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pystablemotifs is a Python 3 library for analyzing Boolean networks. Its non-heuristic and exhaustive attractor identification algorithm was previously presented in Rozum et al. (2021). Here, we illustrate its performance improvements over similar methods and discuss how it uses outputs of the attractor identification process to drive a system to one of its attractors from any initial state. We implement six attractor control algorithms, five of which are new in this work. By design, these algorithms can return different control strategies, allowing for synergistic use. We also give a brief overview of the other tools implemented in pystablemotifs.

The source code is on GitHub at https://github.com/jcrozum/pystablemotifs/.

Supplementary data are available at Bioinformatics online.

 

Cytosolic calcium concentration ([Ca²⁺]_cyt) and heterotrimeric G‐proteins are universal eukaryotic signaling elements. In plant guard cells, extracellular calcium (Ca_o) is as strong a stimulus for stomatal closure as the phytohormone abscisic acid (ABA), but underlying mechanisms remain elusive. Here, we report that the sole Arabidopsis heterotrimeric Gβ subunit,AGB1, is required for four guard cell Ca_oresponses: induction of stomatal closure; inhibition of stomatal opening; [Ca²⁺]_cytoscillation; and inositol 1,4,5‐trisphosphate (InsP3) production. Stomata in wild‐type Arabidopsis (Col) and in mutants of the canonical Gα subunit,GPA1, showed inhibition of stomatal opening and promotion of stomatal closure by Ca_o. By contrast, stomatal movements ofagb1mutants andagb1/gpa1double‐mutants, as well as those of theagg1agg2 Gγ double‐mutant, were insensitive to Ca_o. These behaviors contrast withABA‐regulated stomatal movements, which involveGPA1 andAGB1/AGG3 dimers, illustrating differential partitioning of G‐protein subunits among stimuli with similar ultimate impacts, which may facilitate stimulus‐specific encoding.AGB1knockouts retained reactive oxygen species andNOproduction, but lostYC3.6‐detected [Ca²⁺]_cytoscillations in response to Ca_o, initiating only a single [Ca²⁺]_cytspike. Experimentally imposed [Ca²⁺]_cytoscillations restored stomatal closure inagb1. Yeast two‐hybrid and bimolecular complementation fluorescence experiments revealed thatAGB1 interacts with phospholipase Cs (PLCs), and Ca_oinduced InsP3 production in Col but not inagb1. In sum, G‐protein signaling viaAGB1/AGG1/AGG2 is essential for Ca_o‐regulation of stomatal apertures, and stomatal movements in response to Ca_oapparently require Ca²⁺‐induced Ca²⁺release that is likely dependent on Gβγ interaction withPLCs leading to InsP3 production.

 

Abstract Over the last twenty years, dynamic modeling of biomolecular networks has exploded in popularity. Many of the classical tools for understanding dynamical systems are unwieldy in the highly nonlinear, poorly constrained, high-dimensional systems that often arise from these modeling efforts. Understanding complex biological systems is greatly facilitated by purpose-built methods that leverage common features of such models, such as local monotonicity, interaction graph sparsity, and sigmoidal kinetics. Here, we review methods for controlling the systems of ordinary differential equations used to model biomolecular networks. We focus on methods that make use of the structure of the network of interactions to help inform, which variables to target for control, and highlight the computational and experimental advantages of such approaches. We also discuss the importance of nonperturbative methods in biomedical and experimental molecular biology applications, where finely tuned interventions can be difficult to implement. It is well known that feedback loops, and positive feedback loops in particular, play a major determining role in the dynamics of biomolecular networks. In many of the methods we cover here, control over system trajectories is realized by overriding the behavior of key feedback loops. 

Biological systems contain a large number of molecules that have diverse interactions. A fruitful path to understanding these systems is to represent them with interaction networks, and then describe flow processes in the network with a dynamic model. Boolean modeling, the simplest discrete dynamic modeling framework for biological networks, has proven its value in recapitulating experimental results and making predictions. A first step and major roadblock to the widespread use of Boolean networks in biology is the laborious network inference and construction process. Here we present a streamlined network inference method that combines the discovery of a parsimonious network structure and the identification of Boolean functions that determine the dynamics of the system. This inference method is based on a causal logic analysis method that associates a logic type (sufficient or necessary) to node-pair relationships (whether promoting or inhibitory). We use the causal logic framework to assimilate indirect information obtained from perturbation experiments and infer relationships that have not yet been documented experimentally. We apply this inference method to a well-studied process of hormone signaling in plants, the signaling underlying abscisic acid (ABA)—induced stomatal closure. Applying the causal logic inference method significantly reduces the manual work typically required for network and Boolean model construction. The inferred model agrees with the manually curated model. We also test this method by re-inferring a network representing epithelial to mesenchymal transition based on a subset of the information that was initially used to construct the model. We find that the inference method performs well for various likely scenarios of inference input information. We conclude that our method is an effective approach toward inference of biological networks and can become an efficient step in the iterative process between experiments and computations. 

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. 

Plasticity in multicellular organisms involves signaling pathways converting contexts—either natural environmental challenges or laboratory perturbations—into context-specific changes in gene expression. Congruently, the interactions between the signaling molecules and transcription factors (TF) regulating these responses are also context specific. However, when a target gene responds across contexts, the upstream TF identified in one context is often inferred to regulate it across contexts. Reconciling these stable TF–target gene pair inferences with the context-specific nature of homeostatic responses is therefore needed. The induction of the Caenorhabditis elegans genes lipl-3 and lipl-4 is observed in many genetic contexts and is essential to survival during fasting. We find DAF-16/FOXO mediating lipl-4 induction in all contexts tested; hence, lipl-4 regulation seems context independent and compatible with across-context inferences. In contrast, DAF-16–mediated regulation of lipl-3 is context specific. DAF-16 reduces the induction of lipl-3 during fasting, yet it promotes it during oxidative stress. Through discrete dynamic modeling and genetic epistasis, we define that DAF-16 represses HLH-30/TFEB—the main TF activating lipl-3 during fasting. Contrastingly, DAF-16 activates the stress-responsive TF HSF-1 during oxidative stress, which promotes C. elegans survival through induction of lipl-3 . Furthermore, the TF MXL-3 contributes to the dominance of HSF-1 at the expense of HLH-30 during oxidative stress but not during fasting. This study shows how context-specific diverting of functional interactions within a molecular network allows cells to specifically respond to a large number of contexts with a limited number of molecular players, a mode of transcriptional regulation we name “contextualized transcription.” 

We present new applications of parity inversion and time reversal to the emergence of complex behavior from simple dynamical rules in stochastic discrete models. Our parity-based encoding of causal relationships and time-reversal construction efficiently reveal discrete analogs of stable and unstable manifolds. We demonstrate their predictive power by studying decision-making in systems biology and statistical physics models. These applications underpin a novel attractor identification algorithm implemented for Boolean networks under stochastic dynamics. Its speed enables resolving a long-standing open question of how attractor count in critical random Boolean networks scales with network size and whether the scaling matches biological observations. Via 80-fold improvement in probed network size ( N = 16,384), we find the unexpectedly low scaling exponent of 0.12 ± 0.05, approximately one-tenth the analytical upper bound. We demonstrate a general principle: A system’s relationship to its time reversal and state-space inversion constrains its repertoire of emergent behaviors. 

ABSTRACT We describe a previously unreported macroscopic Arabidopsis organ, the cantil, named for its ‘cantilever’ function of holding the pedicel at a distance from the stem. Cantil development is strongest at the first nodes after the vegetative to reproductive inflorescence transition; cantil magnitude and frequency decrease acropetally. Cantils develop in wild-type Arabidopsis accessions (e.g. Col-0, Ws and Di-G) as a consequence of delayed flowering in short days; cantil formation is observed in long days when flowering is delayed by null mutation of the floral regulator FLOWERING LOCUS T. The receptor-like kinase ERECTA is a global positive regulator of cantil formation; therefore, cantils never form in the Arabidopsis strain Ler. ERECTA functions genetically upstream of heterotrimeric G proteins. Cantil expressivity is repressed by the specific heterotrimeric complex subunits GPA1, AGB1 and AGG3, which also play independent roles: GPA1 suppresses distal spurs at cantil termini, while AGB1 and AGG3 suppress ectopic epidermal rippling. These G protein mutant traits are recapitulated in long-day flowering gpa1-3 ft-10 plants, demonstrating that cantils, spurs and ectopic rippling occur as a function of delayed phase transition, rather than as a function of photoperiod per se.