Evolutionary Engineering of Complex Functional Networks

Complex biological networks are responsible for many fundamental processes in living organisms, including signal transduction and genetic expression in biological cells and signal processing in neural networks. These functional networks, a product of the evolution, are characterized by their robustness against damages, mutations and noise. Functionality and robustness are reflected in their architectures which exhibit structures different from random networks and lattices. To design functional networks, robust against local damages and noise, and to study, how the requirements of functionality and robustness are reflected in their architecture, are the objectives of this work. Our studies are performed using a model of flow distribution networks representing a simplification of biological signal transduction systems. In the model, networks process signals (fluxes) passing from input to output nodes, and generate output patterns which define the function of a network. The design of networks with prescribed functions (output patterns) is performed by using an evolutionary process of mutations and selections. Furthermore, not only functionality, but also the requirements of different kinds of robustness are imposed in the network design. Three criteria of robustness are considered: robustness against the deletion of randomly chosen nodes or links and robustness against distributed noise. Remarkable differences between architectures of the designed networks, depending on the criteria of robustness imposed during their construction, are observed. Particularly, motif distributions of these networks are different. Comparing them with real biological networks, we have found that the networks robust against deletion of links show motif distributions which are very similar to those of some neural systems and to the development transcription and signal transduction networks of biological macroorganisms. An evolutionary process, similar to that used to construct robust networks, has been employed in a reverse engineering problem. Using it, we have constructed networks with given Laplacian spectra. We have demostrated that construction of networks with a prescribed Laplacian spectrum is possible. Statistical structural properties of families of cospectral graphs have been analyzed.