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

Abstract

A mathematical method was developed in order to search for latent periodicity in protein amino acid and other symbolical sequences using the dynamic programming and random matrixes. The method permits detection of the latent periodicity with insertions and deletions in the previously unknown positions. The developed method was applied to search for the periodicity in the amino acid sequences of some proteins and the periodicity in EUR/USD exchange rate since 2001. The presence of the long period length with insertions and deletions in amino acid sequences was shown. The period length of 7 amino acids was found in proteins containing supercoiled areas (coiled coil), the period length of 6 and 5 and more amino acids was also demonstrated. The existence of the period length of 6 and 7 days as well as 24 and 25 hours in the analyzed financial time series, which can be detected with insertions and deletions only, is revealed. The reasons of the occurence of the latent periodicity with insertions and deletions in the amino acid sequences and financial time series are discussed.