A social perspective on perceived distances reveals deep community structure.

Community structure, including relationships between and within groups, is foundational to our understanding of the world around us. For dissimilarity-based data, leveraging social concepts of conflict and alignment, we provide an approach for capturing meaningful structural information resulting from induced local comparisons. In particular, a measure of local (community) depth is introduced that leads directly to a probabilistic partitioning conveying locally interpreted closeness (or cohesion). A universal choice of threshold for distinguishing strongly and weakly cohesive pairs permits consideration of both local and global structure. Cases in which one might benefit from use of the approach include data with varying density such as that arising as snapshots of complex processes in which differing mechanisms drive evolution locally. The inherent recalibrating in response to density allows one to sidestep the need for localizing parameters, common to many existing methods. Mathematical results together with applications in linguistics, cultural psychology, and genetics, as well as to benchmark clustering data have been included. Together, these demonstrate how meaningful community structure can be identified without additional inputs (e.g., number of clusters or neighborhood size), optimization criteria, iterative procedures, or distributional assumptions.

Using correlated motions to determine sufficient sampling times for molecular dynamics.

Here we present a time-dependent correlation method that provides insight into how long a system takes to grow into its equal-time (Pearson) correlation. We also show a usage of an extant time-lagged correlation method that indicates the time for parts of a system to become decorrelated, relative to equal-time correlation. Given a completed simulation (or set of simulations), these tools estimate (i) how long of a simulation of the same system would be sufficient to observe the same correlated motions, (ii) if patterns of observed correlated motions indicate events beyond the timescale of the simulation, and (iii) how long of a simulation is needed to observe these longer timescale events. We view this method as a decision-support tool that will aid researchers in determining necessary sampling times. In principle, this tool is extendable to any multidimensional time series data with a notion of correlated fluctuations; however, here we limit our discussion to data from molecular-dynamics simulations.

Cluster-based network proximities for arbitrary nodal subsets.

The concept of a cluster or community in a network context has been of considerable interest in a variety of settings in recent years. In this paper, employing random walks and geodesic distance, we introduce a unified measure of cluster-based proximity between nodes, relative to a given subset of interest. The inherent simplicity and informativeness of the approach could make it of value to researchers in a variety of scientific fields. Applicability is demonstrated via application to clustering for a number of existent data sets (including multipartite networks). We view community detection (i.e. when the full set of network nodes is considered) as simply the limiting instance of clustering (for arbitrary subsets). This perspective should add to the dialogue on what constitutes a cluster or community within a network. In regards to health-relevant attributes in social networks, identification of clusters of individuals with similar attributes can support targeting of collective interventions. The method performs well in comparisons with other approaches, based on comparative measures such as NMI and ARI.

Visualizing correlated motion with HDBSCAN clustering.

Correlated motion analysis provides a method for understanding communication between and dynamic similarities of biopolymer residues and domains. The typical equal-time correlation matrices-frequently visualized with pseudo-colorings or heat maps-quickly convey large regions of highly correlated motion but hide more subtle similarities of motion. Here we propose a complementary method for visualizing correlations within proteins (or general biopolymers) that quickly conveys intuition about which residues have a similar dynamic behavior. For grouping residues, we use the recently developed non-parametric clustering algorithm HDBSCAN. Although the method we propose here can be used to group residues using correlation as a similarity matrix-the most straightforward and intuitive method-it can also be used to more generally determine groups of residues which have similar dynamic properties. We term these latter groups "Dynamic Domains", as they are based not on spatial closeness but rather closeness in the column space of a correlation matrix. We provide examples of this method across three human proteins of varying size and function-the Nf-Kappa-Beta essential modulator, the clotting promoter Thrombin and the mismatch repair protein (dimer) complex MutS-alpha. Although the examples presented here are from all-atom molecular dynamics simulations, this visualization technique can also be used on correlations matrices built from any ensembles of conformations from experiment or computation.

Uncovering Large-Scale Conformational Change in Molecular Dynamics without Prior Knowledge.

As the length of molecular dynamics (MD) trajectories grows with increasing computational power, so does the importance of clustering methods for partitioning trajectories into conformational bins. Of the methods available, the vast majority require users to either have some a priori knowledge about the system to be clustered or to tune clustering parameters through trial and error. Here we present non-parametric uses of two modern clustering techniques suitable for first-pass investigation of an MD trajectory. Being non-parametric, these methods require neither prior knowledge nor parameter tuning. The first method, HDBSCAN, is fast-relative to other popular clustering methods-and is able to group unstructured or intrinsically disordered systems (such as intrinsically disordered proteins, or IDPs) into bins that represent global conformational shifts. HDBSCAN is also useful for determining the overall stability of a system-as it tends to group stable systems into one or two bins-and identifying transition events between metastable states. The second method, iMWK-Means, with explicit rescaling followed by K-Means, while slower than HDBSCAN, performs well with stable, structured systems such as folded proteins and is able to identify higher resolution details such as changes in relative position of secondary structural elements. Used in conjunction, these clustering methods allow a user to discern quickly and without prior knowledge the stability of a simulated system and identify both local and global conformational changes.