Session S49: Focus Session: Migration of Cells, Droplets, and Particles on Substrates: Mostly Active Nematics

Collisions of deformable cells lead to collective migration

Collective migration of eukaryotic cells plays a fundamental role in tissue growth, wound healing and immune response. The motion, arising spontaneously or in response to chemical and mechanical stimuli, is also important for understanding life-threatening pathologies, such as cancer and metastasis formation. We present a phase-field model to describe the movement of many self-organized, interacting cells. The model takes into account the main mechanisms of cell motility - actomyosin dynamics, as well as substrate-mediated and cell-cell adhesion. It predicts that collective cell migration emerges spontaneously as a result of inelastic collisions between neighboring cells: collisions lead to a mutual alignment of the cell velocities and to the formation of coherently-moving multi-cellular clusters. Small cell-to-cell adhesion, in turn, reduces the propensity for large-scale collective migration, while higher adhesion leads to the formation of moving bands. Our study provides valuable insight into biological processes associated with collective cell motility.   

A self-propelled particle model with experimentally quantified cell polarization

Self-propelled particle (SPP) models have been used extensively to study collective cell motion, but they do not always accurately capture the long-time behavior observed in experiments. Furthermore, the equation for polarization in these models is not experimentally well-constrained. Therefore we developed a novel method for quantifying polarization in Hs578T breast carcinoma cells in a wound healing geometry. During cell movement, the nucleus orients toward the anterior of a cell while the Golgi body orients towards the posterior; we simultaneously imaged and tracked the Golgi and nuclei and constructed a polarization vector defined by the Golgi-nuclei axis. We find that cells in the bulk are not highly polarized, while those on the edge are highly polarized outward perpendicular to the wound edge. We also study the temporal correlations between a cell's internal polarization determined by the Golgi-nuclei axis and the polarization of its motion determined from nuclei displacements. We incorporate these polarization dynamics into a SPP model, and compare wound healing and long-time diffusion in the model to the experiments. These SPP equations can also be coarse-grained to generate a continuum model.   

Modeling traction forces in collective cell migration

Collective cell migration is an important process in embryonic development, wound healing, and cancer metastasis. We have developed a particle-based simulation for collective cell migration that describes flow patterns and finger formation at the tissue edge observed in wound healing experiments [1]. We can apply methods for calculating intercellular stress to our simulation model, and have thereby provided evidence for the validity of a stress reconstitution method from traction forces used in experiments [2]. To accurately capture experimentally measured traction forces and stresses in the tissue, which are mostly tensile, we have to include intracellular acto-myosin contraction into our simulation. We can then reproduce the experimentally observed behavior of cells moving around a circular obstacle [3], and suggest underlying mechanisms for cell-cell alignment and generation of traction force patterns. [1] Basan, M., J. Elgeti, E. Hannezo, W.-J. Rappel, H. Levine. Proc. Natl. Acad. Sci. USA. 2013. [2] Zimmermann, J., R. L. Hayes, M. Basan, J. N. Onuchic, W.-J. Rappel, H. Levine. Biophys. J. 2014. [3] Kim, J. H., X. Serra-Picamal, D. T. Tambe, ..., J. J. Fredberg. Nature Mater. 2013.   

Mimicking the Interfacial Dynamics of Flowing White Blood Cells

The rolling of particles on surfaces, facilitated by hydrodynamic forces combined with localized surface interactions of the appropriate strengths, spatial arrangements, and ranges, is a technologically useful means of transporting and manipulating particles. One's intuition for the rolling of a marble or a car tire cannot be extrapolated down to microparticle length scales because the microparticle interactions are dominated by electrostatic, van der Waals, and hydrogen bonding interactions rather than a friction that depends on an imposed normal force. Indeed, our microparticle rolling systems are inspired by the rolling of white blood cells on the inner walls of venules as part of the innate immune response: Selectin molecules engage with their counterparts on the opposing surfaces to slow cell motion relative to that for freely flowing cells. In the resulting rolling signature, ligand-receptor binding and crack closing on the front of the cell are balanced with molecular dis-bonding and crack opening at the rear. The contact region is relatively static, allowing other interactions (for instance signaling) to occur for a finite duration. Thus, achieving particle rolling in synthetic systems is important because it facilitates particle-surface interactions in a continuous nonfouling fashion where the contact surface is continually renewed. In developing a synthetic model for this system, we employ polymers to modify flowing particles and /or planar collectors, producing heterogeneous interfaces which can support rolling or produce other motion signatures such as skipping, arrest, or free flow. We identify, in the synthetic system, combinations of variables that produce rolling and demonstrate how the distinction between rolling and arrest is not a simple matter of the adhesion strength between the particles and the collector. Rolling is a cooperative process and the coordination of binding in one location with dis-bonding in another requires appropriate length scales in the design of the interface and in the processing parameters as well.   

Long Range Order of Motile Defects in Active Nematic Liquid Crystals

Active 2D nematic liquid crystals exist in a dynamical steady state in which $+$1/2 and -1/2 defects are spontaneously generated and annihilated at a constant rate. Active stresses in the material are thought to destroy nematic order through the generation of these defects. We present an active nematic mesophase in which motile defects of charge $+$1/2 spontaneously acquire long range order. The system is composed of microtubule filaments and kinesin motor protein clusters which are confined to a flat, 2D oil-water interface. The addition of ATP results in microtubule bundles which exhibit kinesin-driven extensile motion. By tuning the density of the nematic material at the 2D interface, we can tune the order parameter of the $+$1/2 defect ordered mesophase. Additionally, the defect alignment persists over samples at the centimeter scale.   

Defect-Stabilized Phases in Extensile Active Nematics

Active nematics are liquid crystals which are driven out of equilibrium by energy-dissipating active stresses. The equilibrium nematic state is unstable in these materials, leading to beautiful and surprising behaviors including the spontaneous generation of topological defect pairs which stream through the system and later annihilate, yielding a complex, seemingly chaotic dynamical steady-state. In this talk, I will describe the emergence of order from this chaos in the form of previously unknown broken-symmetry phases in which the topological defects themselves undergo orientational ordering. We have identified these defect-ordered phases in two realizations of an active nematic: first, a suspension of extensile bundles of microtubules and molecular motor proteins, and second, a computational model of extending hard rods. I will describe the defect-stabilized phases that manifest in these systems, our current understanding of their origins, and discuss whether such phases may be a general feature of extensile active nematics.   

Worms on a plane: simulation studies of an active nematic phase of flexible chains

We present simulation studies of flexible nematogen ``worms'' composed of soft spheres assembled into flexible polymer-like chains. These elongated, flexible chains are confined to a planar substrate with periodic boundary conditions or else confined within bounding walls. We consider a variety of driving mechanisms including unidirectional gliding and gliding with random reversals. We also model actuation via kinesin motor clusters which attach and travel along a pair of neighboring chains of opposite polarity, producing inter-chain sliding forces and driving the chains in opposite directions. We examine resulting nematic order, defect nucleation, motion, and annihilation, and density fluctuations as a function of chain length, flexibility, density, and driving mechanism. In a geometry where the chains are constrained to move in tandem with tight spacing, we observe spontaneous formation of organized beating. We compare our results to experimental and theoretical studies of gliding bacteria [1] and kinesin-driven microtubules [2]. [1] Peruani et al. PRL 108, 098102 (2012), [2] Sanchez et al, Nature 491,431 (2012).   

Instabilities and patterns in an active nematic film

Experiments on microtubule bundles confined to an oil-water interface have motivated extensive theoretical studies of two-dimensional active nematics. Theoretical models taking into account the interplay between activity, flow and order have remarkably reproduced several experimentally observed features of the defect-dynamics in these ``living'' nematics. Here, we derive minimal description of a two-dimensional active nematic film confined between walls. At high friction, we eliminate the flow to obtain closed equations for the nematic order parameter, with renormalized Frank elastic constants. Active processes can render the ``Frank'' constants negative, resulting in the instability of the uniformly ordered nematic state. The minimal model yields emergent patterns of growing complexity with increasing activity, including bands and turbulent dynamics with a steady density of topological defects, as obtained with the full hydrodynamic equations. We report on the scaling of the length scales of these patterns and of the steady state number of defects with activity and system size.   

Dynamics of an overdamped active nematic liquid crystal

A continuum model for the dynamics of an overdamped (often termed ``dry") active nematic liquid crystal will be presented here. This talk will focus on how such a model can be used to describe the formation and self-propulsion of defects which has been seen in active liquid crystals in experiments and simulations. We will start with a general model which shows phase-separations and structure formation near the critical density (for the isotropic-nematic phase transition), and show how this model can be extended to describe extensile active nematics which are deeper within the ordered phase. The spontaneous formation of defects occurs when the contribution of the extensile stresses, to the dynamics of the order parameter, gives rise to a bend instability. This leads to a steady state of defect formation and annihilation, and the self-propulsion of defects, as is seen in experiments and simulation.   

The geometry and topology of turbulence in active nematics

The problem of low Reynolds number turbulence in active nematic fluids is theoretically addressed. Using numerical simulations I demonstrate that an incompressible turbulent flow, in two-dimensional active nematics, consists of an ensemble of vortices whose areas are exponentially distributed within a range of scales. Building on this evidence, I construct a mean-field theory of active turbulence by which several measurable quantities, including the spectral densities and the correlation functions, can be analytically calculated. Due to the profound connection between the flow geometry and the topological properties of the nematic director, the theory sheds light on the mechanisms leading to the proliferation of topological defects in active nematics and provides a number of testable predictions. A hypothesis, inspired by Onsager's statistical hydrodynamics, is finally introduced to account for the equilibrium probability distribution of the vortex sizes.   

Instabilities and boundary effects in a droplet of active polar liquid crystal

Using the active gel theoretical framework, we have performed analytical calculations and numerical simulations of a droplet of active polar liquid crystal at low Reynolds number. This system is a simplified model of a cytoskeletal network that generates internal stresses by converting chemical energy (in the form of ATP) into mechanical work via molecular motors. A physical understanding of these systems can give an insight into the complex and varied dynamics of eukaryotic cell migration and division. We perform a linear stability analysis on the system by separating the behaviour into two limits. One where the internal polarisation is dominated by the shape of the boundary and one where it is deformed by the activity. We find that the two regimes show different instability thresholds for the activity parameter suggesting interesting behaviour both in and between these limits. We also simulate the system numerically and find the resulting steady state of the droplet for a range of parameters between these two limits.   

Interacting active elastic dimers: Two cells moving on a rigid track

Cell migration in morphogenesis and cancer metastasis typically involves an interplay between different cell types. The rules governing such interplay remain largely unknown, however, a recent experiment studying the interaction between neural crest (NC) cells and placodal cells reveals an example of such rules. The study found that NC cells chase the placodal cells by chemotaxis, while placodal cells run away from NC cells when contacted by them. Motivated by this observation, we construct and study a minimal one-dimensional cell-cell model comprised of two cells with each cell represented by two-beads-connected-by-an-active spring. The active spring for each moving cell models the stress fibers with their myosin-driven contractility (and alpha-actinin extendability), while the friction coefficients of the beads describe the catch/slip bond behavior of the integrins in focal adhesions. We also include a dynamic contact interaction between the two cells, as well as a chemotactic potential, to decipher the chase-and-run dynamics observed in the experiment. We then use our modeling to further generalize the rules governing the interplay between different cell types during collective cell migration.