1,336 research outputs found
Finite lifetime eigenfunctions of coupled systems of harmonic oscillators
We find a Hermite-type basis for which the eigenvalue problem associated to
the operator acting on becomes a three-terms recurrence. Here and are two constant
positive definite matrices with no other restriction. Our main result provides
an explicit characterization of the eigenvectors of that lie in the
span of the first four elements of this basis when .Comment: 11 pages, 1 figure. Some typos where corrected in this new versio
Modelling cytoskeletal traffic: an interplay between passive diffusion and active transport
We introduce the totally asymmetric exclusion process with Langmuir kinetics
(TASEP-LK) on a network as a microscopic model for active motor protein
transport on the cytoskeleton, immersed in the diffusive cytoplasm. We discuss
how the interplay between active transport along a network and infinite
diffusion in a bulk reservoir leads to a heterogeneous matter distribution on
various scales. We find three regimes for steady state transport, corresponding
to the scale of the network, of individual segments or local to sites. At low
exchange rates strong density heterogeneities develop between different
segments in the network. In this regime one has to consider the topological
complexity of the whole network to describe transport. In contrast, at moderate
exchange rates the transport through the network decouples, and the physics is
determined by single segments and the local topology. At last, for very high
exchange rates the homogeneous Langmuir process dominates the stationary state.
We introduce effective rate diagrams for the network to identify these
different regimes. Based on this method we develop an intuitive but generic
picture of how the stationary state of excluded volume processes on complex
networks can be understood in terms of the single-segment phase diagram.Comment: 5 pages, 7 figure
On Kohn’s sums of squares of complex vector fields
This is a survey of some recent alternative way of proving a subelliptic estimate, first proven by J. J. Kohn, for certain sums of squares of complex vector fields. My approach here makes it possible to extend the result also to more general families of complex vector fields, to perturbations of sums of squares operators by a first-order
complex term and furthermore to a pseudodifferential setting
Motor proteins traffic regulation by supply-demand balance of resources
In cells and in vitro assays the number of motor proteins involved in
biological transport processes is far from being unlimited. The cytoskeletal
binding sites are in contact with the same finite reservoir of motors (either
the cytosol or the flow chamber) and hence compete for recruiting the available
motors, potentially depleting the reservoir and affecting cytoskeletal
transport. In this work we provide a theoretical framework to study,
analytically and numerically, how motor density profiles and crowding along
cytoskeletal filaments depend on the competition of motors for their binding
sites. We propose two models in which finite processive motor proteins actively
advance along cytoskeletal filaments and are continuously exchanged with the
motor pool. We first look at homogeneous reservoirs and then examine the
effects of free motor diffusion in the surrounding medium. We consider as a
reference situation recent in vitro experimental setups of kinesin-8 motors
binding and moving along microtubule filaments in a flow chamber. We
investigate how the crowding of linear motor proteins moving on a filament can
be regulated by the balance between supply (concentration of motor proteins in
the flow chamber) and demand (total number of polymerised tubulin
heterodimers). We present analytical results for the density profiles of bound
motors, the reservoir depletion, and propose novel phase diagrams that present
the formation of jams of motor proteins on the filament as a function of two
tuneable experimental parameters: the motor protein concentration and the
concentration of tubulins polymerized into cytoskeletal filaments. Extensive
numerical simulations corroborate the analytical results for parameters in the
experimental range and also address the effects of diffusion of motor proteins
in the reservoir.Comment: 31 pages, 10 figure
Early features of autism spectrum disorder: a cross-sectional study.
BACKGROUND: Autism spectrum disorder is characterized by impairment in social interaction and communication along with repetitive, restricted, and stereotyped behaviors, interests and activities. It is important to detect this condition as soon as possible and promptly begin targeted treatments. This study aimed to report on age at onset, early signs, and mode at onset in 105 Italian patients with autism spectrum disorder, searching for correlations with a series of clinical and instrumental variables. METHODS: This retrospective cross-sectional study considered the following five categories of symptoms at onset: language, social interaction and relationships, stereotyped behavior and activities, motor skills, and regulation. Three modes of presentation were considered: a delay, a stagnation, or a regression of development, which were defined modes of onset of autism spectrum disorder. The age at onset, the category of clinical features, and the mode at onset were considered in the entire sample and statistically analyzed for several clinical variables. Statistical analysis was performed utilizing Fisher Exact test and Chi Square test. RESULTS: The first symptoms between 7 and 12\u2009months were evident in 41.9% of cases, and between 13 and 24\u2009months in 27.6%; no significant differences for the age at onset related to diagnosis, etiopathogenesis, early onset epilepsy, and intelligence quotient level emerged. Social interaction and relationships (93.3%) and language (92.4%) were the categories of early signs more represented in our sample. Delay in spoken language (to be understood as both verbal production and verbal comprehension) was one of the most common (even though not specific) symptoms prompting initial medical consultation for a possible diagnosis of autism spectrum disorder. At onset, patients without intellectual disability manifested stagnation more often than delay or regression of development; patients with a severe/profound intellectual disability more frequently showed delay or regression of development. Language signs at onset were less frequent in cases with regression, whereas motor skill disorders prevailed in cases with delay at onset. Feeding problems were more numerous in cases with delay and stagnation of development. CONCLUSIONS: These data contribute to identifying an early trend of autism spectrum disorder, useful also for pediatricians
Spectral Asymptotic Properties of Semiregular Non-commutative Harmonic Oscillators.
We study here the spectral Weyl asymptotics for a semiregular system, extending to the vector-valued case results of Helffer and Robert, and more recently of Doll, Gannot and Wunsch. The class of systems considered here contains the important example of the Jaynes–Cummings system that describes light-matter interaction
Markov Process of Muscle Motors
We study a Markov random process describing a muscle molecular motor
behavior. Every motor is either bound up with a thin filament or unbound. In
the bound state the motor creates a force proportional to its displacement from
the neutral position. In both states the motor spend an exponential time
depending on the state. The thin filament moves at its velocity proportional to
average of all displacements of all motors. We assume that the time which a
motor stays at the bound state does not depend on its displacement. Then one
can find an exact solution of a non-linear equation appearing in the limit of
infinite number of the motors.Comment: 10 page
The extended structure of the remote cluster B514 in M31. Detection of extra-tidal stars
We present a study of the density profile of the remote M31 globular cluster
B514, obtained from HST/ACS observations. Coupling the analysis of the
distribution of the integrated light with star counts we can reliably follow
the profile of the cluster out to r~35", corresponding to ~130pc. The profile
is well fitted, out to ~15 core radii, by a King Model having C=1.65. With an
estimated core radius r_c=0.38", this corresponds to a tidal radius of r_t~17"
(~65pc). We find that both the light and the star counts profiles show a
departure from the best fit King model for r>~8" - as a surface brightness
excess at large radii, and the star counts profile shows a clear break in
correspondence of the estimated tidal radius. Both features are interpreted as
the signature of the presence of extratidal stars around the cluster. We also
show that B514 has a half-light radius significantly larger than ordinary
globular clusters of the same luminosity. In the M_V vs. log r_h plane, B514
lies in a region inhabited by peculiar clusters, like Omega Cen, G1, NGC2419
and others, as well as by the nuclei of dwarf elliptical galaxies.Comment: 9 pages, 6 figures. Accepted for publication in Astronomy &
Astrophysic
Exclusion processes on networks as models for cytoskeletal transport
We present a study of exclusion processes on networks as models for complex
transport phenomena and in particular for active transport of motor proteins
along the cytoskeleton. We argue that active transport processes on networks
spontaneously develop density heterogeneities at various scales. These
heterogeneities can be regulated through a variety of multi-scale factors, such
as the interplay of exclusion interactions, the non-equilibrium nature of the
transport process and the network topology.
We show how an effective rate approach allows to develop an understanding of
the stationary state of transport processes through complex networks from the
phase diagram of one single segment. For exclusion processes we rationalize
that the stationary state can be classified in three qualitatively different
regimes: a homogeneous phase as well as inhomogeneous network and segment
phases.
In particular, we present here a study of the stationary state on networks of
three paradigmatic models from non-equilibrium statistical physics: the totally
asymmetric simple exclusion process, the partially asymmetric simple exclusion
process and the totally asymmetric simple exclusion process with Langmuir
kinetics. With these models we can interpolate between equilibrium (due to
bi-directional motion along a network or infinite diffusion) and
out-of-equilibrium active directed motion along a network. The study of these
models sheds further light on the emergence of density heterogeneities in
active phenomena.Comment: 55 pages, 26 figure
Stepping and crowding of molecular motors: statistical kinetics from an exclusion process perspective
Motor enzymes are remarkable molecular machines that use the energy derived
from the hydrolysis of a nucleoside triphosphate to generate mechanical
movement, achieved through different steps that constitute their kinetic cycle.
These macromolecules, nowadays investigated with advanced experimental
techniques to unveil their molecular mechanisms and the properties of their
kinetic cycles, are implicated in many biological processes, ranging from
biopolymerisation (e.g. RNA polymerases and ribosomes) to intracellular
transport (motor proteins such as kinesins or dyneins). Although the kinetics
of individual motors is well studied on both theoretical and experimental
grounds, the repercussions of their stepping cycle on the collective dynamics
still remains unclear. Advances in this direction will improve our
comprehension of transport process in the natural intracellular medium, where
processive motor enzymes might operate in crowded conditions. In this work, we
therefore extend the current statistical kinetic analysis to study collective
transport phenomena of motors in terms of lattice gas models belonging to the
exclusion process class. Via numerical simulations, we show how to interpret
and use the randomness calculated from single particle trajectories in crowded
conditions. Importantly, we also show that time fluctuations and non-Poissonian
behavior are intrinsically related to spatial correlations and the emergence of
large, but finite, clusters of co-moving motors. The properties unveiled by our
analysis have important biological implications on the collective transport
characteristics of processive motor enzymes in crowded conditions.Comment: 9 pages, 6 figures, 2 supplementary figure
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