Drude Polarizable Lipid Force Field with Explicit Treatment of Long-Range Dispersion: Parametrization and Validation for Saturated and Monounsaturated Zwitterionic Lipids.

Accurate empirical force fields of lipid molecules are a critical component of molecular dynamics simulation studies aimed at investigating properties of monolayers, bilayers, micelles, vesicles, and liposomes, as well as heterogeneous systems, such as protein-membrane complexes, bacterial cell walls, and more. While the majority of lipid force field-based simulations have been performed using pairwise-additive nonpolarizable models, advances have been made in the development of the polarizable force field based on the classical Drude oscillator model. In the present study, we undertake further optimization of the Drude lipid force field, termed Drude2023, including improved treatment of the phosphate and glycerol linker region of PC and PE headgroups, additional optimization of the alkene group in monounsaturated lipids, and inclusion of long-range Lennard-Jones interactions using the particle-mesh Ewald method. Initial optimization targeted quantum mechanical (QM) data on small model compounds representative of the linker region. Subsequent optimization targeted QM data on larger model compounds, experimental data, and dihedral potentials of mean force from the CHARMM36 additive lipid force field using a parameter reweighting protocol. The use of both experimental and QM target data during the reweighting protocol is shown to produce physically reasonable parameters that reproduce a collection of experimental observables. Target data for optimization included surface area/lipid for DPPC, DSPC, DMPC, and DLPC bilayers and nuclear magnetic resonance (NMR) order parameters for DPPC bilayers. Validation data include prediction of membrane thickness, scattering form factors, electrostatic potential profiles, compressibility moduli, surface area per lipid, water permeability, NMR T1 relaxation times, diffusion constants, and monolayer surface tensions for a variety of saturated and unsaturated lipid mono- and bilayers. Overall, the agreement with experimental data is quite good, though the results are less satisfactory for the NMR T1 relaxation times for carbons near the ester groups. Notable improvements compared to the additive C36 force field were obtained for membrane dipole potentials, lipid diffusion coefficients, and water permeability with the exception of monounsaturated lipid bilayers. It is anticipated that the optimized polarizable Drude2023 force field will help generate more accurate molecular simulations of pure bilayers and heterogeneous systems containing membranes, advancing our understanding of the role of electronic polarization in these systems.

Elusive Intermediate State Key in the Conversion of ATP Hydrolysis into Useful Work Driving the Ca2+ Pump SERCA.

A key event in the ATP-driven transport cycle of the calcium pump sarco/endoplasmic reticulum Ca2+-ATPase (SERCA) occurs when autophosphorylation of the pump with two bound ions Ca2+ triggers a large conformational change that opens a gate on the luminal side of the membrane allowing the release of the ions. It is believed that this conformational transition proceeds through a two-step mechanism, with an initial rearrangement of the three cytoplasmic domains of the pump responsible for ATP binding and hydrolysis followed by the opening of the gate toward the luminal side in the transmembrane region. Here, molecular dynamics computation of the free energy landscapes associated with this transition show how, in response to phosphorylation, the cytoplasmic domains are partially reconfigured into an intermediate state on the path toward the E2 state with a closed luminal gate. It is suggested that the free energy associated with this conformational reorganization must subsequently be used to drive the opening of the gate on the luminal side.

Energy Decomposition Analysis for Interactions of Radicals: Theory and Implementation at the MP2 Level with Application to Hydration of Halogenated Benzene Cations and Complexes between CO2-· and Pyridine and Imidazole.

To study intermolecular interactions involving radicals at the correlated level, the energy decomposition analysis scheme for second-order MoÌ·ller-Plesset perturbation theory based on absolutely localized molecular orbitals (ALMO-MP2-EDA) is generalized to unrestricted and restricted open-shell MP2. The benefit of restricted open-shell MP2 is that it can provide accurate binding energies for radical complexes where density functional theory can be error-prone due to delocalization errors. As a model application, the open-shell ALMO-MP2-EDA is applied to study the first solvation step of halogenated benzene radical cations, where both halogen- and hydrogen-bonded isomers are possible. We determine that the lighter halogens favor the hydrogen-bonded form, while the iodine-substituted species prefers halogen bonding due to larger polarizability and charge transfer at the halogen. As a second application, relevant to the activation of CO2 in photoelectrocatalysis, complexes of CO2-· interacting with both pyridine and imidazole are analyzed with ALMO-MP2-EDA. The results reveal the importance of charge transfer into the π* orbital of the heterocycle in controlling the stability of the carbamate binding mode, which is favored for pyridine but not for imidazole.

Reduced Free Energy Perturbation/Hamiltonian Replica Exchange Molecular Dynamics Method with Unbiased Alchemical Thermodynamic Axis.

Replica-exchange molecular dynamics (REMD) has been proven to efficiently improve the convergence of free-energy perturbation (FEP) calculations involving considerable reorganization of their surrounding. We previously introduced the FEP/(λ,H)-REMD algorithm for ligand binding, in which replicas along the alchemical thermodynamic coupling axis λ were expanded as a series of Hamiltonian boosted replicas along a second axis to form a two-dimensional replica-exchange exchange map [Jiang, W.; Roux, B., J. Chem. Theory Comput. 2010, 6 (9), 2559-2565]. Aiming to achieve a similar performance at a lower computational cost, we propose here a modified version of this algorithm in which only the end-states along the alchemical axis are augmented by boosted replicas. The reduced FEP/(λ,H)-REMD method with one-dimensional unbiased alchemical thermodynamic coupling axis λ is implemented on the basis of generic multiple copy algorithm (MCA) module of the biomolecular simulation program NAMD. The flexible MCA framework of NAMD enables a user to design customized replica-exchange patterns through Tcl scripting in the context of a highly parallelized simulation program without touching the source code. Two Hamiltonian tempering boosting scheme were examined with the new algorithm: a first one based on potential energy rescaling of a preidentified "solute" and a second one via the introduction of flattening torsional free-energy barriers. As two illustrative examples with reliable experiment data, the absolute binding free energies of p-xylene and n-butylbenzene to the nonpolar cavity of the L99A mutant of T4 lysozyme were calculated. The tests demonstrate that the new protocol efficiently enhances the sampling of torsional motions for backbone and side chains around the binding pocket and accelerates the convergence of the free-energy computations.

Understanding Non-Covalent Interactions: Correlated Energy Decomposition Analysis and Applications to Halogen Bonding.

Non-covalent interactions play a primordial role in chemistry. Beyond their quantification, the detailed understanding of their physical processes is necessary to rationalize chemical trends and improve designs of chemical systems. Energy decomposition analyses allow detailed insight into non-covalent interactions by extracting electrostatics, Pauli repulsion, polarization, dispersion and charge transfer components from interaction energies. Recent work has demonstrated that electronic correlation influenced significantly all of these energy components, whereas previous decompositions only partitioned correlation between dispersion and charge transfer. The MP2 energy decomposition analysis with Absolutely Localized Molecular Orbitals (MP2 ALMO-EDA) takes these results fully into account and offers a correlation correction for each extracted component. A recent detailed investigation of the CCSD dispersion energy showed that a small number of virtual orbitals is sufficient to describe dispersion interactions accurately in the long-range, which potentially offers a basis-set independent definition of dispersion. Finally, we present an application of MP2 ALMO-EDA to a series of unusual halogen bonding complexes where charge transfer dominates over the electrostatic σ-hole interaction.

Characterizing the interplay of Pauli repulsion, electrostatics, dispersion and charge transfer in halogen bonding with energy decomposition analysis.

The halogen bond is a class of non-covalent interaction that has attracted considerable attention recently. A widespread theory for describing them is the σ-hole concept, which predicts that the strength of the interaction is proportional to the size of the σ-hole, a region of positive electrostatic potential opposite a σ bond. Previous work shows that in the case of CX3I, with X equal to F, Cl, Br, and I, the σ-hole trend is exactly opposite to the trend in binding energy with common electron pair donors. Using energy decomposition analysis (EDA) applied to a potential energy scan as well as the recent adiabatic EDA technique, we show that the observed trend is a result of charge transfer. Therefore a picture of the halogen bond that excludes charge transfer cannot be complete, and permanent and induced electrostatics do not always provide the dominant stabilizing contributions to halogen bonds. Overall, three universally attractive factors, polarization, dispersion and charge transfer, together with permanent electrostatics, which is usually attractive, drive halogen bonding, against Pauli repulsion.

Efficient Implementation of Energy Decomposition Analysis for Second-Order Møller-Plesset Perturbation Theory and Application to Anion-π Interactions.

Energy decomposition analysis (EDA) is a widely used tool for extracting physical and chemical insights from electronic structure calculations of intermolecular interactions, as well as for the development of advanced force fields for describing those interactions. Recently, the absolutely localized molecular orbital (ALMO) EDA has been extended from the self-consistent field level to the second-order Møller-Plesset (MP2) theory level. This paper reports an efficient implementation of the MP2 ALMO-EDA that scales optimally, employs the resolution of the identity (RI) approximation for post-SCF matrix elements, and is shared-memory parallel. The algorithms necessary to achieve this implementation are described in detail. Performance tests using the aug-cc-pVTZ basis set for water clusters of up to 10 molecules are reported. The timings suggest that the MP2 ALMO-EDA is computationally feasible whenever MP2 energy calculations themselves are feasible, and the cost is dominated by the SCF itself in this size regime. The MP2 ALMO-EDA is applied to study the origin of substituent effects in anion-π interactions between chloride and benzene and mono- through hexafluorobenzene. The effect of fluoro substituents was primarily to change the frozen interaction. Detailed analysis supports the interpretation that anion-π interactions are favorable because of electrostatic interaction with the substituents.

An energy decomposition analysis for second-order Møller-Plesset perturbation theory based on absolutely localized molecular orbitals.

An energy decomposition analysis (EDA) of intermolecular interactions is proposed for second-order Møller-Plesset perturbation theory (MP2) based on absolutely localized molecular orbitals (ALMOs), as an extension to a previous ALMO-based EDA for self-consistent field methods. It decomposes the canonical MP2 binding energy by dividing the double excitations that contribute to the MP2 wave function into classes based on how the excitations involve different molecules. The MP2 contribution to the binding energy is decomposed into four components: frozen interaction, polarization, charge transfer, and dispersion. Charge transfer is defined by excitations that change the number of electrons on a molecule, dispersion by intermolecular excitations that do not transfer charge, and polarization and frozen interactions by intra-molecular excitations. The final two are separated by evaluations of the frozen, isolated wave functions in the presence of the other molecules, with adjustments for orbital response. Unlike previous EDAs for electron correlation methods, this one includes components for the electrostatics, which is vital as adjustment to the electrostatic behavior of the system is in some cases the dominant effect of the treatment of electron correlation. The proposed EDA is then applied to a variety of different systems to demonstrate that all proposed components behave correctly. This includes systems with one molecule and an external electric perturbation to test the separation between polarization and frozen interactions and various bimolecular systems in the equilibrium range and beyond to test the rest of the EDA. We find that it performs well on these tests. We then apply the EDA to a halogen bonded system to investigate the nature of the halogen bond.

Electrostatic Domination of the Effect of Electron Correlation in Intermolecular Interactions.

The electron-electron correlation energy is negative, and attractive dispersion interactions are entirely a correlation effect; therefore, the contribution of correlation to intermolecular binding is commonly assumed to be negative, or binding in nature. However, there are many cases where the long-range correlation binding energy is positive, with certain geometries of the water dimer as a prominent example. Geometries with dipoles misaligned can also have an electrostatically dominated, though negative, long-range correlation binding. In either case, the interaction decays as R(-3). This has its origin in the systematic overestimation of dipole moments by Hartree-Fock theory, leading to a reduction in the calculated electrostatic attraction upon inclusion of correlation. Thus, energy decomposition analyses that include correlation but do not correct mean field electrostatic terms are suboptimal. Attenuated second-order Møller-Plesset theory, which smoothly truncates long-range electron correlation effects to zero, can, paradoxically, have the correct long-range behavior for many intermolecular interactions.