Concepts in Boolean network modeling: What do they all mean?

Schwab, Julian; Kühlwein, Silke D.; Ikonomi, Nensi; Kühl, Michael; Kestler, Hans A.

doi:10.1016/j.csbj.2020.03.001

Cited by 162 publications

(158 citation statements)

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“…Biological networks are considered to be robust toward perturbations. This means that they can adapt to environmental changes, and their functions are resistant to random noise (Kitano, 2002 ; Greenbury et al, 2010 ; Graudenzi et al, 2011 ; Barabási, 2016 ; Schwab et al, 2020 ). Hence, we also evaluated the robustness of our network against noise.…”

Section: Discussionmentioning

confidence: 99%

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Awakening the HSC: Dynamic Modeling of HSC Maintenance Unravels Regulation of the TP53 Pathway and Quiescence

et al. 2020

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Hematopoietic stem cells (HSCs) provide all types of blood cells during the entire life of the organism. HSCs are mainly quiescent and can eventually enter the cell cycle to differentiate. HSCs are maintained and tightly regulated in a particular environment. The stem cell niche regulates dormancy and awakening. Deregulations of this interplay can lead to hematopoietic failure and diseases. In this paper, we present a Boolean network model that recapitulates HSC regulation in virtue of external signals coming from the niche. This Boolean network integrates and summarizes the current knowledge of HSC regulation and is based on extensive literature research. Furthermore, dynamic simulations suggest a novel systemic regulation of TP53 in homeostasis. Thereby, our model indicates that TP53 activity is balanced depending on external stimulations, engaging a regulatory mechanism involving ROS regulators and RAS activated transcription factors. Finally, we investigated different mouse models and compared them to in silico knockout simulations. Here, the model could recapitulate in vivo observed behaviors and thus sustains our results.

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Section: Discussionmentioning

confidence: 99%

“…Attractors denote the long-term behavior of a system, and in a biological context, they are often related to phenotypes (Kauffman, 1993;Thomas and Kaufman, 2001). All states leading to the same attractor are part of its so-called basin of attraction (Hopfensitz et al, 2013;Schwab et al, 2020).…”

Section: Boolean Networkmentioning

confidence: 99%

Awakening the HSC: Dynamic Modeling of HSC Maintenance Unravels Regulation of the TP53 Pathway and Quiescence

et al. 2020

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“…Boolean network models are one of the simplest models to study complex dynamic behavior in biological systems. There are three major paradigms (synchronous, asynchronous and probabilistic) for the mode of transition of a Boolean network from a present state to a succeeding one [93]. We have only considered the synchronous paradigm, in which all nodes of the network take an equivalent amount of time (the clock period) to change their value.…”

Section: Discussionmentioning

confidence: 99%

The Eigenvectors of the Transition Matrix as Predictors of the Dynamics of a Synchronous Boolean Network

Rushdi

Alsogati

2020

JAMCS

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The synchronous Boolean network model is a simple and powerful tool in describing, analyzing and simulating cellular biological networks. This paper seeks a complete understanding of the dynamics of such a model by utilizing conventional matrix methods, rather than scalar methods, or matrix methods employing the non-conventional semi-tensor products (STP) of matrices. The paper starts by relating the network transition matrix to its function matrix via a self-inverse (involutary) state matrix, which has a simple recursive expression, provided a recursive ordering is employed for the underlying basis vector. Once the network transition matrix is obtained, it can be used to generate a wealth of information including its powers, characteristic equation, minimal equation, 1-eigenvectors, and 0-eigenvectors. These might be used to correctly predict both the transient behavior and (more importantly) the cyclic behavior of the network. In a short-cut partial variant of the proposed approach, the step of computing the transition matrix might be by-passed. The reason for this is that the transition matrix and the function matrix are similar matrices that share the same characteristic equation and hence the function matrix might suffice when only the partial information supplied by the characteristic equation is all that is needed. We demonstrate the conceptual simplicity and practical utility of our approach via two illustrative examples. The first example illustrates the computation of 1-eigenvectors (that can be used to identify loops or attractors), while the second example deals with the evaluation of 0-eigenvectors (that can be used to explore transient chains). Since attractors are the main concern in the underlying model, then analysis of the Boolean network might be confined to the determination of 1-eigenvectors only.

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“…Each regulatory component is represented by a node of the graph. The directed edges between these components represent their regulatory interactions that are expressed by Boolean functions (Schwab et al, 2020 [64]). In most approaches to Boolean networks, binarization of high-throughput gene expression data is required to infer the Boolean functions.…”

Section: Boolean Networkmentioning

confidence: 99%

“…Attractors represent the long-term behavior of these state graphs and may characterize cellular phenotypes. When using the asynchronous update, complex attractors can emerge (Schwab et al, 2020 [64]).…”

Section: Boolean Networkmentioning

confidence: 99%

A Complex Systems Analysis of Cancer Networks

Uthamacumaran¹

2019

Preprint

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Cancers are complex, adaptive ecosystems. It remains the lead cause of disease-related, pediatric death in North America. The emerging field of complexity science has redefined cancer as a computational system with intractable, algorithmic complexity. Herein, a tumor and its heterogeneous phenotypes are discussed as dynamical systems having multiple, chaotic attractors. Machine learning, Network science and information theory are discussed as current tools for cancer network reconstruction. The fluid dynamics of cancer-cell fate transitions and chemical pattern formation are briefly reviewed. Deep Learning architectures, delay-embedding algorithms and computational fluid models are proposed for better forecasting gene expression patterns in cancer ecosystems. Cancer cell decision-making is investigated within the framework of complexity theory.

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Concepts in Boolean network modeling: What do they all mean?

Cited by 162 publications

References 123 publications

Awakening the HSC: Dynamic Modeling of HSC Maintenance Unravels Regulation of the TP53 Pathway and Quiescence

Awakening the HSC: Dynamic Modeling of HSC Maintenance Unravels Regulation of the TP53 Pathway and Quiescence

The Eigenvectors of the Transition Matrix as Predictors of the Dynamics of a Synchronous Boolean Network

A Complex Systems Analysis of Cancer Networks

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