Order restricted inference in chronobiology

This paper is motivated by applications in oscillatory systems where researchers are typically interested in discovering components of those systems that display rhythmic temporal patterns. The contributions of this paper are twofold. First, a methodology is developed based on a circular signal plus error model that is defined using order restrictions. This mathematical formulation of rhythmicity is simple, easily interpretable and very flexible, with the latter property derived from the nonparametric formulation of the signal. Second, we address various commonly encountered problems in the analysis of oscillatory systems data. Specifically, we propose a methodology for (a) detecting rhythmic signals in an oscillatory system and (b) estimating the unknown sampling time that occurs when tissues are obtained from subjects whose time of death is unknown. The proposed methodology is computationally efficient, outperforms the existing methods, and is broadly applicable to address a wide range of questions related to oscillatory systems.

A Bootstrap Based Measure Robust to the Choice of Normalization Methods for Detecting Rhythmic Features in High Dimensional Data

Motivation: Gene-expression data obtained from high throughput technologies are subject to various sources of noise and accordingly the raw data are pre-processed before formally analyzed. Normalization of the data is a key pre-processing step, since it removes systematic variations across arrays. There are numerous normalization methods available in the literature. Based on our experience, in the context of oscillatory systems, such as cell-cycle, circadian clock, etc., the choice of the normalization method may substantially impact the determination of a gene to be rhythmic. Thus rhythmicity of a gene can purely be an artifact of how the data were normalized. Since the determination of rhythmic genes is an important component of modern toxicological and pharmacological studies, it is important to determine truly rhythmic genes that are robust to the choice of a normalization method.

Results: In this paper we introduce a rhythmicity measure and a bootstrap methodology to detect rhythmic genes in an oscillatory system. Although the proposed methodology can be used for any high-throughput gene expression data, in this paper we illustrate the proposed methodology using several publicly available circadian clock microarray gene-expression datasets. We demonstrate that the choice of normalization method has very little effect on the proposed methodology. Specifically, for any pair of normalization methods considered in this paper, the resulting values of the rhythmicity measure are highly correlated. Thus it suggests that the proposed measure is robust to the choice of a normalization method. Consequently, the rhythmicity of a gene is potentially not a mere artifact of the normalization method used. Lastly, as demonstrated in the paper, the proposed bootstrap methodology can also be used for simulating data for genes participating in an oscillatory system using a reference dataset.

Availability: A user friendly code implemented in R language can be downloaded from http://www.eio.uva.es/~miguel/robustdetectionprocedure.html

Stochastic properties of the plant circadian clock

Circadian clocks are gene regulatory networks whose role is to help the organisms to cope with variations in environmental conditions such as the day/night cycle. In this work, we explored the effects of molecular noise in single cells on the behaviour of the circadian clock in the plant model species Arabidopsis thaliana. The computational modelling language Bio-PEPA enabled us to give a stochastic interpretation of an existing deterministic model of the clock, and to easily compare the results obtained via stochastic simulation and via numerical solution of the deterministic model. First, the introduction of stochasticity in the model allowed us to estimate the unknown size of the system. Moreover, stochasticity improved the description of the available experimental data in several light conditions: noise-induced fluctuations yield a faster entrainment of the plant clock under certain photoperiods and are able to explain the experimentally observed dampening of the oscillations in plants under constant light conditions. The model predicts that the desynchronization between noisy oscillations in single cells contributes to the observed damped oscillations at the level of the cell population. Analysis of the phase, period and amplitude distributions under various light conditions demonstrated robust entrainment of the plant clock to light/dark cycles which closely matched the available experimental data.