638 research outputs found
Signal focusing through active transport
In biological cells and novel diagnostic devices biochemical receptors need
to be sensitive to extremely small concentration changes of signaling
molecules. The accuracy of such molecular signaling is ultimately limited by
the counting noise imposed by the thermal diffusion of molecules. Many
macromolecules and organelles transiently bind to molecular motors and are then
actively transported. We here show that a random albeit directed delivery of
signaling molecules to within a typical diffusion distance to the receptor
reduces the correlation time of the counting noise, effecting an improved
sensing precision. The conditions for this active focusing are indeed
compatible with observations in living cells. Our results are relevant for a
better understanding of molecular cellular signaling and the design of novel
diagnostic devices.Comment: 5 pages. 3 figures, includes supplementary material (2 pages
Finite-time effects and ultraweak ergodicity breaking in superdiffusive dynamics
We study the ergodic properties of superdiffusive, spatiotemporally coupled
Levy walk processes. For trajectories of finite duration, we reveal a distinct
scatter of the scaling exponents of the time averaged mean squared displacement
delta**2 around the ensemble value 3-alpha (1<alpha<2) ranging from ballistic
motion to subdiffusion, in strong contrast to the behavior of subdiffusive
processes. In addition we find a significant dependence of the
trajectory-to-trajectory average of delta**2 as function of the finite
measurement time. This so-called finite-time amplitude depression and the
scatter of the scaling exponent is vital in the quantitative evaluation of
superdiffusive processes. Comparing the long time average of the second moment
with the ensemble mean squared displacement, these only differ by a constant
factor, an ultraweak ergodicity breaking.Comment: 5 pages, 4 Figures, REVTe
Optimization and universality of Brownian search in quenched heterogeneous media
The kinetics of a variety of transport-controlled processes can be reduced to
the problem of determining the mean time needed to arrive at a given location
for the first time, the so called mean first passage time (MFPT) problem. The
occurrence of occasional large jumps or intermittent patterns combining various
types of motion are known to outperform the standard random walk with respect
to the MFPT, by reducing oversampling of space. Here we show that a regular but
spatially heterogeneous random walk can significantly and universally enhance
the search in any spatial dimension. In a generic minimal model we consider a
spherically symmetric system comprising two concentric regions with piece-wise
constant diffusivity. The MFPT is analyzed under the constraint of conserved
average dynamics, that is, the spatially averaged diffusivity is kept constant.
Our analytical calculations and extensive numerical simulations demonstrate the
existence of an {\em optimal heterogeneity} minimizing the MFPT to the target.
We prove that the MFPT for a random walk is completely dominated by what we
term direct trajectories towards the target and reveal a remarkable
universality of the spatially heterogeneous search with respect to target size
and system dimensionality. In contrast to intermittent strategies, which are
most profitable in low spatial dimensions, the spatially inhomogeneous search
performs best in higher dimensions. Discussing our results alongside recent
experiments on single particle tracking in living cells we argue that the
observed spatial heterogeneity may be beneficial for cellular signaling
processes.Comment: 19 pages, 11 figures, RevTe
In vivo facilitated diffusion model
Under dilute in vitro conditions transcription factors rapidly locate their
target sequence on DNA by using the facilitated diffusion mechanism. However,
whether this strategy of alternating between three-dimensional bulk diffusion
and one-dimensional sliding along the DNA contour is still beneficial in the
crowded interior of cells is highly disputed. Here we use a simple model for
the bacterial genome inside the cell and present a semi-analytical model for
the in vivo target search of transcription factors within the facilitated
diffusion framework. Without having to resort to extensive simulations we
determine the mean search time of a lac repressor in a living E. coli cell by
including parameters deduced from experimental measurements. The results agree
very well with experimental findings, and thus the facilitated diffusion
picture emerges as a quantitative approach to gene regulation in living
bacteria cells. Furthermore we see that the search time is not very sensitive
to the parameters characterizing the DNA configuration and that the cell seems
to operate very close to optimal conditions for target localization. Local
searches as implied by the colocalization mechanism are only found to mildly
accelerate the mean search time within our model.Comment: 19 pages, 9 figures, Supplementary Information directly include
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