Many proteins are regulated by dynamic allostery wherein regulator-induced changes in structure are comparable with thermal fluctuations. Consequently, understanding their mechanisms requires assessment of relationships between and within conformational ensembles of different states. Here we show how machine learning based approaches can be used to simplify this high-dimensional data mining task and also obtain mechanistic insight. In particular, we use these approaches to investigate two fundamental questions in dynamic allostery. First, how do regulators modify inter-site correlations in conformational fluctuations (C)? Second, how are regulator-induced shifts in conformational ensembles at two different sites in a protein related to each other? We address these questions in the context of the human protein tyrosine phosphatase 1E's PDZ2 domain, which is a model protein for studying dynamic allostery. We use molecular dynamics to generate conformational ensembles of the PDZ2 domain in both the regulator-bound and regulator-free states. The employed protocol reproduces methyl deuterium order parameters from NMR. Results from unsupervised clustering of C combined with flow analyses of weighted graphs of C show that regulator binding significantly alters the global signaling network in the protein; however, not by altering the spatial arrangement of strongly interacting amino acid clusters but by modifying the connectivity between clusters. Additionally, we find that regulator-induced shifts in conformational ensembles, which we evaluate by repartitioning ensembles using supervised learning, are, in fact, correlated. This correlation Δ is less extensive compared to C, but in contrast to C, Δ depends inversely on the distance from the regulator binding site. Assuming that Δ is an indicator of the transduction of the regulatory signal leads to the conclusion that the regulatory signal weakens with distance from the regulatory site. Overall, this work provides new approaches to analyze high-dimensional molecular simulation data and also presents applications that yield new insight into dynamic allostery.

Nipah is an emerging paramyxovirus that is of serious concern to human health. It invades host cells using two of its membrane proteins-G and F. G binds to host ephrins and this stimulates G to activate F. Upon activation, F mediates virus-host membrane fusion. Here we focus on mechanisms that underlie the stimulation of G by ephrins. Experiments show that G interacts with ephrin and F through separate sites located on two different domains, the receptor binding domain (RBD) and the F activation domain (FAD). No models explain this allosteric coupling. In fact, the analogous mechanisms in other paramyxoviruses also remain undetermined. The structural organization of G is such that allosteric coupling must involve at least one of the two interfaces-the RBD-FAD interface and/or the RBD-RBD interface. Here we examine using molecular dynamics the effect of ephrin binding on the RBD-RBD interface. We find that despite inducing small changes in individual RBDs, ephrin reorients the RBD-RBD interface extensively, and in a manner that will enhance solvent exposure of the FAD. While this finding supports a proposed model of G stimulation, we also find from additional simulations that ephrin induces a similar RBD-RBD reorientation in a stimulation-deficient G mutant, V 209 VG / AAA. Together, our simulations suggest that while inter-RBD reorientation may be important, it is not, by itself, a sufficient condition for G stimulation. Additionally, we find that the mutation affects the conformational ensemble of RBD globally, including the RBD-FAD interface, suggesting the latter's role in G stimulation. Because ephrin induces small changes in individual RBDs, a proper analysis of conformational ensembles required that they are compared directly-we employ a method we developed recently, which we now release at SimTK, and show that it also performs excellently for non-Gaussian distributions.

Recent advances in nanotechnology bring to the forefront a new class of extrinsic constraints for remodeling lipid bilayers. In this next-generation technology, membranes are supported over nanoporous substrates. The nanometer-sized pores in the substrate are too small for bilayers to follow the substrate topology; consequently, the bilayers hang over the pores. Experiments demonstrate that nanoporous substrates remodel lipid bilayers differently from continuous substrates. The underlying molecular mechanisms, however, remain largely undetermined. Here we use molecular dynamics (MD) simulations to probe the effects of silica-type hydroxylation and charge densities on adsorbed palmitoyl-oleoylphosphatidylcholine (POPC) bilayers. We find that a 50% porous substrate decorated with a surface density of 4.6 hydroxyls/nm(2) adsorbs a POPC bilayer at a distance of 4.5 Å, a result consistent with neutron reflectivity experiments conducted on topologically similar silica constructs under highly acidic conditions. Although such an adsorption distance suggests that the interaction between the bilayer and the substrate will be buffered by water molecules, we find that the substrate does interact directly with the bilayer. The substrate modifies several properties of the bilayer-it dampens transverse lipid fluctuations, reduces lipid diffusion rates, and modifies transverse charge densities significantly. Additionally, it affects lipid properties differently in the two leaflets. Compared to substrates functionalized with sparser surface hydroxylation densities, this substrate adheres to bilayers at smaller distances and also remodels POPC more extensively, suggesting a direct correspondence between substrate hydrophilicity and membrane properties. A partial deprotonation of surface hydroxyls, as expected of a silica substrate under mildly acidic conditions, however, produces an inverse effect: it increases the substrate-bilayer distance, which we attribute to the formation of an electric double layer over the negatively charged substrate, and restores, at least partially, leaflet asymmetry and headgroup orientations. Overall, this study highlights the intrinsic complexity of lipid-substrate interactions and suggests the prospect of making two surface attributes-dipole densities and charge densities-work antagonistically toward remodeling lipid bilayer properties.

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Abstract. The surface area per lipid is an important quantity useful in characterizing lipid bilayer structure and dynamics. However, simply dividing the flat surface area covered by the number of lipids does not give a sufficient characterization of surface dynamics in cases where parts of the lipid leaflets have curvaceous trajectories in three dimensions. An algorithm is proposed for modeling surface area per lipid using a three-dimensional tessellated grid. In this way both the vertical, as well as the more commonly considered the horizontal, fluctuations of lipids are used to accurately determine the area covered. This algorithm can reveal differences in dynamics between leaflets under different conditions that are otherwise invisible with a conventional flat surface study. Keywords