Publications

We present a statistical learning framework for robust identification of differential equations from noisy spatio-temporal data. We address two issues that have so far limited the application of such methods, namely their robustness against noise and the need for manual parameter tuning, by proposing stability-based model selection to determine the level of regularization required for reproducible inference. This avoids manual parameter tuning and improves robustness against noise in the data. Our stability selection approach, termed PDE-STRIDE, can be combined with any sparsity-promoting regression method and provides an interpretable criterion for model component importance. We show that the particular combination of stability selection with the iterative hard-thresholding algorithm from compressed sensing provides a fast and robust framework for equation inference that outperforms previous approaches with respect to accuracy, amount of data required, and robustness. We illustrate the performance of PDE-STRIDE on a range of simulated benchmark problems, and we demonstrate the applicability of PDE-STRIDE on real-world data by considering purely data-driven inference of the protein interaction network for embryonic polarization in Caenorhabditis elegans. Using fluorescence microscopy images of C. elegans zygotes as input data, PDE-STRIDE is able to learn the molecular interactions of the proteins.

We present data structures and algorithms for native implementations of discrete convolution operators over Adaptive Particle Representations (APR) of images on parallel computer architectures. The APR is a content-adaptive image representation that locally adapts the sampling resolution to the image signal. It has been developed as an alternative to pixel representations for large, sparse images as they typically occur in fluorescence microscopy. It has been shown to reduce the memory and runtime costs of storing, visualizing, and processing such images. This, however, requires that image processing natively operates on APRs, without intermediately reverting to pixels. Designing efficient and scalable APR-native image processing primitives, however, is complicated by the APR’s irregular memory structure. Here, we provide the algorithmic building blocks required to efficiently and natively process APR images using a wide range of algorithms that can be formulated in terms of discrete convolutions. We show that APR convolution naturally leads to scale-adaptive algorithms that efficiently parallelize on multi-core CPU and GPU architectures. We quantify the speedups in comparison to pixel-based algorithms and convolutions on evenly sampled data. We achieve pixel-equivalent throughputs of up to 1TB/s on a single Nvidia GeForce RTX 2080 gaming GPU, requiring up to two orders of magnitude less memory than a pixel-based implementation.

Kidney Precision Medicine Project (KPMP) is building a spatially specified human kidney tissue atlas in health and disease with single-cell resolution. Here, we describe the construction of an integrated reference map of cells, pathways, and genes using unaffected regions of nephrectomy tissues and undiseased human biopsies from 56 adult subjects. We use single-cell/nucleus transcriptomics, subsegmental laser microdissection transcriptomics and proteomics, near-single-cell proteomics, 3D and CODEX imaging, and spatial metabolomics to hierarchically identify genes, pathways, and cells. Integrated data from these different technologies coherently identify cell types/subtypes within different nephron segments and the interstitium. These profiles describe cell-level functional organization of the kidney following its physiological functions and link cell subtypes to genes, proteins, metabolites, and pathways. They further show that messenger RNA levels along the nephron are congruent with the subsegmental physiological activity. This reference atlas provides a framework for the classification of kidney disease when multiple molecular mechanisms underlie convergent clinical phenotypes.

Although membranous nephropathy (MN) is one of the most common causes of nephrotic syndrome, the molecular characteristics of the kidney damage in MN remain poorly defined. In this study, the authors applied a machine-learning framework to predict diagnosis on the basis of gene expression in microdissected kidney tissue from patients with glomerulonephropathies. They found that MN has a glomerular transcriptional signature that distinguishes it from other glomerulonephropathies and identified a set of MN-specific genes differentially expressed across two independent cohorts and robustly recovered in an additional validation cohort. They also found the MN-specific genes are enriched in targets of transcription factor NF-κB and are predominantly expressed in podocytes. This work provides a molecular snapshot of MN and elucidates transcriptional alterations specific to this disease.

The cytoskeleton -- a collection of polymeric filaments, molecular motors, and crosslinkers -- is a foundational example of active matter, and in the cell assembles into organelles that guide basic biological functions. Simulation of cytoskeletal assemblies is an important tool for modeling cellular processes and understanding their surprising material properties. Here we present aLENS, a novel computational framework to surmount the limits of conventional simulation methods. We model molecular motors with crosslinking kinetics that adhere to a thermodynamic energy landscape, and integrate the system dynamics while efficiently and stably enforcing hard-body repulsion between filaments -- molecular potentials are entirely avoided in imposing steric constraints. Utilizing parallel computing, we simulate different mixtures of tens to hundreds of thousands of cytoskeletal filaments and crosslinking motors, recapitulating self-emergent phenomena such as bundle formation and buckling, and elucidating how motor type, thermal fluctuations, internal stresses, and confinement determine the evolution of active matter aggregates.

A conserved phase of gametogenesis is the development of oocytes and sperm within cell clusters (germline cysts) that arise through serial divisions of a founder cell. The resulting cell lineage trees (CLTs) exhibit diverse topologies across animals and can give rise to numerous emergent behaviors. Despite their centrality, sex-specific differences underlying the evolution and patterning of these cell trees are unknown. In Drosophila melanogaster, oocytes develop within a highly invariant and maximally branched 16-cell tree whose topology is constrained by the fusome – a branched membranous organelle critical for proper mitosis in females; the same division pattern and topology are widely thought to occur during spermatogenesis. Using highly-resolved three-dimensional reconstructions based on a supervised learning algorithm, we show that cell divisions in male cysts can deviate from the maximally branched pattern, leading to greater topological variability. Furthermore, in contrast to females, fusome fragmentation is common, suggesting germ cell mitoses can occur in its absence. These findings thus add to the repertoire of CLT formation strategies, highlighting the diversity of mechanisms employed during gametogenesis in the animal kingdom.

Quaternions are important for a wide variety of rotation-related problems in computer graphics, machine vision, and robotics. We study the nontrivial geometry of the relationship between quaternions and rotation matrices by exploiting the adjugate matrix of the characteristic equation of a related eigenvalue problem to obtain the manifold of the space of a quaternion eigenvector. We argue that quaternions parameterized by their corresponding rotation matrices cannot be expressed, for example, in machine learning tasks, as single-valued functions: the quaternion solution must instead be treated as a manifold, with different algebraic solutions for each of several single-valued sectors represented by the adjugate matrix. We conclude with novel constructions exploiting the quaternion adjugate variables to revisit several classic pose estimation applications: 2D point-cloud matching, 2D point-cloud-to-projection matching, 3D point-cloud matching, 3D orthographic point-cloud-to-projection matching, and 3D perspective point-cloud-to-projection matching. We find an exact solution to the 3D orthographic least squares pose extraction problem, and apply it successfully also to the perspective pose extraction problem with results that improve on existing methods.

Continuum kinetic theories provide an important tool for the analysis and simulation of particle suspensions. When those particles are anisotropic, the addition of a particle orientation vector to the kinetic description yields a dimensional theory which becomes intractable to simulate, especially in three dimensions or near states where the particles are highly aligned. Coarse-grained theories that track only moments of the particle distribution functions provide a more efficient simulation framework, but require closure assumptions. For the particular case where the particles are apolar, the Bingham closure has been found to agree well with the underlying kinetic theory; yet the closure is non-trivial to compute, requiring the solution of an often nearly-singular nonlinear equation at every spatial discretization point at every timestep. In this paper, we present a robust, accurate, and efficient numerical scheme for evaluating the Bingham closure, with a controllable error/efficiency tradeoff. To demonstrate the utility of the method, we carry out high-resolution simulations of a coarse-grained continuum model for a suspension of active particles in parameter regimes inaccessible to kinetic theories. Analysis of these simulations reveals that inaccurately computing the closure can act to effectively limit spatial resolution in the coarse-grained fields. Pushing these simulations to the high spatial resolutions enabled by our method reveals a coupling between vorticity and topological defects in the suspension director field, as well as signatures of energy transfer between scales in this active fluid model.

Neurons from layer II of the entorhinal cortex (ECII) are the first to accumulate tau protein aggregates and degenerate during prodromal Alzheimer’s disease. Here, we use a data-driven functional genomics approach to model ECII neurons in silico and identify the proto-oncogene DEK as a potential driver of tau pathology. By modulating DEK levels in EC neurons in vitro and in vivo, we first validate the accuracy and cell-type specificity of our network predictions. We then show that Dek silencing changes the inducibility of immediate early genes and alters neuron excitability, leading to dysregulation of neuronal plasticity genes. We further find that loss of function of DEK leads to tau accumulation in the soma of ECII neurons, reactivity of surrounding microglia, and eventually microglia-mediated neuron loss. This study validates a pathological gene discovery tool that opens new therapeutic avenues and sheds light on a novel pathway driving tau pathology in vulnerable neurons.

Labeled protein-based biomaterials have become popular for various biomedical applications such as tissue-engineered, therapeutic, and diagnostic scaffolds. Labeling of protein biomaterials, including with ultrasmall superparamagnetic iron oxide (USPIO) nanoparticles, has enabled a wide variety of imaging and therapeutic techniques. These USPIO-based biomaterials are widely studied in magnetic resonance imaging (MRI), thermotherapy, and magnetically-driven drug delivery, which provide a method for direct and non-invasive monitoring of implants or drug delivery agents. Where most developments have been made using polymers or collagen hydrogels, shown here is the use of a rationally designed protein as the building block for a meso-scale fiber. While USPIOs have been chemically conjugated to antibodies, glycoproteins, and tissue-engineered scaffolds for targeting or improved biocompatibility and stability, these constructs have predominantly served as diagnostic agents and often involve harsh conditions for USPIO synthesis. Here, we present an engineered protein–iron oxide hybrid material comprised of an azide-functionalized coiled-coil protein with small molecule binding capacity conjugated via bioorthogonal azide–alkyne cycloaddition to an alkyne-bearing iron oxide templating peptide, CMms6, for USPIO biomineralization under mild conditions. The coiled-coil protein, dubbed Q, has been previously shown to form nanofibers and, upon small molecule binding, further assembles into mesofibers via encapsulation and aggregation. The resulting hybrid material is capable of doxorubicin encapsulation as well as sensitive weighted MRI darkening for strong imaging capability that is uniquely derived from a coiled-coil protein.