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.

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.

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.

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

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.

We propose a simple and efficient method to calculate the electronic self-energy in dynamical mean-field theory (DMFT), addressing a numerical instability often encountered when solving the Dyson equation. Our approach formulates the Dyson equation as a constrained optimization problem with a simple quadratic objective. The constraints on the self-energy are obtained via direct measurement of the leading order terms of its asymptotic expansion within a continuous time quantum Monte Carlo framework, and the use of the compact discrete Lehmann representation of the self-energy yields an optimization problem in a modest number of unknowns. We benchmark our method for the non-interacting Bethe lattice, as well as DMFT calculations for both model systems and \textit{ab-initio} applications.

Bacterial motility in spatially structured environments impacts a variety of natural and engineering processes. Constructing models to predict, control, and design bacterial motility for these processes remains challenging because bacteria and active swimmers have complex interactions with surfaces and because the precise environment geometry is unknown. Here, we present a method for deriving bacterial diffusion coefficients in disordered media in terms of cell and environmental parameters. The approach abstracts the dynamics in the full geometry to “surface states,” which encode how cells interact with surfaces in the environment. Then, a long-time diffusion equation can be derived analytically from the state model. Applying this method to a run-and-tumble particle in a 2D Lorentz gas environment provides analytical predictions that show good agreement with particle simulations. Like past studies, we observe that the diffusivity depends nonmonotonically on the cell’s run length. Using the analytical expressions, we derive the optimal run length, revealing an intuitive dependence on environmental length scales. Furthermore, we find that rescaling length and time by the average distance and time between trap events collapses all of the diffusivities onto a single curve, which we derive analytically. Thus, our approach extracts interpretable, macroscopic diffusive behavior from complex microscopic dynamics, and provides tools and intuitions for understanding bacterial diffusion in disordered media.