Publications

Amphipathic helices (AHs) are secondary structures that can facilitate binding of proteins to the membrane by folding into a helix with hydrophobic and hydrophilic faces that interact with the same surfaces in the lipid membrane. Septins are cytoskeletal proteins that preferentially bind to domains of micron-scale curvature on the cell membrane. Studies have shown that AH domains in septin are essential for curvature sensing. We present the first computational study of septin AH interactions with lipid bilayers. Using all-atom simulations and metadynamics-enhanced sampling, we study the effect of charge distribution at the flanking ends of septin AH on the energy for helical folding and its consequences on the binding configuration and affinity to the membrane. This is relevant to septins, since the net positive charge on the flanking C-terminal amino acids is a conserved property across several organisms. Simulations revealed that the energy barrier for folding in the neutral-capped AH is much larger than the charge-capped AH, leading to a small fraction of AH folding and integration to the membrane compared to a significantly folded configuration in the bound charge-capped AH. These observations are consistent with the binding measurements of synthetic AH constructs with variable helicity to lipid vesicles. Additionally, we examined an extended AH sequence including eight amino acids upstream and downstream of the AH to mimic the native protein. Again, simulations and experiments show that the extended peptide, with a net positive charge at C-terminus, adopts a strong helical configuration in solution, giving rise to a higher membrane affinity. Altogether, these results identify the energy cost for folding of AHs as a regulator of AH binding configuration and affinity and provide a basic template for parameterizing AH-membrane interactions as a starting point for the future multiscale simulations for septin-membrane interactions.

Amphipathic helices (AHs) are secondary structures that can facilitate binding of proteins to the membrane by folding into a helix with hydrophobic and hydrophilic faces that interact with the same surfaces in the lipid membrane. Septins are cytoskeletal proteins that preferentially bind to domains of micron-scale curvature on the cell membrane. Studies have shown that AH domains in septin are essential for curvature sensing. We present the first computational study of septin AH interactions with lipid bilayers. Using all-atom simulations and metadynamics-enhanced sampling, we study the effect of charge distribution at the flanking ends of septin AH on the energy for helical folding and its consequences on the binding configuration and affinity to the membrane. This is relevant to septins, since the net positive charge on the flanking C-terminal amino acids is a conserved property across several organisms. Simulations revealed that the energy barrier for folding in the neutral-capped AH is much larger than the charge-capped AH, leading to a small fraction of AH folding and integration to the membrane compared to a significantly folded configuration in the bound charge-capped AH. These observations are consistent with the binding measurements of synthetic AH constructs with variable helicity to lipid vesicles. Additionally, we examined an extended AH sequence including eight amino acids upstream and downstream of the AH to mimic the native protein. Again, simulations and experiments show that the extended peptide, with a net positive charge at C-terminus, adopts a strong helical configuration in solution, giving rise to a higher membrane affinity. Altogether, these results identify the energy cost for folding of AHs as a regulator of AH binding configuration and affinity and provide a basic template for parameterizing AH-membrane interactions as a starting point for the future multiscale simulations for septin-membrane interactions.

Germline-soma segregation is crucial for fertility. Primordial germ cells (PGCs) arise early in development and are the very first cells to form in the Drosophila embryo. At the time of PGC formation, the embryo is a syncytium where nuclei divide within a common cytoplasm. Whereas invaginating plasma membrane furrows enclose nuclei to form somatic lineages during the 14th nuclear division cycle, PGCs emerge from the syncytium during the 9th division cycle in a mechanistically distinct process. PGC formation depends on maternally deposited germ granules localized at the embryo’s posterior pole. Germ granules trigger protrusion of membrane buds that enlarge to surround several nuclei that reach the posterior pole. Buds are remodeled to cells through mitotic division and constriction of the bud neck. Previous studies implicated F-actin,1 actin regulators,2,3 and contractile ring components4 in mitotic furrow formation, but what drives bud emergence and how germ granules provoke reshaping of the plasma membrane remain unknown. Here, we investigate the mechanism of germ-granule-induced bud formation. Treating the embryo as a pressurized elastic shell, we used mathematical modeling to examine possible mechanical mechanisms for local membrane protrusion. One mechanism, outward buckling produced by polymerization of a branched F-actin network, is supported by experimental data. Further, we show that germ granules modify membrane lipid composition, promoting local branched F-actin polymerization that initiates PGC formation. We propose that a mechanism for membrane lipid regulation of F-actin dynamics in migrating cells has been adapted for PGC formation in response to spatial cues provided by germ granules.

Despite the parallels between problems in computer vision and cryo-electron microscopy (cryo-EM), many state-of-the-art approaches from computer vision have yet to be adapted for cryo-EM. Within the computer-vision research community, implicits such as neural radiance fields (NeRFs) have enabled the detailed reconstruction of 3D objects from few images at different camera-viewing angles. While other neural implicits, specifically density fields, have been used to map conformational heterogeneity from noisy cryo-EM projection images, most approaches represent volume with an implicit function in Fourier space, which has disadvantages compared with solving the problem in real space, complicating, for instance, masking, constraining physics or geometry, and assessing local resolution. In this work, we build on a recent development in neural implicits, a multi-resolution hash-encoding framework called instant-NGP, that we use to represent the scalar volume directly in real space and apply it to the cryo-EM density-map reconstruction problem (InstaMap). We demonstrate that for both synthetic and real data, InstaMap for homogeneous reconstruction achieves higher resolution at shorter training stages than five other real-spaced representations. We propose a solution to noise overfitting, demonstrate that InstaMap is both lightweight and fast to train, implement masking from a user-provided input mask and extend it to molecular-shape heterogeneity via bending space using a per-image vector field.

Single-molecule experiments are a unique tool to characterize the structural dynamics of biomolecules. However, reconstructing molecular details from noisy single-molecule data is challenging. Simulation-based inference (SBI) integrates statistical inference, physics-based simulators, and machine learning and is emerging as a powerful framework for analysing complex experimental data. Recent advances in deep learning have accelerated the development of new SBI methods, enabling the application of Bayesian inference to an ever-increasing number of scientific problems. Here, we review the nascent application of SBI to the analysis of single-molecule experiments. We introduce parametric Bayesian inference and discuss its limitations. We then overview emerging deep-learning-based SBI methods to perform Bayesian inference for complex models encoded in computer simulators. We illustrate the first applications of SBI to single-molecule force-spectroscopy and cryo-electron microscopy experiments. SBI allows us to leverage powerful computer algorithms modeling complex biomolecular phenomena to connect scientific models and experiments in a principled way.

Electrons can form an ordered solid crystal phase ascribed to the interplay between Coulomb repulsion and kinetic energy. Tuning these energy scales can drive a phase transition from electron solid to liquid, i.e. melting of Wigner crystal. Generalized Wigner crystals (GWCs) pinned to moire superlattices have been reported by optical and scanning-probe-based methods. Using transport measurements to investigate GWCs is vital to a complete characterization, however, still poses a significant challenge due to difficulties in making reliable electrical contacts. Here, we report the electrical transport detection of GWCs at fractional fillings nu = 2/5, 1/2, 3/5, 2/3, 8/9, 10/9, and 4/3 in twisted bilayer MoSe2. We further observe that these GWCs undergo continuous quantum melting transitions to liquid phases by tuning doping density, magnetic and displacement fields, manifested by quantum critical scaling behaviors. Our findings establish twisted bilayer MoSe2 as a novel system to study strongly correlated states of matter and their quantum phase transitions.

Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for the optimal control problem of such hybrid dynamical systems based on solving the equations derived from the hybrid minimum principle (HMP). The algorithm is an iterative scheme following the spirit of the method of successive approximations (MSA), and it is robust to undesired collisions observed in the initial guesses. We propose several techniques to address the additional numerical challenges introduced by the presence of discontinuities. The algorithm is tested on disc collision problems whose optimal solutions exhibit one or multiple collisions. Linear convergence in terms of iteration steps and asymptotic first-order accuracy in terms of time discretization are observed when the algorithm is implemented with the forward-Euler scheme. The numerical results demonstrate that the proposed algorithm has better accuracy and convergence than direct methods based on gradient descent. Furthermore, the algorithm is also simpler, more accurate, and more stable than a deep reinforcement learning method.

From an eagle spotting a fish in shimmering water to a scientist extracting patterns from noisy data, many cognitive tasks require untangling overlapping signals. Neural circuits achieve this by transforming complex sensory inputs into distinct, separable representations that guide behavior. Data-visualization techniques convey the geometry of these transformations, and decoding approaches quantify performance efficiency. However, we lack a framework for linking these two key aspects. Here we address this gap by introducing a data-driven analysis framework, which we call Geometry Linked to Untangling Efficiency (GLUE) with manifold capacity theory, that links changes in the geometrical properties of neural activity patterns to representational untangling at the computational level. We applied GLUE to over seven neuroscience datasets—spanning multiple organisms, tasks, and recording techniques—and found that task-relevant representations untangle in many domains, including along the cortical hierarchy, through learning, and over the course of intrinsic neural dynamics. Furthermore, GLUE can characterize the underlying geometric mechanisms of representational untangling, and explain how it facilitates efficient and robust computation. Beyond neuroscience, GLUE provides a powerful framework for quantifying information organization in data-intensive fields such as structural genomics and interpretable AI, where analyzing high-dimensional representations remains a fundamental challenge.

Cryo-electron microscopy (cryo-EM) experiments take 2D snapshots of individual proteins. In principle, these snapshots contain not only the main biomolecular conformations but also scarcely populated states and rare transitions between intermediates. This makes cryo-EM a powerful tool, not only for investigating the structure of biomolecules at high resolution but also for inferring the entire conformational ensemble distribution. Some recent works have reported conformational state populations by counting particle-images from cryo-EM. We wish to caution the community that these measurements are highly susceptible to noise and should not be relied upon as a precise estimate of the thermodynamic landscape of a biomolecule for understanding its biological function. Here, we demonstrate that the extremely noisy nature of cryo-EM images and uncertainty in the viewing orientations of biomolecules lead to ambiguities when assigning images to structures. If ignored, this ambiguity can introduce inherent bias when determining the populations of conformational states through individual particle assignment. We further show that modeling the conformational probability distribution using the entire image dataset mitigates these biases

Cryo-electron microscopy (cryo-EM) experiments take 2D snapshots of individual proteins. In principle, these snapshots contain not only the main biomolecular conformations but also scarcely populated states and rare transitions between intermediates. This makes cryo-EM a powerful tool, not only for investigating the structure of biomolecules at high resolution but also for inferring the entire conformational ensemble distribution. Some recent works have reported conformational state populations by counting particle-images from cryo-EM. We wish to caution the community that these measurements are highly susceptible to noise and should not be relied upon as a precise estimate of the thermodynamic landscape of a biomolecule for understanding its biological function. Here, we demonstrate that the extremely noisy nature of cryo-EM images and uncertainty in the viewing orientations of biomolecules lead to ambiguities when assigning images to structures. If ignored, this ambiguity can introduce inherent bias when determining the populations of conformational states through individual particle assignment. We further show that modeling the conformational probability distribution using the entire image dataset mitigates these biases