Publications

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.

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.

Tissue deformations during morphogenesis can be active, driven by internal processes, or passive, resulting from stresses applied at their boundaries. Here, we introduce the Drosophila hindgut primordium as a model for studying boundary-driven tissue morphogenesis. We characterize its deformations and show that its complex shape changes can be a passive consequence of the deformations of the active regions of the embryo that surround it. First, we find an intermediate characteristic triangular shape in the 3D deformations of the hindgut. We construct a minimal model of the hindgut primordium as an elastic ring deformed by active midgut invagination and germ band extension on an ellipsoidal surface, which robustly captures the symmetry-breaking into this triangular shape. We then quantify the 3D kinematics of the tissue by a set of contours and discover that the hindgut deforms in two stages: an initial translation on the curved embryo surface followed by a rapid breaking of shape symmetry. We extend our model to show that the contour kinematics in both stages are consistent with our passive picture. Our results suggest that the role of in-plane deformations during hindgut morphogenesis is to translate the tissue to a region with anisotropic embryonic curvature and show that uniform boundary conditions are sufficient to generate the observed nonuniform shape change. Our work thus provides a possible explanation for the various characteristic shapes of blastopore-equivalents in different organisms and a framework for the mechanical emergence of global morphologies in complex developmental systems.

Rational computational design is crucial to the pursuit of novel drugs and therapeutic agents. Meso-scale cyclic peptides, which consist of 7-40 amino acid residues, are of particular interest due to their conformational rigidity, binding specificity, degradation resistance, and potential cell permeability. Because there are few natural cyclic peptides, de novo design involving non-canonical amino acids is a potentially useful goal. Here, we develop an efficient pipeline (CyclicChamp) for cyclic peptide design. After converting the cyclic constraint into an error function, we employ a variant of simulated annealing to search for low-energy peptide backbones while maintaining peptide closure. Compared to the previous random sampling approach, which was capable of sampling conformations of cyclic peptides of up to 14 residues, our method both greatly accelerates the computation speed for sampling conformations of small macrocycles (ca. 7 residues), and addresses the high-dimensionality challenge that large macrocycle designs often encounter. As a result, CyclicChamp makes conformational sampling tractable for 15-to 24-residue cyclic peptides, thus permitting the design of macrocycles in this size range. Microsecond-length molecular dynamics simulations on the resulting 15, 20, and 24 amino acid cyclic designs identify designs with kinetic stability. To test their thermodynamic stability, we perform additional replica exchange molecular dynamics simulations and generate free energy surfaces. Three 15-residue designs, one 20-residue and one 24-residue design emerge as promising candidates.

Macrocycles are a promising therapeutic class. The incorporation of heterochiral and non-natural chemical building-blocks presents challenges for rational design, however. With no existing machine learning methods tailored for heterochiral macrocycle design, we developed a novel convolutional autoencoder model to rapidly generate energetically favorable macrocycle backbones for heterochiral design and structure prediction. Our approach surpasses the current state-of-the-art method, Generalized Kinematic loop closure (GenKIC) in the Rosetta software suite. Given the absence of large, available macrocycle datasets, we created a custom dataset in-house and in silico. Our model, CyclicCAE, produces energetically stable backbones and designable structures more rapidly than GenKIC. It enables users to perform energy minimization, generate structurally similar or diverse inputs via MCMC, and conduct inpainting with fixed anchors or motifs. We propose that this novel method will accelerate the development of stable macrocycles, speeding up macrocycle drug design pipelines.

During the first cell fate decision in mammalian embryos the inner cell mass cells, which will give rise to the embryo proper and other extraembryonic tissues, segregate from the trophectoderm cells, the precursors of the placenta. Cell fate segregation proceeds in a gradual manner encompassing two rounds of cell division, as well as cell positional and morphological changes. While it is known that the activity of the Hippo signaling pathway and the subcellular localization of its downstream effector YAP dictate lineage specific gene expression, the response of YAP to these dynamic cellular changes remains incompletely understood. Here we address these questions by quantitative live imaging of endogenously tagged YAP while simultaneously monitoring geometric cellular features and cell cycle progression throughout cell fate segregation. We apply a probabilistic model to our dynamic data, providing a quantitative characterization of the mutual effects of YAP and cellular relative exposed area, which has previously been shown to correlate with subcellular YAP localization in fixed samples. Additionally, we study how nuclear YAP levels are influenced by other factors, such as the decreasing pool of maternally provided YAP that is partitioned to daughter cells through cleavage divisions, cell cycle-associated nuclear volume changes, and a delay after divisions in adjusting YAP levels to new cell positions. Interestingly, we find that establishing low nuclear YAP levels required for the inner cell mass fate is largely achieved by passive cell cycle-associated mechanisms. Moreover, contrary to expectations, we find that mechanical perturbations that result in cell shape changes do not influence YAP localization in the embryo. Together our work identifies how various inputs are integrated over a dynamic developmental time course to shape the levels of a key molecular determinant of the first cell fate choice.

Resolving continuous conformational heterogeneity in single-particle cryo-electron microscopy (cryo-EM) is a field in which new methods are now emerging regularly. Methods range from traditional statistical techniques to state-of-the-art neural network approaches. Such ongoing efforts continue to enhance the ability to explore and understand the continuous conformational variations in cryo-EM data. One of the first methods was the manifold embedding approach or ManifoldEM. However, comparing it with more recent methods has been challenging due to software availability and usability issues. In this work, we introduce a modern Python implementation that is user-friendly, orders of magnitude faster than its previous versions and designed with a developer-ready environment. This implementation allows a more thorough evaluation of the strengths and limitations of methods addressing continuous conformational heterogeneity in cryo-EM, paving the way for further community-driven improvements.

We present a new framework for the fast solution of inhomogeneous elliptic boundary value problems in domains with smooth boundaries. High-order solvers based on adaptive box codes or the fast Fourier transform can efficiently treat the volumetric inhomogeneity, but require care to be taken near the boundary to ensure that the volume data is globally smooth. We avoid function extension or cut-cell quadratures near the boundary by dividing the domain into two regions: a bulk region away from the boundary that is efficiently treated with a truncated free-space box code, and a variable-width boundary-conforming strip region that is treated with a spectral collocation method and accompanying fast direct solver. Particular solutions in each region are then combined with Laplace layer potentials to yield the global solution. The resulting solver has an optimal computational complexity of O(N) for an adaptive discretization with N degrees of freedom. With an efficient two-dimensional (2D) implementation we demonstrate adaptive resolution of volumetric data, boundary data, and geometric features across a wide range of length scales, to typically 10-digit accuracy. The cost of all boundary corrections remains small relative to that of the bulk box code. The extension to 3D is expected to be straightforward in many cases because the strip

A lack of tools for detecting receptor activity in vivo has limited our ability to fully explore receptor-level control of developmental patterning. Here, we extend a new class of biosensors for receptor tyrosine kinase (RTK) activity, the pYtag system, to visualize endogenous RTK activity in Drosophila. We build biosensors for three Drosophila RTKs that function across developmental stages and tissues. By characterizing Torso::pYtag during terminal patterning in the early embryo, we find that Torso activity differs from downstream ERK activity in two surprising ways: Torso activity is narrowly restricted to the poles but produces a broader gradient of ERK, and Torso activity decreases over developmental time while ERK activity is sustained. This decrease in Torso activity is driven by ERK pathway-dependent negative feedback. Our results suggest an updated model of terminal patterning where a narrow domain of Torso activity, tuned in amplitude by negative feedback, locally activates signaling effectors which diffuse through the syncytial embryo to form the ERK gradient. Altogether, this work highlights the usefulness of pYtags for investigating receptor-level regulation of developmental patterning.