Robust regression for periodicity detection in non-uniformly sampled time-course gene expression data

<p>Abstract</p> <p>Background</p> <p>In practice many biological time series measurements, including gene microarrays, are conducted at time points that seem to be interesting in the biologist's opinion and not necessarily at fixed time intervals. In many circumstances we are interested in finding targets that are expressed periodically. To tackle the problems of uneven sampling and unknown type of noise in periodicity detection, we propose to use robust regression.</p> <p>Methods</p> <p>The aim of this paper is to develop a general framework for robust periodicity detection and review and rank different approaches by means of simulations. We also show the results for some real measurement data.</p> <p>Results</p> <p>The simulation results clearly show that when the sampling of time series gets more and more uneven, the methods that assume even sampling become unusable. We find that M-estimation provides a good compromise between robustness and computational efficiency.</p> <p>Conclusion</p> <p>Since uneven sampling occurs often in biological measurements, the robust methods developed in this paper are expected to have many uses. The regression based formulation of the periodicity detection problem easily adapts to non-uniform sampling. Using robust regression helps to reject inconsistently behaving data points.</p> <p>Availability</p> <p>The implementations are currently available for Matlab and will be made available for the users of R as well. More information can be found in the web-supplement <abbrgrp><abbr bid="B1">1</abbr></abbrgrp>.</p

Inducing Ni Sensitivity in the Ni Hyperaccumulator Plant Alyssum inflatum Nyárády (Brassicaceae) by Transforming with CAX1, a Vacuolar Membrane Calcium Transporter

The importance of calcium in nickel tolerance was studied in the nickel hyperaccumulator plant Alyssum inflatum by gene transformation of CAX1, a vacuolar membrane transporter that reduces cytosolic calcium. CAX1 from Arabidopsis thaliana with a CaMV35S promoter accompanying a kanamycin resistance gene was transferred into A. inflatum using Agrobacterium tumefaciens. Transformed calli were subcultured three times on kanamycin-rich media and transformation was confirmed by PCR using a specific primer for CAX1. At least 10 callus lines were used as a pool of transformed material. Both transformed and untransformed calli were treated with varying concentrations of either calcium (1–15 mM) or nickel (0– 500 lM) to compare their responses to those ions. Increased external calcium generally led to increased callus biomass, however, the increase was greater for untransformed callus. Further, increased external calcium led to increased callus calcium concentrations. Transformed callus was less nickel tolerant than untransformed callus: under increasing nickel concentrations callus relative growth rate was significantly less for transformed callus. Transformed callus also contained significantly less nickel than untransformed callus when exposed to the highest external nickel concentration (200 lM). We suggest that transformation with CAX1 decreased cytosolic calcium and resulted in decreased nickel tolerance. This in turn suggests that, at low cytosolic calcium concentrations, other nickel tolerance mechanisms (e.g., complexation and vacuolar sequestration) are insufficient for nickel tolerance. We propose that high cytosolic calcium is an important mechanism that results in nickel tolerance by nickel hyperaccumulator plants