Active matter comprises individual units that convert energy into mechanical motion. In many examples, such as bacterial systems and biofilament assays, constituent units are elongated and can give rise to local nematic orientational order. Such `active nematics' systems have attracted much attention from both theorists and experimentalists. However, despite intense research efforts, data-driven quantitative modeling has not been achieved, a situation mainly due to the lack of systematic experimental data and to the large number of parameters of current models. Here we introduce a new active nematics system made of swarming filamentous bacteria. We simultaneously measure orientation and velocity fields and show that the complex spatiotemporal dynamics of our system can be quantitatively reproduced by a new type of microscopic model for active suspensions whose important parameters are all estimated from comprehensive experimental data. This provides unprecedented access to key effective parameters and mechanisms governing active nematics. Our approach is applicable to different types of dense suspensions and shows a path towards more quantitative active matter research.
Recent studies have shown that packings of cells, both eukaryotic cellular tissues and growing or swarming bacterial colonies, can often be understood as active nematic fluids. A key property of volume-conserving active nematic model systems is chaotic self-mixing characterized by motile topological defects. However, for active nematics driven by growth rather than motility, less is understood about mixing and defect motion. Mixing could affect evolutionary outcomes in bacterial colonies by counteracting the tendency to spatially segregate into monoclonal sectors, which reduces the local genet…
Growing tissue and bacterial colonies are active matter systems where cell divisions and cellular motion generate active stress. Although they operate in the non-equilibrium regime, these biological systems can form large-scale ordered structures such as nematically aligned cells, topological defects, and fingerings. Mechanical instabilities also play an essential role during growth by generating large structural folding. How active matter dynamics and mechanical instabilities together develop large-scale order in growing tissue is not well understood. Here, we use chain forming Bacillus subti…
Living active collectives have evolved with remarkable self-patterning ability to meet the physical and biological constraints for growth and survival. However, how complex multicellular patterns emerge from a single founder cell remains elusive. Here, by recourse to an agent-based model, we track the three-dimensional (3D) morphodynamics and cell orientational order of growing bacterial biofilms encased by agarose gels. Confined growth causes spatiotemporally heterogeneous stress buildup in the biofilm. High hydrostatic and low shear stresses at the core of the biofilm promote viscous-to-elas…
Active systems comprised of self-propelled units show fascinating transitions from Brownian-like dynamics to collective coherent motion. Swirling of swimming bacteria is a spectacular example. This study demonstrates that a nematic liquid crystal environment patterned as a spiral vortex controls individual-to-collective transition in bacterial swirls and defines whether they expand or shrink. In dilute dispersions, the bacteria swim along open spiral trajectories, following the pre-imposed molecular orientation. The trajectories are nonpolar. As their concentration exceeds some threshold, the …
Efficient nutrient mixing is crucial for the survival of bacterial colonies and other living systems. This raises the question of whether the optimization of mixing through the emergence of active turbulent motion in bacterial swarms played a role in the evolution of bacterial shapes. Here, to address this question, we solve the hydrodynamic equation for active nematics coupled with an advection-diffusion equation for the nutrients. The latter models a conserved activity field and mimics the conservation of nutrients in bacterial swarms. At the interface between active and passive nematic phas…
A paradigm for internally driven matter is the active nematic liquid crystal, whereby the equations of a conventional nematic are supplemented by a minimal active stress that violates time reversal symmetry. In practice, active fluids may have not only liquid crystalline but also viscoelastic polymer degrees of freedom. Here we explore the resulting interplay by coupling an active nematic to a minimal model of polymer rheology. We find that adding polymer can greatly increase the complexity of spontaneous flow, but can also have calming effects, thereby increasing the net throughput of spontan…
Motivated by results for the propagation of active-passive interfaces of bacterial Serratia marcescens swarms [Nat. Comm., 9, 5373 (2018)] we use a hydrodynamic multiphase model to investigate the propagation of interfaces of active nematics on substrates. We characterize the active nematic phase of the model and discuss its description of the statistical dynamics of the swarms. We show that the velocicity correlation functions and the energy spectrum of the active turbulent phase of the model scale with the active length, for a range of activities. In addition, the energy spectrum exhibits tw…
We have conducted two quantitative tests of predictions based on the Halperin-Lubensky-Ma (HLM) theory of fluctuation-induced first-order phase transitions. First, we explore the effect of an external magnetic field on the nematic-smectic-A (NA) transition in a liquid crystal. Second, we examine the dependence of the first-order discontinuity as a function of mixture concentration in pure 8CB and three 8CB-10CB mixtures. We find the first quantitative evidence for deviations from the HLM theory.
Continuum hydrodynamic models of active liquid crystals have been used to describe dynamic self-organising systems such as bacterial swarms and cytoskeletal gels. A key prediction of such models is the existence of self-stabilising kink states that spontaneously generate fluid flow in quasi-one dimensional channels. Using simple stability arguments and numerical calculations we extend previous studies to give a complete characterisation of the phase space for both contractile and extensile particles (ie pullers and pushers) moving in a narrow channel as a function of their flow alignment prope…
Transport and Energetics of Bacterial Rectification
Courant Institute of Mathematical Sciences, New York University（纽约大学柯朗数学科学研究所）；Center for Soft Matter Research, Department of Physics, New York University（纽约大学物理系软物质研究中心）；Department of Chemical Engineering and Materials Science, University of Minnesota（明尼苏达大学化学工程与材料科学系）；Simons Center for Computational Physical Chemistry, Department of Chemistry, New York University（纽约大学化学系西蒙斯计算物理化学中心）
Active polymers play a central role in many biological systems, from bacterial flagella to cellular cytoskeletons. Minimal models of semiflexible active filaments have been used to study a variety of interesting phenomena in active systems, such as defect dynamics in active nematics, clustering and laning in motility assays, and conformational properties of chromatin in eukaryotic cells. In this paper, we map a semiflexible polymer to an exactly solvable active Rouse chain, which enables us to analytically compute configurational and dynamical properties of active polymers with arbitrary rigid…
Self-sustained turbulent structures have been observed in a wide range of living fluids, yet no quantitative theory exists to explain their properties. We report experiments on active turbulence in highly concentrated 3D suspensions of Bacillus subtilis and compare them with a minimal fourth-order vector-field theory for incompressible bacterial dynamics. Velocimetry of bacteria and surrounding fluid, determined by imaging cells and tracking colloidal tracers, yields consistent results for velocity statistics and correlations over two orders of magnitude in kinetic energy, revealing a decrease…
Active nematics are the nonequilibrium analog of passive liquid crystals in which anisotropic units consume free energy to drive emergent behavior. Similar to liquid crystal (LC) molecules in displays, ordering and dynamics in active nematics are sensitive to boundary conditions; however, unlike passive liquid crystals, active nematics, such as those composed of living matter, have the potential to regulate their boundaries through self-generated stresses. Here, using bacterial biofilms confined by a hydrogel as a model system, we show how a three-dimensional, living nematic can actively shape…
In growing active matter systems, a large collection of engineered or living autonomous units metabolize free energy and create order at different length scales as they proliferate and migrate collectively. One such example is bacterial biofilms, which are surface-attached aggregates of bacterial cells embedded in an extracellular matrix. However, how bacterial growth coordinates with cell-surface interactions to create distinctive, long-range order in biofilms remains elusive. Here we report a collective cell reorientation cascade in growing Vibrio cholerae biofilms, leading to a differential…
Active fluids, such as cytoskeletal filaments, bacterial colonies and epithelial cell layers, exhibit distinctive orientational coherence, often characterized by nematic order and topological defects. By contrast, little is known about positional coherence -- i.e., how a hidden dynamic skeleton organizes the underlying chaotic motion -- despite this being one of their most prominent and experimentally accessible features. Using a combination of dynamical systems theory, experiments on two-dimensional mixtures of microtubules and kinesin and hydrodynamic simulations, we characterize positional …
Bacterial suspensions--a premier example of active fluids--show an unusual response to shear stresses. Instead of increasing the viscosity of the suspending fluid, the emergent collective motions of swimming bacteria can turn a suspension into a "superfluid" with zero apparent viscosity. Although the existence of active "superfluids" has been demonstrated in bulk rheological measurements, the microscopic origin and dynamics of such an exotic phase have not been experimentally probed. Here, using high-speed confocal rheometry, we study the dynamics of concentrated bacterial suspensions under si…
We provide a quantitative description of the helicoid--to--spiral transition in thin ribbons of nematic elastomers using an elementary calculation based on a Koiter-type plate with incompatible reference configuration. Our calculation confirms that such transition is ruled by the competition between stretching energy and bending energy.
Interaction between active materials and the boundaries of geometrical confinement is key to many emergent phenomena in active systems. For living active matter consisting of animal cells or motile bacteria, the confinement boundary is often a deformable interface, and it has been unclear how activity-induced interface dynamics might lead to morphogenesis and pattern formation. Here we studied the evolution of bacterial active matter confined by a deformable boundary. We discovered that an ordered morphological pattern emerged at the interface characterized by periodically-spaced interfacial p…
Recent experiments on active materials, such as dense bacterial suspensions and microtubule-kinesin motor mixtures, show a promising potential for achieving self-sustained flows. However, to develop active microfluidics it is necessary to understand the behaviour of active systems confined to channels. Therefore here we use continuum simulations to investigate the behaviour of active fluids in a two-dimensional channel. Motivated by the fact that most experimental systems show no ordering in the absence of activity, we concentrate on temperatures where there is no nematic order in the passive …
The understanding of self-organization in the twist-bend nematic $(N_\text{TB})$ phase, identified in 2011 in liquid crystal dimers, is at the forefront of soft matter research worldwide. This new nematic phase develops structural chirality in the isotropic $(I)$ and the uniaxial nematic $(N_\text{U})$ phases, despite the fact that the molecules forming the structure are chemically achiral. Molecular, shape-induced flexopolarization provides a viable mechanism for a qualitative understanding of $N_\text{TB}$ and the related phase transitions. The key question that remains is whether with this …
In microtubule-based active nematics, motor-driven extensile motion of microtubule bundles powers chaotic large-scale dynamics. We quantify the interfilament sliding motion both in isolated bundles and in a dense active nematic. The extension speed of an isolated microtubule pair is comparable to the molecular motor stepping speed. In contrast, the net extension in dense 2D active nematics is significantly slower; the interfilament sliding speeds are widely distributed about the average and the filaments exhibit both contractile and extensile relative motion. These measurements highlight the c…
Spontaneous oscillations and geometric cutoff in confined bacterial swarms
Center of Materials Science and Optoelectronics Engineering, College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences (UCAS)（中国科学院大学材料科学与光电技术学院物质科学与光电工程中心）；Department of Physics, Hong Kong Baptist University（香港浸会大学物理系）；Center for Interdisciplinary Studies, Westlake University（西湖大学交叉研究中心）
Despite the fact that quantitative experimental data have been available for more than forty years now, nematoacoustics still poses intriguing theoretical and experimental problems. In this paper, we prove that the main observed features of acoustic wave propagation through a nematic liquid crystal cell -- namely, the anisotropy of sound velocity and its frequency dependence -- may be plausibly explained by a first-gradient continuum theory characterized by a hyperelastic anisotropic response from an evolving relaxed configuration. We compare and contrast our proposal with a competing theory w…
We combine experiments, theory, and simulations to investigate the coexistence of nonequilibrium phases emerging from interacting colloidal particles that are electrokinetically propelled in a nematic liquid crystal solvent. We directly determine the mechanical pressure within the radial assemblies and measure a non-equilibrium equation of state for this athermal driven system. A generic model combines phoretic propulsion with the interplay between electrostatic effects and liquid-crystal-mediated hydrodynamics, which are effectively cast into a long-range interparticle repulsion, while elasti…
A range of monodomain nematic liquid crystal elastomers containing differing proportions of photo-isomerisable mesogenic moieties, which turn from a rod-like to a kinked shape upon ultraviolet (UV) irradiation, was studied. Depending on the proportion and positional role of the photo-sensitive groups in the crosslinked polymer network, different types and magnitudes of response were found. The principle consequence of such photo-isomerisation is the destabilisation of the nematic phase, whose order parameter depends on temperature in a near-critical fashion. Accordingly, the effect of UV-irrad…
A continuum description is essential for understanding a variety of collective phenomena in active matter. However, building quantitative continuum models of active matter from first principles can be extremely challenging due to both the gaps in our knowledge and the complicated structure of nonlinear interactions. Here we use a novel physically-informed data-driven approach to construct a complete mathematical model of an active nematic from experimental data describing kinesin-driven microtubule bundles confined to an oil-water interface. We find that the structure of the model is similar t…
Many types of bacteria swim by rotating a bundle of helical filaments also called flagella. Each filament is driven by a rotary motor and a very flexible hook transmits the motor torque to the filament. We model it by discretizing Kirchhoff's elastic-rod theory and develop a coarse-grained approach for driving the helical filament by a motor torque. A rotating flagellum generates a thrust force, which pushes the cell body forward and which increases with the motor torque. We fix the rotating flagellum in space and show that it buckles under the thrust force at a critical motor torque. Buckling…
