Publications

The structure of compound eyes in arthropods has been the subject of many studies, revealing important biological principles. Until recently, these studies were constrained by the two-dimensional nature of available ultrastructural data. By taking advantage of the novel three-dimensional ultrastructural dataset obtained using volume electron microscopy, we present the first cellular-level reconstruction of the whole compound eye of an insect, the miniaturized parasitoid wasp Megaphragma viggianii. The compound eye of the female M. viggianii consists of 29 ommatidia and contains 478 cells. Despite the almost anucleate brain, all cells of the compound eye contain nuclei. As in larger insects, the dorsal rim area of the eye in M. viggianii contains ommatidia that are believed to be specialized in polarized light detection as reflected in their corneal and retinal morphology. We report the presence of three ‘ectopic’ photoreceptors. Our results offer new insights into the miniaturization of compound eyes and scaling of sensory organs in general.

A direct solver is introduced for solving overdetermined linear systems involving nonuniform discrete Fourier transform matrices. Such matrices can be transformed into a Cauchy-like form that has hierarchical low rank structure. The rank structure of this matrix is explained, and it is shown that the ranks of the relevant submatrices grow only logarithmically with the number of columns of the matrix. A fast rank-structured hierarchical approximation method based on this analysis is developed, along with a hierarchical least-squares solver for these and related systems. This result is a direct method for inverting nonuniform discrete transforms with a complexity that is usually nearly linear with respect to the degrees of freedom in the problem. This solver is benchmarked against various iterative and direct solvers in the setting of inverting the one-dimensional type-II (or forward) transform, for a range of condition numbers and problem sizes (up to (4 10

Human perceptual sensitivity often improves with training, a phenomenon known as “perceptual learning.” Another important perceptual dimension is appearance, the subjective sense of stimulus magnitude. Are training-induced improvements in sensitivity accompanied by more accurate appearance? Here, we examined this question by measuring both discrimination (sensitivity) and estimation (appearance) responses to near-horizontal motion directions, which are known to be repulsed away from horizontal. Participants performed discrimination and estimation tasks before and after training in either the discrimination or the estimation task or none (control group). Human observers who trained in either discrimination or estimation exhibited improvements in discrimination accuracy, but estimation repulsion did not decrease; instead, it either persisted or increased. Hence, distortions in perception can be exacerbated after perceptual learning. We developed a computational observer model in which perceptual learning arises from increases in the precision of underlying neural representations, which explains this counterintuitive finding. For each observer, the fitted model accounted for discrimination performance, the distribution of estimates, and their changes with training. Our empirical findings and modeling suggest that learning enhances distinctions between categories, a potentially important aspect of real-world perception and perceptual learning.

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.

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.

The genome contains genetic information essential for cell's life. The genome's spatial organization inside the cell nucleus is critical for its proper function including gene regulation. The two major genomic compartments -- euchromatin and heterochromatin -- contain largely transcriptionally active and silenced genes, respectively, and exhibit distinct dynamics. In this work, we present a hydrodynamic framework that describes the large-scale behavior of euchromatin and heterochromatin, and accounts for the interplay of mechanical forces, active processes, and nuclear confinement. Our model shows contractile stresses from cross-linking proteins lead to the formation of heterochromatin droplets via mechanically driven phase separation. These droplets grow, coalesce, and in nuclear confinement, wet the boundary. Active processes, such as gene transcription in euchromatin, introduce non-equilibrium fluctuations that drive long-range, coherent motions of chromatin as well as the nucleoplasm, and thus alter the genome's spatial organization. These fluctuations also indirectly deform heterochromatin droplets, by continuously changing their shape. Taken together, our findings reveal how active forces, mechanical stresses and hydrodynamic flows contribute to the genome's organization at large scales and provide a physical framework for understanding chromatin organization and dynamics in live cells.

imulating membrane proteins accurately combines two challenges into one: properly capturing the structure and dynamics of proteins as well as correctly representing the membrane environment in which they are usually embedded. Beginning with pioneering efforts in the 1980s and 1990s,1−7 both challenges have been met with increasing success over the years. Simulations of membrane proteins in realistic cellular contexts over many microseconds are now common.Concomitant advances in the determination of membrane protein structures, with over 50 unique structures determined 8 annually have further expanded the reach of simulations in this area. This Special Issue highlights a number of recent molecular dynamics (MD) simulations of membrane proteins and covers a wide range of applications and specialized techniques.

Hamiltonian Monte Carlo (HMC) is the mainstay of applied Bayesian inference for differentiable models. However, HMC still struggles to sample from hierarchical models that induce densities with multiscale geometry: a large step size is needed to efficiently explore low curvature regions while a small step size is needed to accurately explore high curvature regions. We introduce the delayed rejection generalized HMC (DR-G-HMC) sampler that overcomes this challenge by employing dynamic step size selection, inspired by differential equation solvers. In generalized HMC, each iteration does a single leapfrog step. DR-G-HMC sequentially makes proposals with geometrically decreasing step sizes upon rejection of earlier proposals. This simulates Hamiltonian dynamics that can adjust its step size along a (stochastic) Hamiltonian trajectory to deal with regions of high curvature. DR-G-HMC makes generalized HMC competitive by decreasing the number of rejections which otherwise cause inefficient backtracking and prevents directed movement. We present experiments to demonstrate that DR-G-HMC (1) correctly samples from multiscale densities, (2) makes generalized HMC methods competitive with the state of the art No-U-Turn sampler, and (3) is robust to tuning parameters.