Archives: Events

Long-range forces between bodies in active matter

A single non-spherical body placed in an active fluid generates currents. When two or more passive bodies are placed in an active fluid these currents lead to long-range interactions. Using a multipole expansion their leading-order behaviors will be characterized in terms of single-body properties. The interactions are showed to decay as a power law with the distance between the bodies, be anisotropic, and not obey an action-reaction principle. The interactions lead to rich dynamics of the bodies, illustrated by the spontaneous synchronized rotation of pinned non-chiral bodies and the formation of traveling bound pairs. The occurrence of these phenomena depends on tunable properties of the bodies, thus opening new possibilities for self-assembly mediated by active fluids.

Pattern Formation in Active Cytoskeletal Systems

Living cells rely on the self-organization mechanisms of cytoskeleton to adapt to their requirements. In processes such as cell division, or cellular motility rely on the controlled self-assembly and disassembly of well defined active cytoskeletal structures interacting with lipid membranes. One important and promising strategy to identify the underlying governing principles is to quantify the underlying physical processes in model systems mimicking functional units of living cell. Here I’ll present in vitro minimal model systems, which allow the identification of the ordering effects emerging in such collective systems. In a first part I will present recent results of a high density motility essay, how weak local interactions can be sensitively tuned to lead to different symmetries of the pattern forming system. In a second model system consisting of active microtubule and actin filament systems which show pattern formation resulting from topological constraints. I will discuss how a balance of local force exertion and tension generation results in shape transformations, blebbing, invagination or tethering of lipid membranes.

Microscopic efficiency sets the kinetics and structure of active fluids

In contrast with systems driven by an external field, the energy injection in active matter is local and independent for each particle, opening the possibility of a phase separation even with purely repulsive interactions. While such a phenomenon has been studied extensively, understanding how the microscopic energy fluxes control the emerging collective behavior, and its connection with entropy production [1, 2], has remained an elusive goal.

Based on methods of stochastic thermodynamics, we define a particle based efficiency as the proportion of injected power which effectively leads to collisional slowing down of the dynamics. We demonstrate that there exist generic relations between such an efficiency and transport properties quantified via the effective diffusion and mobility of an internal tracer. Moreover, we show that the spatial profile of efficiency controls the structure of a phase separated state by setting the form of the interface between dilute and dense phases. We also discuss how the instantaneous efficiency reveals failures in compact structures, such as fractures and moving defects.

These recent findings shed a new light on the control of active fluid properties by microscopic efficiency. It opens the door to the design of new active systems based on monitoring locally internal energy fluxes.

The Role of Boundaries in 2D Active Nematics

We present experimental and theoretical studies of 2D active nematics confined to a disk with parallel boundary conditions and a topological charge of +1. For large diameters, the nematic is unconfined, exhibiting turbulent flow with pairs of +1/2 and -1/2 defects created and destroyed at a steady state. As confinement is increased, the director adopts a yin yang pattern characterized by a pair of co-rotating +1/2 defects, which undergo spontaneous and continuous flow. Upon further confinement the system transitions from the yin yang state to a dipolar configuration of two +1/2 defects resembling a confined passive nematic. Theory predicts this configuration to be static, but in experiment the director field in the center of the disk rotates like a solid body.

We compute the dynamics in disks with total topological charge of +1, 0 and -1. In contrast to the case of passive nematics, for active nematics the yin yang pattern of two +1/2 defects in the center of the disk and circulating flow is persistent for all three charges, with the topologically required -1/2 defects relegated to the boundary. This insensitivity to topological constraints distinguishes active from passive liquid crystals.

Active hydrodynamics of interphase chromatin: coarse-grained modeling

The three-dimensional spatiotemporal organization of genetic material inside the cell nucleus remains an open question in cellular biology. During the time between two cell divisions, the functional form of DNA in cells, known as chromatin, fills the cell nucleus in its uncondensed polymeric form, which allows the transcriptional machinery to access DNA. Recent in vivo imaging experiments have cast light on the existence of coherent chromatin motions inside the nucleus, in the form of large-scale correlated displacements on the scale of microns and lasting for seconds. To elucidate the mechanisms for such motions, we have developed a coarse-grained active polymer model where chromatin is represented as a confined flexible chain acted upon by active molecular motors, which perform work and thus exert dipolar forces on the system. Numerical simulations of this model that account for steric and hydrodynamic interactions as well as internal chain mechanics demonstrate the emergence of coherent motions in systems involving extensile dipoles, which are accompanied by large-scale chain reconfigurations and local nematic ordering. Comparisons with experiments show good qualitative agreement and support the hypothesis that long-ranged hydrodynamic couplings between chromatin-associated active motors are responsible for the observed coherent dynamics.

Filament Bending Promotes Dynamic Stability in Soft Active Nematics

The actomyosin cytoskeleton is an active semi-flexible polymer network whose non-equilibrium behaviors coordinate both cell elasticity and fluidity to maintain or change cell shape. Unlike the induction of contractile flows, the maintenance of dynamic stability in highly labile yet internally pre-stressed active materials remains unknown. To this end, we synthesize a biomimetic active nematic liquid crystal from long semi-flexible actin filaments driven out-of-equilibrium by myosin motor activity. We identify diverse actomyosin interactions that govern the dynamic architecture and mechanical response of the network to active stresses. These responses include dynamic steady states, in which myosin reversibly bends actin filaments, whose curvatures show anomalous and strongly coupled fluctuations across a broad spectrum of filament bending modes. These fluctuations break detailed balance, enhance network elasticity, while maintaining dynamic stability. Furthermore, the actomyosin interactions that maintain dynamic stability are fundamentally distinct from those that drive contractile flows of actomyosin networks.

Flocking round and round

I will discuss the new features that arise when polar flocking takes place on the round 2-sphere rather than in the plane. The topology of the 2-sphere requires that flocking states exhibit defects even in the steady state. In the presence of spontaneous flow the system also supports long-wavelength propagating sound modes gapped by the (constant) spatial curvature. I will discuss the steady state profile of such an active polar flock and show that curvature and active flow together result in symmetry-protected topological modes localized to a great circle. These modes are the analogue of edge states in electronic quantum Hall systems and provide unidirectional channels for information transport in the flock, robust against disorder and backscattering.

Rigidity and flocking transitions in dense tissues

The mechanical properties of epithelial tissues, which are typically composed of a single layer of tightly bound cells, play an important role in development and disease. Our goal is to develop theoretical and computational tools to help explain collective cell migration patterns and mechanical behavior in these tissues. In this talk, I will highlight the interplay between tissue rigidity and collective cell migration using two different models. The first model augments a Self-Propelled Voronoi model that describes epithelial cells in dense tissue as motile polygons covering the plane by introducing a local feedback that aligns cell polarization with the cell velocity. This alignment promotes solidification and drives transitions to both flocking liquid and solid states, qualitatively affecting the morphology of dynamical heterogeneities near the onset of tissue rigidity. This is akin to what observed in jammed epithelial monolayers, which are unjammed by the addition of endocytic proteins. Next, I will describe a hydrodynamic model for bulk tissues that couples cell shapes, tissue rigidity, and cell-substrate interactions by assuming that cells exert traction forces preferentially along gradients in the in-plane tissue stiffness, as suggested by recent experiments. An analysis of the steady states of the model leads to the identification a new “morphotactic” parameter that controls pattern formation in real tissues.

Active Mechanics in the Cell

Many fundamental phenomena in eukaryotic cells — nuclear migration, spindle positioning, chromosome segregation — involve the interaction of (often transitory) mechanical structures with boundaries and fluids. I will discuss the recent interactions of mathematical modeling and simulation with experimental measurements of active biomechanical
processes within the cell.

Reversible reaction dynamics of self-diffusiophoretic Janus motors

The dynamics of a Janus motor with reversible surface reactions that is
driven out of equilibrium fluxes of reactants and products will be described.
Coupled Langevin equations for the motor velocity and reaction rate that are
consistent with microscopic reversibility are used to derive a fluctuation
formula for the joint probability to find the motor at position r after n
reactive events have occurred in a time t. Thermodynamic consistency requires
the existence of a contribution to the Langevin equations that is reciprocal
to self-propulsion by diffusiophoresis and causes the reaction rate to depend
on an externally applied force. A reversible microscopic model that can be
used to study such phenomena will be discussed.