High-resolution 3D imaging of osteocytes and computational modelling in mechanobiology: insights on bone development, ageing, health and disease.

Osteocytes are involved in mechanosensation and mechanotransduction in bone and hence, are key to bone adaptation in response to development, ageing and disease. Thus, detailed knowledge of the three-dimensional (3D) structure of the osteocyte network (ON) and the surrounding lacuno-canalicular network (LCN) is essential. Enhanced understanding of the ON&LCN will contribute to a better understanding of bone mechanics on cellular and sub-cellular scales, for instance through improved computational models of bone mechanotransduction. Until now, the location of the ON within the hard bone matrix and the sub-µm dimensions of the ON&LCN have posed significant challenges for 3D imaging. This review identifies relevant microstructural phenotypes of the ON&LCN in health and disease and summarises how light microscopy, electron microscopy and X-ray imaging techniques have been used in studies of osteocyte anatomy, pathology and mechanobiology to date. In this review, we assess the requirements for ON&LCN imaging and examine the state of the art in the fields of imaging and computational modelling as well as recent advances in high-resolution 3D imaging. Suggestions for future investigations using volume electron microscopy are indicated and we present new data on the ON&LCN using serial block-face scanning electron microscopy. A correlative approach using these high-resolution 3D imaging techniques in conjunction with in silico modelling in bone mechanobiology will increase understanding of osteocyte function and, ultimately, lead to improved pathways for diagnosis and treatment of bone diseases such as osteoporosis.

How changing root system architecture can help tackle a reduction in soil phosphate (P) levels for better plant P acquisition.

The readily available global rock phosphate (P) reserves may run out within the next 50-130 years, causing soils to have a reduced P concentration which will affect plant P uptake. Using a combination of mathematical modelling and experimental data, we investigated potential plant-based options for optimizing crop P uptake in reduced soil P environments. By varying the P concentration within a well-mixed agricultural soil, for high and low P (35.5-12.5 mg L(-1) respectively using Olsen's P index), we investigated branching distributions within a wheat root system that maximize P uptake. Changing the root branching distribution from linear (evenly spaced branches) to strongly exponential (a greater number of branches at the top of the soil) improves P uptake by 142% for low-P soils when root mass is kept constant between simulations. This causes the roots to emerge earlier and mimics topsoil foraging. Manipulating root branching patterns, to maximize P uptake, is not enough on its own to overcome the drop in soil P from high to low P. Further mechanisms have to be considered to fully understand the impact of P reduction on plant development.

Mathematical modelling of the Phloem: the importance of diffusion on sugar transport at osmotic equilibrium.

Plants rely on the conducting vessels of the phloem to transport the products of photosynthesis from the leaves to the roots, or to any other organs, for growth, metabolism, and storage. Transport within the phloem is due to an osmotically-generated pressure gradient and is hence inherently nonlinear. Since convection dominates over diffusion in the main bulk flow, the effects of diffusive transport have generally been neglected by previous authors. However, diffusion is important due to boundary layers that form at the ends of the phloem, and at the leaf-stem and stem-root boundaries. We present a mathematical model of transport which includes the effects of diffusion. We solve the system analytically in the limit of high Münch number which corresponds to osmotic equilibrium and numerically for all parameter values. We find that the bulk solution is dependent on the diffusion-dominated boundary layers. Hence, even for large Péclet number, it is not always correct to neglect diffusion. We consider the cases of passive and active sugar loading and unloading. We show that for active unloading, the solutions diverge with increasing Péclet. For passive unloading, the convergence of the solutions is dependent on the magnitude of loading. Diffusion also permits the modelling of an axial efflux of sugar in the root zone which may be important for the growing root tip and for promoting symbiotic biological interactions in the soil. Therefore, diffusion is an essential mechanism for transport in the phloem and must be included to accurately predict flow.

A mathematical model of water and nutrient transport in xylem vessels of a wheat plant.

At a time of increasing global demand for food, dwindling land and resources, and escalating pressures from climate change, the farming industry is undergoing financial strain, with a need to improve efficiency and crop yields. In order to improve efficiencies in farming, and in fertiliser usage in particular, understanding must be gained of the fertiliser-to-crop-yield pathway. We model one aspect of this pathway; the transport of nutrients within the vascular tissues of a crop plant from roots to leaves. We present a mathematical model of the transport of nutrients within the xylem vessels in response to the evapotranspiration of water. We determine seven different classes of flow, including positive unidirectional flow, which is optimal for nutrient transport from the roots to the leaves; and root multidirectional flow, which is similar to the hydraulic lift process observed in plants. We also investigate the effect of diffusion on nutrient transport and find that diffusion can be significant at the vessel termini especially if there is an axial efflux of nutrient, and at night when transpiration is minimal. Models such as these can then be coupled to whole-plant models to be used for optimisation of nutrient delivery scenarios.

A dual porosity model of nutrient uptake by root hairs.

• The importance of root hairs in the uptake of sparingly soluble nutrients is understood qualitatively, but not quantitatively, and this limits efforts to breed plants tolerant of nutrient-deficient soils. • Here, we develop a mathematical model of nutrient uptake by root hairs allowing for hair geometry and the details of nutrient transport through soil, including diffusion within and between soil particles. We give illustrative results for phosphate uptake. • Compared with conventional 'single porosity' models, this 'dual porosity' model predicts greater root uptake because more nutrient is available by slow release from within soil particles. Also the effect of soil moisture is less important with the dual porosity model because the effective volume available for diffusion in the soil is larger, and the predicted effects of hair length and density are different. • Consistent with experimental observations, with the dual porosity model, increases in hair length give greater increases in uptake than increases in hair density per unit main root length. The effect of hair density is less in dry soil because the minimum concentration in solution for net influx is reached more rapidly. The effect of hair length is much less sensitive to soil moisture.