92 research outputs found
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
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
Blinking statistics of a molecular beacon triggered by end-denaturation of DNA
We use a master equation approach based on the Poland-Scheraga free energy
for DNA denaturation to investigate the (un)zipping dynamics of a denaturation
wedge in a stretch of DNA, that is clamped at one end. In particular, we
quantify the blinking dynamics of a fluorophore-quencher pair mounted within
the denaturation wedge. We also study the behavioural changes in the presence
of proteins, that selectively bind to single-stranded DNA. We show that such a
setup could be well-suited as an easy-to-implement nanodevice for sensing
environmental conditions in small volumes.Comment: 14 pages, 5 figures, LaTeX, IOP style. Accepted to J Phys Cond Mat
special issue on diffusio
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
Tracer particle diffusion in a system with hardcore interacting particles
In this study, inspired by the work of K. Nakazato and K. Kitahara [Prog.
Theor. Phys. 64, 2261 (1980)], we consider the theoretical problem of tracer
particle diffusion in an environment of diffusing hardcore interacting crowder
particles. The tracer particle has a different diffusion constant from the
crowder particles. Based on a transformation of the generating function, we
provide an exact formal expansion for the tracer particle probability density,
valid for any lattice in the thermodynamic limit. By applying this formal
solution to dynamics on regular Bravais lattices we provide a closed form
approximation for the tracer particle diffusion constant which extends the
Nakazato and Kitahara results to include also b.c.c. and f.c.c. lattices.
Finally, we compare our analytical results to simulations in two and three
dimensions.Comment: 28 pages with appendix, 5 figure. To appear in JSTA
Single-file diffusion with non-thermal initial conditions
Single-file diffusion is a theoretically challenging many-body problem where
the calculation of even the simplest observables, e.g. mean square
displacement, for a tracer particle requires a heavy mathematical machinery.
There is therefore a need for simple approaches which predict qualitatively
correct behaviours. Here we put forward one such method which we use to
investigate the influence of non-thermal initial conditions on the dynamics of
a tracer particle. With our new approach we reproduce, up to scaling, several
known asymptotic results for the tracer particle mean square displacement.Comment: 4 pages, 1 figur
Dissimilar bouncy walkers
We consider the dynamics of a one-dimensional system consisting of dissimilar
hardcore interacting (bouncy) random walkers. The walkers' (diffusing
particles') friction constants xi_n, where n labels different bouncy walkers,
are drawn from a distribution rho(xi_n). We provide an approximate analytic
solution to this recent single-file problem by combining harmonization and
effective medium techniques. Two classes of systems are identified: when
rho(xi_n) is heavy-tailed, rho(xi_n)=A xi_n^(-1-\alpha) (0<alpha<1) for large
xi_n, we identify a new universality class in which density relaxations,
characterized by the dynamic structure factor S(Q,t), follows a Mittag-Leffler
relaxation, and the the mean square displacement of a tracer particle (MSD)
grows as t^delta with time t, where delta=alpha/(1+\alpha). If instead rho is
light-tailedsuch that the mean friction constant exist, S(Q,t) decays
exponentially and the MSD scales as t^(1/2). We also derive tracer particle
force response relations. All results are corroborated by simulations and
explained in a simplified model.Comment: 11 pages, to appear in Journal of Chemical Physic
Breathing dynamics in heteropolymer DNA
While the statistical mechanical description of DNA has a long tradition,
renewed interest in DNA melting from a physics perspective is nourished by
measurements of the fluctuation dynamics of local denaturation bubbles by
single molecule spectroscopy. The dynamical opening of DNA bubbles (DNA
breathing) is supposedly crucial for biological functioning during, for
instance, transcription initiation and DNA's interaction with selectively
single-stranded DNA binding proteins. Motivated by this, we consider the bubble
breathing dynamics in a heteropolymer DNA based on a (2+1)-variable master
equation and complementary stochastic Gillespie simulations, providing the
bubble size and the position of the bubble along the sequence as a function of
time. We utilize new experimental data that independently obtain stacking and
hydrogen bonding contributions to DNA stability. We calculate the spectrum of
relaxation times and the experimentally measurable autocorrelation function of
a fluorophore-quencher tagged base-pair, and demonstrate good agreement with
fluorescence correlation experiments. A significant dependence of opening
probability and waiting time between bubble events on the local DNA sequence is
revealed and quantified for a promoter sequence of the T7 phage. The strong
dependence on sequence, temperature and salt concentration for the breathing
dynamics of DNA found here points at a good potential for nanosensing
applications by utilizing short fluorophore-quencher dressed DNA constructs.Comment: 11 pages, 8 figure
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