Biological regulatory networks are less nonlinear than expected by chance

Nonlinearity is a characteristic of complex biological regulatory networks that has implications ranging from therapy to control. To better understand its nature, we analyzed a suite of published Boolean network models, containing a variety of complex nonlinear interactions, with an approach involving a probabilistic generalization of Boolean logic that George Boole himself had proposed. Leveraging the continuous-nature of this formulation using Taylor-decomposition methods revealed the distinct layers of nonlinearity of the models. A comparison of the resulting series of model approximations with the corresponding sets of randomized ensembles furthermore revealed that the biological networks are relatively more linearly approximable. We hypothesize that this is a result of optimization by natural selection for the purpose of controllability.

Informeasure: an R/Bioconductor package to quantify nonlinear dependence between variables in biological networks from an information theory perspective

Using information measures to infer biological regulatory networks can observe nonlinear relationship between variables, but it is computationally challenging and there is currently no convenient tool available. We here describe an information theory R package named Informeasure that devotes to quantifying nonlinear dependence between variables in biological regulatory networks from an information theory perspective. This package compiles most of the information measures currently available: mutual information, conditional mutual information, interaction information, partial information decomposition and part mutual information. The first estimator is used to infer bivariate networks while the last four estimators are dedicated to analysis of trivariate networks. The base installation of this turn-key package allows users to approach these information measures out of the box. Informeasure is implemented in R program and is available as an R/Bioconductor package at https://bioconductor.org/packages/Informeasure.

DReSS: a method to quantitatively describe the influence of structural perturbations on state spaces of genetic regulatory networks

Structures of genetic regulatory networks are not fixed. These structural perturbations can cause changes to the reachability of systems’ state spaces. As system structures are related to genotypes and state spaces are related to phenotypes, it is important to study the relationship between structures and state spaces. However, there is still no method can quantitively describe the reachability differences of two state spaces caused by structural perturbations. Therefore, Difference in Reachability between State Spaces (DReSS) is proposed. DReSS index family can quantitively describe differences of reachability, attractor sets between two state spaces and can help find the key structure in a system, which may influence system’s state space significantly. First, basic properties of DReSS including non-negativity, symmetry and subadditivity are proved. Then, typical examples are shown to explain the meaning of DReSS and the differences between DReSS and traditional graph distance. Finally, differences of DReSS distribution between real biological regulatory networks and random networks are compared. Results show most structural perturbations in biological networks tend to affect reachability inside and between attractor basins rather than to affect attractor set itself when compared with random networks, which illustrates that most genotype differences tend to influence the proportion of different phenotypes and only a few ones can create new phenotypes. DReSS can provide researchers with a new insight to study the relation between genotypes and phenotypes.

Semi-automatic model revision of Boolean regulatory networks: confronting time-series observations with (a)synchronous dynamics

MotivationComplex cellular processes can be represented by biological regulatory networks. Computational models of such networks have successfully allowed the reprodution of known behaviour and to have a better understanding of the associated cellular processes. However, the construction of these models is still mainly a manual task, and therefore prone to error. Additionally, as new data is acquired, existing models must be revised. Here, we propose a model revision approach of Boolean logical models capable of repairing inconsistent models confronted with time-series observations. Moreover, we account for both synchronous and asynchronous dynamics.ResultsThe proposed tool is tested on five well known biological models. Different time-series observations are generated, consistent with these models. Then, the models are corrupted with different random changes. The proposed tool is able to repair the majority of the corrupted models, considering the generated time-series observations. Moreover, all the optimal solutions to repair the models are produced.Contact{[email protected],[email protected]}