Synchronization of mutual time-varying delay-coupled temporal Boolean networks

This paper presents mutual time-varying delay-coupled temporal Boolean network model and investigates synchronization issue for mutual time-varying delay-coupled temporal Boolean networks. The necessary and sufficient conditions for the synchronization are given, and the check criterion of the upper bound is presented. An example is given to illustrate the correctness of the theoretical analysis.

Delay Partial Synchronization of Mutual Delay Coupled Boolean Networks

This paper studies the delay partial synchronization for mutual delay-coupled Boolean networks. First, the mutual delay-coupled Boolean network model is presented. Second, some necessary and sufficient conditions are derived to ensure the delay partial synchronization of the mutual delay-coupled Boolean networks. The upper bound of synchronization time is obtained. Finally, an example is provided to illustrate the efficiency of the theoretical analysis.

Topography of epithelial–mesenchymal plasticity

The transition between epithelial and mesenchymal states has fundamental importance for embryonic development, stem cell reprogramming, and cancer progression. Here, we construct a topographic map underlying epithelial–mesenchymal transitions using a combination of numerical simulations of a Boolean network model and the analysis of bulk and single-cell gene expression data. The map reveals a multitude of metastable hybrid phenotypic states, separating stable epithelial and mesenchymal states, and is reminiscent of the free energy measured in glassy materials and disordered solids. Our work not only elucidates the nature of hybrid mesenchymal/epithelial states but also provides a general strategy to construct a topographic representation of phenotypic plasticity from gene expression data using statistical physics methods.

How causal analysis can reveal autonomy in models of biological systems

Standard techniques for studying biological systems largely focus on their dynamical or, more recently, their informational properties, usually taking either a reductionist or holistic perspective. Yet, studying only individual system elements or the dynamics of the system as a whole disregards the organizational structure of the system—whether there are subsets of elements with joint causes or effects, and whether the system is strongly integrated or composed of several loosely interacting components. Integrated information theory offers a theoretical framework to (1) investigate the compositional cause–effect structure of a system and to (2) identify causal borders of highly integrated elements comprising local maxima of intrinsic cause–effect power. Here we apply this comprehensive causal analysis to a Boolean network model of the fission yeast ( Schizosaccharomyces pombe ) cell cycle. We demonstrate that this biological model features a non-trivial causal architecture, whose discovery may provide insights about the real cell cycle that could not be gained from holistic or reductionist approaches. We also show how some specific properties of this underlying causal architecture relate to the biological notion of autonomy. Ultimately, we suggest that analysing the causal organization of a system, including key features like intrinsic control and stable causal borders, should prove relevant for distinguishing life from non-life, and thus could also illuminate the origin of life problem. This article is part of the themed issue ‘Reconceptualizing the origins of life’.

Simulating heterogeneous populations using Boolean models

Certain biological processes such as cancer development and immune activation are controlled by rare cellular events that are difficult to capture computationally through simulations of individual cells. Here we show that when cellular states are described using a Boolean network model, one can exactly simulate the dynamics of non-interacting, highly heterogeneous populations directly, without having to model the various subpopulations. This strategy captures even the rarest outcomes of the model with no sampling error. Our method can incorporate heterogeneity in both cell state and, by augmenting the model, the underlying rules of the network as well (i.e. mutations). We demonstrate our method by using it to simulate a heterogeneous population of Boolean networks modeling the T-cell receptor, spanning ~ 1020 distinct cellular states and mutational profiles.