Publications 2015-2019

Bistability in the synchronization of actuated microfilaments
by H. Guo, L. Fauci, M. Shelley, and E. Kanso
submitted (2017)

Connecting macroscopic dynamics with microscopic properties in active microtubule network contraction
by P. Foster, W. Yan, S. Fuerthauer, M. Shelley, and D. Needleman
submitted (2017)

Flexibly imposing periodicity in kernel independent FMM: A Multipole-To-Local operator approach
by W. Yan and M. Shelley
submitted (2017)

Activity-induced instability in 1D microfluidic crystals
by A.C. Hou Tsang, M. Shelley, and E. Kanso
submitted (2017)

Guiding microscale swimmers using teardrop-shaped posts
by M. Davies Wykes, X. Zhong, J. Tong, T. Adachi, Y. Liu, L. Ristroph, M. Ward, M. Shelley, and J. Zhang, in Soft Matter 13, 4681-4688 (2017).

Abstract: he swimming direction of biological or artificial microscale swimmers tends to be randomised over long time-scales by thermal fluctuations. Bacteria use various strategies to bias swimming behaviour and achieve directed motion against a flow, maintain alignment with gravity or travel up a chemical gradient. Herein, we explore a purely geometric means of biasing the motion of artificial nanorod swimmers. These artificial swimmers are bimetallic rods, powered by a chemical fuel, which swim on a substrate printed with teardrop-shaped posts. The artificial swimmers are hydrodynamically attracted to the posts, swimming alongside the post perimeter for long times before leaving. The rods experience a higher rate of departure from the higher curvature end of the teardrop shape, thereby introducing a bias into their motion. This bias increases with swimming speed and can be translated into a macroscopic directional motion over long times by using arrays of teardrop-shaped posts aligned along a single direction. This method provides a protocol for concentrating swimmers, sorting swimmers according to different speeds, and could enable artificial swimmers to transport cargo to desired locations.

Analytical structure, dynamics, and reduction of a kinetic model of an active fluid
by T. Gao, M. Betterton, A. Huang, and M. Shelley
in Physical Review Fluids 2, 093302 (2017).

Abstract:We analyze one of the simplest active suspensions with complex dynamics: a suspension of immotile “extensor” particles that exert active extensile dipolar stresses on the fluid in which they are immersed. This is relevant to several experimental systems, such as recently studied tripartite rods that create extensile flows by consuming a chemical fuel. We first describe the system through a Doi-Onsager kinetic theory based on microscopic modeling. This theory captures the active stresses produced by the particles that can drive hydrodynamic instabilities, as well as the steric interactions of rodlike particles that lead to nematic alignment. This active nematic system yields complex flows and disclination defect dynamics very similar to phenomenological Landau–deGennes Q-tensor theories for active nematic fluids, as well as by more complex Doi-Onsager theories for polar microtubule–motor-protein systems. We apply the quasiequilibrium Bingham closure, used to study suspensions of passive microscopic rods, to develop a nonstandard Q-tensor theory. We demonstrate through simulation that this BQ-tensor theory gives an excellent analytical and statistical accounting of the suspension's complex dynamics, at a far reduced computational cost. Finally, we apply the BQ-tensor model to study the dynamics of extensor suspensions in circular and biconcave domains. In circular domains, we reproduce previous results for systems with weak nematic alignment, but for strong alignment we find unusual dynamics with activity-controlled defect production and absorption at the boundaries of the domain. In biconcave domains, a Fredericks-like transition occurs as the width of the neck connecting the two disks is varied.

A computational model of the flight dynamics and aerodynamics of a jellyfish-like flying machine
by F. Fang, K. Ho, L. Ristroph, and M. Shelley
in Journal of Fluid Mechanics 819, 621-655 (2017).

Abstract: We explore theoretically the aerodynamics of a recently fabricated jellyfish-like flying machine (Ristroph & Childress, J. R. Soc. Interface , vol. 11 (92), 2014, 20130992). This experimental device achieves flight and hovering by opening and closing opposing sets of wings. It displays orientational or postural flight stability without additional control surfaces or feedback control. Our model ‘machine’ consists of two mirror-symmetric massless flapping wings connected to a volumeless body with mass and moment of inertia. A vortex sheet shedding and wake model is used for the flow simulation. Use of the fast multipole method allows us to simulate for long times and resolve complex wakes. We use our model to explore the design parameters that maintain body hovering and ascent, and investigate the performance of steady ascent states. We find that ascent speed and efficiency increase as the wings are brought closer, due to a mirror-image ‘ground-effect’ between the wings. Steady ascent is approached exponentially in time, which suggests a linear relationship between the aerodynamic force and ascent speed. We investigate the orientational stability of hovering and ascent states by examining the flyer’s free response to perturbation from a transitory external torque. Our results show that bottom-heavy flyers (centre of mass below the geometric centre) are capable of recovering from large tilts, whereas the orientation of the top-heavy flyers diverges. These results are consistent with the experimental observations in Ristroph & Childress ( J. R. Soc. Interface , vol. 11 (92), 2014, 20130992), and shed light upon future designs of flapping-wing micro aerial vehicles that use jet-based mechanisms.

Fast accurate methods for simulating fiber suspensions applied to cellular mechanics
by E. Nazockdast, A. Rahimian, D. Zorin, and M. Shelley
in Journal of Computational Physics 329, 173-209 (2017)

Abstract: We present a novel platform for the large-scale simulation of three-dimensional fibrous structures immersed in a Stokesian fluid and evolving under confinement or in free-space in three dimensions. One of the main motivations for this work is to study the dynamics of fiber assemblies within biological cells. For this, we also incorporate the key biophysical elements that determine the dynamics of these assemblies, which include the polymerization and depolymerization kinetics of fibers, their interactions with molecular motors and other objects, their flexibility, and hydrodynamic coupling. This work, to our knowledge, is the first technique to include many-body hydrodynamic interactions (HIs), and the resulting fluid flows, in cellular assemblies of flexible fibers....

The effect of microtubule-cytoplasm interactions on pronuclear migration
by E. Nazockdast, A. Rahimian, D. Needleman, and M. Shelley
in Molecular Biology of the Cell, now online (2017).

Abstract: The proper positioning of the mitotic spindle is crucial for asymmetric cell division and generating cell diversity during development. Proper position in the single-cell embryo of Caenorhabditis elegans is achieved initially by the migration and rotation of the pronuclear complex (PNC) and its two associated centrosomal arrays of microtubules (MTs). We present here the first systematic theoretical study of how these O(1000) centrosomal microtubules (MTs) interact through the immersing cytoplasm, the cell periphery and PNC, and with each other, to achieve proper position. This study is made possible through our development of a highly efficient and parallelized computational framework that accounts explicitly for long-ranged hydrodynamic interactions (HIs) between the MTs, while also capturing their flexibility, dynamic instability, and interactions with molecular motors and boundaries. First, we show through direct simulation that previous estimates of the PNC drag coefficient, based on either ignoring or partially including HIs, lead to misprediction of the active forces and time-scales of migration. We then directly study the dynamics of PNC migration under various force-transduction models, including the pushing or pulling of MTs at the cortex, and the pulling of MTs by cytoplasmically-bound force generators. While achieving proper position and orientation on physiologically reasonable time-scales does not uniquely choose a model, we find that each model produces a different signature in its induced cytoplasmic flow and MT conformations. We suggest then that cytoplasmic flows and MT conformations can be used to differentiate between mechanisms and to determine their contribution to the migration process.  

C. elegans chromosomes connect to centrosomes by anchoring into the spindle network
by S. Redemann et al
in Nature Communications (2017) 8, 15288.

Abstract: The mitotic spindle ensures the faithful segregation of chromosomes. To discover the nature of the crucial centrosome-to-chromosome connection during mitosis, we combined the first large-scale serial electron tomography of whole mitotic spindles in early C. elegans embryos with live-cell imaging. Using tomography, we reconstructed the positions of all microtubules in 3D, and identified their plus- and minus-ends. We classified them as kinetochore (KMTs), spindle (SMTs), or astral microtubules (AMTs) according to their positions, and quantified distinct properties of each class. While our light microscopy and mutant studies show that microtubules are nucleated from the centrosomes, we find only a few KMTs are directly connected to the centrosomes. Indeed, by quantitatively analysing several models of microtubule growth, we conclude that minus-ends of KMTs have selectively detached and depolymerized from the centrosome. In toto, our results show that the connection between centrosomes and chromosomes is mediated by an anchoring into the entire spindle network and that any direct connections through KMTs are few and likely very transient.

Forces positioning the mitotic spindle in the cell; Theories, and now experiments
by H. Wu, E. Nazockdast, M. Shelley, and D. Needleman
in BioEssays 39,
1600212 (2017)

Abstract: The position of the spindle determines the position of the cleavage plane, and is thus crucial for cell division. Although spindle positioning has been extensively studied, the underlying forces ultimately responsible for moving the spindle remain poorly understood. A recent pioneering study by Garzon-Coral et al. uses magnetic tweezers to perform the first direct measurements of the forces involved in positioning the mitotic spindle. Combining this with molecular perturbations and geometrical effects, they use their data to argue that the forces that keep the spindle in its proper position for cell division arise from astral microtubules growing and pushing against the cell's cortex. Here, we review these ground-breaking experiments, the various biomechanical models for spindle positioning that they seek to differentiate, and discuss new questions raised by these measurements.

Dynamic self-assembly of microscale rotors and swimmers
by M. Davies Wykes, J. Palacci, T. Adachi, L. Ristroph, X. Zhong, M. Ward, J. Zhang, and M. Shelley
In Soft Matter 12, 4584-4589 (2016)

Abstract: Biological systems often involve the self-assembly of basic components into complex and functioning structures. Artificial systems that mimic such processes can provide a well-controlled setting to explore the principles involved and also synthesize useful micromachines. Our experiments show that immotile, but active, components self-assemble into two types of structure that exhibit the fundamental forms of motility: translation and rotation. Specifically, micron-scale metallic rods are designed to induce extensile surface flows in the presence of a chemical fuel; these rods interact with each other and pair up to form either a swimmer or a rotor. Such pairs can transition reversibly between these two configurations, leading to kinetics reminiscent of bacterial run-and-tumble motion.

Elastic fibers in flows
by A. Lindner and M. Shelley
in Fluid-structure interactions at low Reynolds numbers, eds. C. Duprat and H. A. Stone, Royal Society of Chemistry (2016)

Introduction:  A very common class of fluid-structure interaction problems involves the dynamics of flexible fibers immersed in a Stokesian fluid. In biology this arises in modeling the flagellae or cilia involved in micro-organismal locomotion and mucal transport, in determining the shape of biofilm streamers, and in understanding how biopolymers such as microtubules respond to the active coupling afforded by motor proteins. In engineering it arises in the paper processing industry, where wood pulp suspensions can show the abrupt appearance of normal stress differences, and in micro-fluidic engineering where flow control using flexible particles has lately been explored. Flow induced buckling of fibers is an important determinant on fiber transport in those flows, as well as for the fluid mechanical stresses that develop...

The dynamics of microtubule/motor-protein assemblies in biology and physics
by M. Shelley
In Annual Reviews of Fluid Mechanics 48, 487-506 (2016)

Abstract: Many important processes in the cell are mediated by stiff microtubule polymers and the active motor proteins moving upon them. This includes the transport of subcellular structures (nuclei, chromosomes, organelles),  and the self-assembly and positioning of the mitotic spindle. Very little is yet understood of these processes but they all present fascinating problems in fluid/structure interactions. Microtubules and motor proteins are also the building blocks of new "bio-synthetic" active suspensions driven by motor-protein activity. These reduced systems can probed, and modeled, more easily than the fully biological ones and show their own aspects of self-assembly and complex dynamics. I will review recent work modeling such systems as  uid/structure interaction problems, and as multiscale complex  fluids.

Active contraction of microtubule networks
by P. Foster, S. Furthauer, M. Shelley, and D. Needleman
in eLife, 10837 (2015)

Abstract: Many cellular processes are driven by cytoskeletal assemblies. It remains unclear how cytoskeletal filaments and motor proteins organize into cellular scale structures and how molecular properties of cytoskeletal components affect the large scale behaviors of these systems. Here we investigate the self-organization of stabilized microtubules in Xenopus oocyte extracts and find that they can form macroscopic networks that spontaneously contract. We propose that these contractions are driven by the clustering of microtubule minus ends by dynein. Based on this idea, we construct an active fluid theory of network contractions which predicts a dependence of the timescale of contraction on initial network geometry, a development of density inhomogeneities during contraction, a constant final network density, and a strong influence of dynein inhibition on the rate of contraction, all in quantitative agreement with experiments. These results demonstrate that the motor-driven clustering of filament ends is a generic mechanism leading to contraction

Multiscale modeling and simulation of microtubule�motor-protein assemblies
by T. Gao, R. Blackwell, M. Glaser, D. Betterton, and M. Shelley
In Physical Review E 92, 062709 (2015)

Abstract: Microtubules and motor proteins self-organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by adenosine triphosphate�consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield such larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-motor systems in which Brownian dynamics simulations of polar microtubules driven by motors are used to study microscopic organization and stresses created by motor-mediated microtubule interactions. We identify polarity-sorting and crosslink tether relaxation as two polar-specific sources of active destabilizing stress. We then develop a continuum Doi-Onsager model that captures polarity sorting and the hydrodynamic flows generated by these polar-specific active stresses. In simulations of active nematic flows on immersed surfaces, the active stresses drive turbulent flow dynamics and continuous generation and annihilation of disclination defects. The dynamics follow from two instabilities, and accounting for the immersed nature of the experiment yields unambiguous characteristic length and time scales. When turning off the hydrodynamics in the Doi-Onsager model, we capture formation of polar lanes as observed in the Brownian dynamics simulation.

Hydrodynamic schooling of flapping swimmers
by A. Becker, H. Masoud, J. Newbolt, M. Shelley, and L. Ristroph
in Nature Communications
6, 8514 (2015)

Abstract: Fish schools and bird flocks are fascinating examples of collective behaviours in which many individuals generate and interact with complex flows. Motivated by animal groups on the move, here we explore how the locomotion of many bodies emerges from their flow-mediated interactions. Through experiments and simulations of arrays of flapping wings that propel within a collective wake, we discover distinct modes characterized by the group swimming speed and the spatial phase shift between trajectories of neighbouring wings. For identical flapping motions, slow and fast modes coexist and correspond to constructive and destructive wing�wake interactions. Simulations show that swimming in a group can enhance speed and save power, and we capture the key phenomena in a mathematical model based on memory or the storage and recollection of information in the flow field. These results also show that fluid dynamic interactions alone are sufficient to generate coherent collective locomotion, and thus might suggest new ways to characterize the role of flows in animal groups.

Multiscale polar theory of Microtubule and Motor-Protein Assemblies
by T. Gao, R. Blackwell, M. Glaser, M. Betterton, and M. Shelley
in Physical Review Letters 114, 048101 (2015)

Abstract: Microtubules and motor proteins are building blocks of self-organized subcellular biological structures such as the mitotic spindle and the centrosomal microtubule array. These same ingredients can form new �bioactive� liquid-crystalline fluids that are intrinsically out of equilibrium and which display complex flows and defect dynamics. It is not yet well understood how microscopic activity, which involves polarity dependent interactions between motor proteins and microtubules, yields such larger-scale dynamical structures. In our multiscale theory, Brownian dynamics simulations of polar microtubule ensembles driven by cross-linking motors allow us to study microscopic organization and stresses. Polarity sorting and crosslink relaxation emerge as two polar-specific sources of active destabilizing stress. On larger length scales, our continuum Doi-Onsager theory captures the hydrodynamic flows generated by polarity-dependent active stresses. The results connect local polar structure to flow structures and defect dynamics.

Transport and buckling dynamics of an elastic fiber in in a viscous cellular flow
By N. Quennouz, M. Shelley, O. du Roure, and A. Lindner
in Journal of Fluid Mechanics 769, 387-402 (2015).

Abstract: We study, using both experiment and theory, the coupling of transport and shape dynamics for elastomeric fibres moving through an inhomogeneous flow. The cellular flow, created electromagnetically in our experiment, comprises many identical cells of counter-rotating vortices, with a global flow geometry characterized by a backbone of stable and unstable manifolds connecting hyperbolic stagnation points. Our mathematical model is based upon slender-body theory for the Stokes equations, with the fibres modelled as inextensible elastica. Above a certain threshold of the control parameter, the elasto-viscous number, transport of fibres is mediated by their episodic buckling by compressive stagnation point flows, lending an effectively chaotic component to their dynamics. We use simulations of the model to construct phase diagrams of the fibre state (buckled or not) near stagnation points in terms of two variables that arise in characterizing the transport dynamics. We show that this reduced statistical description quantitatively captures our experimental observations. By carefully reproducing the experimental protocols and time scales of observation within our numerical simulations, we also quantitatively explain features of the measured buckling probability curve as a function of the effective flow forcing. Finally, we show within both experiment and simulation the existence of short and long time scales in the evolution of fibre conformation.

Theory of active suspensions
by D. Saintillan and M. Shelley
in Complex Fluids in Biological Systems, S. Spagnolie (ed.), Springer-Verlag

Abstract: Active suspensions, of which a bath of swimming microorganisms is a paradigmatic example, denote large collections of individual particles or macromolecules capable of converting fuel into mechanical work and microstructural stresses. Such systems, which have excited much research in the last decade, exhibit complex dynamical behaviors such as large-scale correlated motions and pattern formation due to hydrodynamic interactions. In this chapter, we summarize efforts to model these systems using particle simulations and continuum kinetic theories. After reviewing results from experiments and simulations, we present a general kinetic model for a suspension of self-propelled rod-like particles and discuss its stability and nonlinear dynamics. We then address extensions of this model that capture the effect of steric interactions in concentrated systems, the impact of confinement and interactions with boundaries, and the effect of the suspending medium rheology. Finally, we discuss new active systems such as those that involve the interactions of biopolymers with immersed motor proteins, and surface-bound suspensions of chemically-powered particles.