7,406 research outputs found
Relaxation oscillations in a class of delay-differential equations.
We study a class of delay differential equations which have been used to model hematological stem cell regulation and dynamics. Under certain circumstances the model exhibits self-sustained oscillations, with periods which can be significantly longer than the basic cell cycle time. We show that the long periods in the oscillations occur when the cell generation rate is small, and we provide an asymptotic analysis of the model in this case. This analysis bears a close resemblance to the analysis of relaxation oscillators (such as the Van der Pol oscillator), except that in our case the slow manifold is infinite dimensional. Despite this, a fairly complete analysis of the problem is possible
Dynamic behavior of stochastic gene expression models in the presence of bursting
This paper considers the behavior of discrete and continuous mathematical
models for gene expression in the presence of transcriptional/translational
bursting. We treat this problem in generality with respect to the distribution
of the burst size as well as the frequency of bursting, and our results are
applicable to both inducible and repressible expression patterns in prokaryotes
and eukaryotes. We have given numerous examples of the applicability of our
results, especially in the experimentally observed situation that burst size is
geometrically or exponentially distributed.Comment: 22 page
Recommended from our members
The relationship between membrane damage, release of protein and loss of viability in Escherichia coli exposed to high hydrostatic pressure
The aim of this work was to examine a possible association between resistance of two Escherichia coli strains to high hydrostatic pressure and the susceptibility of their cell membranes to pressure-induced damage. Cells were exposed to pressures between 100 and 700 MPa at room temperature (~20C) in phosphate-buffered-saline. In the more pressure-sensitive strain E. coli 8164, loss of viability occurred at pressures between 100 MPa and 300 MPa and coincided with irreversible loss of membrane integrity as indicated by uptake of propidium iodide (PI) and leakage of protein of molecular mass between 9 and 78 kDa from the cells. Protein release increased to a maximum at 400 MPa then decreased, possibly due to intracellular aggregation at the higher pressures. In the pressure-resistant strain E. coli J1, PI was taken up during pressure treatment but not after decompression indicating that cells were able to reseal their membranes. Loss of viability in strain J1 coincided with the transient loss of membrane integrity between approximately 200 MPa and 600 MPa. In E. coli J1 leakage of protein occurred before loss of viability and the released protein was of low molecular mass, between 8 and 11 kDa and may have been of periplasmic origin. In these two strains differences in pressure resistance appeared to be related to differences in the ability of their membranes to withstand disruption by pressure. However it appears that transient loss of membrane integrity during pressure can lead to cell death irrespective of whether cells can reseal their membranes afterwards
The effect of stellar-mass black holes on the structural evolution of massive star clusters
We present the results of realistic N-body modelling of massive star clusters
in the Magellanic Clouds, aimed at investigating a dynamical origin for the
radius-age trend observed in these systems. We find that stellar-mass black
holes, formed in the supernova explosions of the most massive cluster stars,
can constitute a dynamically important population. If a significant number of
black holes are retained (here we assume complete retention), these objects
rapidly form a dense core where interactions are common, resulting in the
scattering of black holes into the cluster halo, and the ejection of black
holes from the cluster. These two processes heat the stellar component,
resulting in prolonged core expansion of a magnitude matching the observations.
Significant core evolution is also observed in Magellanic Cloud clusters at
early times. We find that this does not result from the action of black holes,
but can be reproduced by the effects of mass-loss due to rapid stellar
evolution in a primordially mass segregated cluster.Comment: Accepted for publication in MNRAS Letters; 2 figures, 1 tabl
What measurable zero point fluctuations can(not) tell us about dark energy
We show that laboratory experiments cannot measure the absolute value of dark
energy. All known experiments rely on electromagnetic interactions. They are
thus insensitive to particles and fields that interact only weakly with
ordinary matter. In addition, Josephson junction experiments only measure
differences in vacuum energy similar to Casimir force measurements. Gravity,
however, couples to the absolute value. Finally we note that Casimir force
measurements have tested zero point fluctuations up to energies of ~10 eV, well
above the dark energy scale of ~0.01 eV. Hence, the proposed cut-off in the
fluctuation spectrum is ruled out experimentally.Comment: 4 page
An augmented moment method for stochastic ensembles with delayed couplings: I. Langevin model
By employing a semi-analytical dynamical mean-field approximation theory
previously proposed by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 041903
(2003)], we have developed an augmented moment method (AMM) in order to discuss
dynamics of an -unit ensemble described by linear and nonlinear Langevin
equations with delays. In AMM, original -dimensional {\it stochastic} delay
differential equations (SDDEs) are transformed to infinite-dimensional {\it
deterministic} DEs for means and correlations of local as well as global
variables. Infinite-order DEs arising from the non-Markovian property of SDDE,
are terminated at the finite level in the level- AMM (AMM), which
yields -dimensional deterministic DEs. Model calculations have been made
for linear and nonlinear Langevin models. The stationary solution of AMM for
the linear Langevin model with N=1 is nicely compared to the exact result. The
synchronization induced by an applied single spike is shown to be enhanced in
the nonlinear Langevin ensemble with model parameters locating at the
transition between oscillating and non-oscillating states. Results calculated
by AMM6 are in good agreement with those obtained by direct simulations.Comment: 18 pages, 3 figures, changed the title with re-arranged figures,
accepted in Phys. Rev. E with some change
- …