Metachronal wave and hydrodynamic interaction for deterministic switching rowers

We employ a model system, called rowers, as a generic physical framework to define the problem of the coordinated motion of cilia (the metachronal wave) as a far from equilibrium process. Rowers are active (two-state) oscillators interacting solely through forces of hydrodynamic origin. In this work, we consider the case of fully deterministic dynamics, find analytical solutions of the equation of motion in the long wavelength (continuum) limit, and investigate numerically the short wavelength limit. We prove the existence of metachronal waves below a characteristic wavelength. Such waves are unstable and become stable only if the sign of the coupling is reversed. We also find that with normal hydrodynamic interaction the metachronal pattern has the form of stable trains of traveling wave packets sustained by the onset of anti-coordinated beating of consecutive rowers.Comment: 11 pages, 7 figure

Self-organization and Mechanical Properties of Active Filament Bundles

A phenomenological description for active bundles of polar filaments is presented. The activity of the bundle results from crosslinks, that induce relative displacements between the aligned filaments. Our generic description is based on momentum conservation within the bundle. By specifying the internal forces, a simple minimal model for the bundle dynamics is obtained, capturing generic dynamic behaviors. In particular, contracted states as well as solitary and oscillatory waves appear through dynamic instabilities. The introduction of filament adhesion leads to self-organized persistent filament transport. Furthermore, calculating the tension, homogeneous bundles are shown to be able to actively contract and to perform work against external forces. Our description is motivated by dynamic phenomena in the cytoskeleton and could apply to stress-fibers and self-organization phenomena during cell-locomotion.Comment: 19 pages, 10 figure

A simple self-organized swimmer driven by molecular motors

We investigate a self-organized swimmer at low Reynolds numbers. The microscopic swimmer is composed of three spheres that are connected by two identical active linker arms. Each linker arm contains molecular motors and elastic elements and can oscillate spontaneously. We find that such a system immersed in a viscous fluid can self-organize into a state of directed swimming. The swimmer provides a simple system to study important aspects of the swimming of micro-organisms.Comment: 6 pages, 4 figure

Self-organized Beating and Swimming of Internally Driven Filaments

We study a simple two-dimensional model for motion of an elastic filament subject to internally generated stresses and show that wave-like propagating shapes which can propel the filament can be induced by a self-organized mechanism via a dynamic instability. The resulting patterns of motion do not depend on the microscopic mechanism of the instability but only of the filament rigidity and hydrodynamic friction. Our results suggest that simplified systems, consisting only of molecular motors and filaments could be able to show beating motion and self-propulsion.Comment: 8 pages, 2 figures, REVTe

Twirling and Whirling: Viscous Dynamics of Rotating Elastica

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by a novel pair of coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two dynamical regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.Comment: To be published in Physical Review Letter

Force and Motion Generation of Molecular Motors: A Generic Description

We review the properties of biological motor proteins which move along linear filaments that are polar and periodic. The physics of the operation of such motors can be described by simple stochastic models which are coupled to a chemical reaction. We analyze the essential features of force and motion generation and discuss the general properties of single motors in the framework of two-state models. Systems which contain large numbers of motors such as muscles and flagella motivate the study of many interacting motors within the framework of simple models. In this case, collective effects can lead to new types of behaviors such as dynamic instabilities of the steady states and oscillatory motion.Comment: 29 pages, 9 figure

Molecular motors robustly drive active gels to a critically connected state

Living systems often exhibit internal driving: active, molecular processes drive nonequilibrium phenomena such as metabolism or migration. Active gels constitute a fascinating class of internally driven matter, where molecular motors exert localized stresses inside polymer networks. There is evidence that network crosslinking is required to allow motors to induce macroscopic contraction. Yet a quantitative understanding of how network connectivity enables contraction is lacking. Here we show experimentally that myosin motors contract crosslinked actin polymer networks to clusters with a scale-free size distribution. This critical behavior occurs over an unexpectedly broad range of crosslink concentrations. To understand this robustness, we develop a quantitative model of contractile networks that takes into account network restructuring: motors reduce connectivity by forcing crosslinks to unbind. Paradoxically, to coordinate global contractions, motor activity should be low. Otherwise, motors drive initially well-connected networks to a critical state where ruptures form across the entire network.Comment: Main text: 21 pages, 5 figures. Supplementary Information: 13 pages, 8 figure

Defining the effective temperature of a quantum driven system from current-current correlation functions

We calculate current-current correlation functions and find an expression for the zero-frequency noise of multiterminal systems driven by harmonically time-dependent voltages within the Keldysh non-equilibrium Green's functions formalism. We also propose a fluctuation-dissipation relation for current-current correlation functions to define an effective temperature. We discuss the behavior of this temperature and compare it with the local temperature determined by a thermometer and with the effective temperature defined from a single-particle fluctuation-dissipation relation. We show that for low frequencies all the definitions of the temperature coincide.Comment: 11 pages, 5 figure

Coupling and Elastic Loading Affect the Active Response by the Inner Ear Hair Cell Bundles

Active hair bundle motility has been proposed to underlie the amplification mechanism in the auditory endorgans of non-mammals and in the vestibular systems of all vertebrates, and to constitute a crucial component of cochlear amplification in mammals. We used semi-intact in vitro preparations of the bullfrog sacculus to study the effects of elastic mechanical loading on both natively coupled and freely oscillating hair bundles. For the latter, we attached glass fibers of different stiffness to the stereocilia and observed the induced changes in the spontaneous bundle movement. When driven with sinusoidal deflections, hair bundles displayed phase-locked response indicative of an Arnold Tongue, with the frequency selectivity highest at low amplitudes and decreasing under stronger stimulation. A striking broadening of the mode-locked response was seen with increasing stiffness of the load, until approximate impedance matching, where the phase-locked response remained flat over the physiological range of frequencies. When the otolithic membrane was left intact atop the preparation, the natural loading of the bundles likewise decreased their frequency selectivity with respect to that observed in freely oscillating bundles. To probe for signatures of the active process under natural loading and coupling conditions, we applied transient mechanical stimuli to the otolithic membrane. Following the pulses, the underlying bundles displayed active movement in the opposite direction, analogous to the twitches observed in individual cells. Tracking features in the otolithic membrane indicated that it moved in phase with the bundles. Hence, synchronous active motility evoked in the system of coupled hair bundles by external input is sufficient to displace large overlying structures

Possibility spaces and the notion of novelty: from music to biology

International audienceWe provide a new perspective on the relation between the space of description of an object and the appearance of novelties. One of the aims of this perspective is to facilitate the interaction between mathematics and historical sciences. The definition of novelties is paradoxical: if one can define in advance the possibles, then they are not genuinely new. By analyzing the situation in set theory, we show that defining generic (i.e., shared) and specific (i.e., individual) properties of elements of a set are radically different notions. As a result, generic and specific definitions of possibilities cannot be conflated. We argue that genuinely stating possibilities requires that their meaning has to be made explicit. For example, in physics, properties playing theoretical roles are generic; then, generic reasoning is sufficient to define possibilities. By contrast, in music, we argue that specific properties matter, and generic definitions become insufficient. Then, the notion of new possibilities becomes relevant and irreducible. In biology, among other examples, the generic definition of the space of DNA sequences is insufficient to state phenotypic possibilities even if we assume complete genetic determinism. The generic properties of this space are relevant for sequencing or DNA duplication, but they are inadequate to understand phenotypes. We develop a strong concept of biological novelties which justifies the notion of new possibilities and is more robust than the notion of changing description spaces. These biological novelties are not generic outcomes from an initial situation. They are specific and this specificity is associated with biological functions, that is to say, with a specific causal structure. Thus, we think that in contrast with physics, the concept of new possibilities is necessary for biology