Publications

The evolution of landscapes, landforms, and other natural structures involves highly interactive physical and chemical processes that often lead to intriguing shapes and recurring motifs. Particularly intricate and fine-scale features characterize the so-called karst morphologies formed by mineral dissolution into water. An archetypal form is the tall, slender, and sharply tipped karst pinnacle or rock spire that appears in multitudes in striking landforms called stone forests, but whose formative mechanisms remain unclear due to complex, fluctuating, and incompletely understood developmental conditions. Here, we demonstrate that exceedingly sharp spires also form under the far-simpler conditions of a solid dissolving into a surrounding liquid. Laboratory experiments on solidified sugars in water show that needlelike pinnacles, as well as bed-of-nails-like arrays of pinnacles, emerge robustly from the dissolution of solids with smooth initial shapes. Although the liquid is initially quiescent and no external flow is imposed, persistent flows are generated along the solid boundary as dense, solute-laden fluid descends under gravity. We use these observations to motivate a mathematical model that links such boundary-layer flows to the shape evolution of the solid. Dissolution induces these natural convective flows that, in turn, enhance dissolution rates, and simulations show that this feedback drives the shape toward a finite-time singularity or blow-up of apex curvature that is cut off once the pinnacle tip reaches microscales. This autogenic mechanism produces ultra-fine structures as an attracting state or natural consequence of the coupled processes at work in the closed solid-fluid system.

Registration of histology images from multiple sources is a pressing problem in large-scale studies of spatial -omics data. Researchers often perform “common coordinate registration,” akin to segmentation, in which samples are partitioned based on tissue type to allow for quantitative comparison of similar regions across samples. Accuracy in such registration requires both high image resolution and global awareness, which mark a difficult balancing act for contemporary deep learning architectures. We present a novel convolutional neural network (CNN) architecture that combines (1) a local classification CNN that extracts features from image patches sampled sparsely across the tissue surface, and (2) a global segmentation CNN that operates on these extracted features. This hybrid network can be trained in an end-to-end manner, and we demonstrate its relative merits over competing approaches on a reference histology dataset as well as two published spatial transcriptomics datasets. We believe that this paradigm will greatly enhance our ability to process spatial -omics data, and has general purpose applications for the processing of high-resolution histology images on commercially available GPUs.

Living matter moves, deforms, and organizes itself. In cells this is made possible by networks of polymer filaments and crosslinking molecules that connect filaments to each other and that act as motors to do mechanical work on the network. For the case of highly cross-linked filament networks, we discuss how the material properties of assemblies emerge from the forces exerted by microscopic agents. First, we introduce a phenomenological model that characterizes the forces that crosslink populations exert between filaments. Second, we derive a theory that predicts the material properties of highly crosslinked filament networks, given the crosslinks present. Third, we discuss which properties of crosslinks set the material properties and behavior of highly crosslinked cytoskeletal networks. The work presented here, will enable the better understanding of cytoskeletal mechanics and its molecular underpinnings. This theory is also a first step towards a theory of how molecular perturbations impact cytoskeletal organization, and provides a framework for designing cytoskeletal networks with desirable properties in the lab.

A major obstacle to treating Alzheimer’s disease (AD) is our lack of understanding of the molecular mechanisms underlying selective neuronal vulnerability, a key characteristic of the disease. Here, we present a framework integrating high-quality neuron-type-specific molecular profiles across the lifetime of the healthy mouse, which we generated using bacTRAP, with postmortem human functional genomics and quantitative genetics data. We demonstrate human-mouse conservation of cellular taxonomy at the molecular level for neurons vulnerable and resistant in AD, identify specific genes and pathways associated with AD neuropathology, and pinpoint a specific functional gene module underlying selective vulnerability, enriched in processes associated with axonal remodeling, and affected by amyloid accumulation and aging. We have made all cell-type-specific profiles and functional networks available at http://alz.princeton.edu. Overall, our study provides a molecular framework for understanding the complex interplay between Aβ, aging, and neurodegeneration within the most vulnerable neurons in AD.

A generic flow distribution network typically does not deliver its load at a uniform rate across a service area, instead oversupplying regions near the nutrient source while leaving downstream regions undersupplied. In this work we demonstrate how a local adaptive rule coupling tissue growth with nutrient density results in a flow network that self-organizes to deliver nutrients uniformly. This geometric adaptive rule can be generalized and imported to mechanics-based adaptive models to address the effects spatial gradients in nutrients or growth factors in tissues.

Loss of normal tissue architecture is a hallmark of oncogenic transformation1. In developing organisms, tissues architectures are sculpted by mechanical forces during morphogenesis2. However, the origins and consequences of tissue architecture during tumorigenesis remain elusive. In skin, premalignant basal cell carcinomas form ‘buds’, while invasive squamous cell carcinomas initiate as ‘folds’. Here, using computational modelling, genetic manipulations and biophysical measurements, we identify the biophysical underpinnings and biological consequences of these tumour architectures. Cell proliferation and actomyosin contractility dominate tissue architectures in monolayer, but not multilayer, epithelia. In stratified epidermis, meanwhile, softening and enhanced remodelling of the basement membrane promote tumour budding, while stiffening of the basement membrane promotes folding. Additional key forces stem from the stratification and differentiation of progenitor cells. Tumour-specific suprabasal stiffness gradients are generated as oncogenic lesions progress towards malignancy, which we computationally predict will alter extensile tensions on the tumour basement membrane. The pathophysiologic ramifications of this prediction are profound. Genetically decreasing the stiffness of basement membranes increases membrane tensions in silico and potentiates the progression of invasive squamous cell carcinomas in vivo. Our findings suggest that mechanical forces—exerted from above and below progenitors of multilayered epithelia—function to shape premalignant tumour architectures and influence tumour progression.

We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle collisions. This algorithm extends the well-known complementarity method for non-smooth multi-body dynamics to resolve collisions in dense rigid body suspensions. This approach formulates the collision resolution problem as a linear complementarity problem with geometric `non-overlapping' constraints imposed at each timestep. It is then reformulated as a constrained quadratic programming problem and the Barzilai-Borwein projected gradient descent method is applied for its solution. This framework is designed to be applicable for any convex particle shape, e.g., spheres and spherocylinders, and applicable to any Stokes mobility solver, including the Rotne-Prager-Yamakawa approximation, Stokesian Dynamics, and PDE solvers (e.g., boundary integral and immersed boundary methods). In particular, this method imposes Newton's Third Law and records the entire contact network. Further, we describe a fast, parallel, and spectrally-accurate boundary integral method tailored for spherical particles, capable of resolving lubrication effects. We show weak and strong parallel scalings up to 8×104 particles with approximately 4×107 degrees of freedom on 1792 cores. We demonstrate the versatility of this framework with several examples, including sedimentation of particle clusters, and active matter systems composed of ensembles of particles driven to rotate.

The translational power of human microbiome studies is limited by high interindividual variation. We describe a dimensionality reduction tool, compositional tensor factorization (CTF), that incorporates information from the same host across multiple samples to reveal patterns driving differences in microbial composition across phenotypes. CTF identifies robust patterns in sparse compositional datasets, allowing for the detection of microbial changes associated with specific phenotypes that are reproducible across datasets.

Fibrin is the three-dimensional mechanical scaffold of protective blood clots that stop bleeding and pathological thrombi that obstruct blood vessels. Fibrin must be mechanically tough to withstand rupture, after which life-threatening pieces (thrombotic emboli) are carried downstream by blood flow. Despite multiple studies on fibrin viscoelasticity, mechanisms of fibrin rupture remain unknown. Here, we examined mechanically and structurally the strain-driven rupture of human blood plasma–derived fibrin clots where clotting was triggered with tissue factor. Toughness, i.e., resistance to rupture, quantified by the critical energy release rate (a measure of the propensity for clot embolization) of physiologically relevant fibrin gels was determined to be 7.6 ± 0.45 J/m2. Finite element (FE) simulations using fibrin material models that account for forced protein unfolding independently supported this measured toughness and showed that breaking of fibers ahead the crack at a critical stretch is the mechanism of rupture of blood clots, including thrombotic embolization.

Tissue morphogenesis relies on repeated use of dynamic behaviors at the levels of intracellular structures, individual cells, and cell groups. Rapidly accumulating live imaging datasets make it increasingly important to formalize and automate the task of mapping recurrent dynamic behaviors (motifs), as it is done in speech recognition and other data mining applications. Here, we present a “template-based search” approach for accurate mapping of sub- to multi-cellular morphogenetic motifs using a time series data mining framework. We formulated the task of motif mapping as a subsequence matching problem and solved it using dynamic time warping, while relying on high throughput graph-theoretic algorithms for efficient exploration of the search space. This formulation allows our algorithm to accurately identify the complete duration of each instance and automatically label different stages throughout its progress, such as cell cycle phases during cell division. To illustrate our approach, we mapped cell intercalations during germband extension in the early Drosophila embryo. Our framework enabled statistical analysis of intercalary cell behaviors in wild-type and mutant embryos, comparison of temporal dynamics in contracting and growing junctions in different genotypes, and the identification of a novel mode of iterative cell intercalation. Our formulation of tissue morphogenesis using time series opens new avenues for systematic decomposition of tissue morphogenesis.