BioModels: ten-year anniversary

BioModels (http://www.ebi.ac.uk/biomodels/) is a repository of mathematical models of biological processes. A large set of models is curated to verify both correspondence to the biological process that the model seeks to represent, and reproducibility of the simulation results as described in the corresponding peer-reviewed publication. Many models submitted to the database are annotated, cross-referencing its components to external resources such as database records, and terms from controlled vocabularies and ontologies. BioModels comprises two main branches: one is composed of models derived from literature, while the second is generated through automated processes. BioModels currently hosts over 1200 models derived directly from the literature, as well as in excess of 140 000 models automatically generated from pathway resources. This represents an approximate 60-fold growth for literature-based model numbers alone, since BioModels’ first release a decade ago. This article describes updates to the resource over this period, which include changes to the user interface, the annotation profiles of models in the curation pipeline, major infrastructure changes, ability to perform online simulations and the availability of model content in Linked Data form. We also outline planned improvements to cope with a diverse array of new challenges.

The impact of mathematical modeling on the understanding of diabetes and related complications

Diabetes is a chronic and complex multifactorial disease caused by persistent hyperglycemia and for which underlying pathogenesis is still not completely understood. The mathematical modeling of glucose homeostasis, diabetic condition, and its associated complications is rapidly growing and provides new insights into the underlying mechanisms involved. Here, we discuss contributions to the diabetes modeling field over the past five decades, highlighting the areas where more focused research is required.

An Integrative Systems Perspective on Plant Phosphate Research

The case for improving crop phosphorus-use-efficiency is widely recognized. Although much is known about the molecular and regulatory mechanisms, improvements have been hampered by the extreme complexity of phosphorus (P) dynamics, which involves soil chemistry; plant-soil interactions; uptake, transport, utilization and remobilization within plants; and agricultural practices. The urgency and direction of phosphate research is also dependent upon the finite sources of P, availability of stocks to farmers and reducing environmental hazards. This work introduces integrative systems approaches as a way to represent and understand this complexity, so that meaningful links can be established between genotype, environment, crop traits and yield. It aims to provide a large set of pointers to potential genes and research practice, with a view to encouraging members of the plant-phosphate research community to adopt such approaches so that, together, we can aid efforts in global food security.

A Transcriptomic Comparison of Two Bambara Groundnut Landraces under Dehydration Stress

The ability to grow crops under low-water conditions is a significant advantage in relation to global food security. Bambara groundnut is an underutilised crop grown by subsistence farmers in Africa and is known to survive in regions of water deficit. This study focuses on the analysis of the transcriptomic changes in two bambara groundnut landraces in response to dehydration stress. A cross-species hybridisation approach based on the Soybean Affymetrix GeneChip array has been employed. The differential gene expression analysis of a water-limited treatment, however, showed that the two landraces responded with almost completely different sets of genes. Hence, both landraces with very similar genotypes (as assessed by the hybridisation of genomic DNA onto the Soybean Affymetrix GeneChip) showed contrasting transcriptional behaviour in response to dehydration stress. In addition, both genotypes showed a high expression of dehydration-associated genes, even under water-sufficient conditions. Several gene regulators were identified as potentially important. Some are already known, such as WRKY40, but others may also be considered, namely PRR7, ATAUX2-11, CONSTANS-like 1, MYB60, AGL-83, and a Zinc-finger protein. These data provide a basis for drought trait research in the bambara groundnut, which will facilitate functional genomics studies. An analysis of this dataset has identified that both genotypes appear to be in a dehydration-ready state, even in the absence of dehydration stress, and may have adapted in different ways to achieve drought resistance. This will help in understanding the mechanisms underlying the ability of crops to produce viable yields under drought conditions. In addition, cross-species hybridisation to the soybean microarray has been shown to be informative for investigating the bambara groundnut transcriptome.

Integrated root phenotypes for improved rice performance under low nitrogen availability

Greater nitrogen efficiency would substantially reduce the economic, energy and environmental costs of rice production. We hypothesized that synergistic balancing of the costs and benefits for soil exploration among root architectural phenes is beneficial under suboptimal nitrogen availability. An enhanced implementation of the functional-structural model OpenSimRoot for rice integrated with the ORYZA_v3 crop model was used to evaluate the utility of combinations of root architectural phenes, namely nodal root angle, the proportion of smaller diameter nodal roots, nodal root number; and L-type and S-type lateral branching densities, for plant growth under low nitrogen. Multiple integrated root phenotypes were identified with greater shoot biomass under low nitrogen than the reference cultivar IR64. The superiority of these phenotypes was due to synergism among root phenes rather than the expected additive effects of phene states. Representative optimal phenotypes were predicted to have up to 80% greater grain yield with low N supply in the rainfed dry direct-seeded agroecosystem over future weather conditions, compared to IR64. These phenotypes merit consideration as root ideotypes for breeding rice cultivars with improved yield under rainfed dry direct-seeded conditions with limited nitrogen availability. The importance of phene synergism for the performance of integrated phenotypes has implications for crop breeding.

Reconstructing promoter activity from Lux bioluminescent reporters

The bacterial Lux system is used as a gene expression reporter. It is fast, sensitive and non-destructive, enabling high frequency measurements. Originally developed for bacterial cells, it has also been adapted for eukaryotic cells, and can be used for whole cell biosensors, or in real time with live animals without the need for euthanasia. However, correct interpretation of bioluminescent data is limited: the bioluminescence is different from gene expression because of nonlinear molecular and enzyme dynamics of the Lux system. We have developed a computational approach that, for the first time, allows users of Lux assays to infer gene transcription levels from the light output. This approach is based upon a new mathematical model for Lux activity, that includes the actions of LuxAB, LuxEC and Fre, with improved mechanisms for all reactions, as well as synthesis and turn-over of Lux proteins. The model is calibrated with new experimental data for the LuxAB and Fre reactions from Photorhabdus luminescens—the source of modern Lux reporters—while literature data has been used for LuxEC. Importantly, the data show clear evidence for previously unreported product inhibition for the LuxAB reaction. Model simulations show that predicted bioluminescent profiles can be very different from changes in gene expression, with transient peaks of light output, very similar to light output seen in some experimental data sets. By incorporating the calibrated model into a Bayesian inference scheme, we can reverse engineer promoter activity from the bioluminescence. We show examples where a decrease in bioluminescence would be better interpreted as a switching off of the promoter, or where an increase in bioluminescence would be better interpreted as a longer period of gene expression. This approach could benefit all users of Lux technology.

Bioluminescent reporters are used in many areas of biology as fast, sensitive and non-destructive measures of gene expression. They have been developed for bacteria, adapted now for other kinds of organisms, and recently been used for whole cell biosensors, and for real-time live animal models for infection without the need for euthanasia. However, users of Lux technologies rely on the light output being similar to the gene expression they wish to measure. We show that this is not the case. Rather, there is a nonlinear relationship between the two: light output can be misleading and so limits the way that such data can be interpreted. We have developed a new computational method that, for the first time, allows users of Lux reporters to infer accurate gene transcription levels from bioluminescent data. We show examples where a small decrease in light would be better interpreted as promoter being switched off, or where an increase in light would be better interpreted as promoter activity for a longer time.

Regulatory feedback response mechanisms to phosphate starvation in rice

Phosphorus is a growth-limiting nutrient for plants. The growing scarcity of phosphate stocks threatens global food security. Phosphate-uptake regulation is so complex and incompletely known that attempts to improve phosphorus use efficiency have had extremely limited success. This study improves our understanding of the molecular mechanisms underlying phosphate uptake by investigating the transcriptional dynamics of two regulators: the Ubiquitin ligase PHO2 and the long non-coding RNA IPS1. Temporal measurements of RNA levels have been integrated into mechanistic mathematical models using advanced statistical techniques. Models based solely on current knowledge could not adequately explain the temporal expression profiles. Further modeling and bioinformatics analysis have led to the prediction of three regulatory features: the PHO2 protein mediates the degradation of its own transcriptional activator to maintain constant PHO2 mRNA levels; the binding affinity of the transcriptional activator of PHO2 is impaired by a phosphate-sensitive transcriptional repressor/inhibitor; and the extremely high levels of IPS1 and its rapid disappearance upon Pi re-supply are best explained by Pi-sensitive RNA protection. This work offers both new opportunities for plant phosphate research that will be essential for informing the development of phosphate efficient crop varieties, and a foundation for the development of models integrating phosphate with other stress responses.

Food security is a global priority. One aspect of this is the ability to grow crops in poorer soils with less fertilizer input, of which phosphate is both essential and resource limited. This study provides a quantitative understanding of the genetic regulation of phosphate uptake in rice upon its deficiency. The mathematical models developed in this article lead to three hypotheses for the gaps identified in current knowledge. One of these hypotheses has previously only been reported in animals while the other prompted laboratory experiments, revealing an extra level of regulation at short timescales. These models provide the basis for crop systems biologists to study other aspects of phosphate regulation, including its internal utilisation, external availability and foraging, and, more crucially, in response to other stresses.

RootSlice-A novel functional-structural model for root anatomical phenotypes

Root anatomy is an important determinant of root metabolic costs, soil exploration, and soil resource capture. Root anatomy varies substantially within and among plant species. RootSlice is a multicellular functional-structural model of root anatomy developed to facilitate the analysis and understanding of root anatomical phenotypes. RootSlice can capture phenotypically accurate root anatomy in three dimensions of different root classes and developmental zones, of both monocotyledonous and dicotyledonous species. Several case studies are presented illustrating the capabilities of the model. For maize nodal roots, the model illustrated the role of vacuole expansion in cell elongation; and confirmed the individual and synergistic role of increasing root cortical aerenchyma and reducing the number of cortical cell files in reducing root metabolic costs. Integration of RootSlice for different root zones as the temporal properties of the nodal roots in the whole-plant and soil model OpenSimRoot/maize enabled the multiscale evaluation of root anatomical phenotypes, highlighting the role of aerenchyma formation in enhancing the utility of cortical cell files for improving plant performance over varying soil nitrogen supply. Such integrative in silico approaches present avenues for exploring the fitness landscape of root anatomical phenotypes.

A role for fermentation in aerobic conditions as revealed by computational analysis of maize root metabolism during growth by cell elongation

The root is a well-studied example of cell specialisation, yet little is known about the metabolism that supports the transport functions and growth of different root cell types. To address this, we used computational modelling to study metabolism in the elongation zone of a maize lateral root. A functional-structural model captured the cell-anatomical features of the root and modelled how they changed as the root elongated. From these data, we derived constraints for a flux balance analysis model that predicted metabolic fluxes of the 11 concentric rings of cells in the root. We discovered a distinct metabolic flux pattern in the cortical cell rings, endodermis and pericycle (but absent in the epidermis) that involved a high rate of glycolysis and production of the fermentation end-products lactate and ethanol. This aerobic fermentation was confirmed experimentally by metabolite analysis. The use of fermentation in the model was not obligatory but was the most efficient way to meet the specific demands for energy, reducing power and carbon skeletons of expanding cells. Cytosolic acidification was avoided in the fermentative mode due to the substantial consumption of protons by lipid synthesis. These results expand our understanding of fermentative metabolism beyond that of hypoxic niches and suggest that fermentation could play an important role in the metabolism of aerobic tissues.

In silico evidence for the utility of parsimonious root phenotypes for improved vegetative growth and carbon sequestration under drought

Drought is a primary constraint to crop yields and climate change is expected to increase the frequency and severity of drought stress in the future. It has been hypothesized that crops can be made more resistant to drought and better able to sequester atmospheric carbon in the soil by selecting appropriate root phenotypes. We introduce OpenSimRoot_v2, an upgraded version of the functional-structural plant/soil model OpenSimRoot, and use it to test the utility of a maize root phenotype with fewer and steeper axial roots, reduced lateral root branching density, and more aerenchyma formation (i.e. the 'Steep, Cheap, and Deep' (SCD) ideotype) and different combinations of underlying SCD root phene states under rainfed and drought conditions in three distinct maize growing pedoclimatic environments in the USA, Nigeria, and Mexico. In all environments where plants are subjected to drought stress the SCD ideotype as well as several intermediate phenotypes lead to greater shoot biomass after 42 days. As an additional advantage, the amount of carbon deposited below 50 cm in the soil is twice as great for the SCD phenotype as for the reference phenotype in 5 out of 6 simulated environments. We conclude that crop growth and deep soil carbon deposition can be improved by breeding maize plants with fewer axial roots, reduced lateral root branching density, and more aerenchyma formation.