22,565 research outputs found
Kinetic approaches to lactose operon induction and bimodality
The quasi-equilibrium approximation is acceptable when molecular interactions
are fast enough compared to circuit dynamics, but is no longer allowed when
cellular activities are governed by rare events. A typical example is the
lactose operon (lac), one of the most famous paradigms of transcription
regulation, for which several theories still coexist to describe its behaviors.
The lac system is generally analyzed by using equilibrium constants,
contradicting single-event hypotheses long suggested by Novick and Weiner
(1957). Enzyme induction as an all-or-none phenomenon. Proc. Natl. Acad. Sci.
USA 43, 553-566) and recently refined in the study of (Choi et al., 2008. A
stochastic single-molecule event triggers phenotype switching of a bacterial
cell. Science 322, 442-446). In the present report, a lac repressor
(LacI)-mediated DNA immunoprecipitation experiment reveals that the natural
LacI-lac DNA complex built in vivo is extremely tight and long-lived compared
to the time scale of lac expression dynamics, which could functionally
disconnect the abortive expression bursts and forbid using the standard modes
of lac bistability. As alternatives, purely kinetic mechanisms are examined for
their capacity to restrict induction through: (i) widely scattered derepression
related to the arrival time variance of a predominantly backward asymmetric
random walk and (ii) an induction threshold arising in a single window of
derepression without recourse to nonlinear multimeric binding and Hill
functions. Considering the complete disengagement of the lac repressor from the
lac promoter as the probabilistic consequence of a transient stepwise
mechanism, is sufficient to explain the sigmoidal lac responses as functions of
time and of inducer concentration. This sigmoidal shape can be misleadingly
interpreted as a phenomenon of equilibrium cooperativity classically used to
explain bistability, but which has been reported to be weak in this system
On Maltsev Digraphs
This is an Open Access article, first published by E-CJ on 25 February 2015.We study digraphs preserved by a Maltsev operation: Maltsev digraphs. We show that these digraphs retract either onto a directed path or to the disjoint union of directed cycles, showing in this way that the constraint satisfaction problem for Maltsev digraphs is in logspace, L. We then generalize results from Kazda (2011) to show that a Maltsev digraph is preserved not only by a majority operation, but by a class of other operations (e.g., minority, Pixley) and obtain a O(|VG|4)-time algorithm to recognize Maltsev digraphs. We also prove analogous results for digraphs preserved by conservative Maltsev operations which we use to establish that the list homomorphism problem for Maltsev digraphs is in L. We then give a polynomial time characterisation of Maltsev digraphs admitting a conservative 2-semilattice operation. Finally, we give a simple inductive construction of directed acyclic digraphs preserved by a Maltsev operation, and relate them with series parallel digraphs.Peer reviewedFinal Published versio
Join-Idle-Queue with Service Elasticity: Large-Scale Asymptotics of a Non-monotone System
We consider the model of a token-based joint auto-scaling and load balancing
strategy, proposed in a recent paper by Mukherjee, Dhara, Borst, and van
Leeuwaarden (SIGMETRICS '17, arXiv:1703.08373), which offers an efficient
scalable implementation and yet achieves asymptotically optimal steady-state
delay performance and energy consumption as the number of servers .
In the above work, the asymptotic results are obtained under the assumption
that the queues have fixed-size finite buffers, and therefore the fundamental
question of stability of the proposed scheme with infinite buffers was left
open. In this paper, we address this fundamental stability question. The system
stability under the usual subcritical load assumption is not automatic.
Moreover, the stability may not even hold for all . The key challenge stems
from the fact that the process lacks monotonicity, which has been the powerful
primary tool for establishing stability in load balancing models. We develop a
novel method to prove that the subcritically loaded system is stable for large
enough , and establish convergence of steady-state distributions to the
optimal one, as . The method goes beyond the state of the art
techniques -- it uses an induction-based idea and a "weak monotonicity"
property of the model; this technique is of independent interest and may have
broader applicability.Comment: 30 page
Localizing the Latent Structure Canonical Uncertainty: Entropy Profiles for Hidden Markov Models
This report addresses state inference for hidden Markov models. These models
rely on unobserved states, which often have a meaningful interpretation. This
makes it necessary to develop diagnostic tools for quantification of state
uncertainty. The entropy of the state sequence that explains an observed
sequence for a given hidden Markov chain model can be considered as the
canonical measure of state sequence uncertainty. This canonical measure of
state sequence uncertainty is not reflected by the classic multivariate state
profiles computed by the smoothing algorithm, which summarizes the possible
state sequences. Here, we introduce a new type of profiles which have the
following properties: (i) these profiles of conditional entropies are a
decomposition of the canonical measure of state sequence uncertainty along the
sequence and makes it possible to localize this uncertainty, (ii) these
profiles are univariate and thus remain easily interpretable on tree
structures. We show how to extend the smoothing algorithms for hidden Markov
chain and tree models to compute these entropy profiles efficiently.Comment: Submitted to Journal of Machine Learning Research; No RR-7896 (2012
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