A density-based approach for the modelling of root architecture: application to Maritime pine (Pinus pinaster Ait.) root systems

Modeling root system growth around obstacles

State-of-the-Art models of Root System Architecture (RSA) do not allow simulating root growth around rigid obstacles. Yet, the presence of obstacles can be highly disruptive to the root system. We grew wheat seedlings in sealed petri dishes without obstacle and in custom 3D-printed rhizoboxes containing obstacles. Time-lapse photography was used to reconstruct the wheat root morphology network. We used the reconstructed wheat root network without obstacle to calibrate an RSA model implemented in the R-SWMS software. The root network with obstacles allowed calibrating the parameters of a new function that models the influence of rigid obstacles on wheat root growth. Experimental results show that the presence of a rigid obstacle does not affect the growth rate of the wheat root axes, but that it does influence the root trajectory after the main axis has passed the obstacle. The growth recovery time, i.e. the time for the main root axis to recover its geotropism-driven growth, is proportional to the time during which the main axis grows along the obstacle. Qualitative and quantitative comparisons between experimental and numerical results show that the proposed model successfully simulates wheat RSA growth around obstacles. Our results suggest that wheat roots follow patterns that could inspire the design of adaptive engineering flow networks.

Preferential Root Tropisms in 2D Wet Granular Media with Structural Inhomogeneities

We investigate certain aspects of the physical mechanisms of root growth in a granular medium and how these roots adapt to changes in water distribution induced by the presence of structural inhomogeneities in the form of solid intrusions. Physical intrusions such as a square rod added into the 2D granular medium maintain robust capillary action, pumping water from the more saturated areas at the bottom of the cell towards the less saturated areas near the top of the cell while the rest of the medium is slowly devoid of water via evaporation. The intrusion induces "preferential tropism" of roots by first generating a humidity gradient that attracts the root to grow towards it. Then it guides the roots and permits them to grow deeper into more saturated regions in the soil. This further allows more efficient access to available water in the deeper sections of the medium thereby resulting to increased plant lifetime.

Connecting the dots between computational tools to analyse soil-root water relations

In recent years, many computational tools, such as image analysis, data management, process-based simulation, and upscaling tools, have been developed to help quantify and understand water flow in the soil-root system, at multiple scales (tissue, organ, plant, and population). Several of these tools work together or at least are compatible. However, for the uninformed researcher, they might seem disconnected, forming an unclear and disorganized succession of tools. In this article, we show how different studies can be further developed by connecting them to analyse soil-root water relations in a comprehensive and structured network. This 'explicit network of soil-root computational tools' informs readers about existing tools and helps them understand how their data (past and future) might fit within the network. We also demonstrate the novel possibilities of scale-consistent parameterizations made possible by the network with a set of case studies from the literature. Finally, we discuss existing gaps in the network and how we can move forward to fill them.

Environmental Control of Root System Biology

The plant root system traverses one of the most complex environments on earth. Understanding how roots support plant life on land requires knowing how soil properties affect the availability of nutrients and water and how roots manipulate the soil environment to optimize acquisition of these resources. Imaging of roots in soil allows the integrated analysis and modeling of environmental interactions occurring at micro- to macroscales. Advances in phenotyping of root systems is driving innovation in cross-platform-compatible methods for data analysis. Root systems acclimate to the environment through architectural changes that act at the root-type level as well as through tissue-specific changes that affect the metabolic needs of the root and the efficiency of nutrient uptake. A molecular understanding of the signaling mechanisms that guide local and systemic signaling is providing insight into the regulatory logic of environmental responses and has identified points where crosstalk between pathways occurs.

Analysis of root growth from a phenotyping data set using a density-based model

Major research efforts are targeting the improved performance of root systems for more efficient use of water and nutrients by crops. However, characterizing root system architecture (RSA) is challenging, because roots are difficult objects to observe and analyse. A model-based analysis of RSA traits from phenotyping image data is presented. The model can successfully back-calculate growth parameters without the need to measure individual roots. The mathematical model uses partial differential equations to describe root system development. Methods based on kernel estimators were used to quantify root density distributions from experimental image data, and different optimization approaches to parameterize the model were tested. The model was tested on root images of a set of 89 Brassica rapa L. individuals of the same genotype grown for 14 d after sowing on blue filter paper. Optimized root growth parameters enabled the final (modelled) length of the main root axes to be matched within 1% of their mean values observed in experiments. Parameterized values for elongation rates were within ±4% of the values measured directly on images. Future work should investigate the time dependency of growth parameters using time-lapse image data. The approach is a potentially powerful quantitative technique for identifying crop genotypes with more efficient root systems, using (even incomplete) data from high-throughput phenotyping systems.

Root growth models: towards a new generation of continuous approaches

Models of root system growth emerged in the early 1970s, and were based on mathematical representations of root length distribution in soil. The last decade has seen the development of more complex architectural models and the use of computer-intensive approaches to study developmental and environmental processes in greater detail. There is a pressing need for predictive technologies that can integrate root system knowledge, scaling from molecular to ensembles of plants. This paper makes the case for more widespread use of simpler models of root systems based on continuous descriptions of their structure. A new theoretical framework is presented that describes the dynamics of root density distributions as a function of individual root developmental parameters such as rates of lateral root initiation, elongation, mortality, and gravitropsm. The simulations resulting from such equations can be performed most efficiently in discretized domains that deform as a result of growth, and that can be used to model the growth of many interacting root systems. The modelling principles described help to bridge the gap between continuum and architectural approaches, and enhance our understanding of the spatial development of root systems. Our simulations suggest that root systems develop in travelling wave patterns of meristems, revealing order in otherwise spatially complex and heterogeneous systems. Such knowledge should assist physiologists and geneticists to appreciate how meristem dynamics contribute to the pattern of growth and functioning of root systems in the field.

The dynamics of root meristem distribution in the soil

Plants must develop efficient root architectures to secure access to nutrients and water in soil. This is achieved during plant development through a series of expansion and branching processes, mostly in the proximity of root apical meristems, where the plant senses the environment and explores immediate regions of the soil. We have developed a new approach to study the dynamics of root meristem distribution in soil, using the relationship between the increase in root length density and the root meristem density. Initiated at the seed, the location of root meristems in barley seedlings was shown to propagate, wave-like, through the soil, leaving behind a permanent network of roots for the plant to acquire water and nutrients. Data from observations on barley roots were used to construct mathematical models to describe the density of root meristems in space. These models suggested that the morphology of the waves of meristems was a function of specific root developmental processes. The waves of meristems observed in root systems of barley seedlings exploring the soil might represent a more general and fundamental aspect of plant rooting strategies for securing soil resources.

Lorentzian model of roots for understory yellow birch and sugar maple saplings

Total 66 small (<50m(2)), 24 medium (101-200m(2)) and 36 large (201-500m(2)) canopy gaps at the three sites of yellow birch (Betula alleghaniensis Britton) and sugar maple (Acer saccharum Marsh) forests were established in southern Québec, Canada. Half of the gaps were covered by 8x8m(2) shading cloths to mimic a closed canopy. From these gaps, 46 understory yellow birch and 46 sugar maple saplings with different tree ages and sizes were sampled. Single- and multi-variable linear and nonlinear models of root biomass and traits (root surface area, volume, length and endings) were developed and examined. Lorentzian model as a multi-variable nonlinear model was firstly applied to the simulations using both base diameter and height, and performed the best fit to total root biomass in both species with the highest correlation coefficients (R(2)=0.96 and 0.98) and smallest root mean squared deviations (RMSD=7.85 and 7.02) among all the examined models. The model also accurately simulated small fine root (2.0mm in diameter), coarse fine root (>2.0-5.0mm) and coarse root (>5.0mm) biomass (R(2)=0.87-0.99; RMSD=2.24-6.41), and the root traits (R(2)=0.71-0.99; RMSD=0.19-19.38). The study showed yellow birch roots were longer, larger, had more endings (tips) and grew faster than sugar maple roots. The root traits were largely distributed to small fine roots, sharply decreased from small fine roots to coarse fine roots, the fewest in coarse roots except for root volume. When trees were large, coarse root biomass increased more rapidly than fine root biomass, but vise versa when the trees were small.

Plant architecture: a dynamic, multilevel and comprehensive approach to plant form, structure and ontogeny

BACKGROUND AND AIMS

The architecture of a plant depends on the nature and relative arrangement of each of its parts; it is, at any given time, the expression of an equilibrium between endogenous growth processes and exogenous constraints exerted by the environment. The aim of architectural analysis is, by means of observation and sometimes experimentation, to identify and understand these endogenous processes and to separate them from the plasticity of their expression resulting from external influences.

SCOPE

Using the identification of several morphological criteria and considering the plant as a whole, from germination to death, architectural analysis is essentially a detailed, multilevel, comprehensive and dynamic approach to plant development. Despite their recent origin, architectural concepts and analysis methods provide a powerful tool for studying plant form and ontogeny. Completed by precise morphological observations and appropriated quantitative methods of analysis, recent researches in this field have greatly increased our understanding of plant structure and development and have led to the establishment of a real conceptual and methodological framework for plant form and structure analysis and representation. This paper is a summarized update of current knowledge on plant architecture and morphology; its implication and possible role in various aspects of modern plant biology is also discussed.