L-System model for the growth of arbuscular mycorrhizal fungi, both within and outside of their host roots

A triangular model of fractal growth with application to adsorptive spin-coating of polymers

Over the last 40 years, applied mathematicians and physicists have proposed a number of mathematical models that produce structures exhibiting a fractal dimension. This work has coincided with the discovery that objects with fractal dimension are relatively common in the natural and human-produced worlds. One particularly successful model of fractal growth is the diffusion limited aggregation (DLA) model, a model as notable for its simplicity as for its complex and varied behavior. It has been modified and used to simulate fractal growth processes in numerous experimental and empirical contexts. In this work, we present an alternative fractal growth model that is based on a growing mass that bonds to particles in a surrounding medium and then exerts a force on them in an iterative process of growth and contraction. The resulting structure is a spreading triangular network rather than an aggregate of spheres, and the model is conceptually straightforward. To the best of our knowledge, this model is unique and differs in its dynamics and behavior from the DLA model and related particle aggregation models. We explore the behavior of the model, demonstrate the range of model output, and show that model output can have a variable fractal dimension between 1.5 and 1.83 that depends on model parameters. We also apply the model to simulating the development of polymer thin films prepared using spin-coating which also exhibit variable fractal dimensions. We demonstrate how the model can be adjusted to different dewetting conditions as well as how it can be used to simulate the modification of the polymer morphology under solvent annealing.

Mycorrhizal associations change root functionality: a 3D modelling study on competitive interactions between plants for light and nutrients

Recent studies show that the variation in root functional traits can be explained by a two-dimensional trait framework, containing a 'collaboration' axis in addition to the classical fast-slow 'conservation' axis. This collaboration axis spans from thin and highly branched roots that employ a 'do-it-yourself' strategy to thick and sparsely branched roots that 'outsource' nutrient uptake to symbiotic arbuscular mycorrhizal fungi (AMF). Here, we explore the functionality of this collaboration axis by quantifying how interactions with AMF change the impact of root traits on plant performance. To this end, we developed a novel functional-structural plant (FSP) modelling approach that simulates plants competing for light and nutrients in the presence or absence of AMF. Our simulation results support the notion that in the absence of AMF, plants rely on thin, highly branched roots for their nutrient uptake. The presence of AMF, however, promotes thick, unbranched roots as an alternative strategy for uptake of immobile phosphorus, but not for mobile nitrogen. This provides further support for a root trait framework that accommodates for the interactive effect of roots and AMF. Our modelling study offers unique opportunities to incorporate soil microbial interactions into root functionality as it integrates consequences of belowground trait expression.

A functional-structural model of upland rice root systems reveals the importance of laterals and growing root tips for phosphate uptake from wet and dry soils

BACKGROUND AND AIMS

Upland rice is often grown where water and phosphorus (P) are limited. To better understand the interaction between water and P availability, functional-structural models that mechanistically represent small-scale nutrient gradients and water dynamics in the rhizosphere are needed.

METHODS

Rice was grown in large columns using a P-deficient soil at three P supplies in the topsoil (deficient, sub-optimal and non-limiting) in combination with two water regimes (field capacity vs. drying periods). Root system characteristics, such as nodal root number, lateral types, interbranch distance, root diameters and the distribution of biomass with depth, as well as water and P uptake, were measured. Based on the observed root data, 3-D root systems were reconstructed by calibrating the structural architecure model CRootBox for each scenario. Water flow and P transport in the soil to each of the individual root segments of the generated 3-D root architectures were simulated using a multiscale flow and transport model. Total water and P uptake were then computed by adding up the uptake by all the root segments.

KEY RESULTS

Measurements showed that root architecture was significantly affected by the treatments. The moist, high P scenario had 2.8 times the root mass, double the number of nodal roots and more S-type laterals than the dry, low P scenario. Likewise, measured plant P uptake increased >3-fold by increasing P and water supply. However, drying periods reduced P uptake at high but not at low P supply. Simulation results adequately predicted P uptake in all scenarios when the Michaelis-Menten constant (Km) was corrected for diffusion limitation. They showed that the key drivers for P uptake are the different types of laterals (i.e. S- and L-type) and growing root tips. The L-type laterals become more important for overall water and P uptake than the S-type laterals in the dry scenarios. This is true across all the P treatments, but the effect is more pronounced as the P availability decreases.

CONCLUSIONS

This functional-structural model can predict the function of specific rice roots in terms of P and water uptake under different P and water supplies, when the structure of the root system is known. A future challenge is to predict how the structure root systems responds to nutrient and water availability.

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.

Ecology of Contaminant Biotransformation in the Mycosphere: Role of Transport Processes

Fungi and bacteria often share common microhabitats. Their co-occurrence and coevolution give rise to manifold ecological interactions in the mycosphere, here defined as the microhabitats surrounding and affected by hyphae and mycelia. The extensive structure of mycelia provides ideal "logistic networks" for transport of bacteria and matter in structurally and chemically heterogeneous soil ecosystems. We describe the characteristics of the mycosphere as a unique and highly dynamic bacterial habitat and a hot spot for contaminant biotransformation. In particular, we emphasize the role of the mycosphere for (i) bacterial dispersal and colonization of subsurface interfaces and new habitats, (ii) matter transport processes and contaminant bioaccessibility, and (iii) the functional stability of microbial ecosystems when exposed to environmental fluctuations such as stress or disturbances. Adopting concepts from ecological theory, the chapter disentangles bacterial-fungal impacts on contaminant biotransformation in a systemic approach that interlinks empirical data from microbial ecosystems with simulation data from computational models. This approach provides generic information on key factors, processes, and ecological principles that drive microbial contaminant biotransformation in soil. We highlight that the transport processes create favorable habitat conditions for efficient bacterial contaminant degradation in the mycosphere. In-depth observation, understanding, and prediction of the role of mycosphere transport processes will support the use of bacterial-fungal interactions in nature-based solutions for contaminant biotransformation in natural and man-made ecosystems, respectively.

CRootBox: a structural-functional modelling framework for root systems

Background and Aims

Root architecture development determines the sites in soil where roots provide input of carbon and take up water and solutes. However, root architecture is difficult to determine experimentally when grown in opaque soil. Thus, root architecture models have been widely used and been further developed into functional-structural models that simulate the fate of water and solutes in the soil-root system. The root architecture model CRootBox presented here is a flexible framework to model root architecture and its interactions with static and dynamic soil environments.

Methods

CRootBox is a C++-based root architecture model with Python binding, so that CRootBox can be included via a shared library into any Python code. Output formats include VTP, DGF, RSML and a plain text file containing coordinates of root nodes. Furthermore, a database of published root architecture parameters was created. The capabilities of CRootBox for the unconfined growth of single root systems, as well as the different parameter sets, are highlighted in a freely available web application.

Key results

The capabilities of CRootBox are demonstrated through five different cases: (1) free growth of individual root systems; (2) growth of root systems in containers as a way to mimic experimental setups; (3) field-scale simulation; (4) root growth as affected by heterogeneous, static soil conditions; and (5) coupling CRootBox with code from the book Soil physics with Python to dynamically compute water flow in soil, root water uptake and water flow inside roots.

Conclusions

CRootBox is a fast and flexible functional-structural root model that is based on state-of-the-art computational science methods. Its aim is to facilitate modelling of root responses to environmental conditions as well as the impact of roots on soil. In the future, this approach will be extended to the above-ground part of the plant.