Assessing the Reproducibility of Clustering of Molecular Dynamics Conformations on Self-Organizing Maps

The goal of most clustering algorithms is to find the optimal number of clusters (i.e. fewest number of clusters). However, analysis of molecular conformations of biological macromolecules obtained from computer simulations may benefit from a larger array of clusters. The Self-Organizing Map (SOM) clustering method has the advantage of generating large numbers of clusters, but often gives ambiguous results. In this work, SOMs have been shown to be reproducible when the same conformational dataset is independently clustered multiple times (~100), with the help of the Cramérs V-index (C_v). The ability of C_v to determine which SOMs are reproduced is generalizable across different SOM source codes. The conformational ensembles produced from MD (molecular dynamics) and REMD (replica exchange molecular dynamics) simulations of the penta peptide Met-enkephalin (MET) and the 34 amino acid protein human Parathyroid Hormone (hPTH) were used to evaluate SOM reproducibility. The training length for the SOM has a huge impact on the reproducibility. Analysis of MET conformational data definitively determined that toroidal SOMs cluster data better than bordered maps due to the fact that toroidal maps do not have an edge effect. For the source code from MATLAB, it was determined that the learning rate function should be LINEAR with an initial learning rate factor of 0.05 and the SOM should be trained by a sequential algorithm. The trained SOMs can be used as a supervised classification for another dataset. The toroidal 10×10 hexagonal SOMs produced from the MATLAB program for hPTH conformational data produced three sets of reproducible clusters (27%, 15%, and 13% of 100 independent runs) which find similar partitionings to those of smaller 6×6 SOMs. The χ^2 values produced as part of the C_v calculation were used to locate clusters with identical conformational memberships on independently trained SOMs, even those with different dimensions. The χ^2 values could relate the different SOM partitionings to each other.

Optimizing Computational Frameworks to Study the Influence of the Protein Environment on the Individual Site Energies of Chromophores in Photosystem II of Photosynthesis

Photosynthesis is a process in which electromagnetic radiation is converted into chemical energy. Photosystems capture photons with chromophores and transfer their energy to reaction centers using chromophores as a medium. In the reaction center, the excitation energy is used to perform chemical reactions. Knowledge of chromophore site energies is crucial to the understanding of excitation energy transfer pathways in photosystems and the ability to compute the site energies in a fast and accurate manner is mandatory for investigating how protein dynamics ef-fect the site energies and ultimately energy pathways with time. In this work we developed two software frameworks designed to optimize the calculations of chro-mophore site energies within a protein environment. The first is for performing quantum mechanical energy optimizations on molecules and the second is for com-puting site energies of chromophores in a fast and accurate manner using the polar-izability embedding method. The two frameworks allow for the fast and accurate calculation of chromophore site energies within proteins, ultimately allowing for the effect of protein dynamics on energy pathways to be studied. We use these frame-works to compute the site energies of the eight chromophores in the reaction center of photosystem II (PSII) using a 1.9 Å resolution x-ray structure of photosystem II. We compare our results to conflicting experimental data obtained from both isolat-ed intact PSII core preparations and the minimal reaction center preparation of PSII, and find our work more supportive of the former.