405 research outputs found
Bistability, oscillations and bidirectional motion of ensemble of hydrodynamically-coupled molecular motors
We analyze the collective behavior of hydrodynamically coupled molecular
motors. We show that the local fluxes induced by motors displacement can induce
the experimentally observed bidirectional motion of cargoes and vesicles. By
means of a mean--field approach we show that sustained oscillations as well as
bistable collective motor motion arise even for very large collection of
motors, when thermal noise is irrelevant. The analysis clarifies the physical
mechanisms responsible for such dynamics by identifying the relevant coupling
parameter and its dependence on the geometry of the hydrodynamic coupling as
well as on system size. We quantify the phase diagram for the different phases
that characterize the collective motion of hydrodynamically coupled motors and
show that sustained oscillations can be reached for biologically relevant
parameters, hence demonstrating the relevance of hydrodynamic interactions in
intracellular transport
A practical density functional for polydisperse polymers
The Flory Huggins equation of state for monodisperse polymers can be turned
into a density functional by adding a square gradient term, with a coefficient
fixed by appeal to RPA (random phase approximation). We present instead a model
nonlocal functional in which each polymer is replaced by a deterministic,
penetrable particle of known shape. This reproduces the RPA and square gradient
theories in the small deviation and/or weak gradient limits, and can readily be
extended to polydisperse chains. The utility of the new functional is shown for
the case of a polydisperse polymer solution at coexistence in a poor solvent.Comment: 9 pages, 3 figure
Optimality of contraction-driven crawling
We study a model of cell motility where the condition of optimal trade-off
between performance and metabolic cost can be made precise. In this model a
steadily crawling fragment is represented by a layer of active gel placed on a
frictional surface and driven by contraction only. We find analytically the
distribution of contractile elements (pullers) ensuring that the efficiency of
self-propulsion is maximal. We then show that natural assumptions about
advection and diffusion of pullers produce a distribution that is remarkably
close to the optimal one and is qualitatively similar to the one observed in
experiments on fish keratocytes
Polarity patterns of stress fibers
Stress fibers are contractile actomyosin bundles commonly observed in the
cytoskeleton of metazoan cells. The spatial profile of the polarity of actin
filaments inside contractile actomyosin bundles is either monotonic (graded) or
periodic (alternating). In the framework of linear irreversible thermodynamics,
we write the constitutive equations for a polar, active, elastic
one-dimensional medium. An analysis of the resulting equations for the dynamics
of polarity shows that the transition from graded to alternating polarity
patterns is a nonequilibrium Lifshitz point. Active contractility is a
necessary condition for the emergence of sarcomeric, alternating polarity
patterns.Comment: 5 pages, 3 figure
Mechanical Instabilities of Biological Tubes
We study theoretically the shapes of biological tubes affected by various
pathologies. When epithelial cells grow at an uncontrolled rate, the negative
tension produced by their division provokes a buckling instability. Several
shapes are investigated : varicose, enlarged, sinusoidal or sausage-like, all
of which are found in pathologies of tracheal, renal tubes or arteries. The
final shape depends crucially on the mechanical parameters of the tissues :
Young modulus, wall-to-lumen ratio, homeostatic pressure. We argue that since
tissues must be in quasistatic mechanical equilibrium, abnormal shapes convey
information as to what causes the pathology. We calculate a phase diagram of
tubular instabilities which could be a helpful guide for investigating the
underlying genetic regulation
Generic phase diagram of active polar films
We study theoretically the phase diagram of compressible active polar gels
such as the actin network of eukaryotic cells. Using generalized hydrodynamics
equations, we perform a linear stability analysis of the uniform states in the
case of an infinite bidimensional active gel to obtain the dynamic phase
diagram of active polar films. We predict in particular modulated flowing
phases, and a macroscopic phase separation at high activity. This qualitatively
accounts for experimental observations of various active systems, such as
acto-myosin gels, microtubules and kinesins in vitro solutions, or swimming
bacterial colonies.Comment: 4 pages, 1 figur
Molecular Weight Dependence of Spreading Rates of Ultrathin Polymeric Films
We study experimentally the molecular weight dependence of spreading
rates of molecularly thin precursor films, growing at the bottom of droplets of
polymer liquids. In accord with previous observations, we find that the radial
extension R(t) of the film grows with time as R(t) = (D_{exp} t)^{1/2}. Our
data substantiate the M-dependence of D_{exp}; we show that it follows D_{exp}
\sim M^{-\gamma}, where the exponent \gamma is dependent on the chemical
composition of the solid surface, determining its frictional properties with
respect to the molecular transport. In the specific case of hydrophilic
substrates, the frictional properties can be modified by the change of the
relative humidity (RH). We find that \gamma \approx 1 at low RH and tends to
zero when RH gets progressively increased. We propose simple theoretical
arguments which explain the observed behavior in the limits of low and high RH.Comment: 4 pages, 2 figures, to appear in PR
Dynamics of Spreading of Small Droplets of Chainlike Molecules on Surfaces
Dynamics of spreading of small droplets on surfaces has been studied by the
molecular dynamics method. Simulations have been performed for mixtures of
solvent and dimer, and solvent and tetramer droplets. For solvent particles and
dimers, layering occurs leading to stepped droplet shapes. For tetramers such
shapes occur for relatively deep and strong surface potentials only. For wider
and more shallow potentials, more rapid spreading and rounded droplet shapes
occur. These results are in accordance with experimental data on small non -
volatile polymer droplets. PACS numbers: 68.10Gw, 05.70.Ln, 61.20.Ja, 68.45GdComment: to appear in Europhys. Letters (1994), Latex, 12 page
Influence of solvent quality on polymer solutions: a Monte Carlo study of bulk and interfacial properties
The effect of solvent quality on dilute and semi-dilute regimes of polymers
in solution is studied by means of Monte Carlo simulations. The equation of
state, adsorptions near a hard wall, wall-polymer surface tension and effective
depletion potentials are all calculated as a function of concentration and
solvent quality. We find important differences between polymers in good and
theta solvents. In the dilute regime, the physical properties for polymers in a
theta solvent closely resemble those of ideal polymers. In the semi-dilute
regime, however, significant differences are found.Comment: 10 pages, 13 figure
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