71 research outputs found

### Bayesian inference with information content model check for Langevin equations

The Bayesian data analysis framework has been proven to be a systematic and
effective method of parameter inference and model selection for stochastic
processes. In this work we introduce an information content model check which
may serve as a goodness-of-fit, like the chi-square procedure, to complement
conventional Bayesian analysis. We demonstrate this extended Bayesian framework
on a system of Langevin equations, where coordinate dependent mobilities and
measurement noise hinder the normal mean squared displacement approach.Comment: 10 pages, 7 figures, REVTeX, minor revision

### Universality and non-universality of mobility in heterogeneous single-file systems and Rouse chains

We study analytically the tracer particle mobility in single-file systems
with distributed friction constants. Our system serves as a prototype for
non-equilibrium, heterogeneous, strongly interacting Brownian systems. The long
time dynamics for such a single-file setup belongs to the same universality
class as the Rouse model with dissimilar beads. The friction constants are
drawn from a density $\varrho(\xi)$ and we derive an asymptotically exact
solution for the mobility distribution $P[\mu_0(s)]$, where $\mu_0(s)$ is the
Laplace-space mobility. If $\varrho$ is light-tailed (first moment exists) we
find a self-averaging behaviour: $P[\mu_0(s)]=\delta[\mu_0(s)-\mu(s)]$ with
$\mu(s)\propto s^{1/2}$. When $\varrho(\xi)$ is heavy-tailed,
$\varrho(\xi)\simeq \xi^{-1-\alpha} \ (0<\alpha<1)$ for large $\xi$ we obtain
moments $\langle [\mu_s(0)]^n\rangle \propto s^{\beta n}$ where
$\beta=1/(1+\alpha)$ and no self-averaging. The results are corroborated by
simulations.Comment: 8 pages, 4 figures, REVTeX, to appear in Physical Review

### Dynamics of shape fluctuations of quasi-spherical vesicles revisited

In this paper, the dynamics of spontaneous shape fluctuations of a single,
giant quasi-spherical vesicle formed of a single lipid species is revisited
theoretically. A coherent physical theory for the dynamics is developed based
on a number of fundamental principles and considerations and a systematic
formulation of the theory is also established. From the systematic theoretical
formulation, an analytical description of the dynamics of shape fluctuations of
quasi-spherical vesicles is derived. In particular, in developing the theory we
have made a new interpretation of some of the phenomenological constants in a
canonical continuum description of fluid lipid-bilayer membranes and shown the
consequences of this new interpretation in terms of the characteristics of the
dynamics of vesicle shape fluctuations. Moreover, we have used the systematic
formulation of our theory as a framework against which we have discussed the
previously existing theories and their discrepancies. Finally, we have made a
systematic prediction about the system-dependent characteristics of the
relaxation dynamics of shape fluctuations of quasi-spherical vesicles with a
view of experimental studies of the phenomenon and also discussed, based on our
theory, a recently published experimental work on the topic.Comment: 18 pages, 4 figure

### Applying a potential across a biomembrane: electrostatic contribution to the bending rigidity and membrane instability

We investigate the effect on biomembrane mechanical properties due to the
presence an external potential for a non-conductive non-compressible membrane
surrounded by different electrolytes. By solving the Debye-Huckel and Laplace
equations for the electrostatic potential and using the relevant stress-tensor
we find: in (1.) the small screening length limit, where the Debye screening
length is smaller than the distance between the electrodes, the screening
certifies that all electrostatic interactions are short-range and the major
effect of the applied potential is to decrease the membrane tension and
increase the bending rigidity; explicit expressions for electrostatic
contribution to the tension and bending rigidity are derived as a function of
the applied potential, the Debye screening lengths and the dielectric constants
of the membrane and the solvents. For sufficiently large voltages the negative
contribution to the tension is expected to cause a membrane stretching
instability. For (2.) the dielectric limit, i.e. no salt (and small wavevectors
compared to the distance between the electrodes), when the dielectric constant
on the two sides are different the applied potential induces an effective
(unscreened) membrane charge density, whose long-range interaction is expected
to lead to a membrane undulation instability.Comment: 16 pages, 3 figures, some revisio

### A solution to the subdiffusion-efficiency paradox: Inactive states enhance reaction efficiency at subdiffusion conditions in living cells

Macromolecular crowding in living biological cells effects subdiffusion of
larger biomolecules such as proteins and enzymes. Mimicking this subdiffusion
in terms of random walks on a critical percolation cluster, we here present a
case study of EcoRV restriction enzymes involved in vital cellular defence. We
show that due to its so far elusive propensity to an inactive state the enzyme
avoids non-specific binding and remains well-distributed in the bulk cytoplasm
of the cell. Despite the reduced volume exploration capability of subdiffusion
processes, this mechanism guarantees a high efficiency of the enzyme. By
variation of the non-specific binding constant and the bond occupation
probability on the percolation network, we demonstrate that reduced
non-specific binding are beneficial for efficient subdiffusive enzyme activity
even in relatively small bacteria cells. Our results corroborate a more local
picture of cellular regulation.Comment: 6 plus epsilon pages, 6 figure

### Fitting a function to time-dependent ensemble averaged data

Time-dependent ensemble averages, i.e., trajectory-based averages of some
observable, are of importance in many fields of science. A crucial objective
when interpreting such data is to fit these averages (for instance, squared
displacements) with a function and extract parameters (such as diffusion
constants). A commonly overlooked challenge in such function fitting procedures
is that fluctuations around mean values, by construction, exhibit temporal
correlations. We show that the only available general purpose function fitting
methods, correlated chi-square method and the weighted least squares method
(which neglects correlation), fail at either robust parameter estimation or
accurate error estimation. We remedy this by deriving a new closed-form error
estimation formula for weighted least square fitting. The new formula uses the
full covariance matrix, i.e., rigorously includes temporal correlations, but is
free of the robustness issues, inherent to the correlated chi-square method. We
demonstrate its accuracy in four examples of importance in many fields:
Brownian motion, damped harmonic oscillation, fractional Brownian motion and
continuous time random walks. We also successfully apply our method, weighted
least squares including correlation in error estimation (WLS-ICE), to particle
tracking data. The WLS-ICE method is applicable to arbitrary fit functions, and
we provide a publically available WLS-ICE software.Comment: 47 pages (main text: 15 pages, supplementary: 32 pages

### Real sequence effects on the search dynamics of transcription factors on DNA

Recent experiments show that transcription factors (TFs) indeed use the
facilitated diffusion mechanism to locate their target sequences on DNA in
living bacteria cells: TFs alternate between sliding motion along DNA and
relocation events through the cytoplasm. From simulations and theoretical
analysis we study the TF-sliding motion for a large section of the DNA-sequence
of a common E. coli strain, based on the two-state TF-model with a fast-sliding
search state and a recognition state enabling target detection. For the
probability to detect the target before dissociating from DNA the TF-search
times self-consistently depend heavily on whether or not an auxiliary operator
(an accessible sequence similar to the main operator) is present in the genome
section. Importantly, within our model the extent to which the interconversion
rates between search and recognition states depend on the underlying nucleotide
sequence is varied. A moderate dependence maximises the capability to
distinguish between the main operator and similar sequences. Moreover, these
auxiliary operators serve as starting points for DNA looping with the main
operator, yielding a spectrum of target detection times spanning several orders
of magnitude. Auxiliary operators are shown to act as funnels facilitating
target detection by TFs.Comment: 26 pages, 7 figure

### 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

### Leapover lengths and first passage time statistics for L\'evy flights

Exact results for the first passage time and leapover statistics of symmetric
and one-sided Levy flights (LFs) are derived. LFs with stable index alpha are
shown to have leapover lengths, that are asymptotically power-law distributed
with index alpha for one-sided LFs and, surprisingly, with index alpha/2 for
symmetric LFs. The first passage time distribution scales like a power-law with
index 1/2 as required by the Sparre Andersen theorem for symmetric LFs, whereas
one-sided LFs have a narrow distribution of first passage times. The exact
analytic results are confirmed by extensive simulations.Comment: 4 pages, 5 figures, REVTe

- …