Introduction to BTW

The development of high throughput analysis of mRNA expression has revolutionized the study of complex biological systems. It is now possible to compare the expression levels of thousand of genes in different tissues, cell types, conditions and individuals. Moreover, it is also possible to study how gene expression changes over time.

Dynamic time warping is a class of algorithm that can determine the smallest distance and optimal alignment of two numerical sequences, such as gene expression time series, possibly of different length. Two gene expression time series having small time warping distances indicate that the two genes may share a similar expression over time, and may be involved in similar processes.

To this aim, we developed a symmetric version of the classic time warping algorithm - i.e. the time warping distance aligning from left to right and from right to left is the same. The symmetry allows the computation of the probability that two time points are aligned. High probability regions may indicate a high reliability of the alignment, and may have a biological significance - for example, they may correspond to specific phases of the cell cycle.

In 2001, Aach and Church developed a dynamic time warping variant which is symmetric. For this reason (and with the authorization of the author), we implemented the Aach's algorithm and extended it with the computation of Boltzmann's partition function and pair probabilities.

The web server BTW allows the user-friendly computation of time warping distances and Boltzmann' pair probabilities given input gene expression time series, and to our knowledge it is the first web server dedicated to this task. The user can choose either the Clote's algorithm or the Aach's algorithm.

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