Free Energies of Hydrated Halide Anions: High Through-Put Computations on Clusters to Treat Rough Energy-Landscapes

With a longer-term goal of addressing the comparative behavior of the aqueous halides F−, Cl−, Br−, and I− on the basis of quasi-chemical theory (QCT), here we study structures and free energies of hydration clusters for those anions. We confirm that energetically optimal (H2O)nX clusters, with X = Cl−, Br−, and I−, exhibit surface hydration structures. Computed free energies, based on optimized surface hydration structures utilizing a harmonic approximation, typically (but not always) disagree with experimental free energies. To remedy the harmonic approximation, we utilize single-point electronic structure calculations on cluster geometries sampled from an AIMD (ab initio molecular dynamics) simulation stream. This rough-landscape procedure is broadly satisfactory and suggests unfavorable ligand crowding as the physical effect addressed. Nevertheless, this procedure can break down when n≳4, with the characteristic discrepancy resulting from a relaxed definition of clustering in the identification of (H2O)nX clusters, including ramified structures natural in physical cluster theories. With ramified structures, the central equation for the present rough-landscape approach can acquire some inconsistency. Extension of these physical cluster theories in the direction of QCT should remedy that issue, and should be the next step in this research direction.

Free Energies of Hydrated Halide Anions: High throughput Computations on Clusters to Treat Rough Energy-Landscapes

With a longer-term goal of addressing the comparative behavior of the aqueous halides F$^-$, Cl$^-$, Br$^-$, and I$^-$ on the basis of quasi-chemical theory (QCT), here we study structures and free energies of hydration clusters for those anions. We confirm that energetically optimal $(\mathrm{H_2O})_n\mathrm{X}$ clusters, with X = Cl$^-$, Br$^-$, and I$^-$, exhibit \emph{surface} hydration structures. Computed free energies based on optimized surface hydration structures utilizing a harmonic approximation, typically (but not always) disagree with experimental free energies. To remedy the harmonic approximation, we utilize single-point electronic structure calculations on cluster geometries sampled from an AIMD (\emph{ab initio} molecular dynamics) simulation stream. This \emph{rough-landscape} procedure is broadly satisfactory and suggests unfavorable ligand crowding as the physical effect corrected. Nevertheless, this procedure can break down when $n \gtrsim 4$, with the characteristic discrepancy resulting from a relaxed definition of clustering in the identification of $(\mathrm{H_2O})_n\mathrm{X}$ clusters, including ramified structures natural in \emph{physical cluster theories.} With ramified structures, the central equation for the present rough-landscape approach can acquire some inconsistency. Extension of these physical cluster theories in the direction of QCT should remedy that issue, and should be the next step in this research direction.

Thermodynamic Properties of Heisenberg Spin Systems

We present the simulation results of magnetic 2D and 3D structures with direct (for both of them) and Dzyaloshinskii-Moriya (DMI) (for 2D lattice) interactions in the frame of the Heisenberg model. We have adapted the multipath Metropolis algorithm for systems with complex types of exchange interactions and rough energy landscapes. We show the temperature behavior of magnetization, energy, and heat capacity, and reveal its critical temperatures and order parameter.

REVO: Resampling of Ensembles by Variation Optimization

Conventional molecular dynamics simulations are incapable of sampling many important interactions in biomolecular systems due to their high dimensionality and rough energy landscapes. To observe rare events and calculate transition rates in these systems, enhanced sampling is a necessity. In particular, the study of ligand-protein interactions necessitates a diverse ensemble of protein conformations and transition states, and for many systems this occurs on prohibitively long timescales. Previous strategies such as WExplore that can be used to determine these types of ensembles are hindered by problems related to the regioning of conformational space. Here we propose a novel, regionless, enhanced sampling method that is based on the weighted ensemble framework. In this method, a value referred to as “trajectory variation” is optimized after each cycle through cloning and merging operations. This method allows for a more consistent measurement of observables and broader sampling resulting in the efficient exploration of previously unexplored conformations. We demonstrate the performance of this algorithm with the N-dimensional random walk and the unbinding of the trypsin-benzamidine system. The system is analyzed using conformation space networks, the residence time of benzamidine is confirmed, and a new unbinding pathway for the trypsin-benzamidine system is found. We expect that REVO will be a useful general tool to broadly explore free energy landscapes.

REVO: Resampling of Ensembles by Variation Optimization

Conventional molecular dynamics simulations are incapable of sampling many important interactions in biomolecular systems due to their high dimensionality and rough energy landscapes. To observe rare events and calculate transition rates in these systems, enhanced sampling is a necessity. In particular, the study of ligand-protein interactions necessitates a diverse ensemble of protein conformations and transition states, and for many systems this occurs on prohibitively long timescales. Previous strategies such as WExplore that can be used to determine these types of ensembles are hindered by problems related to the regioning of conformational space. Here we propose a novel, regionless, enhanced sampling method that is based on the weighted ensemble framework. In this method, a value referred to as “trajectory variation” is optimized after each cycle through cloning and merging operations. This method allows for a more consistent measurement of observables and broader sampling resulting in the efficient exploration of previously unexplored conformations. We demonstrate the performance of this algorithm with the N-dimensional random walk and the unbinding of the trypsin-benzamidine system. The system is analyzed using conformation space networks, the residence time of benzamidine is confirmed, and a new unbinding pathway for the trypsin-benzamidine system is found. We expect that REVO will be a useful general tool to broadly explore free energy landscapes.

REVO: Resampling of Ensembles by Variation Optimization

Conventional molecular dynamics simulations are incapable of sampling many important interactions in biomolecular systems due to their high dimensionality and rough energy landscapes. To observe rare events and calculate transition rates in these systems, enhanced sampling is a necessity. In particular, the study of ligand-protein interactions necessitates a diverse ensemble of protein conformations and transition states, and for many systems this occurs on prohibitively long timescales. Previous strategies such as WExplore that can be used to determine these types of ensembles are hindered by problems related to the regioning of conformational space. Here we propose a novel, regionless, enhanced sampling method that is based on the weighted ensemble framework. In this method, a value referred to as “trajectory variation” is optimized after each cycle through cloning and merging operations. This method allows for a more consistent measurement of observables and broader sampling resulting in the efficient exploration of previously unexplored conformations. We demonstrate the performance of this algorithm with the N-dimensional random walk and the unbinding of the trypsin-benzamidine system. The system is analyzed using conformation space networks, the residence time of benzamidine is confirmed, and a new unbinding pathway for the trypsin-benzamidine system is found. We expect that REVO will be a useful general tool to broadly explore free energy landscapes.

REVO: Resampling of Ensembles by Variation Optimization

Conventional molecular dynamics simulations are incapable of sampling many important interactions in biomolecular systems due to their high dimensionality and rough energy landscapes. To observe rare events and calculate transition rates in these systems, enhanced sampling is a necessity. In particular, the study of ligand-protein interactions necessitates a diverse ensemble of protein conformations and transition states, and for many systems this occurs on prohibitively long timescales. Previous strategies such as WExplore that can be used to determine these types of ensembles are hindered by problems related to the regioning of conformational space. Here we propose a novel, regionless, enhanced sampling method that is based on the weighted ensemble framework. In this method, a value referred to as “trajectory variation” is optimized after each cycle through cloning and merging operations. This method allows for a more consistent measurement of observables and broader sampling resulting in the efficient exploration of previously unexplored conformations. We demonstrate the performance of this algorithm with the N-dimensional random walk and the unbinding of the trypsin-benzamidine system. The system is analyzed using conformation space networks, the residence time of benzamidine is confirmed, and a new unbinding pathway for the trypsin-benzamidine system is found. We expect that REVO will be a useful general tool to broadly explore free energy landscapes.