Reducing the number of mean-square deviation calculations with floating close structure in metadynamics.

Metadynamics is an important collective-coordinate-based enhanced sampling simulation method. Its performance depends significantly on the capability of collective coordinates to describe the studied molecular processes. Collective coordinates based on comparison with reference landmark structures can be used to enhance sampling in highly complex systems; however, they may slow down simulations due to high number of structure-structure distance (e.g., mean-square deviation) calculations. Here we introduce an approximation of root-mean-square or mean-square deviation that significantly reduces numbers of computationally expensive operations. We evaluate its accuracy and theoretical performance gain with metadynamics simulations on two molecular systems.

Nonlinear vs. linear biasing in Trp-cage folding simulations.

Biased simulations have great potential for the study of slow processes, including protein folding. Atomic motions in molecules are nonlinear, which suggests that simulations with enhanced sampling of collective motions traced by nonlinear dimensionality reduction methods may perform better than linear ones. In this study, we compare an unbiased folding simulation of the Trp-cage miniprotein with metadynamics simulations using both linear (principle component analysis) and nonlinear (Isomap) low dimensional embeddings as collective variables. Folding of the mini-protein was successfully simulated in 200 ns simulation with linear biasing and non-linear motion biasing. The folded state was correctly predicted as the free energy minimum in both simulations. We found that the advantage of linear motion biasing is that it can sample a larger conformational space, whereas the advantage of nonlinear motion biasing lies in slightly better resolution of the resulting free energy surface. In terms of sampling efficiency, both methods are comparable.

NEEMP: software for validation, accurate calculation and fast parameterization of EEM charges.

BACKGROUND: The concept of partial atomic charges was first applied in physical and organic chemistry and was later also adopted in computational chemistry, bioinformatics and chemoinformatics. The electronegativity equalization method (EEM) is the most frequently used approach for calculating partial atomic charges. EEM is fast and its accuracy is comparable to the quantum mechanical charge calculation method for which it was parameterized. Several EEM parameter sets for various types of molecules and QM charge calculation approaches have been published and new ones are still needed and produced. Methodologies for EEM parameterization have been described in a few articles, but a software tool for EEM parameterization and EEM parameter sets validation has not been available until now. RESULTS: We provide the software tool NEEMP (http://ncbr.muni.cz/NEEMP), which offers three main functionalities: EEM parameterization [via linear regression (LR) and differential evolution with local minimization (DE-MIN)]; EEM parameter set validation (i.e., validation of coverage and quality) and EEM charge calculation. NEEMP functionality is shown using a parameterization and a validation case study. The parameterization case study demonstrated that LR is an appropriate approach for smaller and homogeneous datasets and DE-MIN is a suitable solution for larger and heterogeneous datasets. The validation case study showed that EEM parameter set coverage and quality can still be problematic. Therefore, it makes sense to verify the coverage and quality of EEM parameter sets before their use, and NEEMP is an appropriate tool for such verification. Moreover, it seems from both case studies that new EEM parameterizations need to be performed and new EEM parameter sets obtained with high quality and coverage for key structural databases. CONCLUSION: We provide the software tool NEEMP, which is to the best of our knowledge the only available software package that enables EEM parameterization and EEM parameter set validation. Additionally, its DE-MIN parameterization method is an innovative approach, developed by ourselves and first published in this work. In addition, we also prepared four high-quality EEM parameter sets tailored to ligand molecules.Graphical abstract.