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 spatiotemporal 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.

Computational tools for cellular scale biophysics.

Mathematical models are indispensable for disentangling the interactions through which biological components work together to generate the forces and flows that position, mix, and distribute proteins, nutrients, and organelles within the cell. To illuminate the ever more specific questions studied at the edge of biological inquiry, such models inevitably become more complex. Solving, simulating, and learning from these more realistic models requires the development of new analytic techniques, numerical methods, and scalable software. In this review, we discuss some recent developments in tools for understanding how large numbers of cytoskeletal filaments, driven by molecular motors and interacting with the cytoplasm and other structures in their environment, generate fluid flows, instabilities, and material deformations which help drive crucial cellular processes.

Mechanics of spindle orientation in human mitotic cells is determined by pulling forces on astral microtubules and clustering of cortical dynein.

The forces that orient the spindle in human cells remain poorly understood due to a lack of direct mechanical measurements in mammalian systems. We use magnetic tweezers to measure the force on human mitotic spindles. Combining the spindle's measured resistance to rotation, the speed at which it rotates after laser ablating astral microtubules, and estimates of the number of ablated microtubules reveals that each microtubule contacting the cell cortex is subject to ∼5 pN of pulling force, suggesting that each is pulled on by an individual dynein motor. We find that the concentration of dynein at the cell cortex and extent of dynein clustering are key determinants of the spindle's resistance to rotation, with little contribution from cytoplasmic viscosity, which we explain using a biophysically based mathematical model. This work reveals how pulling forces on astral microtubules determine the mechanics of spindle orientation and demonstrates the central role of cortical dynein clustering.

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.

Clustering of cortical dynein regulates the mechanics of spindle orientation in human mitotic cells.

The forces which orient the spindle in human cells remain poorly understood due to a lack of direct mechanical measurements in mammalian systems. We use magnetic tweezers to measure the force on human mitotic spindles. Combining the spindle's measured resistance to rotation, the speed it rotates after laser ablating astral microtubules, and estimates of the number of ablated microtubules reveals that each microtubule contacting the cell cortex is subject to ~1 pN of pulling force, suggesting that each is pulled on by an individual dynein motor. We find that the concentration of dynein at the cell cortex and extent of dynein clustering are key determinants of the spindle's resistance to rotation, with little contribution from cytoplasmic viscosity, which we explain using a biophysically based mathematical model. This work reveals how pulling forces on astral microtubules determine the mechanics of spindle orientation and demonstrates the central role of cortical dynein clustering.

A note about convected time derivatives for flows of complex fluids.

We present a direct derivation of the typical time derivatives used in a continuum description of complex fluid flows, harnessing the principles of the kinematics of line elements. The evolution of the microstructural conformation tensor in a flow and the physical interpretation of different derivatives then follow naturally.

Reversing Neuromuscular Blockade without Nerve Stimulator Guidance in a Postsurgical ICU-An Observational Study.

We aimed to determine if not using residual neuromuscular blockade (RNB) analysis to guide neuromuscular blockade reversal administration in the postsurgical ICU resulted in consequences related to residual weakness. This single-center, prospective study evaluated 104 patients arriving in a postcardiac surgical ICU. After demonstrating spontaneous movement and T > 35.5 °C, all patients underwent RNB evaluation, and neostigmine/glycopyrrolate was then administered. When patients later demonstrated an adequate Rapid Shallow Breathing Index, negative inspiratory force generation, and arterial blood gas values with minimal mechanical ventilatory support, RNB evaluation was repeated in 94 of the 104 patients, and all patients were extubated. Though RNB evaluation was performed, patients were extubated without considering these results. Eleven of one hundred four patients had not achieved a Train-of-Four (TOF) count of four prior to receiving neostigmine. Twenty of ninety-four patients demonstrated a TOF ratio ≤ 90% prior to extubation. Three patients received unplanned postextubation adjunct respiratory support-one for obvious respiratory weakness, one for pain-related splinting compounding baseline disordered breathing but without obvious benefit from BiPAP, and one for a new issue requiring surgery. Residual neuromuscular weakness may have been unrecognized before extubation in 1 of 104 patients administered neostigmine without RNB analysis. ICU-level care may mitigate consequences in such cases.

Self-organized intracellular twisters.

Life in complex systems, such as cities and organisms, comes to a standstill when global coordination of mass, energy, and information flows is disrupted. Global coordination is no less important in single cells, especially in large oocytes and newly formed embryos, which commonly use fast fluid flows for dynamic reorganization of their cytoplasm. Here, we combine theory, computing, and imaging to investigate such flows in the Drosophila oocyte, where streaming has been proposed to spontaneously arise from hydrodynamic interactions among cortically anchored microtubules loaded with cargo-carrying molecular motors. We use a fast, accurate, and scalable numerical approach to investigate fluid-structure interactions of 1000s of flexible fibers and demonstrate the robust emergence and evolution of cell-spanning vortices, or twisters. Dominated by a rigid body rotation and secondary toroidal components, these flows are likely involved in rapid mixing and transport of ooplasmic components.

Self-organized intracellular twisters.

Life in complex systems, such as cities and organisms, comes to a standstill when global coordination of mass, energy, and information flows is disrupted. Global coordination is no less important in single cells, especially in large oocytes and newly formed embryos, which commonly use fast fluid flows for dynamic reorganization of their cytoplasm. Here, we combine theory, computing, and imaging to investigate such flows in the Drosophila oocyte, where streaming has been proposed to spontaneously arise from hydrodynamic interactions among cortically anchored microtubules loaded with cargo-carrying molecular motors. We use a fast, accurate, and scalable numerical approach to investigate fluid-structure interactions of 1000s of flexible fibers and demonstrate the robust emergence and evolution of cell-spanning vortices, or twisters. Dominated by a rigid body rotation and secondary toroidal components, these flows are likely involved in rapid mixing and transport of ooplasmic components.

Collective Motion and Pattern Formation in Phase-Synchronizing Active Fluids.

Many active particles, such as swimming micro-organisms or motor proteins, do work on their environment by going though a periodic sequence of shapes. Interactions between particles can lead to synchronization of their duty cycles. Here, we study the collective dynamics of a suspension of active particles coupled through hydrodynamics. We find that at high enough density the system transitions to a state of collective motion by a mechanism that is distinct from other instabilities in active matter systems. Second, we demonstrate that the emergent nonequilibrium states feature stationary chimera patterns in which synchronized and phase-isotropic regions coexist. Third, we show that in confinement, oscillatory flows and robust unidirectional pumping states exist, and can be selected by choice of alignment boundary conditions. These results point toward a new route to collective motion and pattern formation and could guide the design of new active materials.

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. Developing 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 that 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 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. We apply Elektrum to predict CRISPR-Cas9 off-target editing probabilities and demonstrate that Elektrum achieves improved performance, regularizes neural network architectures and maintains physical interpretability.

Toward the cellular-scale simulation of motor-driven cytoskeletal assemblies.

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 Living Ensemble Simulator), a novel computational framework designed 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 tens to hundreds of thousands of cytoskeletal filaments and crosslinking motors, recapitulating emergent phenomena such as bundle formation and buckling. This simulation framework can help elucidate how motor type, thermal fluctuations, internal stresses, and confinement determine the evolution of cytoskeletal active matter.

Enhanced clamshell swimming with asymmetric beating at low Reynolds number.

A single flexible filament can be actuated to escape from the scallop theorem and generate net propulsion at low Reynolds number. In this work, we study the dynamics of a simple boundary-driven multi-filament swimmer, a two-arm clamshell actuated at the hinged point, using a nonlocal slender body approximation with hydrodynamic interactions. We first consider an elastic clamshell consisted of flexible filaments with intrinsic curvature, and then build segmental models consisted of rigid segments connected by different mechanical joints with different forms of response torques. The simplicity of the system allows us to fully explore the effect of various parameters on the swimming performance. Optimal included angles and elastoviscous numbers are identified. The segmental models capture the characteristic dynamics of the elastic clamshell. We further demonstrate how the swimming performance can be significantly enhanced by the asymmetric beating patterns induced by biased torques.

Hyperuniformity and phase enrichment in vortex and rotor assemblies.

Ensembles of particles rotating in a two-dimensional fluid can exhibit chaotic dynamics yet develop signatures of hidden order. Such rotors are found in the natural world spanning vastly disparate length scales - from the rotor proteins in cellular membranes to models of atmospheric dynamics. Here we show that an initially random distribution of either driven rotors in a viscous membrane, or ideal vortices with minute perturbations, spontaneously self assemble into a distinct arrangement. Despite arising from drastically different physics, these systems share a Hamiltonian structure that sets geometrical conservation laws resulting in prominent structural states. We find that the rotationally invariant interactions isotropically suppress long-wavelength fluctuations - a hallmark of a disordered hyperuniform material. With increasing area fraction, the system orders into a hexagonal lattice. In mixtures of two co-rotating populations, the stronger population will gain order from the other and both will become phase enriched. Finally, we show that classical 2D point vortex systems arise as exact limits of the experimentally accessible microscopic membrane rotors, yielding a new system through which to study topological defects.

A multiscale biophysical model gives quantized metachronal waves in a lattice of beating cilia.

Motile cilia are slender, hair-like cellular appendages that spontaneously oscillate under the action of internal molecular motors and are typically found in dense arrays. These active filaments coordinate their beating to generate metachronal waves that drive long-range fluid transport and locomotion. Until now, our understanding of their collective behavior largely comes from the study of minimal models that coarse grain the relevant biophysics and the hydrodynamics of slender structures. Here we build on a detailed biophysical model to elucidate the emergence of metachronal waves on millimeter scales from nanometer-scale motor activity inside individual cilia. Our study of a one-dimensional lattice of cilia in the presence of hydrodynamic and steric interactions reveals how metachronal waves are formed and maintained. We find that, in homogeneous beds of cilia, these interactions lead to multiple attracting states, all of which are characterized by an integer charge that is conserved. This even allows us to design initial conditions that lead to predictable emergent states. Finally, and very importantly, we show that, in nonuniform ciliary tissues, boundaries and inhomogeneities provide a robust route to metachronal waves.

Active condensation of filaments under spatial confinement.

Living systems exhibit self-organization, a phenomenon that enables organisms to perform functions essential for life. The interior of living cells is a crowded environment in which the self-assembly of cytoskeletal networks is spatially constrained by membranes and organelles. Cytoskeletal filaments undergo active condensation in the presence of crosslinking motor proteins. In past studies, confinement has been shown to alter the morphology of active condensates. Here, we perform simulations to explore systems of filaments and crosslinking motors in a variety of confining geometries. We simulate spatial confinement imposed by hard spherical, cylindrical, and planar boundaries. These systems exhibit non-equilibrium condensation behavior where crosslinking motors condense a fraction of the overall filament population, leading to coexistence of vapor and condensed states. We find that the confinement lengthscale modifies the dynamics and condensate morphology. With end-pausing crosslinking motors, filaments self-organize into half asters and fully-symmetric asters under spherical confinement, polarity-sorted bilayers and bottle-brush-like states under cylindrical confinement, and flattened asters under planar confinement. The number of crosslinking motors controls the size and shape of condensates, with flattened asters becoming hollow and ring-like for larger motor number. End pausing plays a key role affecting condensate morphology: systems with end-pausing motors evolve into aster-like condensates while those with non-end-pausing crosslinking motor proteins evolve into disordered clusters and polarity-sorted bundles.

Tissue fluidity mediated by adherens junction dynamics promotes planar cell polarity-driven ommatidial rotation.

The phenomenon of tissue fluidity-cells' ability to rearrange relative to each other in confluent tissues-has been linked to several morphogenetic processes and diseases, yet few molecular regulators of tissue fluidity are known. Ommatidial rotation (OR), directed by planar cell polarity signaling, occurs during Drosophila eye morphogenesis and shares many features with polarized cellular migration in vertebrates. We utilize in vivo live imaging analysis tools to quantify dynamic cellular morphologies during OR, revealing that OR is driven autonomously by ommatidial cell clusters rotating in successive pulses within a permissive substrate. Through analysis of a rotation-specific nemo mutant, we demonstrate that precise regulation of junctional E-cadherin levels is critical for modulating the mechanical properties of the tissue to allow rotation to progress. Our study defines Nemo as a molecular tool to induce a transition from solid-like tissues to more viscoelastic tissues broadening our molecular understanding of tissue fluidity.

Lévy Walks and Path Chaos in the Dispersal of Elongated Structures Moving across Cellular Vortical Flows.

In cellular vortical flows, namely arrays of counterrotating vortices, short but flexible filaments can show simple random walks through their stretch-coil interactions with flow stagnation points. Here, we study the dynamics of semirigid filaments long enough to broadly sample the vortical field. Using simulation, we find a surprising variety of long-time transport behavior-random walks, ballistic transport, and trapping-depending upon the filament's relative length and effective flexibility. Moreover, we find that filaments execute Lévy walks whose diffusion exponents generally decrease with increasing filament length, until transitioning to Brownian walks. Lyapunov exponents likewise increase with length. Even completely rigid filaments, whose dynamics is finite dimensional, show a surprising variety of transport states and chaos. Fast filament dispersal is related to an underlying geometry of "conveyor belts." Evidence for these various transport states is found in experiments using arrays of counterrotating rollers, immersed in a fluid and transporting a flexible ribbon.

Metallic microswimmers driven up the wall by gravity.

Experiments on autophoretic bimetallic nanorods propelling within a fuel of hydrogen peroxide show that tail-heavy swimmers preferentially orient upwards and ascend along inclined planes. We show that such gravitaxis is strongly facilitated by interactions with solid boundaries, allowing even ultraheavy microswimmers to climb nearly vertical surfaces. Theory and simulations show that the buoyancy or gravitational torque that tends to align the rods is reinforced by a fore-aft drag asymmetry induced by hydrodynamic interactions with the wall.

The many behaviors of deformable active droplets.

Active fluids consume fuel at the microscopic scale, converting this energy into forces that can drive macroscopic motions over scales far larger than their microscopic constituents. In some cases, the mechanisms that give rise to this phenomenon have been well characterized, and can explain experimentally observed behaviors in both bulk fluids and those confined in simple stationary geometries. More recently, active fluids have been encapsulated in viscous drops or elastic shells so as to interact with an outer environment or a deformable boundary. Such systems are not as well understood. In this work, we examine the behavior of droplets of an active nematic fluid. We study their linear stability about the isotropic equilibrium over a wide range of parameters, identifying regions in which different modes of instability dominate. Simulations of their full dynamics are used to identify their nonlinear behavior within each region. When a single mode dominates, the droplets behave simply: as rotors, swimmers, or extensors. When parameters are tuned so that multiple modes have nearly the same growth rate, a pantheon of modes appears, including zigzaggers, washing machines, wanderers, and pulsators.