Intrinsic noise and deviations from criticality in Boolean gene-regulatory networks

Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline between their ordered and disordered phases. Critical networks have been argued to lead to a number of functional advantages such as maximal dynamical range, maximal sensitivity to environmental changes, as well as to an excellent tradeoff between stability and flexibility. Here, we study the effect of noise within the context of Boolean networks trained to learn complex tasks under supervision. We verify that quasi-critical networks are the ones learning in the fastest possible way –even for asynchronous updating rules– and that the larger the task complexity the smaller the distance to criticality. On the other hand, when additional sources of intrinsic noise in the network states and/or in its wiring pattern are introduced, the optimally performing networks become clearly subcritical. These results suggest that in order to compensate for inherent stochasticity, regulatory and other type of biological networks might become subcritical rather than being critical, all the most if the task to be performed has limited complexity.Spanish-MINECO grant FIS2013-43201-P (FEDER funds) for financial suppor

Application of new probabilistic graphical models in the genetic regulatory networks studies

This paper introduces two new probabilistic graphical models for reconstruction of genetic regulatory networks using DNA microarray data. One is an Independence Graph (IG) model with either a forward or a backward search algorithm and the other one is a Gaussian Network (GN) model with a novel greedy search method. The performances of both models were evaluated on four MAPK pathways in yeast and three simulated data sets. Generally, an IG model provides a sparse graph but a GN model produces a dense graph where more information about gene-gene interactions is preserved. Additionally, we found two key limitations in the prediction of genetic regulatory networks using DNA microarray data, the first is the sufficiency of sample size and the second is the complexity of network structures may not be captured without additional data at the protein level. Those limitations are present in all prediction methods which used only DNA microarray data.Comment: 38 pages, 3 figure

A Computational Algebra Approach to the Reverse Engineering of Gene Regulatory Networks

This paper proposes a new method to reverse engineer gene regulatory networks from experimental data. The modeling framework used is time-discrete deterministic dynamical systems, with a finite set of states for each of the variables. The simplest examples of such models are Boolean networks, in which variables have only two possible states. The use of a larger number of possible states allows a finer discretization of experimental data and more than one possible mode of action for the variables, depending on threshold values. Furthermore, with a suitable choice of state set, one can employ powerful tools from computational algebra, that underlie the reverse-engineering algorithm, avoiding costly enumeration strategies. To perform well, the algorithm requires wildtype together with perturbation time courses. This makes it suitable for small to meso-scale networks rather than networks on a genome-wide scale. The complexity of the algorithm is quadratic in the number of variables and cubic in the number of time points. The algorithm is validated on a recently published Boolean network model of segment polarity development in Drosophila melanogaster.Comment: 28 pages, 5 EPS figures, uses elsart.cl

Evolving Gene Regulatory Networks with Mobile DNA Mechanisms

This paper uses a recently presented abstract, tuneable Boolean regulatory network model extended to consider aspects of mobile DNA, such as transposons. The significant role of mobile DNA in the evolution of natural systems is becoming increasingly clear. This paper shows how dynamically controlling network node connectivity and function via transposon-inspired mechanisms can be selected for in computational intelligence tasks to give improved performance. The designs of dynamical networks intended for implementation within the slime mould Physarum polycephalum and for the distributed control of a smart surface are considered.Comment: 7 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1303.722

Time-delayed models of gene regulatory networks

We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternativemodelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems