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Significant efforts in wet and dry laboratories are devoted to resolving molecular structures. In particular, computational methods can now compute thousands of tertiary structures that populate the structure space of a protein molecule of interest. These advances are now allowing us to turn our attention to analysis methodologies that are able to organize the computed structures in order to highlight functionally relevant structural states. In this paper, we propose a methodology that leverages community detection methods, designed originally to detect communities in social networks, to organize computationally probed protein structure spaces. We report a principled comparison of such methods along several metrics on proteins of diverse folds and lengths. We present a rigorous evaluation in the context of decoy selection in template-free protein structure prediction. The results make the case that network-based community detection methods warrant further investigation to advance analysis of protein structure spaces for automated selection of functionally relevant structures.

Molecular dynamics (MD) simulation software allows probing the equilibrium structural dynamics of a molecule of interest, revealing how a molecule navigates its structure space one structure at a time. To obtain a broader view of dynamics, typically one needs to launch many such simulations, obtaining many trajectories. A summarization of the equilibrium dynamics requires integrating the information in the various trajectories, and Markov State Models (MSM) are increasingly being used for this task. At its core, the task involves organizing the structures accessed in simulation into structural states, and then constructing a transition probability matrix revealing the transitions between states. While now considered a mature technology and widely used to summarize equilibrium dynamics, the underlying computational process in the construction of an MSM ignores energetics even though the transition of a molecule between two nearby structures in an MD trajectory is governed by the corresponding energies. In this paper, we connect theory with simulation and analysis of equilibrium dynamics. A molecule navigates the energy landscape underlying the structure space. The structural states that are identified via off-the-shelf clustering algorithms need to be connected to thermodynamically-stable and semi-stable (macro)states among which transitions can then be quantified. Leveraging recent developments in the analysis of energy landscapes that identify basins in the landscape, we evaluate the hypothesis that basins, directly tied to stable and semi-stable states, lead to better models of dynamics. Our analysis indicates that basins lead to MSMs of better quality and thus can be useful to further advance this widely-used technology for summarization of molecular equilibrium dynamics.

The energy landscape that organizes microstates of a molecular system and governs the underlying molecular dynamics exposes the relationship between molecular form/structure, changes to form, and biological activity or function in the cell. However, several challenges stand in the way of leveraging energy landscapes for relating structure and structural dynamics to function. Energy landscapes are high-dimensional, multi-modal, and often overly-rugged. Deep wells or basins in them do not always correspond to stable structural states but are instead the result of inherent inaccuracies in semi-empirical molecular energy functions. Due to these challenges, energetics is typically ignored in computational approaches addressing long-standing central questions in computational biology, such as protein decoy selection. In the latter, the goal is to determine over a possibly large number of computationally-generated three-dimensional structures of a protein those structures that are biologically-active/native. In recent work, we have recast our attention on the protein energy landscape and its role in helping us to advance decoy selection. Here, we summarize some of our successes so far in this direction via unsupervised learning. More importantly, we further advance the argument that the energy landscape holds valuable information to aid and advance the state of protein decoy selection via novel machine learning methodologies that leverage supervised learning. Our focus in this article is on decoy selection for the purpose of a rigorous, quantitative evaluation of how leveraging protein energy landscapes advances an important problem in protein modeling. However, the ideas and concepts presented here are generally useful to make discoveries in studies aiming to relate molecular structure and structural dynamics to function.

Molecular dynamics simulation software now provides us with a view of the structure space accessed by a molecule. Increasingly, Markov state models are proposed to integrate various simulations of a molecule and extract its equilibrium structural dynamics. The approach relies on organizing the structures accessed in simulation into states as an attempt to identify thermodynamically-stable and semi-stable (macro)states among which transitions can then be quantified. Typically, off-the-shelf clustering algorithms are used for this purpose. In this paper, we investigate two additional complementary approaches to state identification that rely on graph embeddings of the structures. In particular, we show that doing so allows revealing basins in the energy landscape associated with the accessed structure space. Moreover, we demonstrate that basins, directly tied to stable and semi-stable states, yield to a better model of dynamics on a proof-of-concept application.

Over the past decade, Markov State Models (MSM) have emerged as powerful methodologies to build discrete models of dynamics over structures obtained from Molecular Dynamics trajectories. The identification of macrostates for the MSM is a central decision that impacts the quality of the MSM but depends on both the selected representation of a structure and the clustering algorithm utilized over the featurized structures. Motivated by a large molecular system in its free and bound state, this paper investigates two directions of research, further reducing the representation dimensionality in a non-parametric, data-driven manner and including more structures in the computation. Rigorous evaluation of the quality of obtained MSMs via various statistical tests in a comparative setting firmly shows that fewer dimensions and more structures result in a better MSM. Many interesting findings emerge from the best MSM, advancing our understanding of the relationship between antibody dynamics and antibody–antigen recognition.

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