Higher order multipole moments for molecular dynamics simulations

In conventional force fields, the electrostatic potential is represented by atom-centred point charges. This choice is in principle arbitrary, but technically convenient. Point charges can be understood as the first term of multipole expansions, which converge with an increasing number of terms towards the accurate representation of the molecular potential given by the electron density distribution. The use of multipole expansions can therefore improve the force field accuracy. Technically, the implementation of atomic multipoles is more involved than the use of point charges. Important points to consider are the orientation of the multipole moments during the trajectory, conformational dependence of the atomic moments and stability of the simulations which are discussed her

Projected and Hidden Markov Models for calculating kinetics and metastable states of complex molecules

Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of molecular dynamics simulation data. However, MSMs approximate the true dynamics by assuming a Markov chain on a clusters discretization of the state space. This approximation is difficult to make for high-dimensional biomolecular systems, and the quality and reproducibility of MSMs has therefore been limited. Here, we discard the assumption that dynamics are Markovian on the discrete clusters. Instead, we only assume that the full phase- space molecular dynamics is Markovian, and a projection of this full dynamics is observed on the discrete states, leading to the concept of Projected Markov Models (PMMs). Robust estimation methods for PMMs are not yet available, but we derive a practically feasible approximation via Hidden Markov Models (HMMs). It is shown how various molecular observables of interest that are often computed from MSMs can be computed from HMMs / PMMs. The new framework is applicable to both, simulation and single-molecule experimental data. We demonstrate its versatility by applications to educative model systems, an 1 ms Anton MD simulation of the BPTI protein, and an optical tweezer force probe trajectory of an RNA hairpin

Rare-Event Sampling: Occupation-Based Performance Measures for Parallel Tempering and Infinite Swapping Monte Carlo Methods

In the present paper we identify a rigorous property of a number of tempering-based Monte Carlo sampling methods, including parallel tempering as well as partial and infinite swapping. Based on this property we develop a variety of performance measures for such rare-event sampling methods that are broadly applicable, informative, and straightforward to implement. We illustrate the use of these performance measures with a series of applications involving the equilibrium properties of simple Lennard-Jones clusters, applications for which the performance levels of partial and infinite swapping approaches are found to be higher than those of conventional parallel tempering.Comment: 18 figure

An Infinite Swapping Approach to the Rare-Event Sampling Problem

We describe a new approach to the rare-event Monte Carlo sampling problem. This technique utilizes a symmetrization strategy to create probability distributions that are more highly connected and thus more easily sampled than their original, potentially sparse counterparts. After discussing the formal outline of the approach and devising techniques for its practical implementation, we illustrate the utility of the technique with a series of numerical applications to Lennard-Jones clusters of varying complexity and rare-event character.Comment: 24 pages, 16 figure

Synthesis of Trichodermin Derivatives and Their Antimicrobial and Cytotoxic Activities

Trichothecene mycotoxins are recognized as highly bioactive compounds that can be used in the design of new useful bioactive molecules. In Trichoderma brevicompactum, the first specific step in trichothecene biosynthesis is carried out by a terpene cyclase, trichodiene synthase, that catalyzes the conversion of farnesyl diphosphate to trichodiene and is encoded by the tri5 gene. Overexpression of tri5 resulted in increased levels of trichodermin, a trichothecene-type toxin, which is a valuable tool in preparing new molecules with a trichothecene skeleton. In this work, we developed the hemisynthesis of trichodermin and trichodermol derivatives in order to evaluate their antimicrobial and cytotoxic activities and to study the chemo-modulation of their bioactivity. Some derivatives with a short chain at the C-4 position displayed selective antimicrobial activity against Candida albicans and they showed MIC values similar to those displayed by trichodermin. It is important to highlight the cytotoxic selectivity observed for compounds 9, 13, and 15, which presented average IC50 values of 2 g/mL and were cytotoxic against tumorigenic cell line MCF-7 (breast carcinoma) and not against Fa2N4 (non-tumoral immortalized human hepatocytes)

Distributed multipole moments in atomistic force fields. implementation and applications

The accuracy of atomistic force fields depends on the complexity of the interatomic potential function as well as on the parametrization of the potential. In conventional force fields, the electrostatic potential is represented by atom-centered point charges. Point charges can be understood as the first term of multipole expansions, which converge with increasing number of terms towards the accurate representation of the molecular potential given by the electron density distribution. Here, the distributed multipole analysis (DMA) is used to obtain atomic multipole moments. The accuracy of distributed multipole potentials is tested for several molecules and compared to point charge potentials. The investigation is focused on convergence of the multipole expansion and conformational dependence. Energies and forces required for molecular dynamics (MD) simulations with atomic multipole potentials are implemented into the CHARMM program. Important points to consider for the implementation are the orientation of the multipole moments and the conformational dependence of multipole parameters. The implementation is applied to different systems: The splitting of the infrared (IR) absorption band for photodissociated CO in Myoglobin is analyzed comparing different multipole models for CO. A relationship is established between the IR frequency and the CO orientation in the binding pocket. The experimental IR spectrum of CO in amorphous ice is reproduced using multipole potentials for CO and water. The relationship between infrared frequencies and ice structures is analyzed. Furthermore, atomic multipole moments are applied to methane and CO clathrate hydrates. Lattice modes are calculated and compared to experiment. The influence of different guest molecules on lattice modes and structure is characterized

Higher order multipole moments for molecular dynamics simulations

In conventional force fields, the electrostatic potential is represented by atom-centred point charges. This choice is in principle arbitrary, but technically convenient. Point charges can be understood as the first term of multipole expansions, which converge with an increasing number of terms towards the accurate representation of the molecular potential given by the electron density distribution. The use of multipole expansions can therefore improve the force field accuracy. Technically, the implementation of atomic multipoles is more involved than the use of point charges. Important points to consider are the orientation of the multipole moments during the trajectory, conformational dependence of the atomic moments and stability of the simulations which are discussed here

Spatial averaging for small molecule diffusion in condensed phase environments

Spatial averaging is a new approach for sampling rare-event problems. The approach modifies the importance function which improves the sampling efficiency while keeping a defined relation to the original statistical distribution. In this work, spatial averaging is applied to multidimensional systems for typical problems arising in physical chemistry. They include (I) a CO molecule diffusing on an amorphous icesurface, (II) a hydrogen molecule probing favorable positions in amorphous ice, and (III) CO migration in myoglobin. The systems encompass a wide range of energy barriers and for all of them spatial averaging is found to outperform conventional Metropolis Monte Carlo. It is also found that optimal simulation parameters are surprisingly similar for the different systems studied, in particular, the radius of the point cloud over which the potential energy function is averaged. For H2 diffusing in amorphous ice it is found that facile migration is possible which is in agreement with previous suggestions from experiment. The free energy barriers involved are typically lower than 1 kcal/mol. Spatial averaging simulations for CO in myoglobin are able to locate all currently characterized metastable states. Overall, it is found that spatial averaging considerably improves the sampling of configurational space

Structure, spectroscopy and dynamics of layered H2O and CO2 ices

Molecular dynamics simulations of structural, spectroscopic and dynamical properties of mixed water–carbon dioxide (H2O–CO2) ices are discussed over temperature ranges relevant to atmospheric and astrophysical conditions. The simulations employ multipolar force fields to represent electrostatic interactions which are essential for spectroscopic and dynamical investigations. It is found that at the water/CO2 interface the water surface acts as a template for the CO2 component. The rotational reorientation times in both bulk phases agree well with experimental observations. A pronounced temperature effect on the CO2 reorientation time is observed between 100 K and 200 K. At the interface, water reorientation times are nearly twice as long compared to water in the bulk. The spectroscopy of such ices is rich in the far-infrared region of the spectrum and can be related to translational and rotational modes. Furthermore, spectroscopic signatures mediated across the water/CO2 interface are found in this frequency range (around 440 cm−1). These results will be particularly important for new airborne experiments such as planned for SOFIA