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Abstract The inference of gene regulatory networks (GRNs) from high-throughput data constitutes a fundamental and challenging task in systems biology. Boolean networks are a popular modeling framework to understand the dynamic nature of GRNs. In the absence of reliable methods to infer the regulatory logic of Boolean GRN models, researchers frequently assume threshold logic as a default. Using the largest repository of published expert-curated Boolean GRN models as best proxy of reality, we systematically compare the ability of two popular threshold formalisms, the Ising and the 01 formalism, to truthfully recover biological functions and biological system dynamics. While Ising rules match fewer biological functions exactly than 01 rules, they yield a better average agreement. In general, more complex regulatory logic proves harder to be represented by either threshold formalism. Informed by these results and a meta-analysis of regulatory logic, we propose modified versions for both formalisms, which provide a better function-level and dynamic agreement with biological GRN models than the usual threshold formalisms. For small biological GRN models with low connectivity, corresponding threshold networks exhibit similar dynamics. However, they generally fail to recover the dynamics of large networks or highly connected networks. In conclusion, this study provides new insights into an important question in computational systems biology: how truthfully do Boolean threshold networks capture the dynamics of GRNs? 

Abstract The concept of control is crucial for effectively understanding and applying biological network models. Key structural features relate to control functions through gene regulation, signaling, or metabolic mechanisms, and computational models need to encode these. Applications often focus on model-based control, such as in biomedicine or metabolic engineering. In a recent paper, the authors developed a theoretical framework of modularity in Boolean networks, which led to a canonical semidirect product decomposition of these systems. In this paper, we present an approach to model-based control that exploits this modular structure, as well as the canalizing features of the regulatory mechanisms. We show how to identify control strategies from the individual modules, and we present a criterion based on canalizing features of the regulatory rules to identify modules that do not contribute to network control and can be excluded. For even moderately sized networks, finding global control inputs is computationally challenging. Our modular approach leads to an efficient approach to solving this problem. We apply it to a published Boolean network model of blood cancer large granular lymphocyte (T-LGL) leukemia to identify a minimal control set that achieves a desired control objective.