Publications

Single-particle cryo-electron microscopy (cryo-EM) is a technique that takes projection images of biomolecules frozen at cryogenic temperatures. A major advantage of this technique is its ability to image single biomolecules in heterogeneous conformations. While this poses a challenge for data analysis, recent algorithmic advances have enabled the recovery of heterogeneous conformations from the noisy imaging data. Here, we review methods for the reconstruction and heterogeneity analysis of cryo-EM images, ranging from linear-transformation-based methods to nonlinear deep generative models. We overview the dimensionality-reduction techniques used in heterogeneous 3D reconstruction methods and specify what information each method can infer from the data. Then, we review the methods that use cryo-EM images to estimate probability distributions over conformations in reduced subspaces or predefined by atomistic simulations. We conclude with the ongoing challenges for the cryo-EM community.

We present an algorithm to solve the dispersive depth-averaged Serre-Green-Naghdi (SGN) equations using patch-based adaptive mesh refinement. These equations require adding additional higher derivative terms to the nonlinear shallow water equations. This has been implemented as a new component of the open source GeoClaw software that is widely used for modeling tsunamis, storm surge, and related hazards, improving its accuracy on shorter wavelength phenomena. The equations require the solution of an elliptic system at each time step. The adaptive algorithm allows different time steps on different refinement levels, and solves the implicit equations level by level. Computational examples are presented to illustrate the stability and accuracy on a radially symmetric test case and two realistic tsunami modeling problems, including a hypothetical asteroid impact creating a short wavelength tsunami for which dispersive terms are necessary.

Several recent works have introduced highly compact representations of single-particle Green's functions in the imaginary time and Matsubara frequency domains, as well as efficient interpolation grids used to recover the representations. In particular, the intermediate representation with sparse sampling and the discrete Lehmann representation (DLR) make use of low rank compression techniques to obtain optimal approximations with controllable accuracy. We consider the use of the DLR in dynamical mean-field theory (DMFT) calculations, and in particular show that the standard full Matsubara frequency grid can be replaced by the compact grid of DLR Matsubara frequency nodes. We test the performance of the method for a DMFT calculation of Sr$_2$RuO$_4$ at temperature $50$K using a continuous-time quantum Monte Carlo impurity solver, and demonstrate that Matsubara frequency quantities can be represented on a grid of only 36 nodes with no reduction in accuracy, or increase in the number of self-consistent iterations, despite the presence of significant Monte Carlo noise.

Resolving chromatin remodeling-linked gene expression changes at cell type resolution is important for understanding disease states. We describe MAGICAL, a hierarchical Bayesian approach that leverages paired scRNA-seq and scATAC-seq data from different conditions to map disease-associated transcription factors, chromatin sites, and genes as regulatory circuits. By simultaneously modeling signal variation across cells and conditions in both omics data types, MAGICAL achieved high accuracy on circuit inference. We applied MAGICAL to study Staphylococcus aureus sepsis from peripheral blood mononuclear single-cell data that we generated from infected subjects with bloodstream infection and from uninfected controls. MAGICAL identified sepsis-associated regulatory circuits predominantly in CD14 monocytes, known to be activated by bacterial sepsis. We addressed the challenging problem of distinguishing host regulatory circuit responses to methicillin-resistant-(MRSA) and methicillin-susceptible Staphylococcus aureus (MSSA) infections. While differential expression analysis failed to show predictive value, MAGICAL identified epigenetic circuit biomarkers that distinguished MRSA from MSSA.

BK virus (BKV; human polyomavirus 1) infections are asymptomatic in most individuals, and the virus persists throughout life without harm. However, BKV is a threat to transplant patients and those with immunosuppressive disorders. Under these circumstances, the virus can replicate robustly in proximal tubule epithelial cells (PT). Cultured renal proximal tubule epithelial cells (RPTE) are permissive to BKV and have been used extensively to characterize different aspects of BKV infection. Recently, lines of hTERT-immortalized RPTE have become available, and preliminary studies indicate they support BKV infection as well. Our results indicate that BKV infection leads to a similar response in primary and immortalized RPTE. In addition, we examined the patterns of global gene expression of primary and immortalized RPTE and compared them with uncultured PT freshly dissociated from human kidney. As expected, PT isolated from the healthy kidney express a number of differentiation-specific genes that are associated with kidney function. However, the expression of most of these genes is absent or repressed in cultured RPTE. Rather, cultured RPTE exhibit a gene expression profile indicative of a stressed or injured kidney. Inoculation of cultured RPTE with BKV results in the suppression of many genes associated with kidney stress. In summary, this study demonstrated similar global gene expression patterns and responses to BKV infection between primary and immortalized RPTE. Moreover, results from bulk transcriptome sequencing (RNA-seq) and SCT experiments revealed distinct transcriptomic signatures representing cell injury and stress in primary RPTE in contrast to the uncultured, freshly dissociated PT from human kidney.

DNA methylation comprises a cumulative record of lifetime exposures superimposed on genetically determined markers. Little is known about methylation dynamics in humans following an acute perturbation, such as infection. We characterized the temporal trajectory of blood epigenetic remodeling in 133 participants in a prospective study of young adults before, during, and after asymptomatic and mildly symptomatic SARS-CoV-2 infection. The differential methylation caused by asymptomatic or mildly symptomatic infections was indistinguishable. While differential gene expression largely returned to baseline levels after the virus became undetectable, some differentially methylated sites persisted for months of follow-up, with a pattern resembling autoimmune or inflammatory disease. We leveraged these responses to construct methylation-based machine learning models that distinguished samples from pre-, during-, and postinfection time periods, and quantitatively predicted the time since infection. The clinical trajectory in the young adults and in a diverse cohort with more severe outcomes was predicted by the similarity of methylation before or early after SARS-CoV-2 infection to the model-defined postinfection state. Unlike the phenomenon of trained immunity, the postacute SARS-CoV-2 epigenetic landscape we identify is antiprotective.

Recently, the stochastic Polyak step size (SPS) has emerged as a competitive adaptive step size scheme for stochastic gradient descent. Here we develop ProxSPS, a proximal variant of SPS that can handle regularization terms. Developing a proximal variant of SPS is particularly important, since SPS requires a lower bound of the objective function to work well. When the objective function is the sum of a loss and a regularizer, available estimates of a lower bound of the sum can be loose. In contrast, ProxSPS only requires a lower bound for the loss which is often readily available. As a consequence, we show that ProxSPS is easier to tune and more stable in the presence of regularization. Furthermore for image classification tasks, ProxSPS performs as well as AdamW with little to no tuning, and results in a network with smaller weight parameters. We also provide an extensive convergence analysis for ProxSPS that includes the non-smooth, smooth, weakly convex and strongly convex setting.

We introduce a layer potential representation for the solution of the transmission problem defined by two dielectric channels, or open waveguides, meeting along the straight-line interface, {x1=0}. The main observation is that the outgoing fundamental solution for the operator Δ+k21+q(x2), acting on functions defined in ℝ2, is easily constructed using the Fourier transform in the x1-variable and the elementary theory of ordinary differential equations. These fundamental solutions can then be used to represent the solution to the transmission problem in half planes. The transmission boundary conditions lead to integral equations along the intersection of the half planes, which, in our normalization, is the x2-axis. We show that, in appropriate Banach spaces, these integral equations are Fredholm equations of second kind, which are therefore generically solvable. We then show that the solutions satisfy an analogue of the Sommerfeld radiation condition that follows from work of Isozaki, Melrose, Vasy, et al. This formulation suggests practicable numerical methods to approximately solve this class of problems.

Many applications in magnetic confinement fusion require the efficient calculation of surface integrals with singular integrands. The singularity subtraction approaches typically used to handle such singularities are complicated to implement and low-order accurate. In contrast, we demonstrate that the Kapur–Rokhlin quadrature scheme is well-suited for the logarithmically singular integrals encountered for a toroidally axisymmetric confinement system, is easy to implement and is high-order accurate. As an illustration, we show how to apply this quadrature scheme for the efficient and accurate calculation of the normal component of the magnetic field due to the plasma current on the plasma boundary, via the virtual-casing principle.

Living systems are intrinsically nonequilibrium: They use metabolically derived chemical energy to power their emergent dynamics and self-organization. A crucial driver of these dynamics is the cellular cytoskeleton, a defining example of an active material where the energy injected by molecular motors cascades across length scales, allowing the material to break the constraints of thermodynamic equilibrium and display emergent nonequilibrium dynamics only possible due to the constant influx of energy. Notwithstanding recent experimental advances in the use of local probes to quantify entropy production and the breaking of detailed balance, little is known about the energetics of active materials or how energy propagates from the molecular to emergent length scales. Here, we use a recently developed picowatt calorimeter to experimentally measure the energetics of an active microtubule gel that displays emergent large-scale flows. We find that only approximately one-billionth of the system’s total energy consumption contributes to these emergent flows. We develop a chemical kinetics model that quantitatively captures how the system’s total thermal dissipation varies with ATP and microtubule concentrations but that breaks down at high motor concentration, signaling an interference between motors. Finally, we estimate how energy losses accumulate across scales. Taken together, these results highlight energetic efficiency as a key consideration for the engineering of active materials and are a powerful step toward developing a nonequilibrium thermodynamics of living systems.