Confidence in Phase Definition for Periodicity in Genes Expression Time Series

<div><p>Circadian oscillation in baseline gene expression plays an important role in the regulation of multiple cellular processes. Most of the knowledge of circadian gene expression is based on studies measuring gene expression over time. Our ability to dissect molecular events in time is determined by the sampling frequency of such experiments. However, the real peaks of gene activity can be at any time on or between the time points at which samples are collected. Thus, some genes with a peak activity near the observation point have their phase of oscillation detected with better precision then those which peak between observation time points. Separating genes for which we can confidently identify peak activity from ambiguous genes can improve the analysis of time series gene expression. In this study we propose a new statistical method to quantify the phase confidence of circadian genes. The numerical performance of the proposed method has been tested using three real gene expression data sets.</p></div

Additional file 2: of Circadian succession of molecular processes in living tissues

Gene Ontology Charts. (XLSX 224 kb

An Example of data resampling using the Maximum Entropy Bootstrap Algorithm.

<p>(Top left panel): A gene expression time series from the IWAT data. (Remaining:) Set of 24 replications randomly chosen from 999 maximum entropy bootstrap samples used in the analysis.</p

IWAT, BAT and Liver data sets: number of circadian genes identified using Fisher’s <i>g</i>-test, Permutation test and JTK-CYCLE respectively.

<p>IWAT, BAT and Liver data sets: number of circadian genes identified using Fisher’s <i>g</i>-test, Permutation test and JTK-CYCLE respectively.</p

The Bootstrap Percentile confidence interval principle.

<p>Schematic of the bootstrap process. We want to estimate a confidence interval for the phase <i>θ</i>(<i>χ</i>). <i>R</i> training sets, <i>χ</i>¹*, …, <i>χ</i>^<i>R</i>* each of size <i>n</i> are generated using an appropriate resampling mechanism. The quantity of interest <i>θ</i>(<i>χ</i>) is computed from each bootstrap training set, and the values </p><p></p><p></p><p><mi>θ</mi><mo stretchy="false">(</mo></p><p><mo>χ</mo><mn>1</mn><mo>*</mo></p><mo stretchy="false">)</mo><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><mi>θ</mi><mo stretchy="false">(</mo><p><mo>χ</mo><mi>R</mi><mo>*</mo></p><mo stretchy="false">)</mo><p></p><p></p><p></p> are used to construct a confidence interval for the quantity <i>θ</i>(<i>χ</i>).<p></p

Number of genes in each phase for the IWAT, BAT and Liver data sets.

<p>Number of genes in each phase for the IWAT, BAT and Liver data sets.</p

IWAT, BAT and Liver data sets: timings (in minutes (m) or in hours (h)) for the proposed method and a variant of it that uses a set of 60 cosine waves with smaller phases generated using the Eq (10).

<p>The number of bootstrap replications <i>R</i> is in {9, 99, 999}.</p

IWAT, BAT and Liver data sets: timings (seconds) for Fisher’s <i>g</i>-test, Permutation test, JTK-CYCLE, and the proposed method on one bootstrap replication.

<p>IWAT, BAT and Liver data sets: timings (seconds) for Fisher’s <i>g</i>-test, Permutation test, JTK-CYCLE, and the proposed method on one bootstrap replication.</p

Additional file 3: of Circadian succession of molecular processes in living tissues

Gene Ontology Clusters. (XLSX 298 kb

Graph of the moving block bootstrap principle.

<p>Graph showing the principal of moving block bootstrap. The moving block bootstrap randomly selects blocks of the original data (top) and concatenate them together (center) to form a resample (bottom).</p