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.

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.

A hydraulic instability drives the cell death decision in the nematode germline

Oocytes are large cells that develop into an embryo upon fertilization1. As interconnected germ cells mature into oocytes, some of them grow-typically at the expense of others that undergo cell death2-4. We present evidence that in the nematode Caenorhabditis elegans, this cell-fate decision is mechanical and related to tissue hydraulics. An analysis of germ cell volumes and material fluxes identifies a hydraulic instability that amplifies volume differences and causes some germ cells to grow and others to shrink, a phenomenon that is related to the two-balloon instability5. Shrinking germ cells are extruded and they die, as we demonstrate by artificially reducing germ cell volumes via thermoviscous pumping6. Our work reveals a hydraulic symmetry-breaking transition central to the decision between life and death in the nematode germline.

Microtubule reorganization during female meiosis in C. elegans

Most female meiotic spindles undergo striking morphological changes while transitioning from metaphase to anaphase. The ultra-structure of meiotic spindles, and how changes to this structure correlate with such dramatic spindle rearrangements remains largely unknown. To address this, we applied light microscopy, large-scale electron tomography and mathematical modeling of female meiotic Caenorhabditis elegans spindles. Combining these approaches, we find that meiotic spindles are dynamic arrays of short microtubules that turn over within seconds. The results show that the metaphase to anaphase transition correlates with an increase in microtubule numbers and a decrease in their average length. Detailed analysis of the tomographic data revealed that the microtubule length changes significantly during the metaphase-to-anaphase transition. This effect is most pronounced for microtubules located within 150 nm of the chromosome surface. To understand the mechanisms that drive this transition, we developed a mathematical model for the microtubule length distribution that considers microtubule growth, catastrophe, and severing. Using Bayesian inference to compare model predictions and data, we find that microtubule turn-over is the major driver of the spindle reorganizations. Our data suggest that in metaphase only a minor fraction of microtubules, those closest to the chromosomes, are severed. The large majority of microtubules, which are not in close contact with chromosomes, do not undergo severing. Instead, their length distribution is fully explained by growth and catastrophe. This suggests that the most prominent drivers of spindle rearrangements are changes in nucleation and catastrophe rate. In addition, we provide evidence that microtubule severing is dependent on katanin.

Co-movement of astral microtubules, organelles and F-actin by dynein and actomyosin forces in frog egg cytoplasm

How bulk cytoplasm generates forces to separate post-anaphase microtubule (MT) asters in Xenopus laevis and other large eggs remains unclear. Previous models proposed that dynein-based, inward organelle transport generates length-dependent pulling forces that move centrosomes and MTs outwards, while other components of cytoplasm are static. We imaged aster movement by dynein and actomyosin forces in Xenopus egg extracts and observed outward co-movement of MTs, endoplasmic reticulum (ER), mitochondria, acidic organelles, F-actin, keratin, and soluble fluorescein. Organelles exhibited a burst of dynein-dependent inward movement at the growing aster periphery, then mostly halted inside the aster, while dynein-coated beads moved to the aster center at a constant rate, suggesting organelle movement is limited by brake proteins or other sources of drag. These observations call for new models in which all components of the cytoplasm comprise a mechanically integrated aster gel that moves collectively in response to dynein and actomyosin forces.

Self-straining of actively crosslinked microtubule networks

Cytoskeletal networks are foundational examples of active matter and central to self-organized structures in the cell. In vivo, these networks are active and densely crosslinked. Relating their large-scale dynamics to the properties of their constituents remains an unsolved problem. Here, we study an in vitro active gel made from aligned microtubules and XCTK2 kinesin motors. Using photobleaching, we demonstrate that the gel's aligned microtubules, driven by motors, continually slide past each other at a speed independent of the local microtubule polarity and motor concentration. This phenomenon is also observed, and remains unexplained, in spindles. We derive a general framework for coarse graining microtubule gels crosslinked by molecular motors from microscopic considerations. Using microtubule-microtubule coupling through a force-velocity relationship for kinesin, this theory naturally explains the experimental results: motors generate an active strain rate in regions of changing polarity, which allows microtubules of opposite polarities to slide past each other without stressing the material.

From cytoskeletal assemblies to living materials

Many subcellular structures contain large numbers of cytoskeletal filaments. Such assemblies underlie much of cell division, motility, signaling, metabolism, and growth. Thus, understanding cell biology requires understanding the properties of networks of cytoskeletal filaments. While there are well established disciplines in biology dedicated to studying isolated proteins - their structure (Structural Biology) and behaviors (Biochemistry) - it is much less clear how to investigate, or even just describe, the structure and behaviors of collections of cytoskeletal filaments. One approach is to use methodologies from Mechanics and Soft Condensed Matter Physics, which have been phenomenally successful in the domains where they have been traditionally applied. From this perspective, collections of cytoskeletal filaments are viewed as materials, albeit very complex, 'active' materials, composed of molecules which use chemical energy to perform mechanical work. A major challenge is to relate these material level properties to the behaviors of the molecular constituents. Here we discuss this materials perspective and review recent work bridging molecular and network scale properties of the cytoskeleton, focusing on the organization of microtubules by dynein as an illustrative example.

Morphogenetic degeneracies in the actomyosin cortex

One of the great challenges in biology is to understand the mechanisms by which morphogenetic processes arise from molecular activities. We investigated this problem in the context of actomyosin-based cortical flow in C. elegans zygotes, where large-scale flows emerge from the collective action of actomyosin filaments and actin binding proteins (ABPs). Large-scale flow dynamics can be captured by active gel theory by considering force balances and conservation laws in the actomyosin cortex. However, which molecular activities contribute to flow dynamics and large-scale physical properties such as viscosity and active torque is largely unknown. By performing a candidate RNAi screen of ABPs and actomyosin regulators we demonstrate that perturbing distinct molecular processes can lead to similar flow phenotypes. This is indicative for a ‘morphogenetic degeneracy’ where multiple molecular processes contribute to the same large-scale physical property. We speculate that morphogenetic degeneracies contribute to the robustness of bulk biological matter in development.

Active contraction of microtubule networks

Many cellular processes are driven by cytoskeletal assemblies. It remains unclear how cytoskeletal filaments and motor proteins organize into cellular scale structures and how molecular properties of cytoskeletal components affect the large-scale behaviors of these systems. Here, we investigate the self-organization of stabilized microtubules in Xenopus oocyte extracts and find that they can form macroscopic networks that spontaneously contract. We propose that these contractions are driven by the clustering of microtubule minus ends by dynein. Based on this idea, we construct an active fluid theory of network contractions, which predicts a dependence of the timescale of contraction on initial network geometry, a development of density inhomogeneities during contraction, a constant final network density, and a strong influence of dynein inhibition on the rate of contraction, all in quantitative agreement with experiments. These results demonstrate that the motor-driven clustering of filament ends is a generic mechanism leading to contraction.

Active torque generation by the actomyosin cell cortex drives left-right symmetry breaking

Many developmental processes break left-right (LR) symmetry with a consistent handedness. LR asymmetry emerges early in development, and in many species the primary determinant of this asymmetry has been linked to the cytoskeleton. However, the nature of the underlying chirally asymmetric cytoskeletal processes has remained elusive. In this study, we combine thin-film active chiral fluid theory with experimental analysis of the C. elegans embryo to show that the actomyosin cortex generates active chiral torques to facilitate chiral symmetry breaking. Active torques drive chiral counter-rotating cortical flow in the zygote, depend on myosin activity, and can be altered through mild changes in Rho signaling. Notably, they also execute the chiral skew event at the 4-cell stage to establish the C. elegans LR body axis. Taken together, our results uncover a novel, large-scale physical activity of the actomyosin cytoskeleton that provides a fundamental mechanism for chiral morphogenesis in development.

Phase-synchronized state of oriented active fluids

We present a theory for self-driven fluids, such as motorized cytoskeletal extracts or microbial suspensions, that takes into account the underlying periodic duty cycle carried by the constituent active particles. We show that an orientationally ordered active fluid can undergo a transition to a state in which the particles synchronize their phases. This spontaneous breaking of time-translation invariance gives rise to flow instabilities distinct from those arising in phase-incoherent active matter. Our work is of relevance to the transport of fluids in living systems and makes predictions for concentrated active-particle suspensions and optically driven colloidal arrays.

Active chiral processes in thin films

We develop a generic description of thin active films that captures key features of flow and rotation patterns emerging from the activity of chiral motors which introduce torque dipoles. We highlight the role of the spin rotation field and show that fluid flows can occur in two ways: by coupling of the spin rotation rate to the velocity field via a surface or by spatial gradients of the spin rotation rate. We discuss our results in the context of patches of bacteria on solid surfaces and groups of rotating cilia. Our theory could apply to active chiral processes in the cell cytoskeleton and in epithelia.

Active chiral fluids

Active processes in biological systems often exhibit chiral asymmetries. Examples are the chirality of cytoskeletal filaments which interact with motor proteins, the chirality of the beat of cilia and flagella as well as the helical trajectories of many biological microswimmers. Here, we derive constitutive material equations for active fluids which account for the effects of active chiral processes. We identify active contributions to the antisymmetric part of the stress as well as active angular momentum fluxes. We discuss four types of elementary chiral motors and their effects on a surrounding fluid. We show that large-scale chiral flows can result from the collective behavior of such motors even in cases where isolated motors do not create a hydrodynamic far field.