Among the various phenomena that can be modeled by Boolean networks, i.e., discrete-time dynamical systems with binary state variables, gene regulatory interactions are especially well known. Therefore, the analysis of Boolean networks is critical, e.g., to identify genetic pathways and to predict the effects of mutations on the cell functionality. Two methodologies (i.e., the semi-tensor product and the Gröbner bases over finite fields) have recently been proposed to tackle the problem of determining cycles and attractors (with the corresponding basin of attraction) for such systems. Here, it is shown that, by suitably coupling methodologies taken from these two fields (i.e., linear algebra and algebraic geometry), it is not only possible to determine cycles and attractors, but also to find closed-form solutions of the Boolean network. Such a goal is pursued by finding an immersion that recasts the Boolean dynamics in a linear form and by computing the closed-form solution of the latter system. The effectiveness of this technique is demonstrated by fully computing the solutions of the Boolean network modeling the differentiation of the Th-lymphocyte, a type of white blood cells involved in the human adaptive immune system.

Menini, L., Possieri, C., Tornambe, A. (2019). Boolean network analysis through the joint use of linear algebra and algebraic geometry. JOURNAL OF THEORETICAL BIOLOGY, 472, 46-53 [10.1016/j.jtbi.2019.04.012].

Boolean network analysis through the joint use of linear algebra and algebraic geometry

Menini L.;Possieri C.;Tornambe A.
2019-01-01

Abstract

Among the various phenomena that can be modeled by Boolean networks, i.e., discrete-time dynamical systems with binary state variables, gene regulatory interactions are especially well known. Therefore, the analysis of Boolean networks is critical, e.g., to identify genetic pathways and to predict the effects of mutations on the cell functionality. Two methodologies (i.e., the semi-tensor product and the Gröbner bases over finite fields) have recently been proposed to tackle the problem of determining cycles and attractors (with the corresponding basin of attraction) for such systems. Here, it is shown that, by suitably coupling methodologies taken from these two fields (i.e., linear algebra and algebraic geometry), it is not only possible to determine cycles and attractors, but also to find closed-form solutions of the Boolean network. Such a goal is pursued by finding an immersion that recasts the Boolean dynamics in a linear form and by computing the closed-form solution of the latter system. The effectiveness of this technique is demonstrated by fully computing the solutions of the Boolean network modeling the differentiation of the Th-lymphocyte, a type of white blood cells involved in the human adaptive immune system.
2019
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore ING-INF/04 - Automatica
English
Algebraic geometry; Boolean networks; Linear algebra; Linear systems
http://www.elsevier.com/inca/publications/store/6/2/2/9/0/4/index.htt
Menini, L., Possieri, C., Tornambe, A. (2019). Boolean network analysis through the joint use of linear algebra and algebraic geometry. JOURNAL OF THEORETICAL BIOLOGY, 472, 46-53 [10.1016/j.jtbi.2019.04.012].
Menini, L; Possieri, C; Tornambe, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/219917
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