Non-Gaussian Statistics of Anomalous Diffusion:
The DNA Sequences of Prokaryotes
Paolo Allegrini,1,2
Marco Buiatti,2,3
Paolo Grigolini,2,3,4
and Bruce J. West4
1Istituto di Biofisica del Consiglio Nazionale delle Ricerche,
Via San Lorenzo 26, 56127 Pisa, Italy
2Dipartimento di Fisica dell'Università di Pisa,
Piazza Torricelli 2, 56100, Pisa, Italy
3 Istituto di Biofisica del Consiglio Nazionale delle Ricerche,
Via S. Lorenzo 26, 56127 Pisa, Italy
4
Center for Nonlinear Science, University of North Texas, P.O. Box 5368,
Denton, Texas 76203-5368
Physical Review E,
58(3):3640-3648 (September 1998)
Abstract
We adopt a non-Gaussian indicator to measure the deviation from
Gaussian statistics of a diffusion process generated by dichotomous
fluctuations with infinite memory. We also make analytical predictions
on the transient behavior of the non-Gaussian indicator as well as on its
stationary value. We then apply this non-Gaussian analysis to the DNA
sequences of prokaryotes adopting a theoretical model where the ``DNA
dynamics'' are assumed to be determined by the statistical superposition
of two independent generators of fluctuations: a generator of fluctuations
with no correlation and a generator of fluctuations with infinite
correlation ``time.'' We study also the influence that the finite length of
the observed sequences has on the non-Gaussian statistics of diffusion.
We find that these non-Gaussian effects are blurred by the joint action
of short-range fluctuation and sequence truncation. Nevertheless, under
proper conditions, fulfilled by all the DNA sequences of prokaryotes that
have been examined, a non-Gaussian signature remains to signal the
correlated nature of the driving process.
