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1. Unsupervised logic-based mechanism inference for network-driven biological processes

   https://doi.org/10.1371/journal.pcbi.1009035  

   Prugger, Martina; Einkemmer, Lukas; Beik, Samantha P.; Wasdin, Perry T.; Harris, Leonard A.; Lopez, Carlos F. (June 2021, PLOS Computational Biology)

   Saucerman, Jeffrey J. (Ed.)

   Modern analytical techniques enable researchers to collect data about cellular states, before and after perturbations. These states can be characterized using analytical techniques, but the inference of regulatory interactions that explain and predict changes in these states remains a challenge. Here we present a generalizable, unsupervised approach to generate parameter-free, logic-based models of cellular processes, described by multiple discrete states. Our algorithm employs a Hamming-distance based approach to formulate, test, and identify optimized logic rules that link two states. Our approach comprises two steps. First, a model with no prior knowledge except for the mapping between initial and attractor states is built. We then employ biological constraints to improve model fidelity. Our algorithm automatically recovers the relevant dynamics for the explored models and recapitulates key aspects of the biochemical species concentration dynamics in the original model. We present the advantages and limitations of our work and discuss how our approach could be used to infer logic-based mechanisms of signaling, gene-regulatory, or other input-output processes describable by the Boolean formalism. 

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2. Control of Gene Regulatory Networks using Bayesian Inverse Reinforcement Learning

   https://doi.org/10.1109/TCBB.2018.2830357  

   Imani, Mahdi; Braga-Neto, Ulisses (April 2018, IEEE/ACM Transactions on Computational Biology and Bioinformatics)

   Control of gene regulatory networks (GRNs) to shift gene expression from undesirable states to desirable ones has received much attention in recent years. Most of the existing methods assume that the cost of intervention at each state and time point, referred to as the immediate cost function, is fully known. In this paper, we employ the Partially-Observed Boolean Dynamical System (POBDS) signal model for a time sequence of noisy expression measurement from a Boolean GRN and develop a Bayesian Inverse Reinforcement Learning (BIRL) approach to address the realistic case in which the only available knowledge regarding the immediate cost function is provided by the sequence of measurements and interventions recorded in an experimental setting by an expert. The Boolean Kalman Smoother (BKS) algorithm is used for optimally mapping the available gene-expression data into a sequence of Boolean states, and then the BIRL method is efficiently combined with the Q-learning algorithm for quantification of the immediate cost function. The performance of the proposed methodology is investigated by applying a state-feedback controller to two GRN models: a melanoma WNT5A Boolean network and a p53-MDM2 negative feedback loop Boolean network, when the cost of the undesirable states, and thus the identity of the undesirable genes, is learned using the proposed methodology. 

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3. The Dynamics of Canalizing Boolean Networks

   https://doi.org/10.1155/2020/3687961  

   Paul, Elijah; Pogudin, Gleb; Qin, William; Laubenbacher, Reinhard (January 2020, Complexity)

   Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by regulatory rules driving the dynamics that have certain so-called canalizing properties. In this paper, we investigate the dynamics of a random Boolean network with such properties using analytical methods and simulations. From our simulations, we observe that Boolean networks with higher canalizing depth have generally fewer attractors, the attractors are smaller, and the basins are larger, with implications for the stability and robustness of the models. These properties are relevant to many biological applications. Moreover, our results show that, from the standpoint of the attractor structure, high canalizing depth, compared to relatively small positive canalizing depth, has a very modest impact on dynamics. Motivated by these observations, we conduct mathematical study of the attractor structure of a random Boolean network of canalizing depth one (i.e., the smallest positive depth). For every positive integer ℓ , we give an explicit formula for the limit of the expected number of attractors of length ℓ in an n -state random Boolean network as n goes to infinity. 

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4. The logic behind neural control of breathing pattern

   https://doi.org/10.1038/s41598-019-45011-7  

   Ben-Tal, Alona; Wang, Yunjiao; Leite, Maria C. A. (June 2019, Scientific Reports)

   Abstract The respiratory rhythm generator is spectacular in its ability to support a wide range of activities and adapt to changing environmental conditions, yet its operating mechanisms remain elusive. We show how selective control of inspiration and expiration times can be achieved in a new representation of the neural system (called a Boolean network). The new framework enables us to predict the behavior of neural networks based on properties of neurons, not their values. Hence, it reveals the logic behind the neural mechanisms that control the breathing pattern. Our network mimics many features seen in the respiratory network such as the transition from a 3-phase to 2-phase to 1-phase rhythm, providing novel insights and new testable predictions. 

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5. Structure-based approach to identifying small sets of driver nodes in biological networks

   https://doi.org/10.1063/5.0080843  

   Newby, Eli; Tejeda Zañudo, Jorge Gómez; Albert, Réka (June 2022, Chaos: An Interdisciplinary Journal of Nonlinear Science)

   In network control theory, driving all the nodes in the Feedback Vertex Set (FVS) by node-state override forces the network into one of its attractors (long-term dynamic behaviors). The FVS is often composed of more nodes than can be realistically manipulated in a system; for example, only up to three nodes can be controlled in intracellular networks, while their FVS may contain more than 10 nodes. Thus, we developed an approach to rank subsets of the FVS on Boolean models of intracellular networks using topological, dynamics-independent measures. We investigated the use of seven topological prediction measures sorted into three categories—centrality measures, propagation measures, and cycle-based measures. Using each measure, every subset was ranked and then evaluated against two dynamics-based metrics that measure the ability of interventions to drive the system toward or away from its attractors: To Control and Away Control. After examining an array of biological networks, we found that the FVS subsets that ranked in the top according to the propagation metrics can most effectively control the network. This result was independently corroborated on a second array of different Boolean models of biological networks. Consequently, overriding the entire FVS is not required to drive a biological network to one of its attractors, and this method provides a way to reliably identify effective FVS subsets without the knowledge of the network dynamics. 

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