Biological networks : a thermodynamical approach

Many real systems can be represented by networks, that is a set of nodes connected to each other. The study of these systems as such has proven extremely useful as it gives access to a series of parameters that characterise their non-trivial architecture. This architecture is the product of many factors from the evolutionary mechanisms that shape the system during its growth to the functional dynamics on a shorter time scale. Gaining knowledge on the architecture is then of importance but faces many challenges in particular in the study of biological networks. The first challenge is in terms of the method used to generate networks as we need to adopt an approach that, we expect, would allow us to understand those constraints and forces that shape the network. The second challenge is that of understanding the relationship between the architecture of the system and its dynamics and functionality. The third challenge is to get access using suitable techniques to the network architecture from expression data, such as mRNA abundances, for example. We first show in this thesis that it is possible to generate networks from a thermodynamical viewpoint. This approach allows us to relate the architecture of network to some constraints. Furthermore, we show that some information on the structure resides in the non-randomness of the links between nodes. If we were to draw an analogy with traditional thermodynamics, networks could be modelled in a first approximation as perfect gases. On a dynamical network of our design, we show a dependence of the architecture on the distribution of the level of expression of the nodes. Surprisingly, the distribution of the periods of those networks is a power-law and independent of the underlying architecture of the system. By comparing the data obtained from our model to experimental mRNA data we found a correlation between the degree of connectivity of genes and their level of abundance. Finally, we show how we can apply a method used traditionally in image reconstruction to inference of networks.