2,312 research outputs found
Stochastic models of intracellular transport
The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an over-damped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of ATP hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review we present a wide range of analytical methods and models of intracellular transport. In the case of diffusive transport, we consider narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion. In the case of active transport, we consider Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state reduction methods, and mean field approximations. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self–organization of subcellular structures
MODELLING THE INFLUENCE OF NUCLEUS ELASTICITY ON CELL INVASION IN FIBER NETWORKS AND MICROCHANNELS
Cell migration in highly constrained extracellular matrices is exploited in scaffold-based tissue engineering and is fundamental in a wide variety of physiological and pathological phenomena, among others in cancer invasion and development. Research into the critical processes involved in cell migration has mainly focused on cell adhesion and proteolytic degradation of the external environment. However, rising evidence has recently shown that a number of cell-derived biophysical and mechanical parameters, among others nucleus stiffness and cell deformability, plays a major role in cell motility, especially in the ameboid-like migration mode in 3D confined tissue structures. We here present an extended cellular Potts model (CPM) first used to simulate a micro-fabricated migration chip, which tests the active invasive behavior of cancer cells into narrow channels. As distinct features of our approach, cells are modeled as compartmentalized discrete objects, differentiated in the nucleus and in the cytosolic region, while the migration chamber is composed of channels of different widths. We find that cell motile phenotype and velocity in open spaces (i.e., 2D flat surfaces or large channels) are not significantly influenced by cell elastic properties. On the contrary, the migratory behavior of cells within subcellular and subnuclear structures strongly relies on the deformability of the cytosol and of the nuclear cluster, respectively. Further, we characterize two migration dynamics: a stepwise way, characterized by fluctuations in cell length, within channels smaller than nucleus dimensions and a smooth sliding (i.e., maintaining constant cell length) behavior within channels larger than the nuclear cluster. These resulting observations are then extended looking at cell migration in an artificial fiber network, which mimics cell invasion in a 3D extracellular matrix. In particular, in this case, we analyze the effect of variations in elasticity of the nucleus on cell movement. In order to summarize, with our simulated migration assays, we demonstrate that the dimensionality of the environment strongly affects the migration phenotype and we suggest that the cytoskeletal and nuclear elastic characteristics correlate with the tumor cell's invasive potentia
Colloidal Aggregation Coupled with Sedimentation: A Comprehensive Overview
An account is made of the experimental, theoretical, and computational developments that led to our current understanding of the colloidal aggregation problem when a gravitational field is present. Starting with unaggregated colloids, a review is made of the advances that led to the founding of the barometric equation for the distribution of colloidal particles in a suspension, noticing that for large bodies, like large colloidal aggregates, their final fate in equilibrium is to be at the bottom of the container. Then, we briefly review the aggregation of colloids in the absence of gravity that has been amply studied by both experiments and simulations. For this purpose, the paradigmatic case of the DLVO interaction is taken as an example. Next, a brief revision is made of the seminal experimental work of C. Allain and collaborators on the colloidal aggregation problem when an external gravitational field is present, centering our study in the nongelling situations, that is, for dilute colloidal suspensions, when only sedimentation and deposition of single clusters occur. Afterward, the development of different computer simulations that treat this case of single cluster sedimentation and deposition is reviewed, and note how the different improvements of the algorithms lead to better correspondences with the experimental systems. We finally discuss further possible improvements of the algorithms and end with proposals for future work
Physics of Microswimmers - Single Particle Motion and Collective Behavior
Locomotion and transport of microorganisms in fluids is an essential aspect
of life. Search for food, orientation toward light, spreading of off-spring,
and the formation of colonies are only possible due to locomotion. Swimming at
the microscale occurs at low Reynolds numbers, where fluid friction and
viscosity dominates over inertia. Here, evolution achieved propulsion
mechanisms, which overcome and even exploit drag. Prominent propulsion
mechanisms are rotating helical flagella, exploited by many bacteria, and
snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and
algae. For artificial microswimmers, alternative concepts to convert chemical
energy or heat into directed motion can be employed, which are potentially more
efficient. The dynamics of microswimmers comprises many facets, which are all
required to achieve locomotion. In this article, we review the physics of
locomotion of biological and synthetic microswimmers, and the collective
behavior of their assemblies. Starting from individual microswimmers, we
describe the various propulsion mechanism of biological and synthetic systems
and address the hydrodynamic aspects of swimming. This comprises
synchronization and the concerted beating of flagella and cilia. In addition,
the swimming behavior next to surfaces is examined. Finally, collective and
cooperate phenomena of various types of isotropic and anisotropic swimmers with
and without hydrodynamic interactions are discussed.Comment: 54 pages, 59 figures, review article, Reports of Progress in Physics
(to appear
From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the L\'evy area of fractional Brownian motion with Hurst index
{Let be a -dimensional fractional Brownian motion
with Hurst index , or more generally a Gaussian process whose paths
have the same local regularity. Defining properly iterated integrals of is
a difficult task because of the low H\"older regularity index of its paths. Yet
rough path theory shows it is the key to the construction of a stochastic
calculus with respect to , or to solving differential equations driven by
.
We intend to show in a series of papers how to desingularize iterated
integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure
defined by a limit in law procedure. Convergence is proved by using "standard"
tools of constructive field theory, in particular cluster expansions and
renormalization. These powerful tools allow optimal estimates, and call for an
extension of Gaussian tools such as for instance the Malliavin calculus.
After a first introductory paper \cite{MagUnt1}, this one concentrates on the
details of the constructive proof of convergence for second-order iterated
integrals, also known as L\'evy area
Magnetism, FeS colloids, and Origins of Life
A number of features of living systems: reversible interactions and weak
bonds underlying motor-dynamics; gel-sol transitions; cellular connected
fractal organization; asymmetry in interactions and organization; quantum
coherent phenomena; to name some, can have a natural accounting via
interactions, which we therefore seek to incorporate by expanding the horizons
of `chemistry-only' approaches to the origins of life. It is suggested that the
magnetic 'face' of the minerals from the inorganic world, recognized to have
played a pivotal role in initiating Life, may throw light on some of these
issues. A magnetic environment in the form of rocks in the Hadean Ocean could
have enabled the accretion and therefore an ordered confinement of
super-paramagnetic colloids within a structured phase. A moderate H-field can
help magnetic nano-particles to not only overcome thermal fluctuations but also
harness them. Such controlled dynamics brings in the possibility of accessing
quantum effects, which together with frustrations in magnetic ordering and
hysteresis (a natural mechanism for a primitive memory) could throw light on
the birth of biological information which, as Abel argues, requires a
combination of order and complexity. This scenario gains strength from
observations of scale-free framboidal forms of the greigite mineral, with a
magnetic basis of assembly. And greigite's metabolic potential plays a key role
in the mound scenario of Russell and coworkers-an expansion of which is
suggested for including magnetism.Comment: 42 pages, 5 figures, to be published in A.R. Memorial volume, Ed
Krishnaswami Alladi, Springer 201
Spatial evolution of human dialects
The geographical pattern of human dialects is a result of history. Here, we
formulate a simple spatial model of language change which shows that the final
result of this historical evolution may, to some extent, be predictable. The
model shows that the boundaries of language dialect regions are controlled by a
length minimizing effect analogous to surface tension, mediated by variations
in population density which can induce curvature, and by the shape of coastline
or similar borders. The predictability of dialect regions arises because these
effects will drive many complex, randomized early states toward one of a
smaller number of stable final configurations. The model is able to reproduce
observations and predictions of dialectologists. These include dialect
continua, isogloss bundling, fanning, the wave-like spread of dialect features
from cities, and the impact of human movement on the number of dialects that an
area can support. The model also provides an analytical form for S\'{e}guy's
Curve giving the relationship between geographical and linguistic distance, and
a generalisation of the curve to account for the presence of a population
centre. A simple modification allows us to analytically characterize the
variation of language use by age in an area undergoing linguistic change
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