1,013 research outputs found
Minimal model fusion rules from 2-groups
The fusion rules for the -minimal model representations of the
Virasoro algebra are shown to come from the group G = \boZ_2^{p+q-5} in the
following manner. There is a partition into disjoint
subsets and a bijection between and the sectors
of the -minimal model such that the fusion rules correspond to where .Comment: 8 pages, amstex, v2.1, uses fonts msam, msbm, no figures, tables
constructed using macros: cellular and related files are included. This paper
will be submitted to Communications in Math. Physics. A compressed dvi file
is available at ftp://math.binghamton.edu/pub/alex/fusionrules.dvi.Z , and
compressed postscript at ftp://math.binghamton.edu/pub/alex/fusionrules.ps.
Robustness from flexibility in the fungal circadian clock
Background
Robustness is a central property of living systems, enabling function to be maintained against environmental perturbations. A key challenge is to identify the structures in biological circuits that confer system-level properties such as robustness. Circadian clocks allow organisms to adapt to the predictable changes of the 24-hour day/night cycle by generating endogenous rhythms that can be entrained to the external cycle. In all organisms, the clock circuits typically comprise multiple interlocked feedback loops controlling the rhythmic expression of key genes. Previously, we showed that such architectures increase the flexibility of the clock's rhythmic behaviour. We now test the relationship between flexibility and robustness, using a mathematical model of the circuit controlling conidiation in the fungus Neurospora crassa.
Results
The circuit modelled in this work consists of a central negative feedback loop, in which the frequency (frq) gene inhibits its transcriptional activator white collar-1 (wc-1), interlocked with a positive feedback loop in which FRQ protein upregulates WC-1 production. Importantly, our model reproduces the observed entrainment of this circuit under light/dark cycles with varying photoperiod and cycle duration. Our simulations show that whilst the level of frq mRNA is driven directly by the light input, the falling phase of FRQ protein, a molecular correlate of conidiation, maintains a constant phase that is uncoupled from the times of dawn and dusk. The model predicts the behaviour of mutants that uncouple WC-1 production from FRQ's positive feedback, and shows that the positive loop enhances the buffering of conidiation phase against seasonal photoperiod changes. This property is quantified using Kitano's measure for the overall robustness of a regulated system output. Further analysis demonstrates that this functional robustness is a consequence of the greater evolutionary flexibility conferred on the circuit by the interlocking loop structure.
Conclusions
Our model shows that the behaviour of the fungal clock in light-dark cycles can be accounted for by a transcription-translation feedback model of the central FRQ-WC oscillator. More generally, we provide an example of a biological circuit in which greater flexibility yields improved robustness, while also introducing novel sensitivity analysis techniques applicable to a broader range of cellular oscillators
Light and circadian regulation of clock components aids flexible responses to environmental signals
The circadian clock measures time across a 24h period, increasing fitness by phasing biological processes to the most appropriate time of day. The interlocking feedback loop mechanism of the clock is conserved across species; however, the number of loops varies. Mathematical and computational analyses have suggested that loop complexity affects the overall flexibility of the oscillator, including its responses to entrainment signals. We used a discriminating experimental assay, at the transition between different photoperiods, in order to test this proposal in a minimal circadian network (in Ostreococcus tauri) and a more complex network (in Arabidopsis thaliana). Transcriptional and translational reporters in O.tauri primarily tracked dawn or dusk, whereas in A.thaliana, a wider range of responses were observed, consistent with its more flexible clock. Model analysis supported the requirement for this diversity of responses among the components of the more complex network. However, these and earlier data showed that the O.tauri network retains surprising flexibility, despite its simple circuit. We found that models constructed from experimental data can show flexibility either from multiple loops and/or from multiple light inputs. Our results suggest that O.tauri has adopted the latter strategy, possibly as a consequence of genomic reduction
Complementary approaches to understanding the plant circadian clock
Circadian clocks are oscillatory genetic networks that help organisms adapt
to the 24-hour day/night cycle. The clock of the green alga Ostreococcus tauri
is the simplest plant clock discovered so far. Its many advantages as an
experimental system facilitate the testing of computational predictions.
We present a model of the Ostreococcus clock in the stochastic process
algebra Bio-PEPA and exploit its mapping to different analysis techniques, such
as ordinary differential equations, stochastic simulation algorithms and
model-checking. The small number of molecules reported for this system tests
the limits of the continuous approximation underlying differential equations.
We investigate the difference between continuous-deterministic and
discrete-stochastic approaches. Stochastic simulation and model-checking allow
us to formulate new hypotheses on the system behaviour, such as the presence of
self-sustained oscillations in single cells under constant light conditions.
We investigate how to model the timing of dawn and dusk in the context of
model-checking, which we use to compute how the probability distributions of
key biochemical species change over time. These show that the relative
variation in expression level is smallest at the time of peak expression,
making peak time an optimal experimental phase marker. Building on these
analyses, we use approaches from evolutionary systems biology to investigate
how changes in the rate of mRNA degradation impacts the phase of a key protein
likely to affect fitness. We explore how robust this circadian clock is towards
such potential mutational changes in its underlying biochemistry. Our work
shows that multiple approaches lead to a more complete understanding of the
clock
The Brunn-Minkowski inequality and a Minkowski problem for A-harmonic Green's function
Abstract
In this article we study two classical problems in convex geometry associated to
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Genome-wide quantitative analysis of DNA methylation from bisulfite sequencing data
Summary: Here we present the open-source R/Bioconductor software package BEAT (BS-Seq Epimutation Analysis Toolkit). It implements all bioinformatics steps required for the quantitative high-resolution analysis of DNA methylation patterns from bisulfite sequencing data, including the detection of regional epimutation events, i.e. loss or gain of DNA methylation at CG positions relative to a reference. Using a binomial mixture model, the BEAT package aggregates methylation counts per genomic position, thereby compensating for low coverage, incomplete conversion and sequencing errors. Availability and implementation: BEAT is freely available as part of Bioconductor at www.bioconductor.org/packages/devel/bioc/html/BEAT.html. The package is distributed under the GNU Lesser General Public License 3.0. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online
A new perspective on the Frenkel-Zhu fusion rule theorem
In this paper we prove a formula for fusion coefficients of affine Kac-Moody
algebras first conjectured by Walton [Wal2], and rediscovered in [Fe]. It is a
reformulation of the Frenkel-Zhu affine fusion rule theorem [FZ], written so
that it can be seen as a beautiful generalization of the classical
Parasarathy-Ranga Rao-Varadarajan tensor product theorem [PRV].Comment: 19 pages, no figures, uses conm-p-l.cls style fil
Quantitative analysis of regulatory flexibility under changing environmental conditions
The circadian clock controls 24-h rhythms in many biological processes, allowing appropriate timing of biological rhythms relative to dawn and dusk. Known clock circuits include multiple, interlocked feedback loops. Theory suggested that multiple loops contribute the flexibility for molecular rhythms to track multiple phases of the external cycle. Clear dawn- and dusk-tracking rhythms illustrate the flexibility of timing in Ipomoea nil. Molecular clock components in Arabidopsis thaliana showed complex, photoperiod-dependent regulation, which was analysed by comparison with three contrasting models. A simple, quantitative measure, Dusk Sensitivity, was introduced to compare the behaviour of clock models with varying loop complexity. Evening-expressed clock genes showed photoperiod-dependent dusk sensitivity, as predicted by the three-loop model, whereas the one- and two-loop models tracked dawn and dusk, respectively. Output genes for starch degradation achieved dusk-tracking expression through light regulation, rather than a dusk-tracking rhythm. Model analysis predicted which biochemical processes could be manipulated to extend dusk tracking. Our results reveal how an operating principle of biological regulators applies specifically to the plant circadian clock
Lagrange structure and quantization
A path-integral quantization method is proposed for dynamical systems whose
classical equations of motion do \textit{not} necessarily follow from the
action principle. The key new notion behind this quantization scheme is the
Lagrange structure which is more general than the Lagrangian formalism in the
same sense as Poisson geometry is more general than the symplectic one. The
Lagrange structure is shown to admit a natural BRST description which is used
to construct an AKSZ-type topological sigma-model. The dynamics of this
sigma-model in dimensions, being localized on the boundary, are proved to
be equivalent to the original theory in dimensions. As the topological
sigma-model has a well defined action, it is path-integral quantized in the
usual way that results in quantization of the original (not necessarily
Lagrangian) theory. When the original equations of motion come from the action
principle, the standard BV path-integral is explicitly deduced from the
proposed quantization scheme. The general quantization scheme is exemplified by
several models including the ones whose classical dynamics are not variational.Comment: Minor corrections, format changed, 40 page
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