From scale invariance to deterministic chaos in DNA sequences: towards a deterministic description of gene organisation in the human genome

We use the continuous wavelet transform to perform a space-scale analysis of the AT and GC
skews (strand asymmetries) in human genomic sequences, which have been shown to correlate
with gene transcription. This study reveals the existence of a characteristic scale `c 25 ± 10 kb
that separates a monofractal long-range correlated noisy regime at small scales (` ¡ `c ) from
relaxational oscillatory behavior at large-scale (` ¿ `c ). We show that these large scale nonlinear
oscillations enlighten an organization of the human genome into adjacent domains ( 400 kb)
with preferential gene orientation. When using classical techniques from dynamical systems the-
ory, we demonstrate that these relaxational oscillations display all the characteristic properties
of the chaotic strange attractor behavior observed nearby homoclinic orbits of Shil'nikov type.
We discuss the possibility that replication and gene regulation processes are governed by a
low-dimensional dynamical system that displays deterministic chaos.
c 2004 Elsevier B.V. All rights reserved.