APPROXIMATE SCALING PROPERTIES OF RNA FREE-ENERGY LANDSCAPES

RNA free energy landscapes are analysed by means of ''time-series'' th at are obtained from random walks restricted to excursion sets. The po wer spectra, the scaling of the jump size distribution, and the scalin g of the curve length measured with different yard stick lengths are u sed to describe the structure of these ''time series''. Although they are stationary by construction, we find that their local behavior is c onsistent with both AR(I) and self-affine processes. Random walks conf ined to excursion sets (i.e., with the restriction that the fitness va lue exceeds a certain threshold at each step) exhibit essentially the same statistics as free random walks. We find that an AR(I) time serie s is in general approximately self-affine on timescales up to approxim ately the correlation length. We present an empirical relation between the correlation parameter rho of the AR(I) model and the exponents ch aracterizing self-affinity. (C) 1996 Academic Press Limited