A surface model of nonlinear, non-steady-state phloem transport

Exploring optimal stomatal control under alternative hypotheses for the regulation of plant sources and sinks

Experimental evidence that nonstomatal limitations to photosynthesis (NSLs) correlate with leaf sugar and/or leaf water status suggests the possibility that stomata adjust to maximise photosynthesis through a trade-off between leaf CO₂ supply and NSLs, potentially involving source-sink interactions. However, the mechanisms regulating NSLs and sink strength, as well as their implications for stomatal control, remain uncertain. We used an analytically solvable model to explore optimal stomatal control under alternative hypotheses for source and sink regulation. We assumed that either leaf sugar concentration or leaf water potential regulates NSLs, and that either phloem turgor pressure or phloem sugar concentration regulates sink phloem unloading. All hypotheses led to realistic stomatal responses to light, CO₂ and air humidity, including conservative behaviour for the intercellular-to-atmospheric CO₂ concentration ratio. Sugar-regulated and water-regulated NSLs are distinguished by the presence/absence of a stomatal closure response to changing sink strength. Turgor-regulated and sugar-regulated phloem unloading are distinguished by the presence/absence of stomatal closure under drought and avoidance/occurrence of negative phloem turgor. Results from girdling and drought experiments on Pinus sylvestris, Betula pendula, Populus tremula and Picea abies saplings are consistent with optimal stomatal control under sugar-regulated NSLs and turgor-regulated unloading. Our analytical results provide a simple representation of stomatal responses to above-ground and below-ground environmental factors and sink activity.

Diurnal dynamics of phloem loading: theoretical consequences for transport efficiency and flow characteristics

Phloem transport is the process by which plants internally distribute assimilates. The loading of assimilates near the photosynthetic source is responsible for generating enough osmotic pressure to drive sap flow towards the sink tissues where assimilates are consumed. Phloem loading is variable and subject to a diurnal cycle. It is dominated by photosynthesis during the day and by degradation of leaf starch to sugars at night. Most studies ignore the effect of the loading cycle on transport and assume that sugar flow operates at equilibrium. In this study, phloem transport was simulated for three successive days using a finite element model of time-dependent Münch-Horwitz equations. The spatial and temporal distributions of phloem pressure, sucrose concentration, sap velocity and sucrose flux were predicted for five different time variations in sucrose loading. Results showed that periodic loading induces an alternance of two distinct transport phases: one with high pressure, concentration and sucrose flux magnitudes and another with low magnitudes. In contrast, phloem water velocity remained remarkably stable. The alternating phases persisted over time and, under source-driven variation, transport did not reach steady-state conditions for the tested configuration. However, the impact of loading dynamics on transport was mitigated by pathway effects. Oscillations were not only delayed as one travelled away from the source, their amplitude was also reduced over distance. That behaviour stabilized the supply of sucrose to the sink, which continued at moderate levels during the dark cycles. This finding suggests that transport would assist night conversion of starch to sugars in the leaf to prevent carbon starvation at distant sinks in the early morning. The propagation velocity of pressure/concentration waves in phloem was predicted to vary by a factor up to 2.5 depending on the time series chosen to describe the dynamics of loading. Finally, the model predicted that up to 87% of the amount of sucrose loaded over 48 h would be unloaded under time-dependent loading, whereas only 76% would under constant-rate loading. This additional efficiency was periodic. It did not increase significantly the overall efficiency of the system but could be responsible for inducing rhythms in sink activity.

Phloem physics: mechanisms, constraints, and perspectives

Plants have evolved specialized vascular tissues for the distribution of energy, water, nutrients, and for communication. The phloem transports sugars from photosynthetic source regions (e.g. mature leaves) to sugar sinks (e.g. developing tissues such as buds, flowers, roots). Moreover, chemical signals such as hormones, RNAs and proteins also move in the phloem. Basic physical processes strongly limit phloem anatomy and function. This paper provides an overview of recent research and perspectives on phloem biomechanics and the physical constraints relevant to sugar transport in plants.

Phloem networks in leaves

The survival of all vascular plants depends on phloem and xylem, which comprise a hydraulically coupled tissue system that transports photosynthates, water, and a variety of other molecules and ions. Although xylem hydraulics has been extensively studied, until recently, comparatively little is known quantitatively about the phloem hydraulic network and how it is functionally coupled to the xylem network, particularly in photosynthetic leaves. Here, we summarize recent advances in quantifying phloem hydraulics in fully expanded mature leaves with different vascular architectures and show that (1) the size of phloem conducting cells across phylogenetically different taxa scales isometrically with respect to xylem conducting cell size, (2) cell transport areas and lengths increase along phloem transport pathways in a manner that can be used to model Münch's pressure-flow hypothesis, and (3) report observations that invalidate da Vinci's and Murray's hydraulic models as plausible constructs for understanding photosynthate transport in the leaf lamina.