Self Organizing Maps to efficiently cluster and functionally interpret protein conformational ensembles

The wide range of protein biological functions, such as enzymatic activity, ligand- and protein-proteininteractions and allosteric regulation, is strictly related to their flexibility and dynamics[1]. To modelthe influence of protein motions across this broad spectrum of events Molecular Dynamics (MD) sim-ulations are now routinely used. The identification of the most functionally relevant conformations isgenerally done by grouping the conformations according to a criterion of geometrical similarity andpopular choices include hierarchical clustering, single, complete and average linkage and k-means [10].These geometrical approaches rely on the assumption that the identified conformational states also corre-spond to the energetic states [10]. Good candidates to improve this match are Artificial Neural Networks(ANNs) which are capable to discover the relationships between the measured variables only from theavailable dataset [9]. Among the class of ANNs, successfully applied to artificial life systems [2], SelfOrganizing Maps (SOMs) [6] represent a particularly powerful data driven model that has been widelyapplied for exploration and clustering of high-dimensional datasets [9, 6]. We recently developed anapproach which combines SOMs and hierarchical clustering to efficiently compare conformational en-sembles obtained from multiple MD simulations of proteins [3]. To reliably apply the SOM analysis tothese specific input data we identified and optimized a small number of SOM parameters. In particular,we confirmed that the map size is a crucial parameter and that a well-selected number of neurons iscrucial both to reduce the computational cost of the analysis and to provide an intermediate topologicalrepresentation of the input conformational space [3]. As a result the original MD trajectories can berepresented by the few conformations that best represent the clusters obtained. Here we make a step fur-ther; the proposed approach consists of processing all the atom positions of each conformation won bya given SOM neuron using a similarity network. Different similarity measures between atoms behaviorare used to compile a similarity matrix which is inputted to a network model [8]. Network algorithmsare then used to automatically discover and interpret the behavior of the original protein conformationalensembles exploiting the atomic coordinates enclosed in the SOM neuron.