Publications

We generalize the interpolative separable density fitting (ISDF) method, used for compressing the four-index electron repulsion integral (ERI) tensor, to incorporate adaptive real space grids for potentially highly localized single-particle basis functions. To do so, we employ a fast adaptive algorithm, the recently-introduced dual-space multilevel kernel-splitting method, to solve the Poisson equation for the ISDF auxiliary basis functions. The adaptive grids are generated using a high-order accurate, black-box procedure that satisfies a user-specified error tolerance. Our algorithm relies on the observation, which we prove, that an adaptive grid resolving the pair densities appearing in the ERI tensor can be straightforwardly constructed from one that resolves the single-particle basis functions, with the number of required grid points differing only by a constant factor. We find that the ISDF compression efficiency for the ERI tensor with highly localized basis sets is comparable to that for smoother basis sets compatible with uniform grids. To demonstrate the performance of our procedure, we consider several molecular systems with all-electron basis sets which are intractable using uniform grid-based methods. Our work establishes a pathway for scalable many-body electronic structure simulations with arbitrary smooth basis functions, making simulations of phenomena like core-level excitations feasible on a large scale.

Having an accurate reaction coordinate (RC) is essential for reliable kinetic characterization of molecular processes, but there are few quantitative metrics to evaluate RC quality. In this study, we consider the dimensionless γ metric from the Exponential Average Time-dependent Rate (EATR) method, which represents the fraction of a biasing potential along the RC that contributes to increasing the rate constant. We demonstrate that γ can be used to test whether the utility of a RC for predicting kinetics with a Metadynamics bias improves as the coordinate is iteratively updated to include new data. We evaluate RCs approximated via the iterative State Predictive Information Bottleneck (SPIB) approach, which was previously shown to be accurate across six protein–ligand dissociation systems. For these same systems, we compute γ values and mean accelerated times τ̅accel. After systematically scanning over fitting parameters, the results show that γ increases closer to 1, while τ̅accel decreases, revealing a consistent inverse correlation. These results demonstrate that γ serves as a practical criterion for RC evaluation and offers guidance for selecting SPIB–derived coordinates yielding quantitative kinetic predictions.

Having an accurate reaction coordinate (RC) is essential for reliable kinetic characterization of molecular processes, but there are few quantitative metrics to evaluate RC quality. In this study, we consider the dimensionless γ metric from the Exponential Average Time-dependent Rate (EATR) method, which represents the fraction of a biasing potential along the RC that contributes to increasing the rate constant. We demonstrate that γ can be used to test whether the utility of a RC for predicting kinetics with a Metadynamics bias improves as the coordinate is iteratively updated to include new data. We evaluate RCs approximated via the iterative State Predictive Information Bottleneck (SPIB) approach, which was previously shown to be accurate across six protein–ligand dissociation systems. For these same systems, we compute γ values and mean accelerated times τ̅accel. After systematically scanning over fitting parameters, the results show that γ increases closer to 1, while τ̅accel decreases, revealing a consistent inverse correlation. These results demonstrate that γ serves as a practical criterion for RC evaluation and offers guidance for selecting SPIB–derived coordinates yielding quantitative kinetic predictions.

The method of fundamental solutions (MFS) is known to be effective for solving 3D Laplace and Stokes Dirichlet boundary value problems in the exterior of a large collection of simple smooth objects. Here, we present new scalable MFS formulations for the corresponding elastance and mobility problems. The elastance problem computes the potentials of conductors with given net charges, while the mobility problem—crucial to rheology and complex fluid applications—computes rigid body velocities given net forces and torques on the particles. The key idea is orthogonal projection of the net charge (or forces and torques) in a rectangular variant of a “completion flow.” The proposal is compatible with one-body preconditioning, resulting in well-conditioned square linear systems amenable to fast multipole accelerated iterative solution, thus a cost linear in the particle number. For large suspensions with moderate lubrication forces, MFS sources on inner proxy-surfaces give accuracy on par with a well-resolved boundary integral formulation. Our several numerical tests include a suspension of 10,000 nearby ellipsoids, using 2.6\times 10^7
total preconditioned degrees of freedom, where GMRES converges to five digits of accuracy in under two hours on one workstation

The mammalian brain processes experience-dependent spatial information through poorly-understood network mechanisms thought to depend on particular network connectivity patterns and activity-dependent synaptic plasticity. However, dedicated input connections that learn to shape information about place cannot easily explain many rodent hippocampal place cell phenomena. For example, representational drift notwithstanding, the discharge of each place cell maps to specific locations in a fixed environment, but the discharge of most cells remap to distinct independent locations across environments, despite the fact that most sub-second cofiring relationships amongst hippocampal neuron pairs persist across environments. Whereas some models of hippocampal spatial information processing rely on the dedicated input connections of a for-purpose connectome (ignoring remapping, representational drift, and maintained cofiring), other models use synaptic plasticity implemented by learning rules to alter random input connections, but struggle with either limited capacity, representational drift, and/or biological implausibility. Here, using a randomly tuned network with feedback inhibition, we examine whether the assumptions of a specific connectome and learning-implemented synaptic plasticity are necessary for diverse place cell phenomena. We find that the random network with non-plastic connections accounts for positional tuning, single place fields in small spaces and multiple place fields in large spaces, mixed selectivity, and remapping, amongst other place cell phenomena. This requires excitatory activity to be sparse and organized across stimuli by divisive normalization. Enabling synaptic plasticity only at the network connections (not at network inputs) accounts for additional place cell phenomena including overdispersion, representational drift, and memory tagging. We show by simulations and analytically that DivSparse, a random network with sparsifying inhibition can explain many features of place cell network activity, suggesting that simple biologically-plausible architectures can realize representations of spatial experience that are robust, flexible, and spontaneous.

We reveal a mechanism that may explain the non-metallic out-of-plane resistivity in layered metals. By carefully examining how the Drude-Boltzmann expression for the $c$-axis conductivity emerges out of the Kubo formula, we find, besides the standard metallic term proportional to the carrier lifetime $\tau$, a non-Drude contribution proportional to $1/\tau$. The Drude behavior breaks down when $1/\tau > 2 \eta^*$, the crossover value $\eta^*$ being small (and hence observable) when the $c$-axis velocities vary rapidly with the distance from the Fermi surface. We consider the Hund metal Sr$_2$RuO$_4$ as a test case, which we study within a realistic dynamical mean-field theory approach. The non-Drude behavior observed experimentally in $c$-axis transport is reproduced and explained by our considerations, showing that earlier invoked extrinsic mechanisms that involve either impurities or phonons are unnecessary. We point out that the small value of $\eta^*$ is due to a peculiar accidental cancellation due to destructive interference characteristic of body-centered tetragonal lattices.

The squeezing of blood cells and vesicles through narrow constrictions, such as splenic slits, pulmonary capillaries, vascular endothelial gaps, and microfluidic channels, is crucial in physiology and biotechnology, with fluid mechanics playing a central role. The diverse geometries of these constrictions, the associated flow conditions, and the unique mechanical properties of cells and vesicles create a rich subject in fluid mechanics emerging from nonlinear dynamics of fluid–structure interactions involving both lubrication and Marangoni flows. Advances in microfluidics, video microscopy, and computational modeling have enabled investigations into these complex processes. This review surveys the key features and approaches, recent prominent studies, and unresolved challenges related to these processes, offering insights for researchers across biomechanics, biomedical engineering, biological physics, hematology, physiology, and applied mathematics.

Motivation Focused Ion Beam Scanning Electron Microscopy (FIB-SEM) is an advanced Volume Electron Microscopy technology with growing applications, featuring thinner sectioning compared to other Volume Electron Microscopes. Such axial resolution is crucial for accurate segmentation and reconstruction of fine structures in biological tissues. However, in reality, the milling thickness is not always uniform across the sample surface, resulting in the axial plane looking distorted. Existing image processing approaches often: (i) assume constant section thickness; (ii) consist of multiple separate processing steps (i.e., not in an end-to-end fashion); (iii) require ground truth images for modeling, which may entail significant labor and be unsuitable for rapid analysis.

Results We develop a deep learning method to correct non-uniform milling artifacts observed in FIB-SEM images. The proposed method is an image-to-image translation technique that can mitigate image distortions in an unsupervised manner. It conducts cross-plane learning within 3D image volumes without any ground truth annotations. We demonstrate the efficacy of our method on a real-world micro-wasp dataset, showcasing significantly improved image quality after correction with qualitative and quantitative analysis.

IgA nephropathy (IgAN), focal segmental glomerulosclerosis (FSGS), membranous nephropathy (MN), and minimal change disease (MCD) account for the majority of idiopathic glomerulopathies (GN). However, there are no powered transcriptomic datasets coupled to genetic data to investigate the genetic mechanisms underlying gene regulation in the context of GN.

The highly conserved extracellular signal–regulated kinase (ERK) regulates diverse cellular processes by phosphorylating a wide range of intracellular substrates. Its catalytic activity relies on phosphorylation by a single upstream kinase, mitogen-activated protein kinase kinase (MEK), which interacts with only a few binding partners. Here, we test whether the asymmetry in protein–protein interaction network architecture influences the coevolution of the MEK–ERK complex. Phylogenetic sequence analysis across metazoan species revealed accelerated divergence in MEK’s intrinsically disordered N-terminal docking motif (docking site [D-site]), whereas ERK remained highly conserved. Structure prediction with AlphaFold2 and extensive molecular dynamics simulations showed that five conserved D-site residues form stable hydrophobic and electrostatic contacts with ERK’s D-recruitment site. Functional assays in Drosophila melanogaster confirmed that these D-site interactions are essential for proper downstream signaling and support an allosteric role for this motif. Our results demonstrate that MEK uses a structurally simple yet evolutionarily adaptable motif to regulate MEK–ERK complex stability and binding dynamics. The D-site is strongly conserved within phylogenetic groups such as insects or terrestrial vertebrates, yet diverges across them, reflecting evolutionary pressures that balance functional conservation with signaling adaptability. The presented approach illustrates how the combined approach using sequencing data, molecular simulations, and targeted perturbations can be used to address fundamental questions about the evolution of protein–protein interaction networks.