492 Publications

Interpretable neural architecture search and transfer learning for understanding CRISPR–Cas9 off-target enzymatic reactions

Finely-tuned enzymatic pathways control cellular processes, and their dysregulation can lead to disease. Creating predictive and interpretable models for these pathways is challenging because of the complexity of the pathways and of the cellular and genomic contexts. Here we introduce Elektrum, a deep learning framework which addresses these challenges with data-driven and biophysically interpretable models for determining the kinetics of biochemical systems. First, it uses in vitro kinetic assays to rapidly hypothesize an ensemble of high-quality Kinetically Interpretable Neural Networks (KINNs) that predict reaction rates. It then employs a novel transfer learning step, where the KINNs are inserted as intermediary layers into deeper convolutional neural networks, fine-tuning the predictions for reaction-dependent in vivo outcomes. Elektrum makes effective use of the limited, but clean in vitro data and the complex, yet plentiful in vivo data that captures cellular context. We apply Elektrum to predict CRISPR-Cas9 off-target editing probabilities and demonstrate that Elektrum achieves state-of-the-art performance, regularizes neural network architectures, and maintains physical interpretability

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Confirmations, correlatons and instabilities of a flexible fiber in an active fluid

S. Weady, D. Stein, Alexandra Zidovska, M. Shelley

Fluid-structure interactions between active and passive components are important for many biological systems to function. A particular example is chromatin in the cell nucleus, where ATP-powered processes drive coherent motions of the chromatin fiber over micron lengths. Motivated by this system, we develop a multiscale model of a long flexible polymer immersed in a suspension of active force dipoles as an analog to a chromatin fiber in an active fluid – the nucleoplasm. Linear analysis identifies an orientational instability driven by hydrodynamic and alignment interactions between the fiber and the suspension, and numerical simulations show activity can drive coherent motions and structured conformations. These results demonstrate how active and passive components, connected through fluid-structure interactions, can generate coherent structures and self-organize on large scales.

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December 6, 2023

Uniqueness and characteristic flow for a non strictly convex singular variational problem

Jean-FrançoisBabadjian, G. Francfort

This work addresses the question of uniqueness of the minimizers of a convex but not strictly convex integral functional with linear growth in a two-dimensional setting. The integrand -- whose precise form derives directly from the theory of perfect plasticity -- behaves quadratically close to the origin and grows linearly once a specific threshold is reached. Thus, in contrast with the only existing literature on uniqueness for functionals with linear growth, that is that which pertains to the generalized least gradient, the integrand is not a norm. We make use of hyperbolic conservation laws hidden in the structure of the problem to tackle uniqueness. Our argument strongly relies on the regularity of a vector field -- the Cauchy stress in the terminology of perfect plasticity -- which allows us to define characteristic lines, and then to employ the method of characteristics. Using the detailed structure of the characteristic landscape evidenced in our preliminary study \cite{BF}, we show that this vector field is actually continuous, save for possibly two points. The different behaviors of the energy density at zero and at infinity imply an inequality constraint on the Cauchy stress. Under a barrier type convexity assumption on the set where the inequality constraint is saturated, we show that uniqueness holds for pure Dirichlet boundary data, a stronger result than that of uniqueness for a given trace on the whole boundary since our minimizers can fail to attain the boundary data.

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2023

A dynamical model of growth and maturation in Drosophila

John J. Tyson , Amirali Monshizadeh , S. Shvartsman, Alexander W. Shingleton

The decision to stop growing and mature into an adult is a critical point in development that determines adult body size, impacting multiple aspects of an adult’s biology. In many animals, growth cessation is a consequence of hormone release that appears to be tied to the attainment of a particular body size or condition. Nevertheless, the size-sensing mechanism animals use to initiate hormone synthesis is poorly understood. Here, we develop a simple mathematical model of growth cessation in Drosophila melanogaster, which is ostensibly triggered by the attainment of a critical weight (CW) early in the last instar. Attainment of CW is correlated with the synthesis of the steroid hormone ecdysone, which causes a larva to stop growing, pupate, and metamorphose into the adult form. Our model suggests that, contrary to expectation, the size-sensing mechanism that initiates metamorphosis occurs before the larva reaches CW; that is, the critical-weight phenomenon is a downstream consequence of an earlier size-dependent developmental decision, not a decision point itself. Further, this size-sensing mechanism does not require a direct assessment of body size but emerges from the interactions between body size, ecdysone, and nutritional signaling. Because many aspects of our model are evolutionarily conserved among all animals, the model may provide a general framework for understanding how animals commit to maturing from their juvenile to adult form.

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Morphogens enable interacting supracellular phases that generate organ architecture

Sichen Yang , Karl H. Palmquist, P. Miller, et al.

During vertebrate organ morphogenesis, large collectives of cells robustly self-organize to form architectural units (bones, villi, follicles) whose form persists into adulthood. Over the past few decades, mechanisms of organ morphogenesis have been developed predominantly through molecular, genetic, and cellular frameworks. More recently, there has been a resurgence of interest in collective cell and tissue mechanics during organ formation. This approach has amplified the need to clarify and unambiguously link events across biological length scales. Doing so may require reassessing canonical models that continue to guide the field. The most recognized model for organ formation centers around morphogens as determinants of gene expression and morphological patterns. The classical view of a morphogen is that morphogen gradients specify differential gene expression in a distinct spatial order. Because morphogen expression colocalizes with emerging feather and hair follicles, the skin has served as a paradigmatic example of such morphogen prepatterning mechanisms.

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November 24, 2023

Microscopic Theory, Analysis, and Interpretation of Conductance Histograms in Molecular Junctions

Leopoldo Mejía, P. Cossio, Ignacio Franco

Molecular electronics break-junction experiments are widely used to investigate fundamental physics and chemistry at the nanoscale. Reproducibility in these experiments relies on measuring conductance on thousands of freshly formed molecular junctions, yielding a broad histogram of conductance events. Experiments typically focus on the most probable conductance, while the information content of the conductance histogram has remained unclear. Here we develop a microscopic theory for the conductance histogram by merging the theory of force-spectroscopy with molecular conductance. The procedure yields analytical equations that accurately fit the conductance histogram of a wide range of molecular junctions and augments the information content that can be extracted from them. Our formulation captures contributions to the conductance dispersion due to conductance changes during the mechanical elongation inherent to the experiments. In turn, the histogram shape is determined by the non-equilibrium stochastic features of junction rupture and formation. The microscopic parameters in the theory capture the junction’s electromechanical properties and can be isolated from separate conductance and rupture force (or junction-lifetime) measurements. The predicted behavior can be used to test the range of validity of the theory, understand the conductance histograms, design molecular junction experiments with enhanced resolution and molecular devices with more reproducible conductance properties.

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Bacterial diffusion in disordered media, by forgetting the media

We study bacterial diffusion in disordered porous media. Interactions with obstacles, at unknown locations, make this problem challenging. We approach it by abstracting the environment to cell states with memoryless transitions. With this, we derive an effective diffusivity that agrees well with simulations in explicit geometries. The diffusivity is non-monotonic, and we solve the optimal run length. We also find a rescaling that causes all of the theory and simulations to collapse. Our results indicate that a small set of microscopic features captures bacterial diffusion in disordered media.

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November 17, 2023

Sculpting the Sphinx

Samuel Boury, S. Weady, Leif Ristroph

This paper is associated with a poster winner of a 2022 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion.

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A model of replicating coupled oscillators generates naturally occurring cell networks

When a founder cell and its progeny divide with incomplete cytokinesis, a network forms in which each intercellular bridge corresponds to a past mitotic event. Such networks are required for gamete production in many animals, and different species have evolved diverse final network topologies. Although mechanisms regulating network assembly have been identified in particular organisms, we lack a quantitative framework to understand network assembly and inter-species variability. Motivated by cell networks responsible for oocyte production in invertebrates, where the final topology is typically invariant within each species, we devised a mathematical model for generating cell networks, in which each node is an oscillator and, after a full cycle, the node produces a daughter to which it remains connected. These cell cycle oscillations are transient and coupled via diffusion over the edges of the network. By variation of three biologically motivated parameters, our model generates nearly all such networks currently reported across invertebrates. Furthermore, small parameter variations can rationalize cases of intra-species variation. Because cell networks outside of the ovary often form less deterministically, we propose model generalizations to account for sources of stochasticity.

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Cytoplasmic stirring by active carpets

Large cells often rely on cytoplasmic flows for intracellular transport, maintaining homeostasis, and positioning cellular components. Understanding the mechanisms of these flows is essential for gaining insights into cell function, developmental processes, and evolutionary adaptability. Here, we focus on a class of self-organized cytoplasmic stirring mechanisms that result from fluid-structure interactions between cytoskeletal elements at the cell cortex. Drawing inspiration from streaming flows in late-stage fruit fly oocytes, we propose an analytically tractable active carpet theory. This model deciphers the origins and three-dimensional spatio-temporal organization of such flows. Through a combination of simulations and weakly nonlinear theory, we establish the pathway of the streaming flow to its global attractor: a cell-spanning vortical twister. Our study reveals the inherent symmetries of this emergent flow, its low-dimensional structure, and illustrates how complex fluid-structure interaction aligns with classical solutions in Stokes flow. This framework can be easily adapted to elucidate a broad spectrum of self-organized, cortex-driven intracellular flows.

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November 8, 2023
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