190 research outputs found
Descriptions of membrane mechanics from microscopic and effective two-dimensional perspectives
Mechanics of fluid membranes may be described in terms of the concepts of
mechanical deformations and stresses, or in terms of mechanical free-energy
functions. In this paper, each of the two descriptions is developed by viewing
a membrane from two perspectives: a microscopic perspective, in which the
membrane appears as a thin layer of finite thickness and with highly
inhomogeneous material and force distributions in its transverse direction, and
an effective, two-dimensional perspective, in which the membrane is treated as
an infinitely thin surface, with effective material and mechanical properties.
A connection between these two perspectives is then established. Moreover, the
functional dependence of the variation in the mechanical free energy of the
membrane on its mechanical deformations is first studied in the microscopic
perspective. The result is then used to examine to what extent different,
effective mechanical stresses and forces can be derived from a given, effective
functional of the mechanical free energy.Comment: 37 pages, 3 figures, minor change
Directed motion emerging from two coupled random processes: Translocation of a chain through a membrane nanopore driven by binding proteins
We investigate the translocation of a stiff polymer consisting of M monomers
through a nanopore in a membrane, in the presence of binding particles
(chaperones) that bind onto the polymer, and partially prevent backsliding of
the polymer through the pore. The process is characterized by the rates: k for
the polymer to make a diffusive jump through the pore, q for unbinding of a
chaperone, and the rate q kappa for binding (with a binding strength kappa);
except for the case of no binding kappa=0 the presence of the chaperones give
rise to an effective force that drives the translocation process. Based on a
(2+1) variate master equation, we study in detail the coupled dynamics of
diffusive translocation and (partial) rectification by the binding proteins. In
particular, we calculate the mean translocation time as a function of the
various physical parameters.Comment: 22 pages, 5 figures, IOP styl
Enhanced reaction kinetics in biological cells
The cell cytoskeleton is a striking example of "active" medium driven
out-of-equilibrium by ATP hydrolysis. Such activity has been shown recently to
have a spectacular impact on the mechanical and rheological properties of the
cellular medium, as well as on its transport properties : a generic tracer
particle freely diffuses as in a standard equilibrium medium, but also
intermittently binds with random interaction times to motor proteins, which
perform active ballistic excursions along cytoskeletal filaments. Here, we
propose for the first time an analytical model of transport limited reactions
in active media, and show quantitatively how active transport can enhance
reactivity for large enough tracers like vesicles. We derive analytically the
average interaction time with motor proteins which optimizes the reaction rate,
and reveal remarkable universal features of the optimal configuration. We
discuss why active transport may be beneficial in various biological examples:
cell cytoskeleton, membranes and lamellipodia, and tubular structures like
axons.Comment: 10 pages, 2 figure
How Landscape Heterogeneity Frames Optimal Diffusivity in Searching Processes
Theoretical and empirical investigations of search strategies typically have failed to distinguish the distinct roles played by density versus patchiness of resources. It is well known that motility and diffusivity of organisms often increase in environments with low density of resources, but thus far there has been little progress in understanding the specific role of landscape heterogeneity and disorder on random, non-oriented motility. Here we address the general question of how the landscape heterogeneity affects the efficiency of encounter interactions under global constant density of scarce resources. We unveil the key mechanism coupling the landscape structure with optimal search diffusivity. In particular, our main result leads to an empirically testable prediction: enhanced diffusivity (including superdiffusive searches), with shift in the diffusion exponent, favors the success of target encounters in heterogeneous landscapes
Modeling the scaling properties of human mobility
While the fat tailed jump size and the waiting time distributions
characterizing individual human trajectories strongly suggest the relevance of
the continuous time random walk (CTRW) models of human mobility, no one
seriously believes that human traces are truly random. Given the importance of
human mobility, from epidemic modeling to traffic prediction and urban
planning, we need quantitative models that can account for the statistical
characteristics of individual human trajectories. Here we use empirical data on
human mobility, captured by mobile phone traces, to show that the predictions
of the CTRW models are in systematic conflict with the empirical results. We
introduce two principles that govern human trajectories, allowing us to build a
statistically self-consistent microscopic model for individual human mobility.
The model not only accounts for the empirically observed scaling laws but also
allows us to analytically predict most of the pertinent scaling exponents
Kinetics of active surface-mediated diffusion in spherically symmetric domains
We present an exact calculation of the mean first-passage time to a target on
the surface of a 2D or 3D spherical domain, for a molecule alternating phases
of surface diffusion on the domain boundary and phases of bulk diffusion. We
generalize the results of [J. Stat. Phys. {\bf 142}, 657 (2011)] and consider a
biased diffusion in a general annulus with an arbitrary number of regularly
spaced targets on a partially reflecting surface. The presented approach is
based on an integral equation which can be solved analytically. Numerically
validated approximation schemes, which provide more tractable expressions of
the mean first-passage time are also proposed. In the framework of this minimal
model of surface-mediated reactions, we show analytically that the mean
reaction time can be minimized as a function of the desorption rate from the
surface.Comment: Published online in J. Stat. Phy
Non-L\'evy mobility patterns of Mexican Me'Phaa peasants searching for fuelwood
We measured mobility patterns that describe walking trajectories of
individual Me'Phaa peasants searching and collecting fuelwood in the forests of
"La Monta\~na de Guerrero" in Mexico. These one-day excursions typically follow
a mixed pattern of nearly-constant steps when individuals displace from their
homes towards potential collecting sites and a mixed pattern of steps of
different lengths when actually searching for fallen wood in the forest.
Displacements in the searching phase seem not to be compatible with L\'evy
flights described by power-laws with optimal scaling exponents. These findings
however can be interpreted in the light of deterministic searching on heavily
degraded landscapes where the interaction of the individuals with their scarce
environment produces alternative searching strategies than the expected L\'evy
flights. These results have important implications for future management and
restoration of degraded forests and the improvement of the ecological services
they may provide to their inhabitants.Comment: 15 pages, 4 figures. First version submitted to Human Ecology. The
final publication will be available at http://www.springerlink.co
First passage and first hitting times of Lévy flights and Lévy walks
Abstract For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it (‘leapovers’), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms
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