407 research outputs found
Non-equilibrium dynamics of gene expression and the Jarzynski equality
In order to express specific genes at the right time, the transcription of
genes is regulated by the presence and absence of transcription factor
molecules. With transcription factor concentrations undergoing constant
changes, gene transcription takes place out of equilibrium. In this paper we
discuss a simple mapping between dynamic models of gene expression and
stochastic systems driven out of equilibrium. Using this mapping, results of
nonequilibrium statistical mechanics such as the Jarzynski equality and the
fluctuation theorem are demonstrated for gene expression dynamics. Applications
of this approach include the determination of regulatory interactions between
genes from experimental gene expression data
1D quantum models with correlated disorder vs. classical oscillators with coloured noise
We perform an analytical study of the correspondence between a classical
oscillator with frequency perturbed by a coloured noise and the one-dimensional
Anderson-type model with correlated diagonal disorder. It is rigorously shown
that localisation of electronic states in the quantum model corresponds to
exponential divergence of nearby trajectories of the classical random
oscillator. We discuss the relation between the localisation length for the
quantum model and the rate of energy growth for the stochastic oscillator.
Finally, we examine the problem of electron transmission through a finite
disordered barrier by considering the evolution of the classical oscillator.Comment: 23 pages, LaTeX fil
Diffusion in Curved Spacetimes
Using simple kinematical arguments, we derive the Fokker-Planck equation for
diffusion processes in curved spacetimes. In the case of Brownian motion, it
coincides with Eckart's relativistic heat equation (albeit in a simpler form),
and therefore provides a microscopic justification for his phenomenological
heat-flux ansatz. Furthermore, we obtain the small-time asymptotic expansion of
the mean square displacement of Brownian motion in static spacetimes. Beyond
general relativity itself, this result has potential applications in analogue
gravitational systems.Comment: 14 pages, substantially revised versio
Stability of adhesion clusters under constant force
We solve the stochastic equations for a cluster of parallel bonds with shared
constant loading, rebinding and the completely dissociated state as an
absorbing boundary. In the small force regime, cluster lifetime grows only
logarithmically with bond number for weak rebinding, but exponentially for
strong rebinding. Therefore rebinding is essential to ensure physiological
lifetimes. The number of bonds decays exponentially with time for most cases,
but in the intermediate force regime, a small increase in loading can lead to
much faster decay. This effect might be used by cell-matrix adhesions to induce
signaling events through cytoskeletal loading.Comment: Revtex, 4 pages, 4 Postscript files include
Efficient Stochastic Simulations of Complex Reaction Networks on Surfaces
Surfaces serve as highly efficient catalysts for a vast variety of chemical
reactions. Typically, such surface reactions involve billions of molecules
which diffuse and react over macroscopic areas. Therefore, stochastic
fluctuations are negligible and the reaction rates can be evaluated using rate
equations, which are based on the mean-field approximation. However, in case
that the surface is partitioned into a large number of disconnected microscopic
domains, the number of reactants in each domain becomes small and it strongly
fluctuates. This is, in fact, the situation in the interstellar medium, where
some crucial reactions take place on the surfaces of microscopic dust grains.
In this case rate equations fail and the simulation of surface reactions
requires stochastic methods such as the master equation. However, in the case
of complex reaction networks, the master equation becomes infeasible because
the number of equations proliferates exponentially. To solve this problem, we
introduce a stochastic method based on moment equations. In this method the
number of equations is dramatically reduced to just one equation for each
reactive species and one equation for each reaction. Moreover, the equations
can be easily constructed using a diagrammatic approach. We demonstrate the
method for a set of astrophysically relevant networks of increasing complexity.
It is expected to be applicable in many other contexts in which problems that
exhibit analogous structure appear, such as surface catalysis in nanoscale
systems, aerosol chemistry in stratospheric clouds and genetic networks in
cells
Generalization of escape rate from a metastable state driven by external cross-correlated noise processes
We propose generalization of escape rate from a metastable state for
externally driven correlated noise processes in one dimension. In addition to
the internal non-Markovian thermal fluctuations, the external correlated noise
processes we consider are Gaussian, stationary in nature and are of
Ornstein-Uhlenbeck type. Based on a Fokker-Planck description of the effective
noise processes with finite memory we derive the generalized escape rate from a
metastable state in the moderate to large damping limit and investigate the
effect of degree of correlation on the resulting rate. Comparison of the
theoretical expression with numerical simulation gives a satisfactory agreement
and shows that by increasing the degree of external noise correlation one can
enhance the escape rate through the dressed effective noise strength.Comment: 9 pages, 1 figur
Kinetic theory of age-structured stochastic birth-death processes
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov-–Born–-Green–-Kirkwood-–Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution
On the Aggregation of Inertial Particles in Random Flows
We describe a criterion for particles suspended in a randomly moving fluid to
aggregate. Aggregation occurs when the expectation value of a random variable
is negative. This random variable evolves under a stochastic differential
equation. We analyse this equation in detail in the limit where the correlation
time of the velocity field of the fluid is very short, such that the stochastic
differential equation is a Langevin equation.Comment: 16 pages, 2 figure
Absolute photoionization cross section measurements of the Kr I-isoelectronic sequence
Photoionization spectra have been recorded in the 4s, 4p and 3d resonance regions for the Kr Iisoelectronic sequence using both the dual laser produced plasma technique (at DCU) to produce photoabsorption spectra, and the merged ion beam and synchrotron radiation technique (at ASTRID) to measure absolute photoionization cross sections. Profile parameters are compared for the 4s − np resonances of Rb+ and Sr2+. Many new 4p " ns, md transitions are identified with the aid of Hartree-Fock calculations, and consistent quantum defects are observed for the various ns and md Rydberg series. Absolute single and double photoionization cross sections recorded in the 3d region for Rb+ and Sr2+ ions show preferential decay via double photoionization. This is only the second report where both the DLP technique and the merged beam technique have been used simultaneously to record photoionization spectra, and the advantages of both techniques (i.e. better resolution in the case of DLP and values for absolute photoionization cross sections in the case of the merged beam technique) are highlighted
Dynamics of gene expression and the regulatory inference problem
From the response to external stimuli to cell division and death, the
dynamics of living cells is based on the expression of specific genes at
specific times. The decision when to express a gene is implemented by the
binding and unbinding of transcription factor molecules to regulatory DNA.
Here, we construct stochastic models of gene expression dynamics and test them
on experimental time-series data of messenger-RNA concentrations. The models
are used to infer biophysical parameters of gene transcription, including the
statistics of transcription factor-DNA binding and the target genes controlled
by a given transcription factor.Comment: revised version to appear in Europhys. Lett., new titl
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