Modern experimental techniques such as Hi--C make it possible to measure the probability that different chromosomal regions are close in space. Usually, these measurements are characterized by the scaling of the contact probability as a function of the genomic distance between regions. In this work, we introduce a multifractal analysis of chromosomal contact maps. Our analysis shows that Hi--C maps display a non-trivial multifractal spectrum.We introduce a simple analytical model that describes the structure of chromosomes as a hierarchical set of domains nested in each other and we solve it exactly. The predicted multifractal spectrum is characterized by a phase transition between two phases with different fractal dimension, in excellent agreement with experimental data. These results support the view that there is no privileged level in the hierarchy of conformational domains. Within the same model, the scaling exponent of the contact probability can also be calculated. We argue that such procedure leads to a much more precise estimate of the contact probability exponent than previous approaches . By applying this method to experimental data, we demonstrate that it can capture subtle conformational differences a
Modern biological techniques such as Hi--C permit to measure probabilities that different chromosomal regions are close in space. These probabilities can be visualised as matrices called contact maps. Contact maps are characterized by self-similar blocks along the diagonal, corresponding to a hierarchy of tightly packed chromosomal domains. Statistical properties of these maps, and thus of chromosomal interactions, are usually summarized by the scaling of the contact probability as a function of the genomic distance . This approach is fraught with limitations, since such scaling is usually rather noisy. Here, we introduce a multifractal analysis of chromosomal contact maps. Our analysis reveals that Hi--C maps are bifractal, i.e. they are complex geometrical objects characterized by two distinct fractal dimensions. To rationalize this observation, we introduce a model that describes chromosomes as a hierarchical set of domains nested in each other and we solve it exactly. The predicted multifractal spectrum is in excellent quantitative agreement with experimental data. Our theory yields to a more robust estimation of the scaling exponent of the contact probability than existing methods . By applying this method to experimental data, we detect subtle conformational changes among chromosomes during differentiation of human stem cells.
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between regions. In this work,
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display a non-trivial multifractal spectrum.We introduce a simple analytical
are bifractal, i.e. they are complex geometrical objects characterized by two distinct fractal dimensions. To rationalize this observation, we introduce a
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characterized by a phase transition between two phases with different fractal dimension, in excellent
in excellent quantitative
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These results support the view that there is no privileged level in the hierarchy of conformational domains. Within the same model, the
Our theory yields to a more robust estimation of the
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can also be calculated. We argue that such procedure leads to a much more precise estimate of the contact probability exponent than previous approaches
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demonstrate that it can capture subtle conformational differences a
detect subtle conformational changes among chromosomes during differentiation of human stem cells.