peptides and proteins. This 1^st generation polarizable model is shown to maintain the folded state of the studied systems on the 100 ns timescale in explicit solvent MD simulations. The Drude model typically yields larger RMS differences as compared to the additive CHARMM36 force field (C36) and shows additional flexibility as compared to the additive model. Comparison with NMR chemical shift data shows a small degradation of the polarizable model with respect to the additive, though the level of agreement may be considered satisfactory, while for residues shown to have significantly underestimated S² order parameters in the additive model, improvements are calculated with the polarizable model. Analysis of dipole moments associated with the peptide backbone and tryptophan side chains show the Drude model to have significantly larger values than those present in C36, with the dipole moments of the peptide backbone enhanced to a greater extent in sheets versus helices and the dipoles of individual moieties observed to undergo significant variations during the MD simulations. Although there are still some limitations, the presented model, termed Drude-2013, is anticipated to yield a molecular picture of peptide and protein structure and function that will be of increased physical validity and internal consistency in a computationally accessible fashion.