Molecular Latent Space Simulators for Distributed and Multimolecular Trajectories.

All atom molecular dynamics (MD) simulations offer a powerful tool for molecular modeling, but the short time steps required for numerical stability of the integrator place many interesting molecular events out of reach of unbiased simulations. The popular and powerful Markov state modeling (MSM) approach can extend these time scales by stitching together multiple short discontinuous trajectories into a single long-time kinetic model but necessitates a configurational coarse-graining of the phase space that entails a loss of spatial and temporal resolution and an exponential increase in complexity for multimolecular systems. Latent space simulators (LSS) present an alternative formalism that employs a dynamical, as opposed to configurational, coarse graining comprising three back-to-back learning problems to (i) identify the molecular system's slowest dynamical processes, (ii) propagate the microscopic system dynamics within this slow subspace, and (iii) generatively reconstruct the trajectory of the system within the molecular phase space. A trained LSS model can generate temporally and spatially continuous synthetic molecular trajectories at orders of magnitude lower cost than MD to improve sampling of rare transition events and metastable states to reduce statistical uncertainties in thermodynamic and kinetic observables. In this work, we extend the LSS formalism to short discontinuous training trajectories generated by distributed computing and to multimolecular systems without incurring exponential scaling in computational cost. First, we develop a distributed LSS model over thousands of short simulations of a 264-residue proteolysis-targeting chimera (PROTAC) complex to generate ultralong continuous trajectories that identify metastable states and collective variables to inform PROTAC therapeutic design and optimization. Second, we develop a multimolecular LSS architecture to generate physically realistic ultralong trajectories of DNA oligomers that can undergo both duplex hybridization and hairpin folding. These trajectories retain thermodynamic and kinetic characteristics of the training data while providing increased precision of folding populations and time scales across simulation temperature and ion concentration.

Predicting the structural basis of targeted protein degradation by integrating molecular dynamics simulations with structural mass spectrometry.

Targeted protein degradation (TPD) is a promising approach in drug discovery for degrading proteins implicated in diseases. A key step in this process is the formation of a ternary complex where a heterobifunctional molecule induces proximity of an E3 ligase to a protein of interest (POI), thus facilitating ubiquitin transfer to the POI. In this work, we characterize 3 steps in the TPD process. (1) We simulate the ternary complex formation of SMARCA2 bromodomain and VHL E3 ligase by combining hydrogen-deuterium exchange mass spectrometry with weighted ensemble molecular dynamics (MD). (2) We characterize the conformational heterogeneity of the ternary complex using Hamiltonian replica exchange simulations and small-angle X-ray scattering. (3) We assess the ubiquitination of the POI in the context of the full Cullin-RING Ligase, confirming experimental ubiquitinomics results. Differences in degradation efficiency can be explained by the proximity of lysine residues on the POI relative to ubiquitin.

Synaptotagmin rings as high-sensitivity regulators of synaptic vesicle docking and fusion.

Synchronous release at neuronal synapses is accomplished by a machinery that senses calcium influx and fuses the synaptic vesicle and plasma membranes to release neurotransmitters. Previous studies suggested the calcium sensor synaptotagmin (Syt) is a facilitator of vesicle docking and both a facilitator and inhibitor of fusion. On phospholipid monolayers, the Syt C2AB domain spontaneously oligomerized into rings that are disassembled by Ca2+, suggesting Syt rings may clamp fusion as membrane-separating "washers" until Ca2+-mediated disassembly triggers fusion and release [J. Wang et al., Proc. Natl. Acad. Sci. U.S.A. 111, 13966-13971 (2014)].). Here, we combined mathematical modeling with experiment to measure the mechanical properties of Syt rings and to test this mechanism. Consistent with experimental results, the model quantitatively recapitulates observed Syt ring-induced dome and volcano shapes on phospholipid monolayers and predicts rings are stabilized by anionic phospholipid bilayers or bulk solution with ATP. The selected ring conformation is highly sensitive to membrane composition and bulk ATP levels, a property that may regulate vesicle docking and fusion in ATP-rich synaptic terminals. We find the Syt molecules hosted by a synaptic vesicle oligomerize into a halo, unbound from the vesicle, but in proximity to sufficiently phosphatidylinositol 4,5-bisphosphate (PIP2)-rich plasma membrane (PM) domains, the PM-bound trans Syt ring conformation is preferred. Thus, the Syt halo serves as landing gear for spatially directed docking at PIP2-rich sites that define the active zones of exocytotic release, positioning the Syt ring to clamp fusion and await calcium. Our results suggest the Syt ring is both a Ca2+-sensitive fusion clamp and a high-fidelity sensor for directed docking.

The neuronal calcium sensor Synaptotagmin-1 and SNARE proteins cooperate to dilate fusion pores.

All membrane fusion reactions proceed through an initial fusion pore, including calcium-triggered release of neurotransmitters and hormones. Expansion of this small pore to release cargo is energetically costly and regulated by cells, but the mechanisms are poorly understood. Here, we show that the neuronal/exocytic calcium sensor Synaptotagmin-1 (Syt1) promotes expansion of fusion pores induced by SNARE proteins. Pore dilation relied on calcium-induced insertion of the tandem C2 domain hydrophobic loops of Syt1 into the membrane, previously shown to reorient the C2 domain. Mathematical modelling suggests that C2B reorientation rotates a bound SNARE complex so that it exerts force on the membranes in a mechanical lever action that increases the height of the fusion pore, provoking pore dilation to offset the bending energy penalty. We conclude that Syt1 exerts novel non-local calcium-dependent mechanical forces on fusion pores that dilate pores and assist neurotransmitter and hormone release.

The role of scaffold reshaping and disassembly in dynamin driven membrane fission.

The large GTPase dynamin catalyzes membrane fission in eukaryotic cells, but despite three decades of experimental work, competing and partially conflicting models persist regarding some of its most basic actions. Here we investigate the mechanical and functional consequences of dynamin scaffold shape changes and disassembly with the help of a geometrically and elastically realistic simulation model of helical dynamin-membrane complexes. Beyond changes of radius and pitch, we emphasize the crucial role of a third functional motion: an effective rotation of the filament around its longitudinal axis, which reflects alternate tilting of dynamin's PH binding domains and creates a membrane torque. We also show that helix elongation impedes fission, hemifission is reached via a small transient pore, and coat disassembly assists fission. Our results have several testable structural consequences and help to reconcile mutual conflicting aspects between the two main present models of dynamin fission-the two-stage and the constrictase model.

SNARE-mediated membrane fusion is a two-stage process driven by entropic forces.

SNARE proteins constitute the core of the exocytotic membrane fusion machinery. Fusion occurs when vesicle-associated and target membrane-associated SNAREs zipper into trans-SNARE complexes ('SNAREpins'), but the number required is controversial and the mechanism of cooperative fusion is poorly understood. We developed a highly coarse-grained molecular dynamics simulation to access the long fusion timescales, which revealed a two-stage process. First, zippering energy was dissipated and cooperative entropic forces assembled the SNAREpins into a ring; second, entropic forces expanded the ring, pressing membranes together and catalyzing fusion. We predict that any number of SNAREs fuses membranes, but fusion is faster with more SNAREs.

Dynamin's helical geometry does not destabilize membranes during fission.

It is now widely accepted that dynamin-mediated fission is a fundamentally mechanical process: dynamin undergoes a GTP-dependent conformational change, constricting the neck between two compartments, somehow inducing their fission. However, the exact connection between dynamin's conformational change and the scission of the neck is still unclear. In this paper, we re-evaluate the suggestion that a change in the pitch or radius of dynamin's helical geometry drives the lipid bilayer through a mechanical instability, similar to a well-known phenomenon occurring in soap films. We find that, contrary to previous claims, there is no such instability. This lends credence to an alternative model, in which dynamin drives the membrane up an energy barrier, allowing thermal fluctuations to take it into the hemifission state.

Constriction by Dynamin: Elasticity versus Adhesion.

Any cellular fission process is completed when the neck connecting almost-separate membrane compartments is severed. This crucial step is somehow accomplished by proteins from the dynamin family, which polymerize into helical spirals around such necks. Much research has been devoted to elucidating the specifics of that somehow, but despite no shortage of ideas, the question is not settled. Pictorially obvious notions of strangling or pushing are difficult to render in mechanically precise terms. Moreover, because dynamin is a GTPase, it is tempting to speculate that it has a motor activity that assists the necessary severing action, but again the underlying mechanics is not obvious. We believe the difficulty to be the mechanically nontrivial nature of confining elastic filaments onto curved surfaces, for which efficient methods to conceptualize the associated forces and torques have only recently appeared. Here we investigate the implications of a conceptually simple yet mechanically challenging model: consider an elastic helical filament confined to a surface mimicking the neck between two membrane compartments, which we assume to take the shape of a catenoid. What can we say about the expected length of such adsorbed filaments, their shapes, and the forces they exert, as a function of the key parameters in the model? While real dynamin is surely more complex, we consider such a minimal model to be the indispensable baseline. Without knowing what such a model can and cannot explain, it is difficult to justify more complex mechanisms, or understand the constraints under which this machinery evolved in the first place.

Curvature Softening and Negative Compressibility of Gel-Phase Lipid Membranes.

We show that gel-phase lipid membranes soften upon bending, leading to curvature localization and a negative compressibility. Using simulations of two very different lipid models to quantify shape and stress-strain relation of buckled membranes, we demonstrate that gel phase bilayers do not behave like Euler elastica and hence are not well described by a quadratic Helfrich Hamiltonian, much unlike their fluid-phase counterparts. We propose a theoretical framework which accounts for the observed softening through an energy density that smoothly crosses over from a quadratic to a linear curvature dependence beyond a critical new scale [Formula: see text](-1). This model captures both the shape and the stress-strain relation for our two sets of simulations and permits the extraction of bending moduli, which are found to be about an order of magnitude larger than the corresponding fluid phase values. We also find surprisingly large crossover lengths [Formula: see text], several times bigger than the bilayer thickness, rendering the exotic elasticity of gel-phase membranes more strongly pronounced than that of homogeneous compressible sheets and artificial metamaterials. We suggest that such membranes have unexpected potential as nanoscale systems with striking materials characteristics.