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Abstract: Sequence organizations are viewed from two points: one is from informationalredundancy or informational correlation IC and another is from k-merfrequency statistics. Two problems are investigated. The first is how the ICsexceed the fluctuation bound and the order emerges from fluctuation in a genomewhen the sequence length attains some critical value. We demonstrated that thetransition from fluctuation to order takes place at about sequence length200-300 thousands bases for human and E coli genome. It means that the lifeemerges from a region between macroscopic and microscopic. The second is aboutthe statistical law of the k-mer organization in a genome under theevolutionary pressure and functional selection. We deduced a sum rule Qk,N onthe k-mer frequency deviations from the randomness in a N-long sequence ofgenome and deduced the relations of Qk,N with k and N. We found that Qk,Nincreases with length N at a constant rate for most genome sequences anddemonstrated that when the functional selection of k-mers is accumulated tosome critical value the ordering takes place. An important finding is the sumrule correlated with the evolutionary complexity of the genome.



Author: Liaofu Luo, Yang Gao, Jun Lu

Source: https://arxiv.org/







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