Abstract
Information capacity of nucleotide sequences measures the unexpectedness of a continuation of a given string of nucleotides, thus having a sound relation to a variety of biological issues. A continuation is defined in a way maximizing the entropy of the ensemble of such continuations. The capacity is defined as a mutual entropy of real frequency dictionary of a sequence with respect to the one bearing the most expected continuations; it does not depend on the length of strings contained in a dictionary. Various genomes exhibit a multi-minima pattern of the dependence of information capacity on the string length, thus reflecting an order within a sequence. The strings with significant deviation of an expected frequency from the real one are the words of increased information value. Such words exhibit a non-random distribution alongside a sequence, thus making it possible to retrieve the correlation between a structure, and a function encoded within a sequence.
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Notes
The theory and methodology described below is applicable to a sequence from an arbitrary (finite) alphabet ℵ, say, for amino acid sequences.
An equality of these two sums stands behind the connection of a sequence into a ring.
Strictly speaking, information capacity is defined for a frequency dictionary, not for a sequence; we shall not make the difference between them, unless a mispresentation occurs.
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Acknowledgments
We are thankful to Prof. Alexander N. Gorban from Leicester University, for valuable discussions and inspiring ideas, and to Dr. Tatyana G. Popova from the Institute of Computational Modelling of RAS for stimulating interest in this work.
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The results present here were partially obtained due to the support from Krasnoyarsk Science Foundation.
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Sadovsky, M.G., Putintseva, J.A. & Shchepanovsky, A.S. Genes, information and sense: complexity and knowledge retrieval. Theory Biosci. 127, 69–78 (2008). https://doi.org/10.1007/s12064-008-0032-1
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DOI: https://doi.org/10.1007/s12064-008-0032-1