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

Abstract

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.

Artefacts in statistical analyses of network motifs: general framework and application to metabolic networks

“…Some dynamical systems are highly sensitive to motifs as small functional devices. A whole range of investigations have identified a deep relationship between network motifs and the robust functioning of systemic processes [7,59,60,66,67]. In order to understand the generality and fundamental nature of these links between topology and dynamics, one needs better knowledge of the intrinsic statistical properties of few-node subgraphs as well as the most minimal dynamical situations, in which such a relationship between topology and dynamics can occur.…”

“…the 'biomass vector' often encountered in constrained-based modelling of metabolic systems). In the following, we will discuss layered random networks (inspired by the KaluzaMikhailov model of evolved flow networks; [59]). …”

Network Heterogeneity and Node Capacity Lead to Heterogeneous Scaling of Fluctuations in Random Walks on Graphs

“…This method has applications as far reaching as the metabolic states of human cells [28]. Its' variants have been used to study which network features are enhanced during a simulated evolution of simple flow networks, when requiring robustness against link or node removal [29] or as a function of task complexity [30].…”

Autonomous learning by simple dynamical systems with delayed feedback

“…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].…”

“…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.…”