90 research outputs found
Exact expressions for the mobility and electrophoretic mobility of a weakly charged sphere in a simple electrolyte
We present (asymptotically) exact expressions for the mobility and
electrophoretic mobility of a weakly charged spherical particle in an
electrolyte solution. This is done by analytically solving the electro and
hydrodynamic equations governing the electric potential and fluid flow with
respect to an electric field and a nonelectric force. The resulting formulae
are cumbersome, but fully explicit and trivial for computation. In the case of
a very small particle compared to the Debye screening length () our
results reproduce proper limits of the classical Debye and Onsager theories,
while in the case of a very large particle () we recover, both, the
non-monotonous charge dependence discovered by Levich (1958) as well as the
scaling estimate given by Long, Viovy, and Ajdari (1996), while adding the
previously unknown coefficients and corrections. The main applicability
condition of our solution is charge smallness in the sense that screening
remains linear.Comment: 6 pages, 1 figur
Many-body effects in tracer particle diffusion with applications for single-protein dynamics on DNA
30% of the DNA in E. coli bacteria is covered by proteins. Such high degree
of crowding affect the dynamics of generic biological processes (e.g. gene
regulation, DNA repair, protein diffusion etc.) in ways that are not yet fully
understood. In this paper, we theoretically address the diffusion constant of a
tracer particle in a one dimensional system surrounded by impenetrable crowder
particles. While the tracer particle always stays on the lattice, crowder
particles may unbind to a surrounding bulk and rebind at another or the same
location. In this scenario we determine how the long time diffusion constant
(after many unbinding events) depends on (i) the unbinding rate of
crowder particles , and (ii) crowder particle line density ,
from simulations (Gillespie algorithm) and analytical calculations. For small
, we find when crowder particles
are immobile on the line, and when
they are diffusing; is the free particle diffusion constant. For large
, we find agreement with mean-field results which do not depend on
. From literature values of and , we show that
the small -limit is relevant for in vivo protein diffusion on a
crowded DNA. Our results applies to single-molecule tracking experiments.Comment: 10 pages, 8 figure
Zero-Crossing Statistics for Non-Markovian Time Series
In applications spaning from image analysis and speech recognition, to energy
dissipation in turbulence and time-to failure of fatigued materials,
researchers and engineers want to calculate how often a stochastic observable
crosses a specific level, such as zero. At first glance this problem looks
simple, but it is in fact theoretically very challenging. And therefore, few
exact results exist. One exception is the celebrated Rice formula that gives
the mean number of zero-crossings in a fixed time interval of a zero-mean
Gaussian stationary processes. In this study we use the so-called Independent
Interval Approximation to go beyond Rice's result and derive analytic
expressions for all higher-order zero-crossing cumulants and moments. Our
results agrees well with simulations for the non-Markovian autoregressive
model
Single-File diffusion in a Box
We study diffusion of (fluorescently) tagged hard-core interacting particles
of finite size in a finite one-dimensional system. We find an exact analytical
expression for the tagged particle probability density using a coordinate
Bethe-ansatz, from which the mean square displacement is calculated. The
analysis show the existence of three regimes of drastically different behavior
for short, intermediate and large times. The results show excellent agreement
with stochastic simulations (Gillespie algorithm). The findings of the Letter
holds promise for the development of novel bio-nano sensors.Comment: 5 pages, 4 figure
Quality Control System Response to Stochastic Growth of Amyloid Fibrils
We introduce a stochastic model describing aggregation of misfolded proteins
and degradation by the protein quality control system in a single cell. In
analogy with existing literature, aggregates can grow, nucleate and fragment
stochastically. We assume that the quality control system acts as an enzyme
that can degrade aggregates at different stages of the growth process, with an
efficiency that decreases with the size of the aggregate. We show how this
stochastic dynamics, depending on the parameter choice, leads to two
qualitatively different behaviors: a homeostatic state, where the quality
control system is stable and aggregates of large sizes are not formed, and an
oscillatory state, where the quality control system periodically breaks down,
allowing for the formation of large aggregates. We discuss how these periodic
breakdowns may constitute a mechanism for the sporadic development of
neurodegenerative diseases.Comment: 14 pages, 4 figures, submitte
Modelling chromosome-wide target search
The most common gene regulation mechanism is when a transcription factor
protein binds to a regulatory sequence to increase or decrease RNA
transcription. However, transcription factors face two main challenges when
searching for these sequences. First, they are vanishingly short relative to
the genome length. Second, many nearly identical sequences are scattered across
the genome, causing proteins to suspend the search. But as pointed out in a
computational study of LacI regulation in Escherichia coli, such almost-targets
may lower search times if considering DNA looping. In this paper, we explore if
this also occurs over chromosome-wide distances. To this end, we developed a
cross-scale computational framework that combines established
facilitated-diffusion models for basepair-level search and a network model
capturing chromosome-wide leaps. To make our model realistic, we used Hi-C data
sets as a proxy for 3D proximity between long-ranged DNA segments and binding
profiles for more than 100 transcription factors. Using our cross-scale model,
we found that median search times to individual targets critically depend on a
network metric combining node strength (sum of link weights) and local
dissociation rates. Also, by randomizing these rates, we found that some actual
3D target configurations stand out as considerably faster or slower than their
random counterparts. This finding hints that chromosomes' 3D structure funnels
essential transcription factors to relevant DNA regions.Comment: 15 pages, 11 figure
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