Searching for LINCS to Stress: Using Text Mining to Automate Reference Chemical Curation.

Adaptive stress response pathways (SRPs) restore cellular homeostasis following perturbation but may activate terminal outcomes like apoptosis, autophagy, or cellular senescence if disruption exceeds critical thresholds. Because SRPs hold the key to vital cellular tipping points, they are targeted for therapeutic interventions and assessed as biomarkers of toxicity. Hence, we are developing a public database of chemicals that perturb SRPs to enable new data-driven tools to improve public health. Here, we report on the automated text-mining pipeline we used to build and curate the first version of this database. We started with 100 reference SRP chemicals gathered from published biomarker studies to bootstrap the database. Second, we used information retrieval to find co-occurrences of reference chemicals with SRP terms in PubMed abstracts and determined pairwise mutual information thresholds to filter biologically relevant relationships. Third, we applied these thresholds to find 1206 putative SRP perturbagens within thousands of substances in the Library of Integrated Network-Based Cellular Signatures (LINCS). To assign SRP activity to LINCS chemicals, domain experts had to manually review at least three publications for each of 1206 chemicals out of 181,805 total abstracts. To accomplish this efficiently, we implemented a machine learning approach to predict SRP classifications from texts to prioritize abstracts. In 5-fold cross-validation testing with a corpus derived from the 100 reference chemicals, artificial neural networks performed the best (F1-macro = 0.678) and prioritized 2479/181,805 abstracts for expert review, which resulted in 457 chemicals annotated with SRP activities. An independent analysis of enriched mechanisms of action and chemical use class supported the text-mined chemical associations (p < 0.05): heat shock inducers were linked with HSP90 and DNA damage inducers to topoisomerase inhibition. This database will enable novel applications of LINCS data to evaluate SRP activities and to further develop tools for biomedical information extraction from the literature.

Exploring the effects of experimental parameters and data modeling approaches on in vitro transcriptomic point-of-departure estimates.

Multiple new approach methods (NAMs) are being developed to rapidly screen large numbers of chemicals to aid in hazard evaluation and risk assessments. High-throughput transcriptomics (HTTr) in human cell lines has been proposed as a first-tier screening approach for determining the types of bioactivity a chemical can cause (activation of specific targets vs. generalized cell stress) and for calculating transcriptional points of departure (tPODs) based on changes in gene expression. In the present study, we examine a range of computational methods to calculate tPODs from HTTr data, using six data sets in which MCF7 cells cultured in two different media formulations were treated with a panel of 44 chemicals for 3 different exposure durations (6, 12, 24 hr). The tPOD calculation methods use data at the level of individual genes and gene set signatures, and compare data processed using the ToxCast Pipeline 2 (tcplfit2), BMDExpress and PLIER (Pathway Level Information ExtractoR). Methods were evaluated by comparing to in vitro PODs from a validated set of high-throughput screening (HTS) assays for a set of estrogenic compounds. Key findings include: (1) for a given chemical and set of experimental conditions, tPODs calculated by different methods can vary by several orders of magnitude; (2) tPODs are at least as sensitive to computational methods as to experimental conditions; (3) in comparison to an external reference set of PODs, some methods give generally higher values, principally PLIER and BMDExpress; and (4) the tPODs from HTTr in this one cell type are mostly higher than the overall PODs from a broad battery of targeted in vitro ToxCast assays, reflecting the need to test chemicals in multiple cell types and readout technologies for in vitro hazard screening.

Ready for regulatory use: NAMs and NGRA for chemical safety assurance.

New approach methodologies (NAMs) that do not use experimental animals are, in certain settings, entirely appropriate for assuring the safety of chemical ingredients, although regulatory adoption has been slow. In this opinion article we discuss how scientific advances that utilize NAMs to certify systemic safety are available now and merit broader acceptance within the framework of next generation risk assessments (NGRA).

Are Non-animal Systemic Safety Assessments Protective? A Toolbox and Workflow.

An important question in toxicological risk assessment is whether non-animal new approach methodologies (NAMs) can be used to make safety decisions that are protective of human health, without being overly conservative. In this work, we propose a core NAM toolbox and workflow for conducting systemic safety assessments for adult consumers. We also present an approach for evaluating how protective and useful the toolbox and workflow are by benchmarking against historical safety decisions. The toolbox includes physiologically based kinetic (PBK) models to estimate systemic Cmax levels in humans, and 3 bioactivity platforms, comprising high-throughput transcriptomics, a cell stress panel, and in vitro pharmacological profiling, from which points of departure are estimated. A Bayesian model was developed to quantify the uncertainty in the Cmax estimates depending on how the PBK models were parameterized. The feasibility of the evaluation approach was tested using 24 exposure scenarios from 10 chemicals, some of which would be considered high risk from a consumer goods perspective (eg, drugs that are systemically bioactive) and some low risk (eg, existing food or cosmetic ingredients). Using novel protectiveness and utility metrics, it was shown that up to 69% (9/13) of the low risk scenarios could be identified as such using the toolbox, whilst being protective against all (5/5) the high-risk ones. The results demonstrated how robust safety decisions could be made without using animal data. This work will enable a full evaluation to assess how protective and useful the toolbox and workflow are across a broader range of chemical-exposure scenarios.

Mapping the dynamics of Nrf2 antioxidant and NFκB inflammatory responses by soft electrophilic chemicals in human liver cells defines the transition from adaptive to adverse responses.

A comprehensive understanding of the dynamic activation and crosstalk between different cellular stress response pathways that drive cell adversity is crucial in chemical safety assessment. Various chemicals have electrophilic properties that drive cell injury responses in particular oxidative stress signaling and inflammatory signaling. Here we used bacterial artificial chromosome-based GFP cellular stress reporters with live cell confocal imaging, to systematically monitor the differential modulation of the dynamics of stress pathway activation by six different soft electrophiles: sulforaphane, andrographolide, diethyl maleate, CDDO-Me, ethacrynic acid and tert-butyl hydroquinone. The various soft electrophiles showed differential potency and dynamics of Nrf2 activation and nuclear translocation. These differences in Nrf2 dynamics correlated with distinct activation pattern of Nrf2 downstream targets SRNX1 and HMOX1. All soft electrophiles caused a strong dose dependent suppression of a cytokine-induced NFĸB response represented by suppression of NFĸB nuclear oscillation and inhibition of the downstream target gene activation A20 and ICAM1, which followed the potency of Nrf2 modulation but occurred at higher concentration close to saturation of Nrf2 activation. RNAi-based depletion of RelA resulted in a prolonged presence of Nrf2 in the nucleus after soft electrophile treatment; depletion of Nrf2 caused the induction of NFĸB signaling and activation of its downstream targets A20 and ICAM1. A systematic transcriptome analysis confirmed these effects by soft electrophiles on Nrf2 and NFκB signaling crosstalk in human induced-pluripotent stem cell-derived hepatocyte-like cells. Altogether our data indicate that modulation of Nrf2 by soft electrophiles may have consequences for efficient inflammatory signaling.

Latent Variables Capture Pathway-Level Points of Departure in High-Throughput Toxicogenomic Data.

Estimation of points of departure (PoDs) from high-throughput transcriptomic data (HTTr) represents a key step in the development of next-generation risk assessment (NGRA). Current approaches mainly rely on single key gene targets, which are constrained by the information currently available in the knowledge base and make interpretation challenging as scientists need to interpret PoDs for thousands of genes or hundreds of pathways. In this work, we aimed to address these issues by developing a computational workflow to investigate the pathway concentration-response relationships in a way that is not fully constrained by known biology and also facilitates interpretation. We employed the Pathway-Level Information ExtractoR (PLIER) to identify latent variables (LVs) describing biological activity and then investigated in vitro LVs' concentration-response relationships using the ToxCast pipeline. We applied this methodology to a published transcriptomic concentration-response data set for 44 chemicals in MCF-7 cells and showed that our workflow can capture known biological activity and discriminate between estrogenic and antiestrogenic compounds as well as activity not aligning with the existing knowledge base, which may be relevant in a risk assessment scenario. Moreover, we were able to identify the known estrogen activity in compounds that are not well-established ER agonists/antagonists supporting the use of the workflow in read-across. Next, we transferred its application to chemical compounds tested in HepG2, HepaRG, and MCF-7 cells and showed that PoD estimates are in strong agreement with those estimated using a recently developed Bayesian approach (cor = 0.89) and in weak agreement with those estimated using a well-established approach such as BMDExpress2 (cor = 0.57). These results demonstrate the effectiveness of using PLIER in a concentration-response scenario to investigate pathway activity in a way that is not fully constrained by the knowledge base and to ease the biological interpretation and support the development of an NGRA framework with the ability to improve current risk assessment strategies for chemicals using new approach methodologies.

Next generation risk assessment (NGRA): Bridging in vitro points-of-departure to human safety assessment using physiologically-based kinetic (PBK) modelling - A case study of doxorubicin with dose metrics considerations.

Using the chemical doxorubicin (DOX), the objective of the present study was to evaluate the impact of dose metrics selection in the new approach method of integrating physiologically-based kinetic (PBK) modelling and relevant human cell-based assays to inform a priori the point of departure for human health risk. We reviewed the literature on the clinical consequences of DOX treatment to identify dosing scenarios with no or mild cardiotoxicity observed. Key concentrations of DOX that induced cardiomyocyte toxicity in vitro were derived from studies of our own and others. A human population-based PBK model of DOX was developed and verified against pharmacokinetic data. The model was then used to predict plasma and extracellular and intracellular heart concentrations of DOX under selected clinical settings and compared with in vitro outcomes, based on several dose metrics: Cmax (maximum concentration) or AUC (area under concentration-time curve) in free or total form of DOX. We found when using in vitro assays to predict cardiotoxicity for DOX, AUC is a better indicator. Our study illustrates that when appropriate dose metrics are used, it is possible to combine PBK modelling with in vitro-derived toxicity information to define margins of safety and predict low-risk human exposure levels.

Identifying and Characterizing Stress Pathways of Concern for Consumer Safety in Next-Generation Risk Assessment.

Many substances for which consumer safety risk assessments need to be conducted are not associated with specific toxicity modes of action, but rather exhibit nonspecific toxicity leading to cell stress. In this work, a cellular stress panel is described, consisting of 36 biomarkers representing mitochondrial toxicity, cell stress, and cell health, measured predominantly using high content imaging. To evaluate the panel, data were generated for 13 substances at exposures consistent with typical use-case scenarios. These included some that have been shown to cause adverse effects in a proportion of exposed humans and have a toxicological mode-of-action associated with cellular stress (eg, doxorubicin, troglitazone, and diclofenac), and some that are not associated with adverse effects due to cellular stress at human-relevant exposures (eg, caffeine, niacinamide, and phenoxyethanol). For each substance, concentration response data were generated for each biomarker at 3 timepoints. A Bayesian model was then developed to quantify the evidence for a biological response, and if present, a credibility range for the estimated point of departure (PoD) was determined. PoDs were compared with the plasma Cmax associated with the typical substance exposures, and indicated a clear differentiation between "low" risk and "high" risk chemical exposure scenarios. Developing robust methods to characterize the in vitro bioactivity of xenobiotics is an important part of non-animal safety assessment. The results presented in this work show that the cellular stress panel can be used, together with other new approach methodologies, to identify chemical exposures that are protective of consumer health.

A Next-Generation Risk Assessment Case Study for Coumarin in Cosmetic Products.

Next-Generation Risk Assessment is defined as an exposure-led, hypothesis-driven risk assessment approach that integrates new approach methodologies (NAMs) to assure safety without the use of animal testing. These principles were applied to a hypothetical safety assessment of 0.1% coumarin in face cream and body lotion. For the purpose of evaluating the use of NAMs, existing animal and human data on coumarin were excluded. Internal concentrations (plasma Cmax) were estimated using a physiologically based kinetic model for dermally applied coumarin. Systemic toxicity was assessed using a battery of in vitro NAMs to identify points of departure (PoDs) for a variety of biological effects such as receptor-mediated and immunomodulatory effects (Eurofins SafetyScreen44 and BioMap Diversity 8 Panel, respectively), and general bioactivity (ToxCast data, an in vitro cell stress panel and high-throughput transcriptomics). In addition, in silico alerts for genotoxicity were followed up with the ToxTracker tool. The PoDs from the in vitro assays were plotted against the calculated in vivo exposure to calculate a margin of safety with associated uncertainty. The predicted Cmax values for face cream and body lotion were lower than all PoDs with margin of safety higher than 100. Furthermore, coumarin was not genotoxic, did not bind to any of the 44 receptors tested and did not show any immunomodulatory effects at consumer-relevant exposures. In conclusion, this case study demonstrated the value of integrating exposure science, computational modeling and in vitro bioactivity data, to reach a safety decision without animal data.

Bridging the Data Gap From in vitro Toxicity Testing to Chemical Safety Assessment Through Computational Modeling.

Chemical toxicity testing is moving steadily toward a human cell and organoid-based in vitro approach for reasons including scientific relevancy, efficiency, cost, and ethical rightfulness. Inferring human health risk from chemical exposure based on in vitro testing data is a challenging task, facing various data gaps along the way. This review identifies these gaps and makes a case for the in silico approach of computational dose-response and extrapolation modeling to address many of the challenges. Mathematical models that can mechanistically describe chemical toxicokinetics (TK) and toxicodynamics (TD), for both in vitro and in vivo conditions, are the founding pieces in this regard. Identifying toxicity pathways and in vitro point of departure (PoD) associated with adverse health outcomes requires an understanding of the molecular key events in the interacting transcriptome, proteome, and metabolome. Such an understanding will in turn help determine the sets of sensitive biomarkers to be measured in vitro and the scope of toxicity pathways to be modeled in silico. In vitro data reporting both pathway perturbation and chemical biokinetics in the culture medium serve to calibrate the toxicity pathway and virtual tissue models, which can then help predict PoDs in response to chemical dosimetry experienced by cells in vivo. Two types of in vitro to in vivo extrapolation (IVIVE) are needed. (1) For toxic effects involving systemic regulations, such as endocrine disruption, organism-level adverse outcome pathway (AOP) models are needed to extrapolate in vitro toxicity pathway perturbation to in vivo PoD. (2) Physiologically-based toxicokinetic (PBTK) modeling is needed to extrapolate in vitro PoD dose metrics into external doses for expected exposure scenarios. Linked PBTK and TD models can explore the parameter space to recapitulate human population variability in response to chemical insults. While challenges remain for applying these modeling tools to support in vitro toxicity testing, they open the door toward population-stratified and personalized risk assessment.

Flutamide Induces Hepatic Cell Death and Mitochondrial Dysfunction via Inhibition of Nrf2-Mediated Heme Oxygenase-1.

Flutamide is a widely used nonsteroidal antiandrogen for prostate cancer therapy, but its clinical application is restricted by the concurrent liver injury. Increasing evidence suggests that flutamide-induced liver injury is associated with oxidative stress, though the precise mechanism is poorly understood. Nuclear factor erythroid 2-related factor 2 (Nrf2) is a master transcription factor regulating endogenous antioxidants including heme oxygenase-1 (HO-1). This study was designed to delineate the role of Nrf2/HO-1 in flutamide-induced hepatic cell injury. Our results showed that flutamide concentration dependently induced cytotoxicity, hydrogen peroxide accumulation, and mitochondrial dysfunction as indicated by mitochondrial membrane potential loss and ATP depletion. The protein expression of Nrf2 and HO-1 was induced by flutamide at 12.5 µM but was downregulated by higher concentrations of flutamide. Silencing either Nrf2 or HO-1 was found to aggravate flutamide-induced hydrogen peroxide accumulation and mitochondrial dysfunction as well as inhibition of the Nrf2 pathway. Moreover, preinduction of HO-1 by Copp significantly attenuated flutamide-induced oxidative stress and mitochondrial dysfunction, while inhibition of HO-1 by Snpp aggravated these deleterious effects. These findings suggest that flutamide-induced hepatic cell death and mitochondrial dysfunction is assoicated with inhibition of Nrf2-mediated HO-1. Pharmacologic intervention of Nrf2/HO-1 may provide a promising therapeutic approach in flutamide-induced liver injury.

Doxorubicin-induced mitophagy and mitochondrial damage is associated with dysregulation of the PINK1/parkin pathway.

The usefulness of doxorubicin (DOX), a potent anticancer agent, is limited by its cardiotoxicity. Mitochondria play a central role in DOX-induced cardiotoxicity though the precise mechanisms are still obscure. Increasing evidence indicates that excessive activation of mitophagy and mitochondrial dysfunction are key causal events leading to DOX-induced cardiac injury. The PINK1/parkin pathway has emerged as a critical pathway in regulation of mitophagy as well as mitochondrial function. The present study was aimed to investigate the role of PINK1/parkin pathway in DOX-induced mitochondrial damage and cardiotoxicity. Our results showed that DOX concentration-dependently induced cytotoxicity and mitochondrial toxic effects including mitochondrial superoxide accumulation, decreased mitochondrial membrane potential and mitochondrial DNA copy number, as well as mitochondrial ultrastructural alterations. DOX induced mitophagy as evidenced by increases of the markers of autophagosomes, LC3, Beclin 1, reduction of p62, and co-localization of LC3 in mitochondria. DOX activated PINK1/parkin pathway and promoted translocation of PINK1/parkin to mitochondria. Meanwhile, DOX inhibited the expression of PGC-1α and its downstream targets nuclear respiratory factor 1 (NRF1) and mitochondrial transcription factor A (TFAM), and reduced the expression of mitochondrial proteins. Inhibition of mitophagy by mdivi-1 was found to attenuate activation of the PINK1/parkin pathway by DOX and preserve mitochondrial biogenesis, consequently mitigating DOX-induced mitochondrial superoxide overproduction and mitochondrial dysfunction. Moreover, scavenging mitochondrial superoxide by Mito-tempo was also found to effectively attenuate activation of the PINK1/parkin pathway and rescue the cells from DOX-induced adverse effects. Taken together, these findings suggest that DOX-induced mitophagy and mitochondrial damage in cardiomyocytes are mediated, at least in part, by dysregulation of the PINK1/parkin pathway.

Data-Driven Modeling of Intracellular Auxin Fluxes Indicates a Dominant Role of the ER in Controlling Nuclear Auxin Uptake.

In plants, the phytohormone auxin acts as a master regulator of developmental processes and environmental responses. The best characterized process in the auxin regulatory network occurs at the subcellular scale, wherein auxin mediates signal transduction into transcriptional programs by triggering the degradation of Aux/IAA transcriptional repressor proteins in the nucleus. However, whether and how auxin movement between the nucleus and the surrounding compartments is regulated remain elusive. Using a fluorescent auxin analog, we show that its diffusion into the nucleus is restricted. By combining mathematical modeling with time course assays on auxin-mediated nuclear signaling and quantitative phenotyping in single plant cell systems, we show that ER-to-nucleus auxin flux represents a major subcellular pathway to directly control nuclear auxin levels. Our findings propose that the homeostatically regulated auxin pool in the ER and ER-to-nucleus auxin fluxes underpin auxin-mediated downstream responses in plant cells.

An individual-based model for collective cancer cell migration explains speed dynamics and phenotype variability in response to growth factors.

Collective cell migration is a common phenotype in epithelial cancers, which is associated with tumor cell metastasis and poor patient survival. However, the interplay between physiologically relevant pro-migratory stimuli and the underlying mechanical cell-cell interactions are poorly understood. We investigated the migratory behavior of different collectively migrating non-small cell lung cancer cell lines in response to motogenic growth factors (e.g. epidermal growth factor) or clinically relevant small compound inhibitors. Depending on the treatment, we observed distinct behaviors in a classical lateral migration assay involving traveling fronts, finger-shapes or the development of cellular bridges. Particle image velocimetry analysis revealed characteristic speed dynamics (evolution of the average speed of all cells in a frame) in all experiments exhibiting initial acceleration and subsequent deceleration of the cell populations. To better understand the mechanical properties of individual cells leading to the observed speed dynamics and the phenotypic differences we developed a mathematical model based on a Langevin approach. This model describes intercellular forces, random motility, and stimulation of active migration by mechanical interaction between cells. Simulations show that the model is able to reproduce the characteristic spatio-temporal speed distributions as well as most migratory phenotypes of the studied cell lines. A specific strength of the proposed model is that it identifies a small set of mechanical features necessary to explain all phenotypic and dynamical features of the migratory response of non-small cell lung cancer cells to chemical stimulation/inhibition. Furthermore, all processes included in the model can be associated with potential molecular components, and are therefore amenable to experimental validation. Thus, the presented mathematical model may help to predict which mechanical aspects involved in non-small cell lung cancer cell migration are affected by the respective therapeutic treatment.

Concomitant expression of far upstream element (FUSE) binding protein (FBP) interacting repressor (FIR) and its splice variants induce migration and invasion of non-small cell lung cancer (NSCLC) cells.

Transcription factors integrate a variety of oncogenic input information, facilitate tumour growth and cell dissemination, and therefore represent promising therapeutic target structures. Because over-expression of DNA-interacting far upstream element binding protein (FBP) supports non-small cell lung cancer (NSCLC) migration, we asked whether its repressor, FBP-interacting repressor (FIR) is functionally inactivated and how FIR might affect NSCLC cell biology. Different FIR splice variants were highly expressed in the majority of NSCLCs, with the highest levels in tumours carrying genomic gains of chromosome 8q24.3, which contained the FIR gene locus. Nuclear FIR expression was significantly enriched at the invasion front of primary NSCLCs, but this did not correlate with tumour cell proliferation. FIR accumulation was associated with worse patient survival and tumour recurrence; in addition, FIR over-expression significantly correlated with lymph node metastasis in squamous cell carcinomas (SCCs). In vitro, we applied newly developed methods and modelling approaches for the quantitative and time-resolved description of the pro-migratory and pro-invasive capacities of SCC cells. siRNA-mediated silencing of all FIR variants significantly reduced the speed and directional movement of tumour cells in all phases of migration. Furthermore, sprouting efficiency and single cell invasiveness were diminished following FIR inhibition. Interestingly, the silencing of FIR isoforms lacking exon 2 (FIR(Δexon2)) alone was sufficient to reduce lateral migration and invasion. In summary, by using scale-spanning data derived from primary human tissues, quantitative cellular analyses and mathematical modelling, we have demonstrated that concomitant over-expression of FIR and its splice variants drives NSCLC migration and dissemination.

A continuum approximation to an off-lattice individual-cell based model of cell migration and adhesion.

Cell-cell adhesion plays a key role in the collective migration of cells and in determining correlations in the relative cell positions and velocities. Recently, it was demonstrated that off-lattice individual cell based models (IBMs) can accurately capture the correlations observed experimentally in a migrating cell population. However, IBMs are often computationally expensive and difficult to analyse mathematically. Traditional continuum-based models, in contrast, are amenable to mathematical analysis and are computationally less demanding, but typically correspond to a mean-field approximation of cell migration and so ignore cell-cell correlations. In this work, we address this problem by using an off-lattice IBM to derive a continuum approximation which does take into account correlations. We furthermore show that a mean-field approximation of the off-lattice IBM leads to a single partial integro-differential equation of the same form as proposed by Sherratt and co-workers to model cell adhesion. The latter is found to be only effective at approximating the ensemble averaged cell number density when mechanical interactions between cells are weak. In contrast, the predictions of our novel continuum model for the time-evolution of the ensemble cell number density distribution and of the density-density correlation function are in close agreement with those obtained from the IBM for a wide range of mechanical interaction strengths. In particular, we observe 'front-like' propagation of cells in simulations using both our IBM and our continuum model, but not in the continuum model simulations obtained using the mean-field approximation.

Sequential induction of auxin efflux and influx carriers regulates lateral root emergence.

In Arabidopsis, lateral roots originate from pericycle cells deep within the primary root. New lateral root primordia (LRP) have to emerge through several overlaying tissues. Here, we report that auxin produced in new LRP is transported towards the outer tissues where it triggers cell separation by inducing both the auxin influx carrier LAX3 and cell-wall enzymes. LAX3 is expressed in just two cell files overlaying new LRP. To understand how this striking pattern of LAX3 expression is regulated, we developed a mathematical model that captures the network regulating its expression and auxin transport within realistic three-dimensional cell and tissue geometries. Our model revealed that, for the LAX3 spatial expression to be robust to natural variations in root tissue geometry, an efflux carrier is required--later identified to be PIN3. To prevent LAX3 from being transiently expressed in multiple cell files, PIN3 and LAX3 must be induced consecutively, which we later demonstrated to be the case. Our study exemplifies how mathematical models can be used to direct experiments to elucidate complex developmental processes.

Modeling regulatory networks to understand plant development: small is beautiful.

We now have unprecedented capability to generate large data sets on the myriad genes and molecular players that regulate plant development. Networks of interactions between systems components can be derived from that data in various ways and can be used to develop mathematical models of various degrees of sophistication. Here, we discuss why, in many cases, it is productive to focus on small networks. We provide a brief and accessible introduction to relevant mathematical and computational approaches to model regulatory networks and discuss examples of small network models that have helped generate new insights into plant biology (where small is beautiful), such as in circadian rhythms, hormone signaling, and tissue patterning. We conclude by outlining some of the key technical and modeling challenges for the future.

Mathematical modeling elucidates the role of transcriptional feedback in gibberellin signaling.

The hormone gibberellin (GA) is a key regulator of plant growth. Many of the components of the gibberellin signal transduction [e.g., GIBBERELLIN INSENSITIVE DWARF 1 (GID1) and DELLA], biosynthesis [e.g., GA 20-oxidase (GA20ox) and GA3ox], and deactivation pathways have been identified. Gibberellin binds its receptor, GID1, to form a complex that mediates the degradation of DELLA proteins. In this way, gibberellin relieves DELLA-dependent growth repression. However, gibberellin regulates expression of GID1, GA20ox, and GA3ox, and there is also evidence that it regulates DELLA expression. In this paper, we use integrated mathematical modeling and experiments to understand how these feedback loops interact to control gibberellin signaling. Model simulations are in good agreement with in vitro data on the signal transduction and biosynthesis pathways and in vivo data on the expression levels of gibberellin-responsive genes. We find that GA-GID1 interactions are characterized by two timescales (because of a lid on GID1 that can open and close slowly relative to GA-GID1 binding and dissociation). Furthermore, the model accurately predicts the response to exogenous gibberellin after a number of chemical and genetic perturbations. Finally, we investigate the role of the various feedback loops in gibberellin signaling. We find that regulation of GA20ox transcription plays a significant role in both modulating the level of endogenous gibberellin and generating overshoots after the removal of exogenous gibberellin. Moreover, although the contribution of other individual feedback loops seems relatively small, GID1 and DELLA transcriptional regulation acts synergistically with GA20ox feedback.

Growth-induced hormone dilution can explain the dynamics of plant root cell elongation.

In the elongation zone of the Arabidopsis thaliana plant root, cells undergo rapid elongation, increasing their length by ∼10-fold over 5 h while maintaining a constant radius. Although progress is being made in understanding how this growth is regulated, little consideration has been given as to how cell elongation affects the distribution of the key regulating hormones. Using a multiscale mathematical model and measurements of growth dynamics, we investigate the distribution of the hormone gibberellin in the root elongation zone. The model quantifies how rapid cell expansion causes gibberellin to dilute, creating a significant gradient in gibberellin levels. By incorporating the gibberellin signaling network, we simulate how gibberellin dilution affects the downstream components, including the growth-repressing DELLA proteins. We predict a gradient in DELLA that provides an explanation of the reduction in growth exhibited as cells move toward the end of the elongation zone. These results are validated at the molecular level by comparing predicted mRNA levels with transcriptomic data. To explore the dynamics further, we simulate perturbed systems in which gibberellin levels are reduced, considering both genetically modified and chemically treated roots. By modeling these cases, we predict how these perturbations affect gibberellin and DELLA levels and thereby provide insight into their altered growth dynamics.