Abstract EN:

A large number of biological systems exhibit scale-free behaviour of one or more variables. Scale-free behaviour reflects a tendency of complex systems to develop long-range correlations, i. E. Correlations that decay very slowly in time and extend over very large distances in space. However, the properties and the functional role of long-range correlations in biological systems are still poorly understood. The aim of this thesis is to shed new light into this issue with three studies in three different biological domains, both by exploring the relationship between the function of the system and its long-range statistical structure, and by investigating how biological systems adapt to a long-range correlated environment. The first study explores how a reasoning task modulates the temporal long-range correlations of the associated brain electrical activity as recorded by EEG. The task consists in searching a rule in triplets of numbers, and hypothesis are tested on the base of a performance feedback. We demonstrate that negative feedback elicits significantly stronger long-range correlations than positive feedback in wide brain areas. In the second study, we develop a high-order measure to investigate the long-range statistical structure of DNA sequences of prokaryotes. We test the hypothesis that prokaryotic DNA statistics is described by a model consisting in the superposition of a long-range correlated component and random noise. We show that the model fits the long-range statistics of several prokaryotic DNA sequences, and suggest a functional explanation of the result. The main aim of the third study was to investigate how neurons in the retina adapts to the wide range, long-range correlated temporal statistics of natural scenes. Adaptation is modelled as the cascade of the two major mechanisms of adaptation in the retina - light adaptation and contrast adaptation - predicting the mean and the variance of the input from the past input values. By testing the model on time series of natural light intensities, we show that such cascade is indeed sufficient to adapt to the natural stimulus by removing most of its long-range correlations, while no linear filtering alone achieves the same goal. This result suggests that contrast adaptation has efficiently developed to exploit the long-range temporal correlations of natural scenes in an optimal way.