66 research outputs found
First-passage dynamics of obstructed tracer particle diffusion in one-dimensional systems
The standard setup for single-file diffusion is diffusing particles in one
dimension which cannot overtake each other, where the dynamics of a tracer
(tagged) particle is of main interest. In this article we generalise this
system and investigate first-passage properties of a tracer particle when
flanked by crowder particles which may, besides diffuse, unbind (rebind) from
(to) the one-dimensional lattice with rates (). The
tracer particle is restricted to diffuse with rate on the lattice. Such a
model is relevant for the understanding of gene regulation where regulatory
proteins are searching for specific binding sites ona crowded DNA. We quantify
the first-passage time distribution, ( is time), numerically using
the Gillespie algorithm, and estimate it analytically. In terms of our key
parameter, the unbinding rate , we study the bridging of two known
regimes: (i) when unbinding is frequent the particles may effectively pass each
other and we recover the standard single particle result
with a renormalized diffusion constant, (ii) when unbinding is rare we recover
well-known single-file diffusion result . The intermediate
cases display rich dynamics, with the characteristic -peak and the
long-time power-law slope both being sensitive to
Directed motion emerging from two coupled random processes: Translocation of a chain through a membrane nanopore driven by binding proteins
We investigate the translocation of a stiff polymer consisting of M monomers
through a nanopore in a membrane, in the presence of binding particles
(chaperones) that bind onto the polymer, and partially prevent backsliding of
the polymer through the pore. The process is characterized by the rates: k for
the polymer to make a diffusive jump through the pore, q for unbinding of a
chaperone, and the rate q kappa for binding (with a binding strength kappa);
except for the case of no binding kappa=0 the presence of the chaperones give
rise to an effective force that drives the translocation process. Based on a
(2+1) variate master equation, we study in detail the coupled dynamics of
diffusive translocation and (partial) rectification by the binding proteins. In
particular, we calculate the mean translocation time as a function of the
various physical parameters.Comment: 22 pages, 5 figures, IOP styl
Extension of nano-confined DNA: quantitative comparison between experiment and theory
The extension of DNA confined to nanochannels has been studied intensively
and in detail. Yet quantitative comparisons between experiments and model
calculations are difficult because most theoretical predictions involve
undetermined prefactors, and because the model parameters (contour length, Kuhn
length, effective width) are difficult to compute reliably, leading to
substantial uncertainties. Here we use a recent asymptotically exact theory for
the DNA extension in the "extended de Gennes regime" that allows us to compare
experimental results with theory. For this purpose we performed new
experiments, measuring the mean DNA extension and its standard deviation while
varying the channel geometry, dye intercalation ratio, and ionic buffer
strength. The experimental results agree very well with theory at high ionic
strengths, indicating that the model parameters are reliable. At low ionic
strengths the agreement is less good. We discuss possible reasons. Our approach
allows, in principle, to measure the Kuhn length and effective width of a
single DNA molecule and more generally of semiflexible polymers in solution.Comment: Revised version, 6 pages, 2 figures, 1 table, supplementary materia
Fluctuations of a driven membrane in an electrolyte
We develop a model for a driven cell- or artificial membrane in an
electrolyte. The system is kept far from equilibrium by the application of a DC
electric field or by concentration gradients, which causes ions to flow through
specific ion-conducting units (representing pumps, channels or natural pores).
We consider the case of planar geometry and Debye-H\"{u}ckel regime, and obtain
the membrane equation of motion within Stokes hydrodynamics. At steady state,
the applied field causes an accumulation of charges close to the membrane,
which, similarly to the equilibrium case, can be described with renormalized
membrane tension and bending modulus. However, as opposed to the equilibrium
situation, we find new terms in the membrane equation of motion, which arise
specifically in the out-of-equilibrium case. We show that these terms lead in
certain conditions to instabilities.Comment: 7 pages, 2 figures. submitted to Europhys. Let
Nanoconfined circular and linear DNA - equilibrium conformations and unfolding kinetics
Studies of circular DNA confined to nanofluidic channels are relevant both
from a fundamental polymer-physics perspective and due to the importance of
circular DNA molecules in vivo. We here observe the unfolding of DNA from the
circular to linear configuration as a light-induced double strand break occurs,
characterize the dynamics, and compare the equilibrium conformational
statistics of linear and circular configurations. This is important because it
allows us to determine to which extent existing statistical theories describe
the extension of confined circular DNA. We find that the ratio of the
extensions of confined linear and circular DNA configurations increases as the
buffer concentration decreases. The experimental results fall between
theoretical predictions for the extended de Gennes regime at weaker confinement
and the Odijk regime at stronger confinement. We show that it is possible to
directly distinguish between circular and linear DNA molecules by measuring the
emission intensity from the DNA. Finally, we determine the rate of unfolding
and show that this rate is larger for more confined DNA, possibly reflecting
the corresponding larger difference in entropy between the circular and linear
configurations.Comment: 21 pages, 7 figures, 1 tabl
Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane
We discuss the electrostatic contribution to the elastic moduli of a cell or
artificial membrane placed in an electrolyte and driven by a DC electric field.
The field drives ion currents across the membrane, through specific channels,
pumps or natural pores. In steady state, charges accumulate in the Debye layers
close to the membrane, modifying the membrane elastic moduli. We first study a
model of a membrane of zero thickness, later generalizing this treatment to
allow for a finite thickness and finite dielectric constant. Our results
clarify and extend the results presented in [D. Lacoste, M. Cosentino
Lagomarsino, and J. F. Joanny, Europhys. Lett., {\bf 77}, 18006 (2007)], by
providing a physical explanation for a destabilizing term proportional to
\kps^3 in the fluctuation spectrum, which we relate to a nonlinear ()
electro-kinetic effect called induced-charge electro-osmosis (ICEO). Recent
studies of ICEO have focused on electrodes and polarizable particles, where an
applied bulk field is perturbed by capacitive charging of the double layer and
drives flow along the field axis toward surface protrusions; in contrast, we
predict "reverse" ICEO flows around driven membranes, due to curvature-induced
tangential fields within a non-equilibrium double layer, which hydrodynamically
enhance protrusions. We also consider the effect of incorporating the dynamics
of a spatially dependent concentration field for the ion channels.Comment: 22 pages, 10 figures. Under review for EPJ
A stitch in time: Efficient computation of genomic DNA melting bubbles
Background: It is of biological interest to make genome-wide predictions of
the locations of DNA melting bubbles using statistical mechanics models.
Computationally, this poses the challenge that a generic search through all
combinations of bubble starts and ends is quadratic.
Results: An efficient algorithm is described, which shows that the time
complexity of the task is O(NlogN) rather than quadratic. The algorithm
exploits that bubble lengths may be limited, but without a prior assumption of
a maximal bubble length. No approximations, such as windowing, have been
introduced to reduce the time complexity. More than just finding the bubbles,
the algorithm produces a stitch profile, which is a probabilistic graphical
model of bubbles and helical regions. The algorithm applies a probability peak
finding method based on a hierarchical analysis of the energy barriers in the
Poland-Scheraga model.
Conclusions: Exact and fast computation of genomic stitch profiles is thus
feasible. Sequences of several megabases have been computed, only limited by
computer memory. Possible applications are the genome-wide comparisons of
bubbles with promotors, TSS, viral integration sites, and other melting-related
regions.Comment: 16 pages, 10 figure
Stacking Interactions in Denaturation of DNA Fragments
A mesoscopic model for heterogeneous DNA denaturation is developed in the
framework of the path integral formalism. The base pair stretchings are treated
as one-dimensional, time dependent paths contributing to the partition
function. The size of the paths ensemble, which measures the degree of
cooperativity of the system, is computed versus temperature consistently with
the model potential physical requirements. It is shown that the ensemble size
strongly varies with the molecule backbone stiffness providing a quantitative
relation between stacking and features of the melting transition. The latter is
an overall smooth crossover which begins from the \emph{adenine-thymine} rich
portions of the fragment. The harmonic stacking coupling shifts, along the
-axis, the occurrence of the multistep denaturation but it does not change
the character of the crossover. The methods to compute the fractions of open
base pairs versus temperature are discussed: by averaging the base pair
displacements over the path ensemble we find that such fractions signal the
multisteps of the transition in good agreement with the indications provided by
the specific heat plots.Comment: European Physical Journal E (2011) in pres
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