In plants, the delivery of the products of photosynthesis is achieved through a hydraulic system labeled as phloem. This semi-permeable plant tissue consists of living cells that contract and expand in response to fluid pressure and flow velocity fluctuations. The Münch pressure flow theory, which is based on osmosis providing the necessary pressure gradient to drive the mass flow of carbohydrates, is currently the most accepted model for such sucrose transport. When this hypothesis is combined with the conservation of fluid mass and momentum as well as sucrose mass, many simplifications must be invoked to mathematically close the problem and to resolve the flow. This study revisits such osmotically driven flows by developing a new two-dimensional numerical model in cylindrical coordinates for an elastic membrane and a concentration-dependent viscosity. It is demonstrated that the interaction between the hydrodynamic and externally supplied geometrical characteristic of the phloem has a significant effect on the front speed of sucrose transport. These results offer a novel perspective about the evolutionary adaptation of plant hydraulic traits to optimize phloem soluble compounds transport efficiency.
more »
« less
Radial–axial transport coordination enhances sugar translocation in the phloem vasculature of plants
Understanding mass transport of photosynthates in the phloem of plants is necessary for predicting plant carbon allocation, productivity, and responses to water and thermal stress. Several hypotheses about optimization of phloem structure and function and limitations of phloem transport under drought have been proposed and tested with models and anatomical data. However, the true impact of radial water exchange of phloem conduits with their surroundings on mass transport of photosynthates has not been addressed. Here, the physics of the Munch mechanism of sugar transport is re-evaluated to include local variations in viscosity resulting from the radial water exchange in two dimensions (axial and radial) using transient flow simulations. Model results show an increase in radial water exchange due to a decrease in sap viscosity leading to increased sugar front speed and axial mass transport across a wide range of phloem conduit lengths. This increase is around 40% for active loaders (e.g. crops) and around 20% for passive loaders (e.g. trees). Thus, sugar transport operates more efficiently than predicted by previous models that ignore these two effects. A faster front speed leads to higher phloem resiliency under drought because more sugar can be transported with a smaller pressure gradient.
more » « less- Award ID(s):
- 1754893
- NSF-PAR ID:
- 10414423
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Plant Physiology
- Volume:
- 189
- Issue:
- 4
- ISSN:
- 0032-0889
- Page Range / eLocation ID:
- p. 2061-2071
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
Abstract The significance of phloem hydrodynamics to plant mortality and survival, which impacts ecosystem‐scale carbon and water cycling, is not in dispute. The phloem provides the conduits for products of photosynthesis to be transported to different parts of the plant for consumption or storage. The M
nch pressure flow hypothesis (PFH) is the leading framework to mathematically represent this transport. It assumes that osmosis provides the necessary pressure differences to drive water and sucrose within the phloem. Mathematical models utilizing the PFH approximate the phloem by a relatively rigid slender semi‐permeable tube. However, the phloem consists of living cells that contract and expand in response to pressure fluctuations. The effect of membrane elasticity on osmotically driven sucrose front speed has rarely been considered and frames the scope here. Laboratory experiments were conducted to elucidate the elastic‐to‐plastic pressure‐deformation relation in membranes and their effect on sucrose front speeds. It is demonstrated that membrane elasticity acts to retard the sucrose front speed. The retardation emerges because of two effects: (a) part of the osmotic pressure is diverted to perform mechanical work to expand the membrane instead of pressurizing water, and (b) expansion of the membrane reduces the sucrose concentration driving osmotic potential due to volume increases and concomitant dilution effects. These results offer a novel perspective about the much discussed presence of sieve plates throughout the phloem acting as structural expansion dampers. -
null (Ed.)Sucrose is among the main products of photosynthesis that are deemed necessary for plant growth and survival. It is produced in the mesophyll cells of leaves and translocated to different parts of the plant through the phloem. Progress in understanding this transport process remains fraught with experimental difficulties, thereby prompting interest in theoretical approaches and laboratory studies. The Münch pressure and mass flow model is one of the accepted hypotheses describing the physics of sucrose transport in the phloem. It is based on osmosis creating an energy potential difference between the source and the sink. The flow responding to this energy potential is assumed laminar and described by the Hagen–Poiseuille equation. This study revisits such osmotically driven flows in tubes with membrane walls by including the effects of Taylor dispersion on mass transport. This effect has been overlooked in phloem flow studies. Taylor dispersion can increase the effective transport of solutes by increasing the apparent diffusion coefficient. It is shown that, in addition to the conventional diffusive correction derived for impermeable tube walls, a new adjustment to the mean advective terms arises because of osmotic effects. Because the molecular Schmidt number is very large for sucrose in water, the sucrose front speed and travel times have a direct dependence on the Péclet number for different ranges of the Münch number. This study establishes upper limits on expected Taylor dispersion enhancement of sucrose transport.more » « less
-
Ryan, Michael (Ed.)Abstract Increasing evidence suggests that tree growth is sink-limited by environmental and internal controls rather than by carbon availability. However, the mechanisms underlying sink-limitations are not fully understood and thus not represented in large-scale vegetation models. We develop a simple, analytically solved, mechanistic, turgor-driven growth model (TDGM) and a phloem transport model (PTM) to explore the mechanics of phloem transport and evaluate three hypotheses. First, phloem transport must be explicitly considered to accurately predict turgor distributions and thus growth. Second, turgor-limitations can explain growth-scaling with size (metabolic scaling). Third, turgor can explain realistic growth rates and increments. We show that mechanistic, sink-limited growth schemes based on plant turgor limitations are feasible for large-scale model implementations with minimal computational demands. Our PTM predicted nearly uniform sugar concentrations along the phloem transport path regardless of phloem conductance, stem water potential gradients and the strength of sink-demands contrary to our first hypothesis, suggesting that phloem transport is not limited generally by phloem transport capacity per se but rather by carbon demand for growth and respiration. These results enabled TDGM implementation without explicit coupling to the PTM, further simplifying computation. We test the TDGM by comparing predictions of whole-tree growth rate to well-established observations (site indices) and allometric theory. Our simple TDGM predicts realistic tree heights, growth rates and metabolic scaling over decadal to centurial timescales, suggesting that tree growth is generally sink and turgor limited. Like observed trees, our TDGM captures tree-size- and resource-based deviations from the classical ¾ power-law metabolic scaling for which turgor is responsible.more » « less
-
Links between the carbon and water economies of plants are coupled by combining the biochemical demand for atmospheric CO2 with gas transfer through stomates, liquid water transport in the soil-xylem hydraulic system and sucrose export in the phloem. We formulated a model to predict stomatal conductance (gs), consistent with the maximum energy circulation concept of Lotka and Odum, by maximizing the sucrose flux out of photosynthesizing leaves. The proposed modeling approach recovers all prior results derived from stomatal optimization theories and profit-maximization arguments for the xylem hydraulic system aimed at predicting gs. The novel features of this approach are its ability to 1) predict the price of losing water in carbon units using xylem and phloem properties (i.e., the marginal water use efficiency) and 2) explain why water molecules become more expensive to exchange for CO2 molecules when soil moisture becomes limiting or when plants acclimate to new elevated atmospheric CO2 concentration. On short time-scales (sub-daily), predicted gs under many environmental stimuli were consistent with measurements reported in the literature, including a general sensitivity of gs to vapor pressure deficit and leaf water potential. During progressive droughts, differences in the coordination among the leaf, xylem, and phloem functioning determine the isohydric-to-anisohydric behavior among plants.more » « less
