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Transport in biological systems often occurs in complex spatial environments involving random structures. Motivated by such applications, we investigate an idealized model for solute transport past an array of point sinks, randomly distributed along a line, which remove solute via first-order kinetics. Random sink locations give rise to long-range spatial correlations in the solute field and influence the mean concentration. We present a non-standard approach in evaluating these features based on rationally approximating integrals of a suitable Green's function, which accommodates contributions varying on short and long lengthscales and has deterministic and stochastic components. We refine the results of classical two-scale methods for a periodic sink array (giving more accurate higher-order corrections with non-local contributions) and find explicit predictions for the fluctuations in concentration and disorder-induced corrections to the mean for both weakly and strongly disordered sink locations. Our predictions are validated across a large region of parameter space. [ABSTRACT FROM AUTHOR]

Background and Aims Diurnal changes in solar position and intensity combined with the structural complexity of plant architecture result in highly variable and dynamic light patterns within the plant canopy. This affects productivity through the complex ways that photosynthesis responds to changes in light intensity. Current methods to characterize light dynamics, such as ray-tracing, are able to produce data with excellent spatio-temporal resolution but are computationally intensive and the resulting data are complex and high-dimensional. This necessitates development of more economical models for summarizing the data and for simulating realistic light patterns over the course of a day. Methods High-resolution reconstructions of field-grown plants are assembled in various configurations to form canopies, and a forward ray-tracing algorithm is applied to the canopies to compute light dynamics at high (1 min) temporal resolution. From the ray-tracer output, the sunlit or shaded state for each patch on the plants is determined, and these data are used to develop a novel stochastic model for the sunlit–shaded patterns. The model is designed to be straightforward to fit to data using maximum likelihood estimation, and fast to simulate from. Key Results For a wide range of contrasting 3-D canopies, the stochastic model is able to summarize, and replicate in simulations, key features of the light dynamics. When light patterns simulated from the stochastic model are used as input to a model of photoinhibition, the predicted reduction in carbon gain is similar to that from calculations based on the (extremely costly) ray-tracer data. Conclusions The model provides a way to summarize highly complex data in a small number of parameters, and a cost-effective way to simulate realistic light patterns. Simulations from the model will be particularly useful for feeding into larger-scale photosynthesis models for calculating how light dynamics affects the photosynthetic productivity of canopies. [ABSTRACT FROM AUTHOR]

Using a popular vertex-based model to describe a spatially disordered planar epithelial monolayer, we examine the relationship between cell shape and mechanical stress at the cell and tissue level. Deriving expressions for stress tensors starting from an energetic formulation of the model, we show that the principal axes of stress for an individual cell align with the principal axes of shape, and we determine the bulk effective tissue pressure when the monolayer is isotropic at the tissue level. Using simulations for a monolayer that is not under peripheral stress, we fit parameters of the model to experimental data for Xenopus embryonic tissue. The model predicts that mechanical interactions can generate mesoscopic patterns within the monolayer that exhibit long-range correlations in cell shape. The model also suggests that the orientation of mechanical and geometric cues for processes such as cell division are likely to be strongly correlated in real epithelia. Some limitations of the model in capturing geometric features of Xenopus epithelial cells are highlighted. [ABSTRACT FROM AUTHOR]

Photoinhibition reduces photosynthetic productivity; however, it is difficult to quantify accurately in complex canopies partly because of a lack of high-resolution structural data on plant canopy architecture, which determines complex fluctuations of light in space and time. Here, we evaluate the effects of photoinhibition on long-term carbon gain (over 1 d) in three different wheat (Triticum aestivum) lines, which are architecturally diverse. We use a unique method for accurate digital three-dimensional reconstruction of canopies growing in the field. The reconstruction method captures unique architectural differences between lines, such as leaf angle, curvature, and leaf density, thus providing a sensitive method of evaluating the productivity of actual canopy structures that previously were difficult or impossible to obtain. We show that complex data on light distribution can be automatically obtained without conventional manual measurements. We use a mathematical model of photosynthesis parameterized by field data consisting of chlorophyll fluorescence, light response curves of carbon dioxide assimilation, and manual confirmation of canopy architecture and light attenuation. Model simulations show that photoinhibition alone can result in substantial reduction in carbon gain, but this is highly dependent on exact canopy architecture and the diurnal dynamics of photoinhibition. The use of such highly realistic canopy reconstructions also allows us to conclude that even a moderate change in leaf angle in upper layers of the wheat canopy led to a large increase in the number of leaves in a severely light-limited state. [ABSTRACT FROM AUTHOR]

In simulations, large-amplitude self-excited oscillations of high-Reynolds-number flow in a finite-length flexible channel often exhibit vigorous repetitive 'slamming' motion, during which the channel briefly becomes almost completely occluded over a very short length scale near its downstream end before rapidly reopening. Here we analyse this near-singular behaviour using an established one-dimensional PDE model of the two-dimensional physical system. Working in a distinguished asympotic limit, we systematically derive a low-order differential/algebraic model for the flow when it is close to the slamming state. The shape of the channel near the constriction is determined by a balance between membrane tension and fluid inertia; this region is also the predominant site of viscous dissipation, which balances energy changes distributed along the channel. The reduced model accurately captures a set of steady solution branches and their stability and shows how slamming is strongly coupled to the properties of the rigid channel downstream of the membrane. A singularity is identified in the low-order model which may explain the violent readjustment of the flow at the end of a slamming event. [ABSTRACT FROM AUTHOR]

Plants have evolved complex mechanisms to balance the efficient use of absorbed light energy in photosynthesis with the capacity to use that energy in assimilation, so avoiding potential damage from excess light. This is particularly important under natural light, which can vary according to weather, solar movement and canopy movement. Photosynthetic acclimation is the means by which plants alter their leaf composition and structure over time to enhance photosynthetic efficiency and productivity. However there is no empirical or theoretical basis for understanding how leaves track historic light levels to determine acclimation status, or whether they do this accurately. We hypothesized that in fluctuating light (varying in both intensity and frequency), the light-response characteristics of a leaf should adjust (dynamically acclimate) to maximize daily carbon gain. Using a framework of mathematical modelling based on light-response curves, we have analysed carbon-gain dynamics under various light patterns. The objective was to develop new tools to quantify the precision with which photosynthesis acclimates according to the environment in which plants exist and to test this tool on existing data. We found an inverse relationship between the optimal maximum photosynthetic capacity and the frequency of low to high light transitions. Using experimental data from the literature we were able to show that the observed patterns for acclimation were consistent with a strategy towards maximizing daily carbon gain. Refinement of the model will further determine the precision of acclimation. [ABSTRACT FROM AUTHOR]

We review the role of anisotropic stress in controlling the growth anisotropy of stems. Instead of stress, growth anisotropy is usually considered in terms of compliance. Anisotropic compliance is typical of cell walls, because they contain aligned cellulose microfibrils, and it appears to be sufficient to explain the growth anisotropy of an isolated cell. Nevertheless, a role for anisotropic stress in the growth of stems is indicated by certain growth responses that appear too rapid to be accounted for by changes in cell-wall compliance and because the outer epidermal wall of most growing stems has microfibrils aligned axially, an arrangement that would favour radial expansion based on cell-wall compliance alone. Efforts to quantify stress anisotropy in the stem have found that it is predominantly axial, and large enough in principle to explain the elongation of the epidermis, despite its axial microfibrils. That the epidermis experiences a stress deriving from the inner tissue, the so-called ‘tissue stress’, has been widely recognized; however, the origin of the dominant axial direction remains obscure. Based on geometry, an isolated cylindrical cell should have an intramural stress anisotropy favouring the transverse direction. Explanations for tissue stress have invoked differential elastic moduli, differential plastic deformation (so-called differential growth), and a phenomenon analogous to the maturation stress generated by secondary cell walls. None of these explanations has been validated. We suggest that understanding the role of stress anisotropy in plant growth requires a deeper understanding of the nature of stress in hierarchical, organic structures. [ABSTRACT FROM PUBLISHER]

Over recent decades, we have gained detailed knowledge of many processes involved in root growth and development. However, with this knowledge come increasing complexity and an increasing need for mechanistic modeling to understand how those individual processes interact. One major challenge is in relating genotypes to phenotypes, requiring us to move beyond the network and cellular scales, to use multiscale modeling to predict emergent dynamics at the tissue and organ levels. In this review, we highlight recent developments in multiscale modeling, illustrating how these are generating new mechanistic insights into the regulation of root growth and development. We consider how these models are motivating new biological data analysis and explore directions for future research. This modeling progress will be crucial as we move from a qualitative to an increasingly quantitative understanding of root biology, generating predictive tools that accelerate the development of improved crop varieties. [ABSTRACT FROM AUTHOR]

We consider small-amplitude deformations of a long thin-walled elastic tube having an initially axially uniform elliptical cross section. The tube is subject to an axial pre-stress, and the deformations result from an applied transmural pressure. An approximate tube law (linking the transmural pressure with the cross-sectional area and its axial derivatives) is derived from shell theory in the distinguished asymptotic limit in which the tube's behaviour is dominated by the restoring forces from the axial pre-stress and azimuthal bending. This is possible because the deformations of the tube induced by both the transmural pressure and the axial forces can be described, to very good approximation, by a single azimuthal mode of deformation of axially varying amplitude. The resulting tube law is compared with numerical solutions of the full shell equations and good agreement is found (provided the tube is sufficiently long and the wall not too thin so that in-plane shearing is negligible). We discuss the applications of our results to the modelling of flow in collapsible tubes. [ABSTRACT FROM PUBLISHER]