Size-and-Shape Space Gaussian Mixture Models for Structural Clustering of Molecular Dynamics Trajectories

Abstract

Determining the optimal number and identity of structural clusters from an ensemble of molecular configurations continues to be a challenge. Recent structural clustering methods have focused on the use of internal coordinates due to the innate rotational and translational invariance of these features. The vast number of possible internal coordinates necessitates a feature space supervision step to make clustering tractable but yields a protocol that can be system type-specific. Particle positions offer an appealing alternative to internal coordinates but suffer from a lack of rotational and translational invariance, as well as a perceived insensitivity to regions of structural dissimilarity. Here, we present a method, denoted shape-GMM, that overcomes the shortcomings of particle positions using a weighted maximum likelihood alignment procedure. This alignment strategy is then built into an expectation maximization Gaussian mixture model (GMM) procedure to capture metastable states in the free-energy landscape. The resulting algorithm distinguishes between a variety of different structures, including those indistinguishable by root-mean-square displacement and pairwise distances, as demonstrated on several model systems. Shape-GMM results on an extensive simulation of the fast-folding HP35 Nle/Nle mutant protein support a four-state folding/unfolding mechanism, which is consistent with previous experimental results and provides kinetic details comparable to previous state-of-the art clustering approaches, as measured by the VAMP-2 score. Currently, training of shape-GMMs is recommended for systems (or subsystems) that can be represented by ≲200 particles and ≲100k configurations to estimate high-dimensional covariance matrices and balance computational expense. Once a shape-GMM is trained, it can be used to predict the cluster identities of millions of configurations.

Building insightful, memory-enriched models to capture long-time biochemical processes from short-time simulations

“…In Fig. 4(c), we show the replacement of U with its average U (obtained over the averaging interval of [20,25] ns). We observe that MSM dynamics predicted using only 25 ns of the MD data set overestimates the equilibration rate, as was the case with alanine dipeptide and the argonaute complex, whereas the U -GME parameterized with the same amount of reference data accurately captures the MD data until ∼ 375 ns.…”

“…As we mentioned in the Introduction, below we do not consider how one identifies these configurational basins (the interested reader can see, for instance, Refs. 18–21, 23–25, and 39), but rather focus on the second problem: given a set of configurations whose dynamics one can only afford for only short times, how does one construct a dynamical framework to accurately and efficiently capture the dynamics of these configurations over all time?…”

“…Identifying the slowest interconverting structures, however, remains a formidable problem. 7,[17][18][19][20][21][22][23][24][25] This difficulty arises from the fact that, to perform a perfect partitioning, one needs detailed knowledge of the full free energy landscape of a complex condensed phase system. Instead, one is generally limited to a set of states that evolve on slow timescales but are not optimally partitioned.…”

Memory unlocks the future of biomolecular dynamics: Transformative tools to uncover physical insights accurately and efficiently

“…While work in the last few decades has produced a robust set of tools to exploit collections of short-time all-atom MD simulations of complex biomolecular systems to identify these elusive and important slow coordinates, this problem of identifying slow degrees of freedom remains an open question of fundamental importance to many fields. 11,[41][42][43][44][45][46][47][48][49] Once these slow coordinates are (perfectly or approximately) identified, one can employ a variety of tools to estimate the transition probabilities 11,42 and construct the simple equation of motion -which takes the form of a simple chemical kinetics problem -for the interconversion of these slow macrostates at the heart of the MSM: 10,42…”

Demultiplexing the heterogeneous conformational ensembles of intrinsically disordered proteins into structurally similar clusters

“…Theoretically well-grounded dimensionality reduction (DR) techniques are now commonly being used in protein conformation analysis to extract the latent low dimensional features and the quantum of information lost during the projection depends heavily on the kind of data set under consideration 67–72 . For example, a highly heterogeneous data set that lies on a high-dimensional manifold as in the case of IDPs is best handled with the non-linear dimension reduction (NLDR) techniques, which generally attempt to keep the nearest neighbors close together.…”