A model comparison study of the flowering time regulatory network in Arabidopsis

Modeling the Flowering Activation Motif during Vernalization in Legumes: A Case Study of M. trancatula

In many plant species, flowering is promoted by the cold treatment or vernalization. The mechanism of vernalization-induced flowering has been extensively studied in Arabidopsis but remains largely unknown in legumes. The orthologs of the FLC gene, a major regulator of vernalization response in Arabidopsis, are absent or non-functional in the vernalization-sensitive legume species. Nevertheless, the legume integrator genes FT and SOC1 are involved in the transition of the vernalization signal to meristem identity genes, including PIM (AP1 ortholog). However, the regulatory contribution of these genes to PIM activation in legumes remains elusive. Here, we presented the theoretical and data-driven analyses of a feed-forward regulatory motif that includes a vernalization-responsive FT gene and several SOC1 genes, which independently activate PIM and thereby mediate floral transition. Our theoretical model showed that the multiple regulatory branches in this regulatory motif facilitated the elimination of no-sense signals and amplified useful signals from the upstream regulator. We further developed and analyzed four data-driven models of PIM activation in Medicago trancatula in vernalized and non-vernalized conditions in wild-type and fta1-1 mutants. The model with FTa1 providing both direct activation and indirect activation via three intermediate activators, SOC1a, SOC1b, and SOC1c, resulted in the most relevant PIM dynamics. In this model, the difference between regulatory inputs of SOC1 genes was nonessential. As a result, in the M. trancatula model, the cumulative action of SOC1a, SOC1b, and SOC1c was favored. Overall, in this study, we first presented the in silico analysis of vernalization-induced flowering in legumes. The considered vernalization network motif can be supplemented with additional regulatory branches as new experimental data become available.

Data-driven dynamical modelling of a pathogen-infected plant gene regulatory network: A comparative analysis

Recent advances in synthetic biology have enabled the design of genetic feedback control circuits that could be implemented to build resilient plants against pathogen attacks. To facilitate the proper design of these genetic feedback control circuits, an accurate model that is able to capture the vital dynamical behaviour of the pathogen-infected plant is required. In this study, using a data-driven modelling approach, we develop and compare four dynamical models (i.e. linear, Michaelis-Menten with Hill coefficient (Hill Function), standard S-System and extended S-System) of a pathogen-infected plant gene regulatory network (GRN). These models are then assessed across several criteria, i.e. ease of identifying the type of gene regulation, the predictive capability, Akaike Information Criterion (AIC) and the robustness to parameter uncertainty to determine its viability of balancing between biological complexity and accuracy when modelling the pathogen-infected plant GRN. Using our defined ranking score, we obtain the following insights to the modelling of GRN. Our analyses show that despite commonly used and provide biological relevance, the Hill Function model ranks the lowest while the extended S-System model ranks highest in the overall comparison. Interestingly, the performance of the linear model is more consistent throughout the comparison, making it the preferred model for this pathogen-infected plant GRN when considering data-driven modelling approach.

The flowering transition pathways converge into a complex gene regulatory network that underlies the phase changes of the shoot apical meristem in Arabidopsis thaliana

Post-embryonic plant development is characterized by a period of vegetative growth during which a combination of intrinsic and extrinsic signals triggers the transition to the reproductive phase. To understand how different flowering inducing and repressing signals are associated with phase transitions of the Shoot Apical Meristem (SAM), we incorporated available data into a dynamic gene regulatory network model for Arabidopsis thaliana. This Flowering Transition Gene Regulatory Network (FT-GRN) formally constitutes a dynamic system-level mechanism based on more than three decades of experimental data on flowering. We provide novel experimental data on the regulatory interactions of one of its twenty-three components: a MADS-box transcription factor XAANTAL2 (XAL2). These data complement the information regarding flowering transition under short days and provides an example of the type of questions that can be addressed by the FT-GRN. The resulting FT-GRN is highly connected and integrates developmental, hormonal, and environmental signals that affect developmental transitions at the SAM. The FT-GRN is a dynamic multi-stable Boolean system, with 2²³ possible initial states, yet it converges into only 32 attractors. The latter are coherent with the expression profiles of the FT-GRN components that have been experimentally described for the developmental stages of the SAM. Furthermore, the attractors are also highly robust to initial states and to simulated perturbations of the interaction functions. The model recovered the meristem phenotypes of previously described single mutants. We also analyzed the attractors landscape that emerges from the postulated FT-GRN, uncovering which set of signals or components are critical for reproductive competence and the time-order transitions observed in the SAM. Finally, in the context of such GRN, the role of XAL2 under short-day conditions could be understood. Therefore, this model constitutes a robust biological module and the first multi-stable, dynamical systems biology mechanism that integrates the genetic flowering pathways to explain SAM phase transitions.

Dynamical Modeling of the Core Gene Network Controlling Transition to Flowering in Pisum sativum

Transition to flowering is an important stage of plant development. Many regulatory modules that control floral transition are conservative across plants. This process is best studied for the model plant Arabidopsis thaliana. The homologues of Arabidopsis genes responsible for the flowering initiation in legumes have been identified, and available data on their expression provide a good basis for gene network modeling. In this study, we developed several dynamical models of a gene network controlling transition to flowering in pea (Pisum sativum) using two different approaches. We used differential equations for modeling a previously proposed gene regulation scheme of floral initiation in pea and tested possible alternative hypothesis about some regulations. As the second approach, we applied neural networks to infer interactions between genes in the network directly from gene expression data. All models were verified on previously published experimental data on the dynamic expression of the main genes in the wild type and in three mutant genotypes. Based on modeling results, we made conclusions about the functionality of the previously proposed interactions in the gene network and about the influence of different growing conditions on the network architecture. It was shown that regulation of the PIM, FTa1, and FTc genes in pea does not correspond to the previously proposed hypotheses. The modeling suggests that short- and long-day growing conditions are characterized by different gene network architectures. Overall, the results obtained can be used to plan new experiments and create more accurate models to study the flowering initiation in pea and, in a broader context, in legumes.

A simplified modelling framework facilitates more complex representations of plant circadian clocks

The circadian clock orchestrates biological processes so that they occur at specific times of the day, thereby facilitating adaptation to diurnal and seasonal environmental changes. In plants, mathematical modelling has been comprehensively integrated with experimental studies to gain a better mechanistic understanding of the complex genetic regulatory network comprising the clock. However, with an increasing number of circadian genes being discovered, there is a pressing need for methods facilitating the expansion of computational models to incorporate these newly-discovered components. Conventionally, plant clock models have comprised differential equation systems based on Michaelis-Menten kinetics. However, the difficulties associated with modifying interactions using this approach-and the concomitant problem of robustly identifying regulation types-has contributed to a complexity bottleneck, with quantitative fits to experimental data rapidly becoming computationally intractable for models possessing more than ≈50 parameters. Here, we address these issues by constructing the first plant clock models based on the S-System formalism originally developed by Savageau for analysing biochemical networks. We show that despite its relative simplicity, this approach yields clock models with comparable accuracy to the conventional Michaelis-Menten formalism. The S-System formulation also confers several key advantages in terms of model construction and expansion. In particular, it simplifies the inclusion of new interactions, whilst also facilitating the modification of regulation types, thereby making it well-suited to network inference. Furthermore, S-System models mitigate the issue of parameter identifiability. Finally, by applying linear systems theory to the models considered, we provide some justification for the increased use of aggregated protein equations in recent plant clock modelling, replacing the separate cytoplasmic/nuclear protein compartments that were characteristic of the earlier models. We conclude that as well as providing a simplified framework for model development, the S-System formalism also possesses significant potential as a robust modelling method for designing synthetic gene circuits.

Deterministic and Stochastic Models of Arabidopsis thaliana Flowering

Experimental studies of the flowering of Arabidopsis thaliana have shown that a large complex gene regulatory network (GRN) is responsible for its regulation. This process has been mathematically modelled with deterministic differential equations by considering the interactions between gene activators and inhibitors (Valentim et al. in PLoS ONE 10(2):e0116973, 2015; van Mourik et al. in BMC Syst Biol 4(1):1, 2010). However, due to complexity of the model, the properties of the network and the roles of the individual genes cannot be deducted from the numerical solution the published work offers. Here, we propose simplifications of the model, based on decoupling of the original GRN to motifs, described with three and two differential equations. A stable solution of the original model is sought by linearisation of the original model which contributes to further investigation of the role of the individual genes to the flowering. Furthermore, we study the role of noise by introducing and investigating two types of stochastic elements into the model. The deterministic and stochastic nonlinear dynamic models of Arabidopsis flowering time are considered by following the deterministic delayed model introduced in Valentim et al. (2015). Steady-state regimes and stability of the deterministic original model are investigated analytically and numerically. By decoupling some concentrations, the system was reduced to emphasise the role played by the transcription factor Suppressor of Overexpression of Constants1 ([Formula: see text]) and the important floral meristem identity genes, Leafy ([Formula: see text]) and Apetala1 ([Formula: see text]). Two-dimensional motifs, based on the dynamics of [Formula: see text] and [Formula: see text], are obtained from the reduced network and parameter ranges ensuring flowering are determined. Their stability analysis shows that [Formula: see text] and [Formula: see text] are regulating each other for flowering, matching experimental findings. New sufficient conditions of mean square stability in the stochastic model are obtained using a stochastic Lyapunov approach. Our numerical simulations demonstrate that the reduced models of Arabidopsis flowering time, describing specific motifs of the GRN, can capture the essential behaviour of the full system and also introduce the conditions of flowering initiation. Additionally, they show that stochastic effects can change the behaviour of the stability region through a stability switch. This study thus contributes to a better understanding of the role of [Formula: see text] and [Formula: see text] in Arabidopsis flowering.

QTL mapping for flowering-time and photoperiod insensitivity of cotton Gossypium darwinii Watt

Most wild and semi-wild species of the genus Gossypium are exhibit photoperiod-sensitive flowering. The wild germplasm cotton is a valuable source of genes for genetic improvement of modern cotton cultivars. A bi-parental cotton population segregating for photoperiodic flowering was developed by crossing a photoperiod insensitive irradiation mutant line with its pre-mutagenesis photoperiodic wild-type G. darwinii Watt genotype. Individuals from the F2 and F3 generations were grown with their parental lines and F1 hybrid progeny in the long day and short night summer condition (natural day-length) of Uzbekistan to evaluate photoperiod sensitivity, i.e., flowering-time during the seasons 2008-2009. Through genotyping the individuals of this bi-parental population segregating for flowering-time, linkage maps were constructed using 212 simple-sequence repeat (SSR) and three cleaved amplified polymorphic sequence (CAPS) markers. Six QTLs directly associated with flowering-time and photoperiodic flowering were discovered in the F2 population, whereas eight QTLs were identified in the F3 population. Two QTLs controlling photoperiodic flowering and duration of flowering were common in both populations. In silico annotations of the flanking DNA sequences of mapped SSRs from sequenced cotton (G. hirsutum L.) genome database has identified several potential 'candidate' genes that are known to be associated with regulation of flowering characteristics of plants. The outcome of this research will expand our understanding of the genetic and molecular mechanisms of photoperiodic flowering. Identified markers should be useful for marker-assisted selection in cotton breeding to improve early flowering characteristics.

Methyl Protodioscin, a Steroidal Saponin, Inhibits Neointima Formation in Vitro and in Vivo

Restenosis (or neointimal hyperplasia) remains a clinical limitation of percutaneous coronary angioplasty. Abnormal proliferation and migration of vascular smooth muscle cells (VSMCs) are known to be involved in the development of restenosis. The present study aimed to investigate the ability and molecular mechanisms of methyl protodioscin (1), a steroidal saponin isolated from the root of Dioscorea nipponica, to inhibit neointimal formation. Our study demonstrated that 1 markedly inhibited the growth and migration of VSMCs (A7r5 cells). A cytometric analysis suggested that 1 induced growth inhibition by arresting VSMCs at the G1 phase of the cell cycle. A rat carotid artery balloon injury model indicated that neointima formation of the balloon-injured vessel was markedly reduced after extravascular administration of 1. Compound 1 decreased the expression levels of ADAM15 (a disintegrin and metalloprotease 15) and its downstream signaling pathways in the VSMCs. Moreover, the expressions and activities of matrix metalloproteinases (MMP-2 and MMP-9) were also suppressed by 1 in a concentration-dependent manner. Additionally, the molecular mechanisms appear to be mediated, in part, through the downregulation of ADAM15, FAK, ERK, and PI3K/Akt.

Modeling plant development: from signals to gene networks

Mathematical modeling has become a common tool in plant developmental biology. Indeed, it allows for the prediction of complex and often unintuitive dynamics of the molecular networks driving plant development. This has enabled the test of their possible involvement in robust and specific developmental processes. Modeling has also been fruitful in predicting new interactions within gene networks, such as the Arabidopsis circadian clock. A new challenge is to integrate patterning issues with tissue growth and biomechanics. The development of new tools to gain resolution in data collection as well as new frameworks to confront models and data might provide even more robust predictions.

CN: a consensus algorithm for inferring gene regulatory networks using the SORDER algorithm and conditional mutual information test

Inferring Gene Regulatory Networks (GRNs) from gene expression data is a major challenge in systems biology. The Path Consistency (PC) algorithm is one of the popular methods in this field. However, as an order dependent algorithm, PC algorithm is not robust because it achieves different network topologies if gene orders are permuted. In addition, the performance of this algorithm depends on the threshold value used for independence tests. Consequently, selecting suitable sequential ordering of nodes and an appropriate threshold value for the inputs of PC algorithm are challenges to infer a good GRN. In this work, we propose a heuristic algorithm, namely SORDER, to find a suitable sequential ordering of nodes. Based on the SORDER algorithm and a suitable interval threshold for Conditional Mutual Information (CMI) tests, a network inference method, namely the Consensus Network (CN), has been developed. In the proposed method, for each edge of the complete graph, a weighted value is defined. This value is considered as the reliability value of dependency between two nodes. The final inferred network, obtained using the CN algorithm, contains edges with a reliability value of dependency of more than a defined threshold. The effectiveness of this method is benchmarked through several networks from the DREAM challenge and the widely used SOS DNA repair network in Escherichia coli. The results indicate that the CN algorithm is suitable for learning GRNs and it considerably improves the precision of network inference. The source of data sets and codes are available at .