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Timetable (CFMW01)

Dynamics of active suspensions, gels, cells and tissues

Monday 24th June 2013 to Friday 28th June 2013

Monday 24th June 2013
09:00 to 09:45 Registration at INI
09:45 to 10:30 R Goldstein (University of Cambridge)
Spontaneous Circulation of Confined Active Suspensions
Many active fluid systems encountered in biology are set in total geometric confinement. Cytoplasmic streaming in plant cells is a prominent and ubiquitous example, in which cargo-carrying molecular motors move along polymer filaments and generate coherent cell-scale flow. In this talk I will summarize theoretical and experimental work in my group that addresses the possibility that the ordered patterns of streaming seen in nature can arise from a process of self-organization.
10:30 to 11:00 Morning Coffee at INI
11:00 to 11:45 Active motion: under external fields and collective dynamics
Active motion of microorganisms or artificial microswimmers, such as active colloids, is an appealing subject which has attracted much attention recently. Since these swimmers move constantly in non-equilibrium, they give rise to novel phenomena which, in particular, occur when external fields are applied or when they move collectively.

The talk reviews our recent work on how active Brownian particles behave in external fields and in confinement. For example, they develop orientational order in a gravitational field [1] and exhibit an interesting instability in dense suspensions when they are bottom-heavy. They also create active fluid pumps in a harmonic trap. Finally, under Poiseuille flow they show nonlinear dynamics reminiscent of the nonlinear pendulum where the bounding walls introduce "dissipation" [2].

We also study the collective motion of so-called squirmers in a quasi 2D geometry by means of multi-particle collision dynamics. We observe dynamical clustering, phase separation, and active jamming which is strongly influenced by hydrodynamic near-field interactions. In dense suspensions rotational diffusion is greatly enhanced and the critical volume fraction for crystallisation is different for pushers and pullers.

[1] M. Enculescu and H. Stark, Phys. Rev. Lett. 106, 208103 (2011). [2] A. Zoettl and H. Stark, Phys. Rev. Lett. 108, 218104 (2012).

Co-authors: Marc Hennes (Institute of Theoretical Physics, Technische Universität Berlin), Katrin Wolff (Institute of Theoretical Physics, Technische Universität Berlin), Andreas Zoettl (Institute of Theoretical Physics, Technische Universität Berlin)

11:45 to 12:30 E Keaveny (Imperial College London)
Optimisation of chiral structures for micro-scale propulsion
In micron-scale hydrodynamics, shape and geometry play a strong role in determining the speed at which a body can move through fluid. This shape dependence is particularly important to the design of many microfluidic devices, including magnetically actuated micro-structures fabricated and studied for biomedical applications. In this talk, I will discuss several important experimentally-realisable micro-structures whose shapes couple their rotations and translations. I will address the optimal design of these devices through an infinite-dimensional optimisation problem, obtaining geometries that maximise speed for a given applied torque. Our optimisations show that attached payloads have a significant effect on optimal micro-structure shapes and current designs can be improved by upwards of 450%.
12:30 to 13:30 Lunch at Wolfson Court
14:00 to 14:30 M Koepf (Technion - Israel Institute of Technology)
A continuum model of epithelial spreading
We present a continuum model of unconstrained epithelial spreading. The tissue is described as a polarizable and chemo-mechanically interacting layer with neo-Hookean elasticity. Our model reproduces the spontaneous formation of finger-like protrusions commonly observed in experiment. Statistics of velocity orientation obtained from numerical simulation show strong alignment in the fingers opposed to an isotropic distribution in the bulk, as has been measured by Reffay et al. (Reffay et al., Biophysical Journal, 2011). The results faithfully reproduce faster relative advance of cells close to the leading edge of the tissue, as well as spatial velocity correlations and stress accumulation within the tissue, which proceeds in form of a "mechanical wave", traveling from the wound edge inwards (cf. Serra-Picamal et al., Nature Physics, 2012).

M H Koepf, L M Pismen: A continuum model of epithelial spreading (2013) submitted

M H Koepf, L M Pismen: Non-equilibrium patterns in polarizable active layers (2013) submitted

Co-author: Leonid M. Pismen (Department of Chemical Engineering, Technion - Israel Institute of Technology, 32000 Haifa, Israel)

14:30 to 15:00 Traveling and resting crystals in crowds of self-propelled particles
When the density within a crowd of self-propelled particles is high enough and when the interactions between these particles are strong enough, then it is plausible to expect that crystallization will occur. We are interested in the formation and in the behavior of such active crystals that are composed of self-propelled particles. To study this kind of materials using a field approach, we combine the classical phase field crystal model by Elder and Grant with the Toner-Tu theory for active media. In this way we obtain an active phase field crystal model. Our approach can further be justified from dynamic density functional theory. The active crystals that we identify can be classified into two groups: either the crystal is resting, meaning that no net density flux is observed, or it is traveling, meaning that the lattice peaks collectively migrate into one direction. As a central result we find that a transition from a resting to a traveling crystal can occur at a threshold value of the active drive. Consequently a variety of different crystalline phases can be identified: resting hexagonal, traveling hexagonal, swinging hexagonal, traveling rhombic, traveling quadratic, resting lamellar, traveling lamellar, resting honeycomb, and traveling honeycomb. Upon quenching from the fluid phase, the traveling crystals emerge through a coarse-graining process from domains of different directions of collective motion. Qualitatively we also studied the impact of additional hydrodynamic interactions between the lattice peaks. Since the properties and response of active crystals can be very different from their equilibrium counterparts, the knowledge of, classification of, and control of the different crystalline states can provide a starting point for the design of new active materials.

Co-author: Hartmut Lowen (Heinrich Heine University Dusseldorf, Germany)

15:00 to 15:30 S Banerjee (Syracuse University)
Collective mechanics of epithelial cell colonies on elastic substrates
Crosstalk between cell-cell and cell-matrix adhesions plays an essential role in the mechanical function of tissues. The traction stresses exerted by cohesive keratinocyte colonies with strong cell-cell adhesions are mostly concentrated at the colony periphery. In contrast, for weak cadherin-based intercellular adhesions, individual cells in a colony interact with their matrix independently, with disorganized distribution of traction stresses extending throughout the colony. In this talk I will present a minimal physical model of the colony as adherent contractile elastic media coupled to an elastic substrate. The model captures the spatial distribution of traction forces seen in experiments. For cell colonies with strong cell-cell adhesions, the total traction force of the colony measured in experiments is found to scale with the colony’s geometrical size. This scaling suggests the emergence of an effective surface tension of magnitude comparable to that measured fo r non-adherent, three-dimensional cell aggregates. The physical model supports the scaling and indicates that the surface tension may be controlled by acto-myosin contractility.

Co-authors: Aaron F. Mertz (Yale University), M. Cristina Marchetti (Syracuse University), Eric R. Dufresne (Yale University), Valerie Horsley (Yale University)

15:30 to 16:00 Afternoon Tea at INI
16:00 to 17:00 Rigidity, Zero Modes, States of Self Stress, and Surface Phonons in Periodic and Diluted Periodic Networks near their Instability Limit
Frames consisting of nodes connected pairwise by rigid rods or central-force springs, possibly with preferred relative angles controlled by bending forces, are useful models for systems as diverse as architectural structures, crystalline and amorphous solids, sphere packings and granular matter, networks of semi-flexible polymers, and protein structure. The rigidity of these networks depends on the average coordination number z of the nodes: If z is small enough, the frames have internal zero-frequency modes, and they are "floppy"; if z is large enough, they have no internal zero modes and they are rigid. The critical point separating these two regimes occurs at a rigidity threshold, which corresponds closely to what is often referred to as the isostatic point, that for central forces in d-dimensions occurs at coordination number zc = 2d. At and near the rigidity threshold, elastic frames exhibit unique and interesting properties, including extreme sensitivity to boundary conditions, power-law scaling of elastic moduli with (z- zc), and diverging length and time scales. This talk will explore elastic and mechanical properties and mode structures of model periodic and diluted periodic lattices, such as the square and kagome lattices with central-force springs, that are just on verge of mechanical instability, and 4-coordinated lattices in two and three dimensions that are stabilized by bending forces. It will discuss the origin and nature of zero modes of these structures under both periodic (PBC) and free boundary conditions (FBC), and it will derive general conditions under which (a) the zero modes under the two boundary conditions are essentially identical and (b) under which zero modes do not appear in the periodic spectrum but do appear as surface Rayleigh waves in the free spectrum. In the former situation, lattices are generally in a type of critical state that admits states of self-stress in which there can be tension in bars with zero force on any node, and distortions away from that state give rise to surface modes under free boundary conditions whose degree of penetration into the bulk diverges at the critical state. This general phenomenon also occurs in sub-isostatic lattices like the honeycomb lattice. The talk will also explore diluted 4-coordinated lattices as models for networks of semi-flexible polymers, discuss the special properties that result when constituent polymers adopt strictly straight configurations.
17:00 to 18:00 Welcome Wine Reception at INI
Tuesday 25th June 2013
09:00 to 09:45 Models of low-Reynolds-number swimmers and colloidal particles in confined domains
The talk will survey some simple mathematical models to gain insights into the dynamics of particles or swimmers of various kinds moving at zero Reynolds numbers in geometrically complex domains bounded by no-slip walls and/or free surfaces.
09:45 to 10:30 Locomotion of helical bodies in viscoelastic fluids
Many microorganisms swim by rotating one or many helical flagella, often propelling themselves through fluids that exhibit both viscous and elastic qualities in response to deformations. In an effort to better understand the complex interaction between the fluid and body in such systems, we have studied numerically the force-free swimming of a rotating helix in a viscoelastic (Oldroyd-B) fluid. The introduction of viscoelasticity can either enhance or retard the swimming speed depending on the body geometry and the properties of the fluid (through a dimensionless Deborah number). The numerical results show how small-amplitude theoretical calculations connect smoothly to large-amplitude experimental measurements.

Co-authors: Bin Liu (Brown University), Thomas R. Powers (Brown University)

10:30 to 11:00 Morning Coffee at INI
11:00 to 11:45 Concentration fluctuations in a bacterial suspension
Recent analyses and simulations have identified an instability of a quiescent bacterial suspension above a threshold concentration, (nL3)crit = (5/C)(L/U\tau), where n is the bacterium number density, L and U the bacterium length and swimming speed, t the mean interval between tumbles, and C a measure of the intrinsic force-dipole. This instability is thought to underlie the large-scale coherent motions observed in experiments. There, however, remains a discrepancy between theory and simulations. While the former predicts a spatially homogeneous instability with coupled orientation and velocity fluctuations, simulations have observed large-scale concentration fluctuations. Even in the stable regime, solutions of the linearized equations reveal significant concentration fluctuations.

We will formulate an analytical solution that illustrates the linearized evolution of the velocity, orientation and concentration fields in a bacterial suspension starting from an arbitrary initial condition. The analysis relies on a remarkable correspondence between orientation fluctuations in a bacterial suspension and vorticity fluctuations in an inviscid fluid. The governing operators in both cases possess singular continuous spectra in addition to discrete modes. The dynamics of the singular orientation modes leads to transient growth of concentration fluctuations in the manner that the singular vorticity modes lead to kinetic energy growth in high-Reynolds-number shearing flows. We will discuss the velocity, orientation and stress correlations, emerging from an uncorrelated Poisson field, both below and above the critical concentration.

We also analyze the role of tumbling as a source of fluctuations. Regarding a tumble as a ‘linear collision’ governed by Poisson statistics allows one to write down the orientation-space noise, and this in turn leads to the analog of the fluctuating hydrodynamic equations for a bacterial suspension.

Co-author: Donald Koch (Chemical and bio-molecular engineering, Cornell University, NY, USA.)

11:45 to 12:30 Hydrodynamic coordination of bacterial motions: from bundles to biomixing
Many bacteria propel themselves though their fluid environment by means of multiple rotating flagella that self-assemble to form bundles. At a larger scale, the fluid motion generated by an individual microbe as it swims affects the motions of its neighbors. Experimental observations indicate the presence of long-range order and enhanced transport in suspensions of bacteria -- these phenomena may be important in many aspects of bacterial dynamics including chemotaxis and development of biofilms. This talk focuses on the role of fluid dynamics in the bundling of flagella and the interactions between swimming organisms.

We first describe theory and simulations of hydrodynamically interacting microorganisms, using very simple models of the individual organisms. In the dilute limit, simple arguments reveal the dependence of swimmer and tracer velocities and diffusivities on concentration. As concentration increases, we show that cases exist in which the swimming motion generates large-scale flows and dramatically enhanced transport in the fluid. A physical argument supported by a mean field theory sheds light on the origin of these effects.

The second part of the talk focuses on the dynamics of the flagellar bundling process, using a mathematical model that incorporates the fluid motion generated by each flagellum as well as the finite flexibility of the flagella. The initial stage of bundling is driven purely by hydrodynamics, while the final state of the bundle is determined by a nontrivial and delicate balance between hydrodynamics and elasticity. As the flexibility of the flagella increases a regime is found where, depending on initial conditions, one finds bundles that are either tight, with the flagella in mechanical contact, or loose, with the flagella intertwined but not touching. That is, multiple coexisting states of bundling are found. The parameter regime at which this multiplicity occurs is comparable to the parameters for a number of bacteria.

12:30 to 13:30 Lunch at Wolfson Court
14:00 to 14:45 J Yeomans (University of Oxford)
Active Nematics
Active systems, such as the cytoskeleton and bacterial suspensions, provide their own energy and hence operate out of thermodynamic equilibrium. Continuum models describing active systems are closely related to those describing liquid crystal hydrodynamics, together with an additional ‘active’ stress term. We discuss how the behaviour of the active continuum models depends on model parameters, such as the strength of the activity and the liquid crystal tumbling parameter, and we compare our results to recent experiments on cytoskeletal gels.
14:45 to 15:30 Hierarchical active matter: from extensible bundles to active gels, streaming liquid crystals and motile emulsions
The emerging field of active matter promises an entirely new category of materials, with highly sought after properties such as autonomous motility and internally generated flows. In this vein, I will describe recent experiments that have focused on reconstituting dynamical structures from purified biochemical components. In particular I will describe recent advances that include: (1) assembly of a minimal model of synthetic cilia capable of generating periodic beating patterns, and conditions under which they exhibit metachronal traveling waves, (2) study of 2D active nematic liquid crystals whose streaming flows are determined by internal fractures and self-healing as well as spontaneous unbinding and recombination of oppositely charged disclination defects, (3) reconstitution of active gels characterized by highly tunable and controllable spontaneous internal flows, and (4) assembly of active emulsions in which aqueous droplets spontaneously crawl when in contact with a ha rd wall.
15:30 to 16:00 Afternoon Tea at INI
16:00 to 16:45 J Toner (University of Oregon)
Rice, Locusts and Chemical Waves: A Hydrodynamic Theory of Polar Active Smectics
We present a hydrodynamic theory of polar active smectics, by which we mean active striped systemsactive systems, both with and without number conservation. For the latter, we find quasi long-ranged smectic order in $d=2$ and long-ranged smectic order in $d=3$. In $d=2$ there is a Kosterlitz-Thouless type phase transition from the smectic phase to the ordered fluid phase driven by increasing the noise strength. For the number conserving case, we find that giant number fluctuations are greatly suppressed by the smectic order; that smectic order is long-ranged in $d=3$; and that nonlinear effects become important in $d=2$.

Co-author: Leiming Chen (The China University of Mining and Technology)

17:00 to 21:00 Walk to Grantchester, pub dinner* (either on Tues or Thu)
Wednesday 26th June 2013
09:00 to 09:45 The Five S's: Chemical Swimming, Sailing, Surfing, Squirming and Swarming
The design of nanoengines that can convert stored chemical energy into motion is an important challenge of nanotechnology, especially for engines that can operate autonomously. Recent experiments have demonstrated that it is possible to power the motion of nanoscale and microscale objects by using surface catalytic reactions -- so-called catalytic nanomotors. The precise mechanism(s) responsible for this motion is(are) still debated, although a number of ideas have been put forth. Here, a very simple mechanism is discussed: A surface chemical reaction creates local concentration gradients of the reactant (the fuel) and product species. As these species diffuse in an attempt to re-establish equilibrium, they entrain the motor causing it to move. This process can be viewed either as osmotic propulsion or as self-diffusiophoresis. The simplest way to break symmetry and achieve motion is by an asymmetric reactivity on the motor surface. The mathematical description of suc h motion is analogous to that used to describe the swimming of microorganisms, hence the name 'chemical swimming.' However, symmetry can also be broken by the motor's shape and, even for uniform reactivity, propulsion can be achieved -- 'chemical sailing.' A motor particle at an air-water interface can change the local concentration of surface-active agents and propel itself -- 'chemical surfing.' And even local variations of hydrodynamic mobility and interactive potential between the motor and the fuel can lead to net motion, a form of 'chemical squirming.' The implications of these mechanisms on the attainable propulsive speeds as a function of reaction rate and fuel concentration will be discussed and compared with Brownian dynamics simulations. It will also be shown that chemically active particles can attract or repel each other through long-range 'Coulomb-like' interactions. And suspensions of active particles can exhibit Debye-like screening leading to 'chemical swarming.'
09:45 to 10:30 R Lipowsky (Max-Planck-Institut für Kolloid- und Grenzflächenforschung)
Remodelling of membrane compartments
Biomembranes undergo continuous remodelling by budding and fission processes, which create new membrane compartments in the form of vesicles, as well as by adhesion and fusion, which combine two such compartments into a single one. The vesicles are transported by teams of molecular motors from donor membranes, where they are created, to acceptor membranes,into which they are incorporated by membrane fusion. In this talk, I will address the energetics and kinetics of these remodelling processes as well as their relevance for intracellular transport.
10:30 to 11:00 Morning Coffee at INI
11:00 to 11:45 Physarum Polycephalum Percolation as a Paradigm for Topological Phase Transitions in Transportation Networks
We study the formation of transportation networks of the true slime mold Physarum polycephalum after fragmentation by shear. Small fragments, called microplasmodia, fuse to form macroplasmodia in a percolation transition. At this topological phase transition, one single giant component forms, connecting most of the previously isolated microplasmodia. Employing the configuration model of graph theory for small link degree, we have found analytically an exact solution for the phase transition.

The universality of percolation may be used as a general gauge in the analysis of transportation networks. Some malignant tissues derive their blood vessels not by angiogenesis, i.e., remodeling of existing vessels, but rather by denovo vascularization like embryos. Since topologically, percolation is independent from detailed mechanisms and even space dimensions, i.e., 2D versus 3D growth, it may serve as a reference point in space and time when comparing the dynamics of network formation in tumors of varying size and shape. Since restricting blood supply via hindering vessel percolation is paramount for suppressing tumor growth, this may foster development of antiangiogenic therapy.

11:45 to 12:30 N Yoshinaga (Tohoku University)
Spontaneous motion and deformation of a droplet driven by chemical reaction
Spontaneous motion has been attracting lots of attention in last decades in nonlinear and nonequilibrium physics partially for its potential application to biological problems such as cell motility. Recently several model experiments showing spontaneous motion have been proposed in order to elucidate underlying mechanism of the motion. The systems in these works consist of relatively simple ingredients, for instance oil droplets in water, but nevertheless the results show rich motion and deformation of the droplet. Importantly, the system breaks symmetry and chooses one direction of motion. In this work, we theoretically derive a set of nonlinear equations exhibiting a transition between stationary and motile states starting from advection-reaction-diffusion equation driven away from an equilibrium state due to chemical reactions. A particular focus is on how hydrodynamic flow destabilizes an isotropic distribution of a concentration of chemicals. We also discuss a shape of the droplet. Due to self-propulsive motion and flow around the droplet, a spherical shape becomes unstable and it elongates perpendicular to the direction of motion. This fact would imply that the self-propulsion driven by chemical reaction is characterized as a pusher in terms of a flow field.
12:30 to 13:00 Lunch at Wolfson Court
14:00 to 14:30 Data mining in swarming models INI 1
14:30 to 16:00 Poster Session at INI
15:30 to 16:00 Afternoon Tea at INI
16:00 to 17:00 Free
19:30 to 22:00 Conference Dinner at Lucy Cavendish College
Thursday 27th June 2013
09:00 to 09:45 F MacKintosh (Vrije Universiteit Amsterdam)
Active stresses and mechanics of intra/extracellular networks
Much like the bones in our bodies, the cytoskeleton consisting of filamentous proteins largely determines the mechanical response and stability of cells. Similarly, extracellular networks contribute to tissue mechanics. Unlike passive materials, however, living cells are kept far out of equilibrium by metabolic processes and energy-consuming molecular motors that generate forces to drive the machinery behind various cellular processes. We describe recent advances both in theoretical modeling of such active gels, as well as experiments on reconstituted in vitro acto-myosin networks and living cells. We show how such internal force generation by motors can lead to dramatic mechanical effects, including strong mechanical stiffening. Furthermore, stochastic motor activity can lead to non-equilibrium diffusive-like motion in cells.
09:45 to 10:30 Cytoskeletal pattern formation: Self organization of driven filaments
Living cells rely on the self organization mechanisms of cytoskeleton to adapt to their requirements. Especially in processes such as cell division, intracellular transport or cellular motility the controlled self assembly to well defined structures, which still allow a dynamic reorganization on different time scales are of outstanding importance. Thereby, the intricate interplay of cytoskeletal filaments, crosslinking proteins and molecular motors a central role. One important and promising strategy to identify the underlying governing principles is to quantify the physical process in model systems mimicking the functional units of living cells. Here I will present in vitro minimal model systems consisting of actin filaments, crosslinking molecules and myosin II exhibiting collective long range order and dynamics. I will discuss how a balance of local force exertion, alignment interactions, crosslinking and hydrodynamics affect the evolving dynamic structures.
10:30 to 11:00 Morning Coffee at INI
11:00 to 11:45 L Truskinovsky (École Polytechnique)
Passive cooperative behavior in striated acto-myosin systems
Passive mechanical response of skeletal muscles at fast time scales is dominated by long range interactions inducing cooperative behavior without breaking the detailed balance. This leads to such unusual 'material properties' as negative equilibrium stiffness and different behavior in force and displacement controlled loading conditions. Careful fitting of experimental data suggests that 'muscle material' is finely tuned to perform close to a critical point.
11:45 to 12:30 A Alexeev (Georgia Institute of Technology)
Hydrodynamics of an elastic swimmer at low Reynolds number
We use fully-coupled three-dimensional computer simulations to examine the hydrodynamics of an elastic swimmer that swims in a viscous Newtonian fluid, and to probe how elasticity and resonance oscillations can be harnessed for efficient locomotion in a low-Reynolds-number environment. Our simulation approach is based on the lattice Boltzmann method. The swimmer is modeled as a rectangular elastic plate. We examine two types of swimmer actuation. In the first case, the elastic swimmer is actuated by imposing sinusoidal oscillations at its root. We also examine internally actuated swimmers that are driven by time varying internal moment producing swimmer bending. We probe the hydrodynamic forces and fluid structures generated by the swimmers and compare different actuation regimes. In particular, we show that the resonance actuation leads by the fastest swimmer propulsion velocity. This fast swimming, however, is inefficient, whereas an efficient swimming can be obtained for o ff-resonance frequencies. Furthermore, we compare our simulations of internally actuated swimmers with the experimental results for swimmers made of piezoelectric macro-fiber composites. The results are useful for designing efficient self-propelling fish-like robots driven by internally powered fins
12:30 to 13:30 Lunch at Wolfson Court
14:00 to 14:45 Growth and instabilities of healthy and cancerous tissues
During development or during tumor growth, cells organize collectively by cell division and apoptosis in a tissue. The aim of our work is to build up theoretical tools to describe the mechanical properties of tissues and to apply them to various biologically relevant situations.

We first show that because of the coupling between cell division and the local stress, a tissue can be considered as a visco-elastic liquid at time scales larger than the cell division time. We then show recent model experiments on cell aggregates showing the effect of mechanical stress on tissue growth.

Finally, we use the hydrodynamic description to discuss the steady state structure of villis which are the protrusions of the surface of the intestine. We describe the formation of villis as a buckling instability of a polar cell monolayer. In addition to the mechanical properties, we also consider the role of stem cells and their differentiation.

14:45 to 15:30 A Balazs (University of Pittsburgh)
Reconfigurable assemblies of active, auto-chemotactic gels
Using computational modeling, we show that self-oscillating Belousov-Zhabotinsky (BZ) gels can both emit and sense a chemical signal and thus, drive neighboring gel pieces to spontaneously self-aggregate, so that the system exhibits auto-chemotaxis. To date, this is the closest system to the ultimate self-recombining material, which can be divided into separated parts and the parts move autonomously to assemble into a structure resembling the original, uncut sample. We also show that the gels’ coordinated motion can be controlled by light, allowing us to achieve selective self-aggregation and control over the shape of the gel aggregates. By exposing the BZ gels to specific patterns of light and dark, we design a BZ gel “train” that leads the movement of its “cargo”. Our findings pave the way for creating reconfigurable materials from self-propelled elements, which autonomously communicate with neighboring units and thereby actively participate in cons tructing the final structure. In essence, the BZ gels resemble pieces of a construction toy that can be reused to build multiple structures and thus, provide a new route for creating dynamically reconfigurable materials.
15:30 to 16:00 Afternoon Tea at INI
16:00 to 16:45 E Farge (Institut Curie)
Mechanogenetic reciprocal coupling in early embryonic differentiation and morphogenesis, and evolutionary involvement in primitive organisms emergence
Biochemical patterning and morphogenetic movements coordinate the design of embryonic development. The molecular processes through which differentiation patterning closely controls the development of morphogenetic movements are today becoming well understood. Recent experimental evidence demonstrates that mechanical cues generated by morphogenesis activate mechano-transduction pathways, which conversely regulate the tissue differentiation and acto-myosin dependent active morphogenesis of embryonic development (1). Such mechanotransduction processes was discovered at Drosophila embryos gastrulation (2). These include the Armadillo/β-catenin dependent mechanical activation of the master differentiation patterning protein Twist (2,3) and the Fog dependent mechanical activation of the master morphogenetic patterning protein Myosin-II (4). Experiments combining genetics and biomechanics physiological perturbations, with theoretical analysis and simulation of the mechanoge netic control of early drosophila development, showed that these mechanotransduction processes are required for the physiological functions of mid-gut differentiation and mesoderm invagination, respectively (2,3,4). They also indicate the evolutionary involvement of such mechanotransductive processes in the emergence of primitive animals first morphogenetic and differentiation patterns (1,2,5).

1 Farge, E. Curr Top Dev Biol 95, 243-265, doi:10.1016/B978-0-12-385065-2.00008-6 (2011). 2 Farge, E. Curr Biol 13, 1365-1377 (2003). 3 Desprat, e al., E. Dev Cell 15, 470-477, doi:S1534-5807(08)00288-8 [pii] 10.1016/j.devcel.2008.07.009 (2008). 4 Pouille, P. A., Ahmadi, et al. Science signaling 2, ra16, doi:scisignal.2000098 [pii] 10.1126/scisignal.2000098 (2009). B. Driquez, A. Bouclet et al , Phys. Biol, Dec;8(6):066007. doi: 10.1088/1478-3975/8/6/066007. Epub 2011 Nov 25. (2011). 5 Brunet1, A. Bouclet, A. et al , in Euro Evo-Devo 2012 (Lisboa).

16:45 to 17:15 D Head (University of Leeds)
Microscopic simulation of active gels: The controlling role of end detachment
We detail results of two microscopic models for active media integrated numerically. In the first, point particles lacking orientational degrees of freedom are driven individually through random force noise, and dissipate energy collectively through inelastic interactions. This leads to large length-scale density fluctuations (aka 'giant number fluctuations') and super-diffusion, and we provide a simple scaling argument that links the two, suggestion a degree of commonality between these two features. A simple mechanism relating this model to those with orientational degrees of freedom is postulated. The second model is of apolar filaments driven by two-headed motile springs mimicking motor proteins, in quasi-2D systems with and without lateral confinement. With confinement, a range of structure formation is observed akin to in vitro experiments and in vivo visualisation of dividing cells. Without confinement, layers, asters and bundled states are found that broadly a gree with the predictions of a simple model. Super-diffusion is also observed for less strongly-bound states, as is a suggestion of giant number fluctuations. It is hoped this bottoms-up approach may lead to analytical theories for active gels valid on length scales on the filaments, relevant to some biological situations.

Co-authors: G. Gompper (Juelich, Germany), W. J. Briels (Twente, The Netherlands), H. Tanaka (Tokyo University)

17:15 to 17:45 Phase transitions and solitons in self-propelled particles: kinetic theory and diagrammatic approach
In this talk, I will summarize our recent progress on the kinetic theory of collective motion. The theory starts with an exact Markov chain for the Vicsek model in phase space and is made tractable by the mean-field-like Molecular Chaos approximation. This leads to an Enskog-like equation which we solve numerically as well as analytically in certain limits. The kinetic equation was also used to rigorously derive the hydrodynamic equations from the microscopic collision rules. We show that our results on the phase diagram and the formation of soliton-like waves agree quantitatively with direct simulations for large particle velocities. We find that the solitons modify the character of the flocking transition from continuous to discontinuous. To understand the behavior in the small velocity limit where mean-field theory is invalid, we developed a diagrammatic approach to systematically include particle correlations and show how they shift the flocking transition.
Friday 28th June 2013
09:00 to 09:45 D Needleman (Harvard University)
The Metaphase Spindle as an Active Liquid Crystal
The spindle is a complex assembly of microtubules, motors, and other associated proteins, which segregates chromosomes during cell division. In metaphase, the spindle exists in a steady-state with a constant flux of molecules and energy continuously modifying and maintaining its architecture. While the self-organization of systems of microtubules and motors have been investigated using theory and experiments, there have been few attempts to test if the proposed theories can be used to understand the dynamics and structure of complex biological systems in vivo. Here we use polarized light microscopy, 3D time-lapse spinning disk confocal microscopy, single molecule imaging, second harmonic generation microscopy, and mechanical measurements to test the validity of continuum models of metaphase spindles. Our results show that a simple continuum model can quantitatively explain spindle structure and dynamics, demonstrate that rigorous physical theories can be used to quantitat ively describe complex subcellular systems, and provide a framework for understanding the structure of the spindle and its response to physical and molecular perturbations.

Co-author: Jan Brugues (Harvard University)

09:45 to 10:30 Modeling dorsal closure during embryonic development of the fruit fly
This talk concerns "dorsal closure", a dynamic and complex process during the embryogenesis of Drosophila. Experiments have documented distinct phases of dorsal closure, each with rich and sometimes contradictory observations. We build a mathematical model to rationalize the results and test various hypotheses put forth by experimenters. The cells are coupled mechanically through the position of the nodes and the elastic forces on the edges. Besides, each cell has radial spokes on which myosin motors can attach and exert contractile forces on the nodes, the myosin dynamics itself being controlled by a signaling molecule. This simple model successfully reproduces the cell and tissue pulsation in the early phase of dorsal closure, as well as the consistent contraction in the slow phase through a cellular ratcheting mechanism.

Co-authors: Qiming Wang (Univ of British Columbia), Len Pismen (Technion)

10:30 to 11:00 Morning Coffee at INI
11:00 to 11:45 I Aronson (Argonne National Laboratory)
Modeling of Cell Movement on Adhesive Substrates
Modeling the movement of living motile cells on substrates is a formidable challenge; regulatory pathways are intertwined and forces that influence cell motion on adhesive substrates are not fully quantified. Here, we present a mathematical model coupling cell shape dynamics, treated in the framework of the Ginzburg-Landau-type equation for auxiliary mass density (phase field), to a partial differential equation describing the mean orientation (polarization of actin filaments) of the cell's cytoskeletal network. In order to maintain the total area of the cell, the phase field equation is subject to a global conservation constraint. Correspondingly, the equation for mean polarization incorporates key elements of cell mechanics: directed polymerization of actin network at the cell membrane, decay of polarization in the bulk of the cell, and formation of actin bundles (stress fibers) in the rear. The model successfully reproduces the primary phenomenology of cell motil ity: discontinuous onset of motion, diversity of cell shapes and shape oscillations, as well as distribution of traction on the surface. The results are in qualitative agreement with recent experiments on the motility of keratocyte cells and cell fragments. The asymmetry of the shapes is captured to a large extent in this simple model, which may prove useful for the interpretation of recent experiments and predictions of cell dynamics under various conditions. We also investigate effects of adhesion and substrate elasticity on the shape and dynamics of moving cells. We demonstrate that on hard adhesive substrates the cells exhibit steady-state motion. A transition to stick-slip motion is observed on soft and weakly adhesive surfaces.

11:45 to 12:30 A poroelastic model for mechanochemical waves and pattern formation in Physarum polycephalum
Many processes in living cells are controlled by biochemical substances regulating active stresses. The cytoplasm is an active material with both viscoelastic and liquid properties. First, we incorporate the active stress into a two-phase model of the cytoplasm which accounts for the spatiotemporal dynamics of the cytoskeleton and the cytosol. The cytoskeleton is described as a solid matrix that together with the cytosol as interstitial fluid constitutes a poroelastic material. We find different forms of mechanochemical waves including traveling, standing and rotating waves by employing linear stability analysis and numerical simulations in one and two spatial dimensions.

In a second step, we expand the chemo-mechanical model in order to model the manifold contraction patterns observed experimentally in protoplasmic droplets of Physarum polycephalum. To achieve this, we combine a biophysically realistic model of a calcium oscillator with the poroelastic model derived in the first part of the talk and assume that the active tension is regulated by calcium. With the help of two-dimensional simulations the model is shown to reproduce the contraction patterns observed in in protoplasmic droplets as well as a number of other traveling and standing wave patterns.

Co-authors: Markus Radszuweit (PTB Berlin), Sergio Alonso (PTB Berlin), Harald Engel (TU Berlin )

12:30 to 13:30 Lunch at Wolfson Court
14:00 to 14:45 Collective behaviour of phoretically active colloids
Interfacial phoretic transport mechanisms can be used to design self-propelled active colloids, due to their force-free nature. In my talk, I will discuss the generic properties of such self-propelled colloids, and examine their collective behaviour when they interact via the gradient of the fields that they also use for self-propulsion. I will present some results on interesting collective effects such as instabilities and emergent dynamical behaviours.
14:45 to 15:30 Vascularization patterns and fluid flow in growing tumours
Growing tumours remodel the vascular network by generating new blood vessels (angiogensis), by co-opting already existing ones and by vessel regression. We want to understand the physical determinants of the emerging tumour vascularization patterns and the characteristics of the resuting blood and interstitial fluid flow. For this purpose we develop a theoretical model combining a dynamically evolving and blood flow carrying pipe network with a non-liear growth process, intercommunicating via nutrient and growth factor fields. With it we discuss mechanisms leading to tumor compartmentalization, hot spot formation, and interstitial fluid flow patterns impeding drug delivery.
15:30 to 16:00 Afternoon Tea at INI
16:00 to 16:25 Cell motility due to active gel flows
The cell cytoskeleton, consisting of filaments and molecular motors (such as actomyosin), can be modelled as a polar or nematic active gel. Here a cell embedded in a surrounding medium is modelled as a drop of active gel. Motility of the model cell depends on flows of the contractile active gel. I will present analytical calculations of velocity fields for different polarisation fields and boundary conditions in two and three dimensions. These solutions will be compared to numerical simulations in which the approximations required for analytical tractability are lifted and steady state polarisations and velocities can be found. Generic features of persistent motion will be discussed and comparisons to available experimental data made.

Co-author: Carl Whitfield (University of Sheffield)

16:25 to 16:50 A New Theory of Micro-Robots: multiple scales & distinguished limits
This paper is devoted to the theory of three types of micro-robots consisting of rigid spheres connected by rods or springs of oscillating lengths:

1. N-sphere linear micro-robot;

2. Dumbbell micro-robot driven by flow oscillations;

3. Triangular micro-robot;

In all three cases the velocities of self-propulsion and the angular velocity of self-rotations have been calculated analytically with the use of the two-timing asymptotic procedure. The results are discussed and compared with the known experiments and with the results of other authors.

16:50 to 17:15 Conditions of hydrodynamic synchronization in models of beating cilia
Motile cilia are highly conserved structures in the evolution of organisms, generating the transport of fluid by periodic beating, through remarkably organized behavior in space and time. It is not known how these spatiotemporal patterns emerge and what sets their properties.

Individual cilia are nonequilibrium systems with many degrees of freedom. However, their description can be represented by simpler effective force laws that drive oscillations, and paralleled with nonlinear phase oscillators studied in physics.

Here I will describe synthetic model phase oscillators, where colloidal particles are driven by optical traps. The complex structural details of the cilia are coarse-grained into the details of how the colloidal particles are driven. We explore experimentally two types of colloidal model, finding in each case the conditions for optimal coupling. The applicability of this approach to biological data is illustrated by successfully mapping the behavior of cilia in the alga Chlamydomonas onto one of the coarse-grained models.

17:15 to 17:40 J Dunkel (University of Cambridge)
Fluid dynamics of bacterial turbulence
Self-sustained turbulent structures have been observed in a wide range of living fluids, yet no quantitative continuum 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 of fluid memory with increasing swimming activity and linear scaling between energy and enstrophy. The best-fit model parameters allow for quantitative agreement with experimental data.

Co-authors: Sebastian Heidenreich (PTB Berlin), Knut Drescher (Princeton University), Rik Wensink (CNRS Orsay), Markus Baer (PTB Berlin), Ray Goldstein (University of Cambridge)

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons