Βιολειτουργίες αλληλουχιών DNA

Abstract

In the current Thesis we explored Dynamical Statistics and its application on eucaryotic and procaryotic organisms. The results are devided into two parts. The rst part is dedicated to the theory of statistics, and especially to Nonextensive Statistics, which represent a possible generalization of random statistics (exponential distributions). This generalization depends on parametric logarithic-like and exponential-like functions (generalized functions) and tends to the ordinary de nitions for speci c values of these parameters. The values of the parameters, except the speci c ones, indicate the existence of correlations. We succeeded to construct two generalized multinomial coe#cients, where each one is based on the respective deformed factorial operator. Their structures are not connected through a q-transformation. Accordingly, the respective multinomial coe#cients describe di erent statistical properties. We distinguished the correlations described by the parameters into internal R and external Q correlations. For speci c values of these parameters we obtain four independent statistical structures. One of them is always the Boltzmann-Gibbs Statistics. For the deformed q-logarithm the rest three statistical structures are Tsallis, R#enyi and Ne-Gaussian. The rst multinomial coe#cient leads us to the de - nition of the respective entropies ST q , SR r and SG q in the ranges q 2 [0; 1], r 2 [0; 1] and q 2 (?1; 1]. The respective probability distributions of the maximum entropy are the q-exponential, ordinary exponential and q-exponential. The second multinomial coe#cient leads us to the de nition of the entropies ST q , SR r and SG q in the ranges q 2 [1;1), r 2 [0; 1] and q 2 [1;1). The respective probability distributions of the maximum entropy are the 2 ? q-exponential, ordinary exponential and 2 ? q-exponential. According to our results, the computation of the maximum probability distributions based on the Jaynes formalism leads in general to incorrect conclusions, while we showed explicitly which are the cases where the above formalism gives us the correct distributions. Applying the Jaynes formalism and considering our results about the maximum probability distributions for the entropy Tsallis ST q , we were able to explain the concavity paradoxon of the the Escort Probability Representation of ST q . The second part of this Thesis considers the application of statistical methods on the genome of di erent eucaryotic and procaryotic (bacteria) organisms. The study is performed with respect to the size distribution of the coding and noncoding regions in DNA. The human organism has been studied widely. The size distributions of the coding and noncoding regions of human DNA present a \bell" shape. This shape in the distributions are similar for all chromosomes. We observed that the two distributions, coding and noncoding, present a global maximum for sequences of the size# 100 bps, which means that the frequency of these sequences is very high around the maximum. .....................................................................................................