Alignment of time-resolved data from high throughput experiments

To better understand the dynamics of the underlying processes in cells, it is necessary to take measurements over a time course. Modern high-throughput technologies are often used for this purpose to measure the behavior of cell products like metabolites, peptides, proteins, mu RNA or mRNA at different points in time. Compared to classical time series, the number of time points is usually very limited and the measurements are taken at irregular time intervals. The main reasons for this are the costs of the experiments and the fact that the dynamic behavior usually shows a strong reaction and fast changes shortly after a stimulus and then slowly converges to a certain stable state. Another reason might simply be missing values. It is common to repeat the experiments and to have replicates in order to carry out a more reliable analysis. The ideal assumptions that the initial stimulus really started exactly at the same time for all replicates and that the replicates are perfectly synchronized are seldom satisfied. Therefore, there is a need to first adjust or align the time-resolved data before further analysis is carried out. Dynamic time warping (DTW) is considered as one of the common alignment techniques for time series data with equidistant time points. In this paper, we modified the DTW algorithm so that it can align sequences with measurements at different, non-equidistant time points with large gaps in between. This type of data is usually known as time-resolved data characterized by irregular time intervals between measurements as well as non-identical time points for different replicates. This new algorithm can be easily used to align time-resolved data from high-throughput experiments and to come across existing problems such as time scarcity and existing noise in the measurements. We propose a modified method of DTW to adapt requirements imposed by time-resolved data by use of monotone cubic interpolation splines. Our presented approach provides a nonlinear alignment of two sequences that neither need to have equi-distant time points nor measurements at identical time points. The proposed method is evaluated with artificial as well as real data. The software is available as an R package tra (Time-Resolved data Alignment) which is freely available at: http://public.ostfalia.de/klawonn/tra.zip.