Developing a mathematical method to search for latent periodicity in protein amino-acid sequences with deletions and insertions

A mathematical method has been developed in order to search for latent periodicity in protein amino-acid and other symbolical sequences using dynamic programming and random matrices. The method allows the detection of the latent periodicity with insertions and deletions at positions that are unknown beforehand. The developed method has been applied to search for the periodicity in the amino-acid sequences of several proteins and in the euro/dollar exchange rate since 2001. The presence of a long period with insertions and deletions in amino-acid sequences is shown. The period length of seven amino acids is observed in the proteins that contain supercoiled regions (a coiled-coil structure) as well as of six, five, or more amino acids. The existence of the period length of 6 and 7 days, as well as 24 and 25 h in the analyzed financial time series is observed; note that this periodicity is detectable only for insertions and deletions. The causes that underlie the occurrence of the latent periodicity with insertions and deletions in amino-acid sequences and financial time series are discussed.