Design and statistical properties of robust functional networks: A model study of biological signal transduction

Vingron

Chaos: An Interdisciplinary Journal of Nonlinear Science

2008

Self Cite

Statistical properties of large ensembles of networks, all designed to have the same functions of signal processing, but robust against different kinds of perturbations, are analyzed. We find that robustness against noise and random local damage plays a dominant role in determining motif distributions of networks and may underlie their classification into network superfamilies.High robustness against local damage and noise is a fundamental property of biological networks [1]. In gene knock-out experiments where effects of genes are studied by making inoperative one gene per experiment, it has been found that only 13% of genes in yeast are essential, so that their absence is lethal [2]. Because many subsystems of the cell are small, they are subject to strong stochastic fluctuations, but this also does not prevent regular cell functioning.To suppress fluctuations and increase stability of dynamical systems, negative feedback loops can be used (cf. [3]) and such mechanisms of noise reduction are indeed employed by the cells. Alternatively, robustness against random damage can be achieved through the use of self-correcting network architectures. Can small self-correcting networks with only tens of elements, typical for functional modules of biological cells, be constructed? What are characteristic statistical properties of functional networks capable of self-correction? Here, these questions are addressed for a class of networks that should produce predefined responses following activation of different input elements. In the realm of biology, this class includes not only signal-transduction networks of the cell, but also genetic networks. Moreover, the entire nervous system of primitive mul-2 ticellular organisms may also be viewed as belonging to such a class. In our analysis, an approach that can be described as constructive biology is chosen.Instead of investigating real biological networks, we consider a simple flow distribution model of signal processing where nonlinear feedbacks are excluded.By running evolutionary optimization algorithms, large ensembles of networks with the same size and the same output patterns, but robust against different kinds of local damage or distributed noise, are designed. This allows us to analyze how statistical properties of self-correcting networks depend on the kind of random perturbations against which they are robust. Special attention is paid to motif distributions of networks [4]. We discover that our designed networks, robust against random link deletions, have motif distributions characteristic for the second superfamily previously identified by U. Alon and coworkers [4], which includes signal transduction and genetic developmental networks of multicellular organisms and the neural system of the nematode Caenorhabditid elegans.Completely different motif distributions, that belong instead to the fourth superfamily, are characteristic for networks designed to be robust against node deletions or against of noise.

Section: Return To Stepmentioning

confidence: 99%

“…In the modified evolutionary optimization algorithm [6], the following steps are performed at each next iteration:…”

Section: Evolutionary Construction Of Robust Network With Predefmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

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

Vingron

Chaos: An Interdisciplinary Journal of Nonlinear Science

2008

Self Cite

“…Combinatorial optimization methods, such as stochastic Metropolis algorithms and simulated annealing, have been used in systems engineering problems [7][8][9][10][11][12][13][14][15][16]. Thus, analogs of biological signal transduction networks [7][8][9][10] and model oscillatory genetic networks with prescribed output patterns or oscillation periods [11,12] could be constructed. Moreover, the designed networks could, through further optimization, be made robust against local structural perturbations, such as deletion of links or nodes, or against noise [7][8][9][10].…”

mentioning

confidence: 99%

“…Thus, analogs of biological signal transduction networks [7][8][9][10] and model oscillatory genetic networks with prescribed output patterns or oscillation periods [11,12] could be constructed. Moreover, the designed networks could, through further optimization, be made robust against local structural perturbations, such as deletion of links or nodes, or against noise [7][8][9][10]. Model genetic networks, which could generate definite stationary expression patterns and thus imitate processes relevant for biological morphogenesis [13] or to produce required temporal responses [14], were developed and investigated.…”

mentioning

confidence: 99%

Autonomous learning by simple dynamical systems with delayed feedback

2014

Phys. Rev. E

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A general scheme for the construction of dynamical systems able to learn generation of the desired kinds of dynamics through adjustment of their internal structure is proposed. The scheme involves intrinsic time-delayed feedback to steer the dynamics towards the target performance. As an example, a system of coupled phase oscillators, which can, by changing the weights of connections between its elements, evolve to a dynamical state with the prescribed (low or high) synchronization level, is considered and investigated.

Evolutionary Engineering of Complex Functional Networks

Kori

Understanding Complex Systems

2008

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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.