Evolutionary Engineering of Complex Functional Networks

Abstract

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.

Self-correcting networks: Function, robustness, and motif distributions in biological signal processing

“…Two mutation schemes have been tried [10]. In the link mutation scheme, a mutation consists in adding a new connection or deleting an existing one from the network.…”

“…The constructive approach for studies of bionetworks has been followed in our recent publications [6][7][8]. Using a simplified model representing an abstraction of biological signal processing, ensembles of networks with the same output functions have been generated, which were additionally designed to be self-correcting against deletion of individual links or nodes, or against the application of distributed quenched noise.…”

“…Evolutionary optimization algorithms were used by us to obtain large ensembles of networks with predefined output patterns, which were robust against different kinds of local damage [6,10]. To collect the data, each evolution was started with a different, independently generated random network.…”

“…In the generated target patterns, only K = 4 output nodes received fluxes when an input node was activated. These four nodes were randomly specified for each input node and their relative activation degrees were also chosen at random [6,10].…”

Autonomous learning by simple dynamical systems with delayed feedback

“…These results could be further extended to flow network models with dynamic responses [7]. For coupled phase oscillators, it was shown that, by running evolutionary optimization, networks that are better entrained by pacemakers could be designed [8,9].…”