The competition between thermal fluctuations and potential forces is the foundation of our understanding of phase transitions and matter in equilibrium. Driving matter out of equilibrium allows for a new class of interactions which are neither attractive nor repulsive but transverse. The existence of such transverse forces immediately raises the question of how they interfere with basic principles of material self-organization. Despite a recent surge of interest, this question remains open. Here, we show that activating transverse forces by homogeneous rotation of colloidal units generically turns otherwise quiescent solids into a crystal whorl state dynamically shaped by self-propelled dislocations. Simulations of both a minimal model and a full hydrodynamics model establish the generic nature of the chaotic dynamics of these self-kneading polycrystals. Using a continuum theory, we explain how odd and Hall stresses conspire to destabilize chiral crystals from within. This chiral instability produces dislocations that are unbound by their self-propulsion. Their proliferation eventually leads to a crystalline whorl state out of reach of equilibrium matter.
Robustness of biological systems is crucial for their survival, however, for many systems its origin is an open question. Here, we analyze one subcellular level system, the microtubule cytoskeleton. Microtubules self-organize into a network, along which cellular components are delivered to their biologically relevant locations. While the dynamics of individual microtubules is sensitive to the organism’s environment and genetics, a similar sensitivity of the overall network would result in pathologies. Our large-scale stochastic simulations show that the self-organization of microtubule networks is robust in a wide parameter range in individual cells. We confirm this robustness in vivo on the tissue-scale using genetic manipulations of Drosophila epithelial cells. Finally, our minimal mathematical model shows that the origin of robustness is the separation of time-scales in microtubule dynamics rates. Altogether, we demonstrate that the tissue-scale self-organization of a microtubule network depends only on cell geometry and the distribution of the microtubule minus-ends.
In the cellular phenomena of cytoplasmic streaming, molecular motors carrying cargo along a network of microtubules entrain the surrounding fluid. The piconewton forces produced by individual motors are sufficient to deform long microtubules, as are the collective fluid flows generated by many moving motors. Studies of streaming during oocyte development in the fruit fly Drosophila melanogaster have shown a transition from a spatially disordered cytoskeleton, supporting flows with only short-ranged correlations, to an ordered state with a cell-spanning vortical flow. To test the hypothesis that this transition is driven by fluid-structure interactions, we study a discrete-filament model and a coarse-grained continuum theory for motors moving on a deformable cytoskeleton, both of which are shown to exhibit a swirling instability to spontaneous large-scale rotational motion, as observed.
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 toward a theory of how molecular perturbations impact cytoskeletal organization, and provides a framework for designing cytoskeletal networks with desirable properties in the lab.
A classical problem in ﬂuid mechanics is the motion of an axisymmetric vor-tex sheet evolving under the action of surface tension, surrounded by an invis-cid ﬂuid. Lagrangian descriptions of these dynamics are well-known, involv-ing complex nonlocal expressions for the radial and longitudinal velocities interms of elliptic integrals. Here we use these prior results to arrive at a remark-ably compact and exact Eulerian evolution equation for the sheet radius r.´; t/in an explicit ﬂux form associated with the conservation of enclosed volume.The ﬂux appears as an integral involving the pairwise mutual induction formulafor vortex loop pairs ﬁrst derived by Helmholtz and Maxwell. We show howthe well-known linear stability results for cylindrical vortex sheets in the pres-ence of surface tension and streaming ﬂows [A. M. Sterling and C. A. Sleicher,J. Fluid Mech. 68, 477 (1975)] can be obtained directly from this formulation.Furthermore, the inviscid limit of the empirical model of Eggers and Dupont[J. Fluid Mech. 262 205 (1994); SIAM J. Appl. Math. 60, 1997 (2000)], whichhas served as the basis for understanding singularity formation in droplet pin-choff, is derived within the present formalism as the leading-order term in anasymptotic analysis for long slender axisymmetric vortex sheets and should pro-vide the starting point for a rigorous analysis of singularity formation.
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.
In cells, cytoskeletal filament networks are responsible for cell movement, growth, and division. Filaments in the cytoskeleton are driven and organized by crosslinking molecular motors. In reconstituted cytoskeletal systems, motor activity is responsible for far-fromequilibrium phenomena such as active stress, self-organized flow, and spontaneous nematic defect generation. How microscopic interactions between motors and filaments lead to larger-scale dynamics remains incompletely understood. To build from motor-filament interactions to predict bulk behavior of cytoskeletal systems, more computationally efficient techniques for modeling motor-filament interactions are needed. Here we derive a coarsegraining hierarchy of explicit and continuum models for crosslinking motors that bind to and walk on filament pairs. We compare the steady-state motor distribution and motorinduced filament motion for the different models and analyze their computational cost. All three models agree well in the limit of fast motor binding kinetics. Evolving a truncated moment expansion of motor density speeds the computation by 103–106
compared to the explicit or continuous-density simulations, suggesting an approach for more efficient simulation of large networks. These tools facilitate further study of motor-filament networks on micrometer to millimeter length scales.
The effective diffusivity of a Brownian tracer in unidirectional flow is well known to be enhanced due to shear by the classic phenomenon of Taylor dispersion. At long times, the average concentration of the tracer follows a simplified advection–diffusion equation with an effective shear-dependent dispersivity. In this work, we make use of the generalized Taylor dispersion theory for periodic domains to analyze tracer dispersion by peristaltic pumping. In channels with small aspect ratios, asymptotic expansions in the lubrication limit are employed to obtain analytical expressions for the dispersion coefficient at both small and high Péclet numbers. Channels of arbitrary aspect ratios are also considered using a boundary integral formulation for the fluid flow coupled to a conservation equation for the effective dispersivity, which is solved using the finite-volume method. Our theoretical calculations, which compare well with results from Brownian dynamics simulations, elucidate the effects of channel geometry and pumping strength on shear-induced dispersion. We further discuss the connection between the present problem and dispersion due to Taylor’s swimming sheet and interpret our results in the purely diffusive regime in the context of Fick–Jacobs theory. Our results provide the theoretical basis for understanding passive scalar transport in peristaltic flow, for instance, in the ureter or in microfluidic peristaltic pumps.
Many different simulation methods for Stokes flow problems involve a common computationally intense task—the summation of a kernel function over O(N2) pairs of points. One popular technique
is the Kernel Independent Fast Multipole Method (KIFMM), which constructs a spatial adaptive octree and places a small number of equivalent multipole and local points around each octree box, and completes the kernel sum with O(N) performance. However, the KIFMM cannot be used directly with nonlinear kernels, can be inefficient for complicated linear kernels, and in general is difficult to implement compared to less-efficient alternatives such as Ewald-type methods. Here we present the Kernel Aggregated Fast Multipole Method (KAFMM), which overcomes these drawbacks by allowing different kernel functions to be used for specific stages of octree traversal. In many cases a simpler linear kernel suffices during the most extensive stage of octree traversal, even for nonlinear kernel summation problems. The KAFMM thereby improves computational efficiency in general and also allows efficient evaluation of some nonlinear kernel functions such as the regularized Stokeslet. We have implemented our method as an open-source software library STKFMM with support for Laplace kernels, the Stokeslet, regularized Stokeslet, Rotne-Prager-Yamakawa (RPY) tensor, and the Stokes double-layer and traction operators. Open and periodic boundary conditions are supported for all kernels, and the no-slip wall boundary condition is supported for the Stokeslet and RPY tensor.
The package is designed to be ready-to-use as well as being readily extensible to additional kernels. Massive parallelism is supported with mixed OpenMP and MPI.
Stoichiometric interactions explain spindle dynamics and scaling across 100 million years of nematode evolution
The spindle shows remarkable diversity, and changes in an integrated fashion, as cells vary over evolution. Here, we provide a mechanistic explanation for variations in the first mitotic spindle in nematodes. We used a combination of quantitative genetics and biophysics to rule out broad classes of models of the regulation of spindle length and dynamics, and to establish the
importance of a balance of cortical pulling forces acting in different directions. These experiments led us to construct a model of cortical pulling forces in which the stoichiometric interactions of microtubules and force generators (each force generator can bind only one microtubule), is key to\ explaining the dynamics of spindle positioning and elongation, and spindle final length and scaling with cell size. This model accounts for variations in all the spindle traits we studied here, both within species and across nematode species spanning over 100 million years of evolution.