FRACTIONAL BROWNIAN-MOTION AS A NONSTATIONARY PROCESS - AN ALTERNATIVE PARADIGM FOR DNA-SEQUENCES

The long-range correlations in DNA sequences are currently interpreted as an example of stationary fractional Brownian motion (FBM). First w e show that the dynamics of a dichotomous stationary process with long -range correlations such as that used to model DNA sequences should co rrespond to Levy statistics and not to FBM. To explain why, in spite o f this, the statistical analysis of the data seems to be compatible wi th FBM, we notice that an initial Gaussian condition, generated by a p rocess foreign to the mechanism establishing the long-range correlatio ns and consequently implying a departure from the stationary condition , is maintained approximately unchanged for very long times. This is s o because due to the nature itself of the long-range correlation proce ss, it takes virtually an infinite time for the system to reach the ge nuine stationary state. Then we discuss a possible generator of initia l Gaussian conditions, based on a folding mechanism of the nucleic aci d in the cell nucleus. The model adopted is compatible with the known biological and physical constraints, namely, it is shown to be consist ent with the information of current biological literature on folding a s well as with the statistical analyses of DNA sequences.