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

Abstract

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 ℓ c ≃25±10 kb that separates a monofractal long-range correlated noisy regime at small scales (ℓ<ℓ c ) from relaxational oscillatory behavior at large-scale (ℓ>ℓ 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 theory, 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.