11,569 research outputs found
Inducing phase-locking and chaos in cellular oscillators by modulating the driving stimuli
Inflammatory responses in eucaryotic cells are often associated with
oscillations in the nuclear-cytoplasmic translocation of the transcription
factor NF-kB. In most laboratory realizations, the oscillations are triggered
by a cytokine stimulus, like the tumor necrosis factor alpha, applied as a step
change to a steady level. Here we use a mathematical model to show that an
oscillatory external stimulus can synchronize the NF-kB oscillations into
states where the ratios of the internal to external frequency are close to
rational numbers. We predict a specific response diagram of the TNF-driven
NF-kB system which exhibits bands of synchronization known as "Arnold tongues".
Our model also suggests that when the amplitude of the external stimulus
exceeds a certain threshold there is the possibility of coexistence of multiple
different synchronized states and eventually chaotic dynamics of the nuclear
NF-kB concentration. This could be used as a way of externally controlling
immune response, DNA repair and apoptotic pathways.Comment: 12 pages, 3 figure
Symbolic dynamics of biological feedback networks
We formulate general rules for a coarse-graining of the dynamics, which we
term `symbolic dynamics', of feedback networks with monotone interactions, such
as most biological modules. Networks which are more complex than simple cyclic
structures can exhibit multiple different symbolic dynamics. Nevertheless, we
show several examples where the symbolic dynamics is dominated by a single
pattern that is very robust to changes in parameters and is consistent with the
dynamics being dictated by a single feedback loop. Our analysis provides a
method for extracting these dominant loops from short time series, even if they
only show transient trajectories.Comment: 4 pages, 4 figure
Trade Policy with Heterogeneous Traders: Do Quotas Get a Bum Rap?
This paper considers the effects of trade policy--tariffs and quotas--when importing is done by competitive traders who are identical ex ante but differ ex post. We show that the standard equivalence results no longer hold and the conventional ranking of tariffs and quotas is turned on its head: quotas are not as bad for welfare as previously believed, while tariffs may restrict trade by more than originally intended. Furthermore, the allocation of property rights (quota licenses) has real effects beyond the distribution of rents; this, in turn, has implications for the effects of corruption on welfare.
Generalized Landau-Pollak Uncertainty Relation
The Landau-Pollak uncertainty relation treats a pair of rank one projection
valued measures and imposes a restriction on their probability distributions.
It gives a nontrivial bound for summation of their maximum values. We give a
generalization of this bound (weak version of the Landau-Pollak uncertainty
relation). Our generalization covers a pair of positive operator valued
measures. A nontrivial but slightly weak inequality that can treat an arbitrary
number of positive operator valued measures is also presented.Comment: Simplified the proofs. To be published in Phys.Rev.
Oscillations and temporal signalling in cells
The development of new techniques to quantitatively measure gene expression
in cells has shed light on a number of systems that display oscillations in
protein concentration. Here we review the different mechanisms which can
produce oscillations in gene expression or protein concentration, using a
framework of simple mathematical models. We focus on three eukaryotic genetic
regulatory networks which show "ultradian" oscillations, with time period of
the order of hours, and involve, respectively, proteins important for
development (Hes1), apoptosis (p53) and immune response (NFkB). We argue that
underlying all three is a common design consisting of a negative feedback loop
with time delay which is responsible for the oscillatory behaviour
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