88 research outputs found
Driven Polymer Translocation Through a Narrow Pore
Motivated by experiments in which a polynucleotide is driven through a
proteinaceous pore by an electric field, we study the diffusive motion of a
polymer threaded through a narrow channel with which it may have strong
interactions. We show that there is a range of polymer lengths in which the
system is approximately translationally invariant, and we develop a
coarse-grained description of this regime. From this description, general
features of the distribution of times for the polymer to pass through the pore
may be deduced. We also introduce a more microscopic model. This model provides
a physically reasonable scenario in which, as in experiments, the polymer's
speed depends sensitively on its chemical composition, and even on its
orientation in the channel. Finally, we point out that the experimental
distribution of times for the polymer to pass through the pore is much broader
than expected from simple estimates, and speculate on why this might be.Comment: 16 pages, 8 figures, RevTex and harvard citation style, submitted to
Biophysical Journa
Exchange of stability as a function of system size in a nonequilibrium system
In equilibrium systems with short-ranged interactions, the relative stability
of different thermodynamic states generally does not depend on system size (as
long as this size is larger than the interaction range). Here, we use a large
deviations approach to show that, in contrast, different states can exchange
stability as system size is varied in a driven, bistable reaction-diffusion
system. This striking effect is related to a shift from a spatially uniform to
a nonuniform transition state and should generically be possible in a wide
range of nonequilibrium physical and biological systems.Comment: 7 pages, 4 figures. Supporting Material included in same file with
main tex
Dynamics of Molecular Motors and Polymer Translocation with Sequence Heterogeneity
The effect of sequence heterogeneity on polynucleotide translocation across a
pore and on simple models of molecular motors such as helicases, DNA
polymerase/exonuclease and RNA polymerase is studied in detail. Pore
translocation of RNA or DNA is biased due to the different chemical
environments on the two sides of the membrane, while the molecular motor motion
is biased through a coupling to chemical energy. An externally applied force
can oppose these biases. For both systems we solve lattice models exactly both
with and without disorder. The models incorporate explicitly the coupling to
the different chemical environments for polymer translocation and the coupling
to the chemical energy (as well as nucleotide pairing energies) for molecular
motors. Using the exact solutions and general arguments we show that the
heterogeneity leads to anomalous dynamics. Most notably, over a range of forces
around the stall force (or stall tension for DNA polymerase/exonuclease
systems) the displacement grows sublinearly as t^\mu with \mu<1. The range over
which this behavior can be observed experimentally is estimated for several
systems and argued to be detectable for appropriate forces and buffers. Similar
sequence heterogeneity effects may arise in the packing of viral DNA.Comment: 42 pages, 12 figure
Physical limits to sensing material properties
Constitutive relations describe how materials respond to external stimuli
such as forces. All materials respond heterogeneously at small scales, which
limits what a localized sensor can discern about the global constitution of a
material. In this paper, we quantify the limits of such constitutional sensing
by determining the optimal measurement protocols for sensors embedded in
disordered media. For an elastic medium, we find that the least fractional
uncertainty with which a sensor can determine a material constant
is approximately
\begin{equation*}
\frac{\delta \lambda_0}{\lambda_0 } \sim \left( \frac{\Delta_{\lambda} }{
\lambda_0^2} \right)^{1/2} \left( \frac{ d }{ a } \right)^{D/2} \left( \frac{
\xi }{ a } \right)^{D/2} \end{equation*} for , , and , where is the size of the sensor, is
its spatial resolution, is the correlation length of fluctuations in the
material constant, is the local variability of the material
constant, and is the dimension of the medium. Our results reveal how one
can construct microscopic devices capable of sensing near these physical
limits, e.g. for medical diagnostics. We show how our theoretical framework can
be applied to an experimental system by estimating a bound on the precision of
cellular mechanosensing in a biopolymer network.Comment: 33 pages, 3 figure
Switch and template pattern formation in a discrete reaction diffusion system inspired by the Drosophila eye
We examine a spatially discrete reaction diffusion model based on the
interactions that create a periodic pattern in the Drosophila eye imaginal
disc. This model is capable of generating a regular hexagonal pattern of gene
expression behind a moving front, as observed in the fly system. In order to
better understand the novel switch and template mechanism behind this pattern
formation, we present here a detailed study of the model's behavior in one
dimension, using a combination of analytic methods and numerical searches of
parameter space. We find that patterns are created robustly provided that there
is an appropriate separation of timescales and that self-activation is
sufficiently strong, and we derive expressions in this limit for the front
speed and the pattern wavelength. Moving fronts in pattern-forming systems near
an initial linear instability generically select a unique pattern, but our
model operates in a strongly nonlinear regime where the final pattern depends
on the initial conditions as well as on parameter values. Our work highlights
the important role that cellularization and cell-autonomous feedback can play
in biological pattern formation
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