Session X01: Biofluids: Collective Behavior and Active Matter IV

Hydrodynamics of Tunable Janus Particles

We use a model recently developed for the many-body hydrodynamics of amphiphilic Janus particles (JPs) under a viscous background flow to investigate distinct particle phases that arise when accounting for asymmetric and polar hydrophobes. We quantify the macroscopic properties of novel JP phases under a linear shear and a Taylor-Green mixing background flow and quantify their macroscopic, complex-fluid behavior. These numerical results provide insight into dynamic control of non-equilibrium active biological systems with similar self-organization.   

Object transport by a confined active nematic suspension, including fixed-point and limit-cycle numerical solutions

The transport of an object by active nematic fluid shows is studied using the continuum model of Gao et al. (Phys. Rev. Fluids, 2017), which includes a slender-body strain response of rod-like agents, Maier-Saupe steric interaction, and a Bingham closure for fourth-moments of the orientation. We mostly consider two-dimensional suspensions of contractors (non-motile puller agents), which are unstable for some parameters, transporting an object in a closed circular container. The motion is often chaotic, characterized by the seemingly random interactions of the object and nematic defects. However, for ranges of parameters there are two unexpected terminal states that can arrise suddenly, even for the same physical parameters: a fixed point solution, in which the net active stress is balanced by a (nearly) hydrostatic pressure, and a limit cycle solution, in which the object endlessly traverses the container. The fixed-point solution is associated with a net +1 nematic "charge" associated with the object, whereas the limit cycle arises when it achieves a neutral 0 nematic "charge". The limit-cycle solution is far from any linear solution and involves the formation of transient -1/2 defect pairs, disrupting the fully aligned nominal base state, and near 90-degree rotation of the nematic order in regions. Both of these basic flows are also shown to arise in more complex geometries.   

The periodic motion of active nematic fluids and the role of particle shape.

Active nematic materials are non-equilibrium fluids composed of rod-like subunits that convert local internal (e.g. chemical) energy into large-scale mechanical motion, which generates a self-stirring fluid. One prominent example of an active nematic utilizes rod-like microtubules—components of the cytoskeleton—and kinesin molecular motors. The microtubules are densely packed in a 2D layer and form an ordered nematic phase. The kinesin motors cross-link the microtubules and cause them to slide relative to one another, creating an extensile flow. The nematic phase contains point-like topological defects that move around one another in a typically chaotic fashion. These defects can be viewed as virtual rods that are responsible for stirring the fluid. The geometric shape of the nematic subunits plays a crucial role in determining whether the defects move periodically. To understand the importance of the geometric shape of these particles and its role in defect behavior, we conducted simulations of the nematohydrodynamic equations, varying the particle aspect ratio.  We observed that when the particles are sufficiently elongated there is a transition from chaotic motion of defects to periodic motion; i.e., if the particles are sufficiently circular, the periodic behavior of the defects disappears. Thus, when modelling active nematics, it is important to use the correct aspect ratio to achieve the proper qualitative behavior.    

Nematic and polar order in a thin layer of rod-shaped bacteria Myxococcus xanthus

Myxococcus xanthus is a rod-shaped bacterium that moves on a solid surface. In a nutrient-rich environment, they form a thin cell layer that behaves as an active liquid crystal, with the system's nematic order leading to half-integer defects [1]. However, our direct experimental measurements of the cell polarity show that as a collective of self-propelled rods [2], the system also exhibits instantaneous local polar order, despite the absence of a torque that forces the polarities of neighboring cells to align. Furthermore, this local polar order is controlled by the reversal frequency of the cells. Lowering the reversal frequency results in enhanced local polar order, stronger forces between the colony and the solid substrate, and increased out-of-plane cell motion. Through modulating their reversal frequency, M. xanthus cells regulate the behavior of the population. Our research reveals the biological significance of an interplay between nematic and polar order in a bacterial population.  

[1] Copenhagen, et al. Nature Physics, 17(2):211–215, 2021. 

[2] Bar, et al. Annual Review of Condensed Matter Physics, 11(1):441–466, 2020.   

Orientational correlations in mammalian cells: unveiling the influence of intercellular and cell-Matrix Interactions

Mammalian cells have unique and complex ways to communicate with each other and establish mutual correlations, akin to human beings and social animals. These correlations are evident in various cellular behaviors, such as collective migration, orientation alignment, and force balance, which hold great significance in understanding different physiological processes but still lack clarity. Spindle-shape myoblasts, as an active system, can spontaneously form nematic order within monolayers, and this process is closely related to intercellular correlations. In our study, we demonstrate that the establishment of long-range orientation correlation among myoblasts is a result of both cell-cell and cell-matrix interactions. By observing the evolution of correlation length with varying cell density and blocking cell proliferation or intercellular protein contacts, we conclude that intercellular interactions influence correlations both physically and biologically. Additionally, we investigate how cell-matrix interaction plays a role in cell correlation using Polydimethylsiloxane (PDMS) substrates with varying stiffness (from 1.8kPa to 500kPa). This complex situation involves focal adhesions acting as motors or friction, actomyosin contractility, cell morphology, and intercellular mechanical communication through substrate deformation. Our research aims to provide valuable insights for further studies on topics such as wound healing, myogenesis, cell jamming, topological defects, 3D morphogenesis, and other collective behaviors.   

Self-organization and hydrodynamics of active rods on fluid membranes

The transport and self-organization of active self-propelled rod-like proteins and biopolymers on the cell membrane and other fluid interfaces is key to many biological processes and functions.  Such systems are shown to exhibit a complex range of collective behaviors, including aggregation, polar and nematic ordering, and complex dynamics of topological defects. Here, we use a continuum description of active polar rods to study the collective dynamics of a dilute suspension of pusher and puller rods in a fluid membrane submerged in a bulk fluid on the interior and exterior. This serves as a simplified model for the assembly of cytoskeletal biopolymers on the cell membrane. The behavior is determined by two dimensionless quantities: (1) the ratio of active to thermal stresses, and (2) the ratio of the rod’s length (L) to Saffman-Delbruck length (l0), where l0 is the ratio of the 2D membrane viscosity to 3D bulk viscosity. Using stability analysis and numerical simulations, we show that the coupling between the membrane’s tangential flows to 3D bulk flows introduces several novel features that are absent in active suspensions in free space 3D and 2D geometries. Specifically, we show that pusher rods undergo a finite wavelength nematic order transition at sufficiently high activities. The wavelength of the ordered domains decreases with increasing L/l0.  Furthermore, we show that in addition to ordering, the pusher suspensions undergo phase transition in density (aggregation) above some critical swimming velocity, which depends on L/l0.   

Collective hydrodynamics of driven particles in viscous membranes: effect of non-Newtonian surface rheology and particle shape

Biological membranes are self-assembled complex fluid interfaces that host proteins, molecular motors, and other macromolecules essential for cellular function. These membranes have a distinct in-plane fluid response with a surface viscosity that has been well characterized. The resulting quasi-two-dimensional fluid dynamical problem describes the motion of embedded proteins or particles. However, the viscous response of biological membranes is often non-Newtonian and the inclusions are rarely simple discs. We use the Lorentz reciprocal theorem to extract the effective long-ranged hydrodynamic interaction among membrane inclusions that arises due to a particular class of surface-pressure dependent rheology. We show that the corrective force that emerges ties back to the interplay between membrane flow and non-constant viscosity, which suggests a mechanism for biologically favorable protein aggregation within membranes. We quantify and describe the mechanism for such a large-scale concentration instability using a mean-field model, which we verify with numerical simulations. Finally, we extend the mean-field model to describe the role of particle shape. The anisotropic mobility and orientability of rod-like particles lead to co-ordinated dynamics that depend on the ratio of membrane viscosity to that of the surrounding fluid. New mechanisms for separation and aggregation emerge from this analysis, suggesting creative strategies to tune assembly on viscous membranes.   

Defect morphologies in active nematics turbulence

In active nematic liquid crystals, activity is able to drive chaotic spatiotemporal flows referred to as active turbulence.  In this regime, the system is cahractaerized by the proliferation of  defects. I will address how active stress affects the morphology of disclination lines of a three dimensional active nematic liquid crystal under chaotic flow. I will discuss how  activity selects a crossover length scale in between the size of small defect loops and the one of long and tangled defect lines of fractal dimension . This length scale crossover is consistent with the scaling of the average separation between defects as a function of activity.  Numerical simlulations, together with a track defect algorithm, show that defects organize as a network of regular contractible  loops that coexisting with wrapping defect lines.   

Spontaneous rotation of disks by active nematics

We consider a two-dimensional active nematic liquid crystal between two concentric circular boundaries. The anchoring conditions are hybrid, meaning that the nematic directors make different constant angles with the inner and outer boundaries. When the activity is zero, the system takes on the "magic spiral" geometry which was proposed by Robert Meyer to elucidate the balance of torques in nematic liquid crystals in equilibrium. When the activity is nonzero and the inner circle bounds a disk which is free to rotate, active flows spin the disk at a speed that depends on the activity, viscosity, liquid crystal parameters, and the size of the gap between the two circles. We calculate the rotation speed analytically using the frozen nematic approximation in which the effect of the flow on the nematic is disregarded, but the viscous flow is accounted for. We examine the accuracy of this approximation by numerically solving the full hydrodynamic equations.   

Collective behavior and mixing dynamics in membranes with active inclusions

Eukaryotic cell membranes are a crowded assembly of molecular motors, ion pumps, and other biomolecular machines embedded in the bilayer matrix. Biomimetic membranes made of polymer assemblies also display similar properties, and are promising candidates for drug delivery applications. We investigate the collective behavior of active inclusions in viscous membranes surrounded by a deep subphase ('free' membranes) and in membranes surrounded by a shallow subphase ('confined' membranes). Our simulations show clustering of particles in free and confined membrane systems where 3D fluid viscous stresses dominate. We rationalize this by examining pair interactions in these systems, which reveals unique nonlinear dynamics that result in aggregation. By contrast, pairs are equally likely to aggregate or separate, which translates to large-scale chaotic motion without aggregation in systems where membrane stresses dominate. We also numerically study lipid spatial re-organization ('mixing') due to the flows induced by the inclusions. Mixing dynamics are explored as a function of concentration of active material, passive anchors, and surface viscosities in both free and confined membranes, which we quantify using standard mixing norms.   

Dynamics of active nematic fluids on arbitrary manifolds: exploring the role of geometry and topology

Recent advances in cell biology and experimental techniques using reconstituted cell extracts have generated significant interest in understanding how geometry and topology influence active fluid dynamics. In this work, we present a comprehensive continuum theory and computational method to explore the dynamics of sharply-aligned active nematic fluids on arbitrary surfaces without topological constraints. The fluid velocity and nematic order parameter are represented as the sections of the complex line bundle of a 2-manifold. We introduce the Levi-Civita connection and surface curvature form within the framework of fiber bundles. By adopting this geometric approach, we introduce a gauge-invariant discretization method that preserves the continuous local-to-global theorems in differential geometry. Furthermore, we establish a nematic Laplacian on complex functions that can accommodate fractional topological charges through the covariant derivative on the complex nematic representation. We formulate advection of the nematic field based on a unifying definition of the Lie derivative, resulting in a stable geometric semi-Lagrangian discretization scheme for transport by the flow. In general, the proposed surface-based method offers an efficient and stable means to investigate the influence of local curvature and global topology on the 2D hydrodynamics of active nematic systems. Moreover, the complex line representation of the nematic field and the unifying Lie advection present a systematic approach for generalizing our method to active $p$-atic systems.   

Biologically Generated Mixing and the Direction of Energy Cascade

It has been proposed that biologically generated turbulence plays an important role in material transport and ocean mixing. Both experimental and numerical studies have reported evidence of the non-negligible mixing by moderate Reynolds number swimmers in quiescent water, such as zooplankton, especially at aggregation scales. However, the interaction between biologically generated agitation and the background flow as a key factor in biologically generated turbulence that could reshape our previous knowledge of biologically generated turbulence, has long been ignored. Here we show that the geometry between the biologically generated agitation and the background hydrodynamic shear can determine both the intensity and direction of the biologically generated turbulent energy cascade. Measuring the migration of a centimeter-scale swimmer-as represented by the brine shrimp Artemia salina-in a shear flow and verifying through an analogue experiment with an artificial jet revealed that different geometries between the biologically generated agitation and the background shear can result in spectral energy transferring toward larger or smaller scales, which consequently intensifies or attenuates the large scale hydrodynamic shear. Our results suggest that the long ignored geometry between the biologically generated agitation and the background flow field is an important factor that should be taken into consideration in future studies of biologically generated turbulence.