A network-based modeling framework reveals the core signal transduction network underlying high carbon dioxide-induced stomatal closure in guard cells.

Stomata are pores on plant aerial surfaces, each bordered by a pair of guard cells. They control gas exchange vital for plant survival. Understanding how guard cells respond to environmental signals such as atmospheric carbon dioxide (CO2) levels is not only insightful to fundamental biology but also relevant to real-world issues of crop productivity under global climate change. In the past decade, multiple important signaling elements for stomatal closure induced by elevated CO2 have been identified. Yet, there is no comprehensive understanding of high CO2-induced stomatal closure. In this work, we assemble a cellular signaling network underlying high CO2-induced stomatal closure by integrating evidence from a comprehensive literature analysis. We further construct a Boolean dynamic model of the network, which allows in silico simulation of the stomatal closure response to high CO2 in wild-type Arabidopsis thaliana plants and in cases of pharmacological or genetic manipulation of network nodes. Our model has a 91% accuracy in capturing known experimental observations. We perform network-based logical analysis and reveal a feedback core of the network, which dictates cellular decisions in closure response to high CO2. Based on these analyses, we predict and experimentally confirm that applying nitric oxide (NO) induces stomatal closure in ambient CO2 and causes hypersensitivity to elevated CO2. Moreover, we predict a negative regulatory relationship between NO and the protein phosphatase ABI2 and find experimentally that NO inhibits ABI2 phosphatase activity. The experimental validation of these model predictions demonstrates the effectiveness of network-based modeling and highlights the decision-making role of the feedback core of the network in signal transduction. We further explore the model's potential in predicting targets of signaling elements not yet connected to the CO2 network. Our combination of network science, in silico model simulation, and experimental assays demonstrates an effective interdisciplinary approach to understanding system-level biology.

Enhanced Resistance to Viruses in Nicotiana edwardsonii 'Columbia' Is Dependent on Salicylic Acid, Correlates with High Glutathione Levels, and Extends to Plant-Pathogenic Bacteria and Abiotic Stress.

Our earlier research showed that an interspecific tobacco hybrid (Nicotiana edwardsonii 'Columbia' [NEC]) displays elevated levels of salicylic acid (SA) and enhanced resistance to localized necrotic symptoms (hypersensitive response [HR]) caused by tobacco mosaic virus (TMV) and tobacco necrosis virus (TNV), as compared with another interspecific hybrid (Nicotiana edwardsonii [NE]) derived from the same parents. In the present study, we investigated whether symptomatic resistance in NEC is indeed associated with the inhibition of TMV and TNV and whether SA plays a role in this process. We demonstrated that enhanced viral resistance in NEC is manifested as both milder local necrotic (HR) symptoms and reduced levels of TMV and TNV. The presence of an adequate amount of SA contributes to the enhanced defense response of NEC to TMV and TNV, as the absence of SA resulted in seriously impaired viral resistance. Elevated levels of subcellular tripeptide glutathione (GSH) in NEC plants in response to viral infection suggest that in addition to SA, GSH may also contribute to the elevated viral resistance of NEC. Furthermore, we found that NEC displays an enhanced resistance not only to viral pathogens but also to bacterial infections and abiotic oxidative stress induced by paraquat treatments. [Formula: see text] Copyright © 2024 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license.

Network medicine framework reveals generic herb-symptom effectiveness of traditional Chinese medicine.

Understanding natural and traditional medicine can lead to world-changing drug discoveries. Despite the therapeutic effectiveness of individual herbs, traditional Chinese medicine (TCM) lacks a scientific foundation and is often considered a myth. In this study, we establish a network medicine framework and reveal the general TCM treatment principle as the topological relationship between disease symptoms and TCM herb targets on the human protein interactome. We find that proteins associated with a symptom form a network module, and the network proximity of an herb's targets to a symptom module is predictive of the herb's effectiveness in treating the symptom. These findings are validated using patient data from a hospital. We highlight the translational value of our framework by predicting herb-symptom treatments with therapeutic potential. Our network medicine framework reveals the scientific foundation of TCM and establishes a paradigm for understanding the molecular basis of natural medicine and predicting disease treatments.

Inferring gene regulatory networks using transcriptional profiles as dynamical attractors.

Genetic regulatory networks (GRNs) regulate the flow of genetic information from the genome to expressed messenger RNAs (mRNAs) and thus are critical to controlling the phenotypic characteristics of cells. Numerous methods exist for profiling mRNA transcript levels and identifying protein-DNA binding interactions at the genome-wide scale. These enable researchers to determine the structure and output of transcriptional regulatory networks, but uncovering the complete structure and regulatory logic of GRNs remains a challenge. The field of GRN inference aims to meet this challenge using computational modeling to derive the structure and logic of GRNs from experimental data and to encode this knowledge in Boolean networks, Bayesian networks, ordinary differential equation (ODE) models, or other modeling frameworks. However, most existing models do not incorporate dynamic transcriptional data since it has historically been less widely available in comparison to "static" transcriptional data. We report the development of an evolutionary algorithm-based ODE modeling approach (named EA) that integrates kinetic transcription data and the theory of attractor matching to infer GRN architecture and regulatory logic. Our method outperformed six leading GRN inference methods, none of which incorporate kinetic transcriptional data, in predicting regulatory connections among TFs when applied to a small-scale engineered synthetic GRN in Saccharomyces cerevisiae. Moreover, we demonstrate the potential of our method to predict unknown transcriptional profiles that would be produced upon genetic perturbation of the GRN governing a two-state cellular phenotypic switch in Candida albicans. We established an iterative refinement strategy to facilitate candidate selection for experimentation; the experimental results in turn provide validation or improvement for the model. In this way, our GRN inference approach can expedite the development of a sophisticated mathematical model that can accurately describe the structure and dynamics of the in vivo GRN.

Predicting cascading extinctions and efficient restoration strategies in plant-pollinator networks via generalized positive feedback loops.

The extinction of a species in a plant-pollinator mutualistic community can cause cascading effects and lead to major biodiversity loss. The ecologically important task of predicting the severity of the cascading effects is made challenging by the complex network of interactions among the species. In this work, we analyze an ensemble of models of communities of plant and pollinator species. These models describe the mutualistic inter-species interactions by Boolean threshold functions. We show that identifying generalized positive feedback loops can help pinpoint the species whose extinction leads to catastrophic and substantial damage to the whole community. We compare these results with the damage percentage caused by the loss of species identified as important by previously studied structural measures and show that positive feedback loops and the information gained from them can identify certain crucial species that the other measures fail to find. We also suggest mitigation measures for two specific purposes: (1) prevent the damage to the community by protecting a subset of the species, and (2) restore the community after the damage by restoring a subset of species. Our analyses indicate that the generalized positive feedback loops predict the most efficient strategies to achieve these purposes. The correct identification of species in each category has important implications for conservation efforts and developing community management strategies.

Models of Cell Processes are Far from the Edge of Chaos.

Complex living systems are thought to exist at the "edge of chaos" separating the ordered dynamics of robust function from the disordered dynamics of rapid environmental adaptation. Here, a deeper inspection of 72 experimentally supported discrete dynamical models of cell processes reveals previously unobserved order on long time scales, suggesting greater rigidity in these systems than was previously conjectured. We find that propagation of internal perturbations is transient in most cases, and that even when large perturbation cascades persist, their phenotypic effects are often minimal. Moreover, we find evidence that stochasticity and desynchronization can lead to increased recovery from regulatory perturbation cascades. Our analysis relies on new measures that quantify the tendency of perturbations to spread through a discrete dynamical system. Computing these measures was not feasible using current methodology; thus, we developed a multipurpose CUDA-based simulation tool, which we have made available as the open-source Python library cubewalkers. Based on novel measures and simulations, our results suggest that-contrary to current theory-cell processes are ordered and far from the edge of chaos.

Leveraging network structure in nonlinear control.

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.

Inference of a Boolean Network From Causal Logic Implications.

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.

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

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.

Whole community invasions and the integration of novel ecosystems.

The impact of invasion by a single non-native species on the function and structure of ecological communities can be significant, and the effects can become more drastic-and harder to predict-when multiple species invade as a group. Here we modify a dynamic Boolean model of plant-pollinator community assembly to consider the invasion of native communities by multiple invasive species that are selected either randomly or such that the invaders constitute a stable community. We show that, compared to random invasion, whole community invasion leads to final stable communities (where the initial process of species turnover has given way to a static or near-static set of species in the community) including both native and non-native species that are larger, more likely to retain native species, and which experience smaller changes to the topological measures of nestedness and connectance. We consider the relationship between the prevalence of mutualistic interactions among native and invasive species in the final stable communities and demonstrate that mutualistic interactions may act as a buffer against significant disruptions to the native community.

pystablemotifs: Python library for attractor identification and control in Boolean networks.

SUMMARY: 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. AVAILABILITY AND IMPLEMENTATION: The source code is on GitHub at https://github.com/jcrozum/pystablemotifs/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Relationships among generalized positive feedback loops determine possible community outcomes in plant-pollinator interaction networks.

Attractors in Boolean network models representing complex systems such as ecological communities correspond to long-term outcomes (e.g., stable communities) in such systems. As a result, identifying efficient methods to find and characterize these attractors allows for a better understanding of the diversity of possible outcomes. Here we analyze networks that model mutualistic communities of plant and pollinator species governed by Boolean threshold functions. We propose a novel attractor identification method based on generalized positive feedback loops and their functional relationships in such networks. We show that these relationships determine the mechanisms by which groups of stable positive feedback loops collectively trap the system in specific regions of the state space and lead to attractors. Put into the ecological context, we show how survival units-small groups of species in which species can maintain a specific survival state-and their relationships determine the final community outcomes in plant-pollinator networks. We find a remarkable diversity of community outcomes: up to an average of 43 attractors possible for networks with 100 species. This diversity is due to the multiplicity of survival units (up to 34) and stable subcommunities (up to 14). The timing of species influx or outflux does not affect the number of attractors, but it may influence their basins of attraction.

Context-specific regulation of lysosomal lipolysis through network-level diverting of transcription factor interactions.

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."

ER+ Breast Cancer Strongly Depends on MCL-1 and BCL-xL Anti-Apoptotic Proteins.

Breast cancer is the most frequent type of cancer and the major cause of mortality in women. The rapid development of various therapeutic options has led to the improvement of treatment outcomes; nevertheless, one-third of estrogen receptor (ER)-positive patients relapse due to cancer cell acquired resistance. Here, we use dynamic BH3 profiling (DBP), a functional predictive assay that measures net changes in apoptotic priming, to find new effective treatments for ER+ breast cancer. We observed anti-apoptotic adaptations upon treatment that pointed to metronomic therapeutic combinations to enhance cytotoxicity and avoid resistance. Indeed, we found that the anti-apoptotic proteins BCL-xL and MCL-1 are crucial for ER+ breast cancer cells resistance to therapy, as they exert a dual inhibition of the pro-apoptotic protein BIM and compensate for each other. In addition, we identified the AKT inhibitor ipatasertib and two BH3 mimetics targeting these anti-apoptotic proteins, S63845 and A-1331852, as new potential therapies for this type of cancer. Therefore, we postulate the sequential inhibition of both proteins using BH3 mimetics as a new treatment option for refractory and relapsed ER+ breast cancer tumors.

Parity and time reversal elucidate both decision-making in empirical models and attractor scaling in critical Boolean networks.

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.

Cell Line-Specific Network Models of ER+ Breast Cancer Identify Potential PI3Kα Inhibitor Resistance Mechanisms and Drug Combinations.

Durable control of invasive solid tumors necessitates identifying therapeutic resistance mechanisms and effective drug combinations. In this work, we used a network-based mathematical model to identify sensitivity regulators and drug combinations for the PI3Kα inhibitor alpelisib in estrogen receptor positive (ER+) PIK3CA-mutant breast cancer. The model-predicted efficacious combination of alpelisib and BH3 mimetics, for example, MCL1 inhibitors, was experimentally validated in ER+ breast cancer cell lines. Consistent with the model, FOXO3 downregulation reduced sensitivity to alpelisib, revealing a novel potential resistance mechanism. Cell line-specific sensitivity to combinations of alpelisib and BH3 mimetics depended on which BCL2 family members were highly expressed. On the basis of these results, newly developed cell line-specific network models were able to recapitulate the observed differential response to alpelisib and BH3 mimetics. This approach illustrates how network-based mathematical models can contribute to overcoming the challenge of cancer drug resistance. SIGNIFICANCE: Network-based mathematical models of oncogenic signaling and experimental validation of its predictions can identify resistance mechanisms for targeted therapies, as this study demonstrates for PI3Kα-specific inhibitors in breast cancer.

Data-Driven Math Model of FLT3-ITD Acute Myeloid Leukemia Reveals Potential Therapeutic Targets.

FLT3-mutant acute myeloid leukemia (AML) is an aggressive form of leukemia with poor prognosis. Treatment with FLT3 inhibitors frequently produces a clinical response, but the disease nevertheless often recurs. Recent studies have revealed system-wide gene expression changes in FLT3-mutant AML cell lines in response to drug treatment. Here we sought a systems-level understanding of how these cells mediate these drug-induced changes. Using RNAseq data from AML cells with an internal tandem duplication FLT3 mutation (FLT3-ITD) under six drug treatment conditions including quizartinib and dexamethasone, we identified seven distinct gene programs representing diverse biological processes involved in AML drug-induced changes. Based on the literature knowledge about genes from these modules, along with public gene regulatory network databases, we constructed a network of FLT3-ITD AML. Applying the BooleaBayes algorithm to this network and the RNAseq data, we created a probabilistic, data-driven dynamical model of acquired resistance to these drugs. Analysis of this model reveals several interventions that may disrupt targeted parts of the system-wide drug response. We anticipate co-targeting these points may result in synergistic treatments that can overcome resistance and prevent eventual recurrence.

Detecting network anomalies using Forman-Ricci curvature and a case study for human brain networks.

We analyze networks of functional correlations between brain regions to identify changes in their structure caused by Attention Deficit Hyperactivity Disorder (ADHD). We express the task for finding changes as a network anomaly detection problem on temporal networks. We propose the use of a curvature measure based on the Forman-Ricci curvature, which expresses higher-order correlations among two connected nodes. Our theoretical result on comparing this Forman-Ricci curvature with another well-known notion of network curvature, namely the Ollivier-Ricci curvature, lends further justification to the assertions that these two notions of network curvatures are not well correlated and therefore one of these curvature measures cannot be used as an universal substitute for the other measure. Our experimental results indicate nine critical edges whose curvature differs dramatically in brains of ADHD patients compared to healthy brains. The importance of these edges is supported by existing neuroscience evidence. We demonstrate that comparative analysis of curvature identifies changes that more traditional approaches, for example analysis of edge weights, would not be able to identify.

Mathematical modeling of the Candida albicans yeast to hyphal transition reveals novel control strategies.

Candida albicans, an opportunistic fungal pathogen, is a significant cause of human infections, particularly in immunocompromised individuals. Phenotypic plasticity between two morphological phenotypes, yeast and hyphae, is a key mechanism by which C. albicans can thrive in many microenvironments and cause disease in the host. Understanding the decision points and key driver genes controlling this important transition and how these genes respond to different environmental signals is critical to understanding how C. albicans causes infections in the host. Here we build and analyze a Boolean dynamical model of the C. albicans yeast to hyphal transition, integrating multiple environmental factors and regulatory mechanisms. We validate the model by a systematic comparison to prior experiments, which led to agreement in 17 out of 22 cases. The discrepancies motivate alternative hypotheses that are testable by follow-up experiments. Analysis of this model revealed two time-constrained windows of opportunity that must be met for the complete transition from the yeast to hyphal phenotype, as well as control strategies that can robustly prevent this transition. We experimentally validate two of these control predictions in C. albicans strains lacking the transcription factor UME6 and the histone deacetylase HDA1, respectively. This model will serve as a strong base from which to develop a systems biology understanding of C. albicans morphogenesis.

Reactive Oxygen Species Contribute to Symptomless, Extreme Resistance to Potato virus X in Tobacco.

Here we show that in tobacco (Nicotiana tabacum cultivar Samsun NN Rx1) the development of Rx1 gene-mediated, symptomless, extreme resistance to Potato virus X (PVX) is preceded by an early, intensive accumulation of the reactive oxygen species (ROS) superoxide (O2·-), evident between 1 and 6 h after inoculation and associated with increased nicotinamide adenine dinucleotide phosphate (NADPH) oxidase activities. This suggests a direct contribution of this ROS to virus restriction during symptomless, extreme resistance. Superoxide inhibition in PVX-inoculated leaves by infiltration of antioxidants (superoxide dismutase [SOD] and catalase [CAT]) partially suppresses extreme resistance in parallel with the appearance of localized leaf necrosis resembling a hypersensitive resistance (HR) response. F1 progeny from crosses of Rx1 and ferritin overproducer (deficient in production of the ROS OH·) tobaccos also display a suppressed extreme resistance to PVX, because significantly increased virus levels are coupled to HR, suggesting a role of the hydroxyl radical (OH·) in this symptomless antiviral defense. In addition, treatment of PVX-susceptible tobacco with a superoxide-generating agent (riboflavin/methionine) results in HR-like symptoms and reduced PVX titers. Finally, by comparing defense responses during PVX-elicited symptomless, extreme resistance and HR-type resistance elicited by Tobacco mosaic virus, we conclude that defense reactions typical of an HR (e.g., induction of cell death/ROS-regulator genes and antioxidants) are early and transient in the course of extreme resistance. Our results demonstrate the contribution of early accumulation of ROS (superoxide, OH·) in limiting PVX replication during symptomless extreme resistance and support earlier findings that virus-elicited HR represents a delayed, slower resistance response than symptomless, extreme resistance.