148 research outputs found
Escape of a Uniform Random Walk from an Interval
We study the first-passage properties of a random walk in the unit interval
in which the length of a single step is uniformly distributed over the finite
range [-a,a]. For a of the order of one, the exit probabilities to each edge of
the interval and the exit time from the interval exhibit anomalous properties
stemming from the change in the minimum number of steps to escape the interval
as a function of the starting point. As a decreases, first-passage properties
approach those of continuum diffusion, but non-diffusive effects remain because
of residual discreteness effectsComment: 8 pages, 8 figures, 2 column revtex4 forma
Precision of readout at the hunchback gene: analyzing short transcription time traces in living fly embryos
The simultaneous expression of the hunchback gene in the numerous nuclei of
the developing fly embryo gives us a unique opportunity to study how
transcription is regulated in living organisms. A recently developed MS2-MCP
technique for imaging nascent messenger RNA in living Drosophila embryos allows
us to quantify the dynamics of the developmental transcription process. The
initial measurement of the morphogens by the hunchback promoter takes place
during very short cell cycles, not only giving each nucleus little time for a
precise readout, but also resulting in short time traces of transcription.
Additionally, the relationship between the measured signal and the promoter
state depends on the molecular design of the reporting probe. We develop an
analysis approach based on tailor made autocorrelation functions that overcomes
the short trace problems and quantifies the dynamics of transcription
initiation. Based on live imaging data, we identify signatures of bursty
transcription initiation from the hunchback promoter. We show that the
precision of the expression of the hunchback gene to measure its position along
the anterior-posterior axis is low both at the boundary and in the anterior
even at cycle 13, suggesting additional post-transcriptional averaging
mechanisms to provide the precision observed in fixed embryos
Averaged residence times of stochastic motions in bounded domains
Two years ago, Blanco and Fournier (Blanco S. and Fournier R., Europhys.
Lett. 2003) calculated the mean first exit time of a domain of a particle
undergoing a randomly reoriented ballistic motion which starts from the
boundary. They showed that it is simply related to the ratio of the volume's
domain over its surface. This work was extended by Mazzolo (Mazzolo A.,
Europhys. Lett. 2004) who studied the case of trajectories which start inside
the volume. In this letter, we propose an alternative formulation of the
problem which allows us to calculate not only the mean exit time, but also the
mean residence time inside a sub-domain. The cases of any combinations of
reflecting and absorbing boundary conditions are considered. Lastly, we
generalize our results for a wide class of stochastic motions.Comment: 7 pages, 3 figure
Imaging Gold Nanoparticles in Living Cells Environments using Heterodyne Digital Holographic Microscopy
This paper describes an imaging microscopic technique based on heterodyne
digital holography where subwavelength-sized gold colloids can be imaged in
cell environment. Surface cellular receptors of 3T3 mouse fibroblasts are
labeled with 40 nm gold nanoparticles, and the biological specimen is imaged in
a total internal reflection configuration with holographic microscopy. Due to a
higher scattering efficiency of the gold nanoparticles versus that of cellular
structures, accurate localization of a gold marker is obtained within a 3D
mapping of the entire sample's scattered field, with a lateral precision of 5
nm and 100 nm in the x,y and in the z directions respectively, demonstrating
the ability of holographic microscopy to locate nanoparticles in living cells
environments
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