Publications

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 full 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.

Cytoskeletal networks are the main actuators of cellular mechanics, and a foundational example for active matter physics. In cytoskeletal networks, motion is generated on small scales by filaments that push and pull on each other via molecular-scale motors. These local actuations give rise to large-scale stresses and motion. To understand how microscopic processes can give rise to self-organized behavior on larger scales it is important to consider what mechanisms mediate long-ranged mechanical interactions in the systems. Two scenarios have been considered in the recent literature. The first scenario is systems that are relatively sparse, in which most of the large-scale momentum transfer is mediated by the solvent in which cytoskeletal filaments are suspended. The second scenario is systems in which filaments are coupled via cross-link molecules throughout. Here, we review the differences and commonalities between the physics of these two regimes. We also survey the literature for the numbers that allow us to place a material within either of these two classes.

The large-scale organization of the genome inside the cell nucleus is critical for the cell’s function. Chromatin – the functional form of DNA in cells – serves as a substrate for active nuclear processes such as transcription, replication and DNA repair. Chromatin’s spatial organization directly affects its accessibility by ATP-powered enzymes, e.g., RNA polymerase II in the case of transcription. In differentiated cells, chromatin is spatially segregated into compartments – euchromatin and heterochromatin – the former being largely transcriptionally active and loosely packed, the latter containing mostly silent genes and densely compacted. The euchromatin/heterochromatin segregation is crucial for proper genomic function, yet the physical principles behind it are far from understood. Here, we model the nucleus as filled with hydrodynamically interacting active Zimm chains – chromosomes – and investigate how large heterochromatic regions form and segregate from euchromatin through their complex interactions. Each chromosome presents a block copolymer composed of heterochromatic blocks, capable of crosslinking that increases chromatin’s local compaction, and euchromatic blocks, subjected to stochastic force dipoles that capture the microscopic stresses exerted by nuclear ATPases. These active stresses lead to a dynamic self-organization of the genome, with its coherent motions driving the mixing of chromosome territories as well as large-scale heterochromatic segregation through crosslinking of distant genomic regions. We study the stresses and flows that arise in the nucleus during the heterochromatic segregation, and identify their signatures in Hi-C proximity maps. Our results reveal the fundamental role of active mechanical processes and hydrodynamic interactions in the kinetics of chromatin compartmentalization and in the emergent large-scale organization of the nucleus.

We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as physics informed neural networks (PINNs). PINNs are popular machine-learning templates that allow for seamless integration of physical equation models with data. Their training amounts to solving an optimization problem over a weighted sum of data-fidelity and equation-fidelity objectives. Conflicts between objectives can arise from scale imbalances, heteroscedasticity in the data, stiffness of the physical equation, or from catastrophic interference during sequential training. We explain the training pathology arising from this and propose a simple yet effective inverse Dirichlet weighting strategy to alleviate the issue. We compare with Sobolev training of neural networks, providing the baseline of analytically ε-optimal training. We demonstrate the effectiveness of inverse Dirichlet weighting in various applications, including a multi-scale model of active turbulence, where we show orders of magnitude improvement in accuracy and convergence over conventional PINN training. For inverse modeling using sequential training, we find that inverse Dirichlet weighting protects a PINN against catastrophic forgetting.

The mammalian mitotic spindle segregates an equal number of chromosomes to daughter cells. Over the course of spindle assembly, many initially erroneous attachments between kinetochores and microtubules are fixed through a process called error correction. Despite the importance of chromosome segregation errors in many human health conditions, we lack quantitative methods to characterize the dynamic error correction process and how it is impaired in disease states. We have developed a novel experimental method and analysis framework to quantify chromosome segregation error correction in human tissue culture cells with live cell confocal imaging of spindle assembly, timed premature chromosome separation, and automated counting of kinetochores after cell division. Using our assay we targeted Aurora B kinase, a key regulator of kinetochore-microtubule attachments, with two small molecules that either inhibited Aurora B activity or perturbed its localization. While both inhibitors increased the steady state error baseline over 10-fold from control, they differed in their initial error states and times to reach steady state. Our results indicate that error correction dynamics, and not just endpoint segregation errors, are important for understanding the involvement of proteins in error correction. Future work will focus on distinguishing the functional roles of different proteins in error correction, characterizing how kinetochore-microtubule affinity and microtubule stability determine error correction dynamics, and constructing and testing a mathematical theory of error correction.

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 ideal vortices in an inviscid fluid, or driven rotors in a viscous membrane, spontaneously self assembles. Despite arising from drastically different physics, these systems share a Hamiltonian structure that sets geometrical conservation laws resulting in distinct 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.

Can non-invasive imaging with fluorescence lifetime imaging microscopy (FLIM) detect metabolic differences in euploid versus aneuploid human blastocysts? FLIM has identified significant metabolic differences between euploid and aneuploid blastocysts. Prior studies have demonstrated that FLIM can detect metabolic differences in mouse oocytes and embryos and in discarded human blastocysts.

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.

Microtubule-based active matter provides insight into the self-organization of motile interacting constituents. We describe several formulations of microtubule-based 3D active isotropic fluids. Dynamics of these fluids is powered by three types of kinesin motors: a processive motor, a non-processive motor, and a motor which is permanently linked to a microtubule backbone. Another modification uses a specific microtubule crosslinker to induce bundle formation instead of a non-specific polymer depletant. In comparison to the already established system, each formulation exhibits distinct properties. These developments reveal the temporal stability of microtubule-based active fluids while extending their reach and the applicability.

Dense assemblies of self-propelling rods (SPRs) may exhibit fascinating collective behaviors and anomalous physical properties that are far away from equilibrium. Using large-scale Brownian dynamics simulations, we investigate the dynamics of disclination defects in 2D fluidized swarming motions of dense dry SPRs (i.e., without hydrodynamic effects) that form notable local positional topological structures that are reminiscent of smectic order. We find the deformations of smectic-like rod layers can create unique polar structures that lead to slow translations and rotations of ±1/2-order defects, which are fundamentally different from the fast streaming defect motions observed in wet active matter. We measure and characterize the statistical properties of topological defects and reveal their connections with the coherent structures. Furthermore, we construct a bottom-up active-liquid-crystal model to analyze the instability of polar lanes, which effectively leads to defect formation between interlocked polar lanes and serves as the origin of the large-scale swarming motions.