38 research outputs found
A method for molecular dynamics on curved surfaces
Dynamics simulations of constrained particles can greatly aid in
understanding the temporal and spatial evolution of biological processes such
as lateral transport along membranes and self-assembly of viruses. Most
theoretical efforts in the field of diffusive transport have focussed on
solving the diffusion equation on curved surfaces, for which it is not
tractable to incorporate particle interactions even though these play a crucial
role in crowded systems. We show here that it is possible to combine standard
constraint algorithms with the classical velocity Verlet scheme to perform
molecular dynamics simulations of particles constrained to an arbitrarily
curved surface, in which such interactions can be taken into account.
Furthermore, unlike Brownian dynamics schemes in local coordinates, our method
is based on Cartesian coordinates allowing for the reuse of many other standard
tools without modifications, including parallelisation through domain
decomposition. We show that by applying the schemes to the Langevin equation
for various surfaces, confined Brownian motion is obtained, which has direct
applications to many biological and physical problems. Finally we present two
practical examples that highlight the applicability of the method: (i) the
influence of crowding and shape on the lateral diffusion of proteins in curved
membranes and (ii) the self-assembly of a coarse-grained virus capsid protein
model.Comment: 30 pages, 5 figure
Confinement without boundaries: Anisotropic diffusion on the surface of a cylinder
Densely packed systems of thermal particles in curved geometries are
frequently encountered in biological and microfluidic systems. In 2D systems,
at sufficiently high surface coverage, diffusive motion is widely known to be
strongly affected by physical confinement, e.g., by the walls. In this Letter,
we explore the effects of confinement by shape, not rigid boundaries, on the
diffusion of particles by confining them to the surface of a cylinder. We find
that both the magnitude and the directionality of lateral diffusion is strongly
influenced by the radius of the cylinder. An anisotropy between diffusion in
the longitudinal and circumferential direction of the cylinder develops. We
demonstrate that the origin of this effect lies in the fact that screw-like
packings of mono- and oligodisperse discs on the surface of a cylinder induce
preferential collective motions in the circumferential direction, but also show
that even in polydisperse systems lacking such order an intrinsic finite size
confinement effect increases diffusivity in the circumferential direction
Active elastohydrodynamics of vesicles in narrow, blind constrictions
Fluid-resistance limited transport of vesicles through narrow constrictions
is a recurring theme in many biological and engineering applications. Inspired
by the motor-driven movement of soft membrane-bound vesicles into closed
neuronal dendritic spines, here we study this problem using a combination of
passive three-dimensional simulations and a simplified semi-analytical theory
for active transport of vesicles that are forced through such constrictions by
molecular motors. We show that the motion of these objects is characterized by
two dimensionless quantities related to the geometry and the strength of
forcing relative to the vesicle elasticity. We use numerical simulations to
characterize the transit time for a vesicle forced by fluid pressure through a
constriction in a channel, and find that relative to an open channel, transport
into a blind end leads to the formation of an effective lubrication layer that
strongly impedes motion. When the fluid pressure forcing is complemented by
forces due to molecular motors that are responsible for vesicle trafficking
into dendritic spines, we find that the competition between motor forcing and
fluid drag results in multistable dynamics reminiscent of the real system. Our
study highlights the role of non-local hydrodynamic effects in determining the
kinetics of vesicular transport in constricted geometries
Forced transport of deformable containers through narrow constrictions
We study, numerically and analytically, the forced transport of deformable
containers through a narrow constriction. Our central aim is to quantify the
competition between the constriction geometry and the active forcing,
regulating whether and at which speed a container may pass through the
constriction and under what conditions it gets stuck. We focus, in particular,
on the interrelation between the force that propels the container and the
radius of the channel, as these are the external variables that may be directly
controlled in both artificial and physiological settings. We present
Lattice-Boltzmann simulations that elucidate in detail the various phases of
translocation, and present simplified analytical models that treat two limiting
types of these membrane containers: deformational energy dominated by the
bending or stretching contribution. In either case we find excellent agreement
with the full simulations, and our results reveal that not only the radius but
also the length of the constriction determines whether or not the container
will pass.Comment: 9 pages, 4 figure
К вопросу об устойчивости сопряжений капитальных выработок глубоких шахт
Наведений аналіз стану сполучень протяжних виробок. Розглянуті умови підтримання
похилих виробок та сполучень на шахті ім. В.М. Бажанова. Визначені розрахункові показники параметрів сполучень виробок. Наведені результати шахтних досліджень за станом
сполучень капітальних похилих виробок шахти ім. В.М. Бажанова.The analysis of the state of pairings of the extended workings is resulted. The terms of maintenance of the sloping workings and pairings are considered on a mine the name of V.M. Bazhanova. The calculation indexes of parameters of pairings of workings are certain. The results of the
mine researches are resulted after the state of pairings of the capital sloping workings of mine the
name of V.M. Bazhanova