Auxin fluxes through plasmodesmata

Characterising the processes that control auxin dynamics is essential to understanding how auxin regulates plant development. Over recent years, several studies have investigated auxin diffusion through plasmodesmata, characterising this cell-to-cell diffusion and demonstrating that it affects auxin distributions. Furthermore, studies have shown that plasmodesmatal auxin diffusion affects developmental processes, including phototropism, lateral root emergence and leaf hyponasty. This short Tansley Insight review describes how these studies have contributed to our understanding of auxin dynamics and discusses potential future directions in this area

Parameter inference to motivate asymptotic model reduction: an analysis of the gibberellin biosynthesis pathway

Developing effective strategies to use models in conjunction with experimental data is essential to understand the dynamics of biological regulatory networks. In this study, we demonstrate how combining parameter estimation with asymptotic analysis can reveal the key features of a network and lead to simplified models that capture the observed network dynamics. Our approach involves fitting the model to experimental data and using the Profile Likelihood to identify small parameters and cases where model dynamics are insensitive to changing particular individual parameters. Such parameter diagnostics provide understanding of the dominant features of the model and motivate asymptotic model reductions to derive simpler models in terms of identifiable parameter groupings. We focus on the particular example of biosynthesis of the plant hormone gibberellin (GA), which controls plant growth and has been mutated in many current crop varieties. This pathway comprises two parallel series of enzyme-substrate reactions, which have previously been modelled using the law of mass action [23]. Considering the GA20ox-mediated steps, we analyse the identifiability of the model parameters using published experimental data; the analysis reveals the ratio between enzyme and GA levels to be small and motivates us to perform a quasi-steady state analysis to derive a reduced model. Fitting the parameters in the reduced model reveals additional features of the pathway and motivates further asymptotic analysis which produces a hierarchy of reduced models. Calculating the Akaike information criterion and parameter confidence intervals enables us to select a parsimonious model with identifiable parameters. As well as demonstrating the benefits of combining parameter estimation and asymptotic analysis, the analysis shows how GA biosynthesis is limited by the final GA20ox-mediated steps in the pathway and generates a simple mathematical description of this part of the GA biosynthesis pathway

Stochastic and deterministic multiscale models for systems biology: an auxin-transport case study

Background: Stochastic and asymptotic methods are powerful tools in developing multiscale systems biology models; however, little has been done in this context to compare the efficacy of these methods. The majority of current systems biology modelling research, including that of auxin transport, uses numerical simulations to study the behaviour of large systems of deterministic ordinary differential equations, with little consideration of alternative modelling frameworks.Results: In this case study, we solve an auxin-transport model using analytical methods, deterministic numerical simulations and stochastic numerical simulations. Although the three approaches in general predict the same behaviour, the approaches provide different information that we use to gain distinct insights into the modelled biological system. We show in particular that the analytical approach readily provides straightforward mathematical expressions for the concentrations and transport speeds, while the stochastic simulations naturally provide information on the variability of the system.Conclusions: Our study provides a constructive comparison which highlights the advantages and disadvantages of each of the considered modelling approaches. This will prove helpful to researchers when weighing up which modelling approach to select. In addition, the paper goes some way to bridging the gap between these approaches, which in the future we hope will lead to integrative hybrid models. © 2010 Twycross et al; licensee BioMed Central Ltd

Long-distance hormone transport via the phloem

Several key plant hormones are synthesised in the shoot and are advected within the phloem to the root tip. In the root tip, these hormones regulate growth and developmental processes, and responses to environmental cues. However, we lack understanding of how environmental factors and biological parameters affect the delivery of hormones to the root tip. In this study, we build on existing models of phloem flow to develop a mathematical model of sugar transport alongside the transport of a generic hormone. We derive the equations for osmotically driven flow in a long, thin pipe with spatially varying membrane properties to capture the phloem loading and unloading zones. Motivated by experimental findings, we formulate solute membrane transport in terms of passive and active components, and incorporate solute unloading via bulk flow (i.e. advection with the water efflux) by including the Staverman reflection coefficient. We use the model to investigate the coupling between the sugar and hormone dynamics. The model predicts that environmental cues that lead to an increase in active sugar loading, an increase in bulk flow sugar unloading or a decrease in the relative root sugar concentration result in an increase in phloem transport velocity. Furthermore, the model reveals that such increases in phloem transport velocity result in an increase in hormone delivery to the root tip for passively loaded hormones

Double or nothing? Cell division and cell size control

Size is a fundamental property that must be tightly regulated to ensure that cells and tissues function efficiently. Dynamic size control allows unicellular organisms to adapt to environmental changes, but cell size is also integral to multicellular development, affecting tissue size and structure. Despite clear evidence for homeostatic cell size maintenance, we are only now beginning to understand cell size regulation in the actively dividing meristematic tissues of higher plants. We discuss here how coupled advances in live cell imaging and modelling are uncovering dynamic mechanisms for size control mediated at the cellular level. We argue that integrated models of cell growth and division will be necessary to predict cell size and fully understand multicellular growth and development

Auxin fluxes through plasmodesmata modify root-tip auxin distribution

© 2020. Published by The Company of Biologists Ltd. Auxin is a key signal regulating plant growth and development. It is well established that auxin dynamics depend on the spatial distribution of efflux and influx carriers on the cell membranes. In this study, we employ a systems approach to characterise an alternative symplastic pathway for auxin mobilisation via plasmodesmata, which function as intercellular pores linking the cytoplasm of adjacent cells. To investigate the role of plasmodesmata in auxin patterning, we developed a multicellular model of the Arabidopsis root tip. We tested the model predictions using the DII-VENUS auxin response reporter, comparing the predicted and observed DII-VENUS distributions using genetic and chemical perturbations designed to affect both carrier-mediated and plasmodesmatal auxin fluxes. The model revealed that carrier-mediated transport alone cannot explain the experimentally determined auxin distribution in the root tip. In contrast, a composite model that incorporates both carrier-mediated and plasmodesmatal auxin fluxes re-capitulates the root-tip auxin distribution. We found that auxin fluxes through plasmodesmata enable auxin reflux and increase total root-tip auxin. We conclude that auxin fluxes through plasmodesmata modify the auxin distribution created by efflux and influx carriers

Differential biosynthesis and cellular permeability explain longitudinal gibberellin gradients in growing roots.

Control over cell growth by mobile regulators underlies much of eukaryotic morphogenesis. In plant roots, cell division and elongation are separated into distinct longitudinal zones and both division and elongation are influenced by the growth regulatory hormone gibberellin (GA). Previously, a multicellular mathematical model predicted a GA maximum at the border of the meristematic and elongation zones. However, GA in roots was recently measured using a genetically encoded fluorescent biosensor, nlsGPS1, and found to be low in the meristematic zone grading to a maximum at the end of the elongation zone. Furthermore, the accumulation rate of exogenous GA was also found to be higher in the elongation zone. It was still unknown which biochemical activities were responsible for these mobile small molecule gradients and whether the spatiotemporal correlation between GA levels and cell length is important for root cell division and elongation patterns. Using a mathematical modeling approach in combination with high-resolution GA measurements in vivo, we now show how differentials in several biosynthetic enzyme steps contribute to the endogenous GA gradient and how differential cellular permeability contributes to an accumulation gradient of exogenous GA. We also analyzed the effects of altered GA distribution in roots and did not find significant phenotypes resulting from increased GA levels or signaling. We did find a substantial temporal delay between complementation of GA distribution and cell division and elongation phenotypes in a GA deficient mutant. Together, our results provide models of how GA gradients are directed and in turn direct root growth

Elementary effects for models with dimensional inputs of arbitrary type and range: Scaling and trajectory generation

The Elementary Effects method is a global sensitivity analysis approach for identifying (un)important parameters in a model. However, it has almost exclusively been used where inputs are dimensionless and take values on [0, 1]. Here, we consider models with dimensional inputs, inputs taking values on arbitrary intervals or discrete inputs. In such cases scaling effects by a function of the input range is essential for correct ranking results. We propose two alternative dimensionless sensitivity indices by normalizing the scaled mean or median of absolute effects. Testing these indices with 9 trajectory generation methods on 4 test functions (including the Penman-Monteith equation for evapotranspiration) reveals that: i) scaled elementary effects are necessary to obtain correct parameter importance rankings; ii) small step-size methods typically produce more accurate rankings; iii) it is beneficial to compute and compare both sensitivity indices; and iv) spread and discrepancy of the simulation points are poor proxies for trajectory generation method performance

Modeling root loss reveals impacts on nutrient uptake and crop development

Abstract Despite the widespread prevalence of root loss in plants, its effects on crop productivity are not fully understood. While root loss reduces the capacity of plants to take up water and nutrients from the soil, it may provide benefits by decreasing the resources required to maintain the root system. Here, we simulated a range of root phenotypes in different soils and root loss scenarios for barley (Hordeum vulgare), common bean (Phaseolus vulgaris) and maize (Zea mays) using and extending the open-source, functional-structural root/soil simulation model OpenSimRoot. The model enabled us to quantify the impact of root loss on shoot dry weight in these scenarios and identify in which scenarios root loss is beneficial, detrimental, or has no effect. The simulations showed that root loss is detrimental for phosphorus uptake in all tested scenarios whereas nitrogen uptake was relatively insensitive to root loss unless main root axes were lost. Loss of axial roots reduced shoot dry weight for all phenotypes in all species and soils, whereas lateral root loss had a smaller impact. In barley and maize plants with high lateral branching density that were not phosphorus-stressed, loss of lateral roots increased shoot dry weight. The fact that shoot dry weight increased due to root loss in these scenarios indicates that plants overproduce roots for some environments, such as those found in high-input agriculture. We conclude that a better understanding of the effects of root loss on plant development is an essential part of optimizing root system phenotypes for maximizing yield