Publications

Many different simulation methods for Stokes flow problems involve a common computationally intense task—the summation of a kernel function over O(N2) pairs of points. One popular technique
is the Kernel Independent Fast Multipole Method (KIFMM), which constructs a spatial adaptive octree and places a small number of equivalent multipole and local points around each octree box, and completes the kernel sum with O(N) performance. However, the KIFMM cannot be used directly with nonlinear kernels, can be inefficient for complicated linear kernels, and in general is difficult to implement compared to less-efficient alternatives such as Ewald-type methods. Here we present the Kernel Aggregated Fast Multipole Method (KAFMM), which overcomes these drawbacks by allowing different kernel functions to be used for specific stages of octree traversal. In many cases a simpler linear kernel suffices during the most extensive stage of octree traversal, even for nonlinear kernel summation problems. The KAFMM thereby improves computational efficiency in general and also allows efficient evaluation of some nonlinear kernel functions such as the regularized Stokeslet. We have implemented our method as an open-source software library STKFMM with support for Laplace kernels, the Stokeslet, regularized Stokeslet, Rotne-Prager-Yamakawa (RPY) tensor, and the Stokes double-layer and traction operators. Open and periodic boundary conditions are supported for all kernels, and the no-slip wall boundary condition is supported for the Stokeslet and RPY tensor.
The package is designed to be ready-to-use as well as being readily extensible to additional kernels. Massive parallelism is supported with mixed OpenMP and MPI.

Structures of membrane proteins are challenging to determine experimentally and currently represent only about 2% of the structures in the ProteinDataBank. Because of this disparity, methods for modeling membrane proteins are fewer and of lower quality than those for modeling soluble proteins. However, better expression, crystallization, and cryo-EM techniques have prompted a recent increase in experimental structures of membrane proteins, which can act as templates to predict the structure of closely related proteins through homology modeling. Because homology modeling relies on a structural template, it is easier and more accurate than fold recognition methods or de novo modeling, which are used when the sequence similarity between the query sequence and the sequence of related proteins in structural databases is below 25%. In homology modeling, a query sequence is mapped onto the coordinates of a single template and refined. With the increase in available templates, several templates often cover overlapping segments of the query sequence. Multi-template modeling can be used to identify the best template for local segments and join them into a single model. Here we provide a protocol for modeling membrane proteins from multiple templates in the Rosetta software suite. This approach takes advantage of several integrated frameworks, namely RosettaScripts, RosettaCM, and RosettaMP with the membrane scoring function.

To guide behavior, the brain extracts relevant features from high-dimensional data streamed by sensory organs. Neuroscience experiments demonstrate that the processing of sensory inputs by cortical neurons is modulated by instructive signals which provide context and task-relevant information. Here, adopting a normative approach, we model these instructive signals as supervisory inputs guiding the projection of the feedforward data. Mathematically, we start with a family of Reduced-Rank Regression (RRR) objective functions which include Reduced Rank (minimum) Mean Square Error (RRMSE) and Canonical Correlation Analysis (CCA), and derive novel offline and online optimization algorithms, which we call Bio-RRR. The online algorithms can be implemented by neural networks whose synaptic learning rules resemble calcium plateau potential dependent plasticity observed in the cortex. We detail how, in our model, the calcium plateau potential can be interpreted as a backpropagating error signal. We demonstrate that, despite relying exclusively on biologically plausible local learning rules, our algorithms perform competitively with existing implementations of RRMSE and CCA.

Learning latent features from time series data is an important problem in both machine learning and brain function. One approach, called Slow Feature Analysis (SFA), leverages the slowness of many salient features relative to the rapidly varying input signals. Furthermore, when trained on naturalistic stimuli, SFA reproduces interesting properties of cells in the primary visual cortex and hippocampus, suggesting that the brain uses temporal slowness as a computational principle for learning latent features. However, despite the potential relevance of SFA for modeling brain function, there is currently no SFA algorithm with a biologically plausible neural network implementation, by which we mean an algorithm operates in the online setting and can be mapped onto a neural network with local synaptic updates. In this work, starting from an SFA objective, we derive an SFA algorithm, called Bio-SFA, with a biologically plausible neural network implementation. We validate Bio-SFA on naturalistic stimuli.

Blind source separation, the problem of separating mixtures of unknown signals into their distinct sources, is an important problem for both biological and engineered signal processing systems. Nonnegative Independent Component Analysis (NICA) is a special case of blind source separation that assumes the mixture is a linear combination of independent, nonnegative sources. In this work, we derive a single-layer neural network implementation of NICA satisfying the following 3 constraints, which are relevant for biological systems and the design of neuromorphic hardware: (i) the network operates in the online setting, (ii) the synaptic learning rules are local, and (iii) the neural outputs are nonnegative.

Supernovae mark the explosive deaths of stars and enrich the cosmos with heavy elements. Future telescopes will discover thousands of new supernovae nightly, creating a need to flag astrophysically interesting events rapidly for followup study. Ideally, such an anomaly detection pipeline would be independent of our current knowledge and be sensitive to unexpected phenomena. Here we present an unsupervised method to search for anomalous time series in real time for transient, multivariate, and aperiodic signals. We use a RNN-based variational autoencoder to encode supernova time series and an isolation forest to search for anomalous events in the learned encoded space. We apply this method to a simulated dataset of 12,159 supernovae, successfully discovering anomalous supernovae and objects with catastrophically incorrect redshift measurements. This work is the first anomaly detection pipeline for supernovae which works with online datastreams.

Tissue development, homeostasis, and repair require cells to sense mechanical forces. Although many molecular actors implicated in cell mechanosensitivity have been extensively studied, the basis by which cells adapt their mechanical responses to their geometry remains poorly defined. López-Gay et al. now identify how two fundamental epithelial structures—stress fibers and tricellular junctions—endow Drosophila cells with an internal ruler to scale their mechanical response with their area. This work explains how cells of different sizes within an epithelial tissue collectively adapt their mechanical response to control tissue shape and proliferation. Scaling of biological properties with size is a core property of other biological systems.

Cyclic symmetry is frequent in protein and peptide homo‐oligomers, but extremely rare within a single chain, as it is not compatible with free N‐ and C‐termini. Here we describe the computational design of mixed‐chirality peptide macrocycles with rigid structures that feature internal cyclic symmetries or improper rotational symmetries inaccessible to natural proteins. Crystal structures of three C2‐ and C3‐symmetric macrocycles, and of six diverse S2‐symmetric macrocycles, match the computationally‐designed models with backbone heavy‐atom RMSD values of 1 Å or better. Crystal structures of an S4‐symmetric macrocycle (consisting of a sequence and structure segment mirrored at each of three successive repeats) designed to bind zinc reveal a large‐scale zinc‐driven conformational change from an S4‐symmetric apo‐state to a nearly inverted S4‐symmetric holo‐state almost identical to the design model. These symmetric structures provide promising starting points for applications ranging from design of cyclic peptide based metal organic frameworks to creation of high affinity binders of symmetric protein homo‐oligomers. More generally, this work demonstrates the power of computational design for exploring symmetries and structures not found in nature, and for creating synthetic switchable systems.

COVID-19 morbidity and mortality are increased via unknown mechanisms in patients with diabetes and kidney disease. SARS-CoV-2 uses angiotensin-converting enzyme 2 (ACE2) for entry into host cells. Because ACE2 is a susceptibility factor for infection, we investigated how diabetic kidney disease and medications alter ACE2 receptor expression in kidneys. Single cell RNA profiling of kidney biopsies from healthy living donors and patients with diabetic kidney disease revealed ACE2 expression primarily in proximal tubular epithelial cells. This cell-specific localization was confirmed by in situ hybridization. ACE2 expression levels were unaltered by exposures to renin-angiotensin-aldosterone system inhibitors in diabetic kidney disease. Bayesian integrative analysis of a large compendium of public -omics datasets identified molecular network modules induced in ACE2-expressing proximal tubular epithelial cells in diabetic kidney disease (searchable at hb.flatironinstitute.org/covid-kidney) that were linked to viral entry, immune activation, endomembrane reorganization, and RNA processing. The diabetic kidney disease ACE2-positive proximal tubular epithelial cell module overlapped with expression patterns seen in SARS-CoV-2–infected cells. Similar cellular programs were seen in ACE2-positive proximal tubular epithelial cells obtained from urine samples of 13 hospitalized patients with COVID-19, suggesting a consistent ACE2-coregulated proximal tubular epithelial cell expression program that may interact with the SARS-CoV-2 infection processes. Thus SARS-CoV-2 receptor networks can seed further research into risk stratification and therapeutic strategies for COVID-19–related kidney damage.

We present the Cosmology and Astrophysics with MachinE Learning Simulations --CAMELS-- project. CAMELS is a suite of 4,233 cosmological simulations of $(25~h^{-1}{\rm Mpc})^3$ volume each: 2,184 state-of-the-art (magneto-)hydrodynamic simulations run with the AREPO and GIZMO codes, employing the same baryonic subgrid physics as the IllustrisTNG and SIMBA simulations, and 2,049 N-body simulations. The goal of the CAMELS project is to provide theory predictions for different observables as a function of cosmology and astrophysics, and it is the largest suite of cosmological (magneto-)hydrodynamic simulations designed to train machine learning algorithms. CAMELS contains thousands of different cosmological and astrophysical models by way of varying $\Omega_m$, $\sigma_8$, and four parameters controlling stellar and AGN feedback, following the evolution of more than 100 billion particles and fluid elements over a combined volume of $(400~h^{-1}{\rm Mpc})^3$. We describe the simulations in detail and characterize the large range of conditions represented in terms of the matter power spectrum, cosmic star formation rate density, galaxy stellar mass function, halo baryon fractions, and several galaxy scaling relations. We show that the IllustrisTNG and SIMBA suites produce roughly similar distributions of galaxy properties over the full parameter space but significantly different halo baryon fractions and baryonic effects on the matter power spectrum. This emphasizes the need for marginalizing over baryonic effects to extract the maximum amount of information from cosmological surveys. We illustrate the unique potential of CAMELS using several machine learning applications, including non-linear interpolation, parameter estimation, symbolic regression, data generation with Generative Adversarial Networks (GANs), dimensionality reduction, and anomaly detection.