Discretised Flux Balance Analysis for Reaction-Diffusion Simulation of Single-Cell Metabolism.

Metabolites have to diffuse within the sub-cellular compartments they occupy to specific locations where enzymes are, so reactions could occur. Conventional flux balance analysis (FBA), a method based on linear programming that is commonly used to model metabolism, implicitly assumes that all enzymatic reactions are not diffusion-limited though that may not always be the case. In this work, we have developed a spatial method that implements FBA on a grid-based system, to enable the exploration of diffusion effects on metabolism. Specifically, the method discretises a living cell into a two-dimensional grid, represents the metabolic reactions in each grid element as well as the diffusion of metabolites to and from neighbouring elements, and simulates the system as a single linear programming problem. We varied the number of rows and columns in the grid to simulate different cell shapes, and the method was able to capture diffusion effects at different shapes. We then used the method to simulate heterogeneous enzyme distribution, which suggested a theoretical effect on variability at the population level. We propose the use of this method, and its future extensions, to explore how spatiotemporal organisation of sub-cellular compartments and the molecules within could affect cell behaviour.

Mathematical models light up plant signaling.

Plants respond to changes in the environment by triggering a suite of regulatory networks that control and synchronize molecular signaling in different tissues, organs, and the whole plant. Molecular studies through genetic and environmental perturbations, particularly in the model plant Arabidopsis thaliana, have revealed many of the mechanisms by which these responses are actuated. In recent years, mathematical modeling has become a complementary tool to the experimental approach that has furthered our understanding of biological mechanisms. In this review, we present modeling examples encompassing a range of different biological processes, in particular those regulated by light. Current issues and future directions in the modeling of plant systems are discussed.

Multiscale digital Arabidopsis predicts individual organ and whole-organism growth.

Understanding how dynamic molecular networks affect whole-organism physiology, analogous to mapping genotype to phenotype, remains a key challenge in biology. Quantitative models that represent processes at multiple scales and link understanding from several research domains can help to tackle this problem. Such integrated models are more common in crop science and ecophysiology than in the research communities that elucidate molecular networks. Several laboratories have modeled particular aspects of growth in Arabidopsis thaliana, but it was unclear whether these existing models could productively be combined. We test this approach by constructing a multiscale model of Arabidopsis rosette growth. Four existing models were integrated with minimal parameter modification (leaf water content and one flowering parameter used measured data). The resulting framework model links genetic regulation and biochemical dynamics to events at the organ and whole-plant levels, helping to understand the combined effects of endogenous and environmental regulators on Arabidopsis growth. The framework model was validated and tested with metabolic, physiological, and biomass data from two laboratories, for five photoperiods, three accessions, and a transgenic line, highlighting the plasticity of plant growth strategies. The model was extended to include stochastic development. Model simulations gave insight into the developmental control of leaf production and provided a quantitative explanation for the pleiotropic developmental phenotype caused by overexpression of miR156, which was an open question. Modular, multiscale models, assembling knowledge from systems biology to ecophysiology, will help to understand and to engineer plant behavior from the genome to the field.

Mechanistic Model-Driven Biodesign in Mammalian Synthetic Biology.

Mathematical modeling plays a vital role in mammalian synthetic biology by providing a framework to design and optimize design circuits and engineered bioprocesses, predict their behavior, and guide experimental design. Here, we review recent models used in the literature, considering mathematical frameworks at the molecular, cellular, and system levels. We report key challenges in the field and discuss opportunities for genome-scale models, machine learning, and cybergenetics to expand the capabilities of model-driven mammalian cell biodesign.

An augmented Arabidopsis phenology model reveals seasonal temperature control of flowering time.

• In this study, we used a combination of theoretical (models) and experimental (field data) approaches to investigate the interaction between light and temperature signalling in the control of Arabidopsis flowering. • We utilised our recently published phenology model that describes the flowering time of Arabidopsis grown under a range of field conditions. We first examined the ability of the model to predict the flowering time of field plantings at different sites and seasons in light of the specific meteorological conditions that pertained. • Our analysis suggested that the synchrony of temperature and light cycles is important in promoting floral initiation. New features were incorporated into the model that improved its predictive accuracy across seasons. Using both laboratory and field data, our study has revealed an important seasonal effect of night temperatures on flowering time. Further model adjustments to describe phytochrome (phy) mutants supported our findings and implicated phyB in the temporal gating of temperature-induced flowering. • Our study suggests that different molecular pathways interact and predominate in natural environments that change seasonally. Temperature effects are mediated largely during the photoperiod during spring/summer (long days) but, as days shorten in the autumn, night temperatures become increasingly important.

Emerging whole-cell modeling principles and methods.

Whole-cell computational models aim to predict cellular phenotypes from genotype by representing the entire genome, the structure and concentration of each molecular species, each molecular interaction, and the extracellular environment. Whole-cell models have great potential to transform bioscience, bioengineering, and medicine. However, numerous challenges remain to achieve whole-cell models. Nevertheless, researchers are beginning to leverage recent progress in measurement technology, bioinformatics, data sharing, rule-based modeling, and multi-algorithmic simulation to build the first whole-cell models. We anticipate that ongoing efforts to develop scalable whole-cell modeling tools will enable dramatically more comprehensive and more accurate models, including models of human cells.

Toward Community Standards and Software for Whole-Cell Modeling.

OBJECTIVE: Whole-cell (WC) modeling is a promising tool for biological research, bioengineering, and medicine. However, substantial work remains to create accurate comprehensive models of complex cells. METHODS: We organized the 2015 Whole-Cell Modeling Summer School to teach WC modeling and evaluate the need for new WC modeling standards and software by recoding a recently published WC model in the Systems Biology Markup Language. RESULTS: Our analysis revealed several challenges to representing WC models using the current standards. CONCLUSION: We, therefore, propose several new WC modeling standards, software, and databases. SIGNIFICANCE: We anticipate that these new standards and software will enable more comprehensive models.

A stress-free walk from Arabidopsis to crops.

Global concerns such as food security and climate change have highlighted an urgent need for improved crop yield. Breakthroughs in Arabidopsis research provide fresh application routes to achieve novel crop varieties that can withstand or avoid stresses imposed by a changing growth environment. This review features advances in CBF-stress signalling that expand opportunities to produce super hardy crops that can withstand multiple abiotic stresses. It examines molecular external coincidence mechanisms that avoid abiotic stresses by confining plant growth and reproduction to favourable times of the year. The potential value of mathematical modelling approaches is discussed in relation to improving crop-stress resistance or avoidance, and forecasting crop performance.

Modeling of glucose regulation and insulin-signaling pathways.

A model of glucose regulation system was combined with a model of insulin-signaling pathways in this study. A feedback loop was added to link the transportation of glucose into cells (by GLUT4 in the insulin-signaling pathways) and the insulin-dependent glucose uptake in the glucose regulation model using the Michaelis-Menten kinetic model. A value of K(m) for GLUT4 was estimated using Genetic Algorithm. The estimated value was found to be 25.3 mM, which was in the range of K(m) values found experimentally from in vivo and in vitro human studies. Based on the results of this study, the combined model enables us to understand the overall dynamics of glucose at the systemic level, monitor the time profile of components in the insulin-signaling pathways at the cellular level and gives a good estimate of the K(m) value of glucose transportation by GLUT4. In conclusion, metabolic modeling such as displayed in this study provides a good predictive method to study the step-by-step reactions in an organism at different levels and should be used in combination with experimental approach to increase our understanding of metabolic disorders such as type 2 diabetes.

Modeling of oscillatory bursting activity of pancreatic beta-cells under regulated glucose stimulation.

A mathematical model to describe the oscillatory bursting activity of pancreatic beta-cells is combined with a model of glucose regulation system in this work to study the bursting pattern under regulated extracellular glucose stimulation. The bursting electrical activity in beta-cells is crucial for the release of insulin, which acts to regulate the blood glucose level. Different types of bursting pattern have been observed experimentally in glucose-stimulated islets both in vivo and in vitro, and the variations in these patterns have been linked to changes in glucose level. The combined model in this study enables us to have a deeper understanding on the regime change of bursting pattern when glucose level changes due to hormonal regulation, especially in the postprandial state. This is especially important as the oscillatory components of electrical activity play significant physiological roles in insulin secretion and some components have been found to be lost in type 2 diabetic patients.