Development and application of a modified dynamic time warping algorithm (DTW-S) to analyses of primate brain expression time series

Yuan Yuan,Martin Vingron,Shengyu Ni,Lin Tang,Yi-Ping Phoebe Chen,Augix Guohua Xu,Philipp Khaitovich,Mehmet Somel

doi:10.1186/1471-2105-12-347

Abstract

BackgroundComparing biological time series data across different conditions, or different specimens, is a common but still challenging task. Algorithms aligning two time series represent a valuable tool for such comparisons. While many powerful computation tools for time series alignment have been developed, they do not provide significance estimates for time shift measurements.ResultsHere, we present an extended version of the original DTW algorithm that allows us to determine the significance of time shift estimates in time series alignments, the DTW-Significance (DTW-S) algorithm. The DTW-S combines important properties of the original algorithm and other published time series alignment tools: DTW-S calculates the optimal alignment for each time point of each gene, it uses interpolated time points for time shift estimation, and it does not require alignment of the time-series end points. As a new feature, we implement a simulation procedure based on parameters estimated from real time series data, on a series-by-series basis, allowing us to determine the false positive rate (FPR) and the significance of the estimated time shift values. We assess the performance of our method using simulation data and real expression time series from two published primate brain expression datasets. Our results show that this method can provide accurate and robust time shift estimates for each time point on a gene-by-gene basis. Using these estimates, we are able to uncover novel features of the biological processes underlying human brain development and maturation.ConclusionsThe DTW-S provides a convenient tool for calculating accurate and robust time shift estimates at each time point for each gene, based on time series data. The estimates can be used to uncover novel biological features of the system being studied. The DTW-S is freely available as an R package TimeShift at http://www.picb.ac.cn/Comparative/data.html.

Highlights

Comparing biological time series data across different conditions, or different specimens, is a common but still challenging task
Testing dynamic time warping (DTW)-S using heterochrony simulations To test the efficiency of time shift estimation by DTWS, we first applied the algorithm to a number of simulated datasets with known heterochrony
Using these error distribution parameters, residual variance constituted approximately 15% of the total variance in the simulated datasets. This percentage of error-related variance is within the range of technical and biological variance, relative to factors such as age and species identity, observed in actual microarray experiments (e.g. [15]). These results demonstrate that DTW-S estimates are robust with respect to the numbers of original data points and interpolated time points

Summary

Introduction

Comparing biological time series data across different conditions, or different specimens, is a common but still challenging task. Algorithms aligning two time series represent a valuable tool for such comparisons. While many powerful computation tools for time series alignment have been developed, they do not provide significance estimates for time shift measurements. Comparing and characterizing temporal changes in gene expression is a routine method to elucidate functional features of biological processes [1,2]. The application of DTW to gene expression data was pioneered by Aach and Church [9] and has been further developed by other groups [10,11,12,13,14]

Methods

Results

Conclusion