Scaling phloem transport: elasticity and pressure-concentration waves

Earlier theoretical analyses of the rate of propagation of pressure-concentration waves in the phloem were performed without adequate attention to the elastic expansion of sieve tube walls. Here, it is shown that the rate of propagation of pressure-concentration waves in phloem sieve tubes is not significantly impeded by wall elasticity, but rather, as previously implicated, by the ratio of sap osmotic pressure to the axial drop in sap hydrostatic pressure. It is also shown that pressure-concentration waves move equally well in both the upstream and downstream directions. These results permit future models to ignore elastic effects, and lend additional theoretical support to the "osmoregulatory flow" hypothesis, which argues that efficient molecular control of the phloem is permitted by maintaining sieve sap hydrostatic pressure at a value that is spatially nearly constant, which in turn permits changes in sieve tube state to be rapidly transmitted throughout the sieve tube via pressure-concentration waves.     

Effect of Water Stress on Turgor Differences and C-Assimilate Movement in Phloem of Ecballium elaterium

The effects of water stress on pressure differences and ¹⁴C-assimilate translocation in sieve tubes of squirting cucumber Ecballium elaterium A. Rich were studied. Water stress was induced by transfer of plants from culture solution to a polyethylene glycol 6,000 solution having an osmotic potential of −18.2 atm. Sieve tube turgor, turgor differences between source and sink, and translocation rate were decreased. After 260 minutes of translocation, only 19% of the total fixed ¹⁴CO₂ had moved out of the leaf, compared to the control value of 62% after the same period of time. The results suggest that water stress slows translocation by lowering sieve tube turgor differences, which are essential for the pressure flow mechanism of conduction.     

Water Flow Across the Sieve-Tube Boundary: Estimating Turgor and Some Implications For Phloem Loading and Unloading. I. Theory

A mathematical model of water and sucrose transport across thesieve tube boundary is presented, based on conservation of matterand the phenomenological equations for plasmodesmatal transportbetween the sieve elements and their associated cells. Plasmodesmataltransport coefficients are discussed. In parts II–IV,the equations developed here are used to assess: (i) the estimationof phloem turgor gradients from osmotic pressure gradients;(ii) plasmodesmatal transport of water and sucrose between thesieve elements and adjacent cells; and (iii) the plausibilityof symplastic and apoplastic phloem loading and unloading insome primary sources and sinks. A list of symbols is given inAppendix 1 of this paper Phloem, turgor, osmotic pressure, loading, unloading, plasmodesmata, Munch hypothesis     

Application of a single-solute non-steady-state phloem model to the study of long-distance assimilate transport

A mass-balanced, finite-difference solution to Münch's osmotically generated pressure-flow hypothesis is developed for the study of non-steady-state sucrose transport in the phloem tissue of plants. Major improvements over previous modeling efforts are the inclusion of wall elasticity, nonlinear functions of viscosity and solute potential, an enhanced calculation of sieve pore resistance, and the introduction of a slope-limiting total variation diminishing method for determining the concentration of sucrose at node boundaries. The numerical properties of the model are discussed, as is the history of the modeling of pressure-driven phloem transport. Idealized results are presented for a sharp, fast-moving concentration front, and the effect of changing sieve tube length on the transport of sucrose in both the steady-state and non-steady-state cases is examined. Most of the resistance to transport is found to be axial, rather than radial (via membrane transport), and most of the axial resistance is due to the sieve plates. Because of the sieve plates, sieve tube elasticity does not provide a significant enhancement to conductivity at high pressure, as previously suspected. The transit time of sucrose through a sieve tube is found to be inversely proportional to the square of the sieve tube's length; following that observation, it is suggested that 20 1-m-long sieve tubes could transport sucrose 20 times faster than a single 20 m sieve tube. Short sieve tubes would be highly sensitive to differentials between loading and unloading rate, and would require close cooperation with adjacent companion cells for proper function.     

Physiological implications of the Münch-Horwitz theory of phloem transport: effects of loading rates*

Abstract Predicted effects of phloem loading rates on the five profiles of unloading rate, osmotic water flux, pressure, transport speed and concentration, in hypothetical sieve tubes with different sink properties, were calculated using the steady-state mathematical expression of the Münch hypothesis of phloem transport. The prediction that increased loading rates always increases the concentration, and generally increase the speed of translocates through the sieve tube, is emphasized since these parameters are accessible for experimental testing. This particular prediction contrasts with a previous prediction (Tyree, Christy, & Ferrier, 1974), that where concentration was held constant at the loading end, concentration along the rest of the sieve tube would decrease, while speed would increase greatly. Where the unloading mechanism was assigned saturable (enzyme-like) kinetics, increased loading rates (in the range well below the V_max of the sink) caused both transport speed and concentration to increase. However, as loading rates approached the V_max of the sinks, speed reached a maximum and then declined, and concentration increased substantially. This was particularly true at very high values of Km, e.g. > 0.1 mol cm^?3.     

Estimation of Osmotic Gradients in Soybean Sieve Tubes by Quantitative Autoradiography: Qualified Support for the MUnch Hypothesis

An attempt was made to evaluate Münch's hypothesis of osmotically generated pressure flow in soybean (Glycine max L.) sieve tubes from velocity measurements and calculations of pressure potentials and sieve tube resistances. Pressure potential was estimated from values for water potentials and osmotic potential. Leaf water potential measurements were made by isopiestic thermocouple psychrometry, while the water potential of the nutrient solution was made with a vapor pressure osmometer. Osmotic potential was measured by first bringing the sucrose pools in the entire plant to the same specific radioactivity by steady-state-labeling of the shoot with constant specific radioactivity ¹⁴CO₂ for 5 to 8 hours. Sucrose concentrations in sieve tubes were calculated from the disintegration rate per unit volume in sieve elements as measured by absolute quantitative microautoradiography of freeze-substituted, Eponembedded source (leaf) and sink (root) tissues.     

Aphid stylectomy reveals an osmotic step between sieve tube and cortical cells in barley roots

The aim of the present study was to quantify osmotic pressuresdirectly in the translocation pathway, from leaf to growingroot tip, in order to understand the forces driving solutesfrom a source to a sink. Solutes move through the translocationpathway down an osmotically derived turgor gradient. Accordinglyaphid stylectomy and single cell sampling techniques have beencombined to examine the osmotic pressure of root phloem andgrowing root cells. Sieve tube sap was obtained from shootsand, for the first time, roots of barley seedlings using aphidstylectomy. Vacuolar sap was also obtained from a variety ofcells in leaf and root tissues using single cell sampling methods.Osmotic pressure of sieve tube sap from roots and shoots wasmeasured at high temporal resolution (within min) and over longperiods of time (up to 24 h). Osmotic pressure did not changesignificantly in the minutes immediately following excision,suggesting that confidence can be placed in the assumption thatstylet exudate is representative of sieve tube sap in vivo.There were no differences in the osmotic pressure of sieve tubesap from shoots (1.240.26 MPa, n = 10) or roots (1.420.15MPa, n = 13). However, osmotic pressure of sap from root corticalcells (0.710.09, n = 12) was about 0.7 MPa lower than thatof the sieve elements from roots, this difference may be maintainedby consumption of incoming solutes at the root tip. Resultsare discussed in the context of pressure driven flow in thephloem and symplastic contact between root tip cells and sievetube. It is hoped that the approach described here will provideimportant insights into the nature of the relationship betweenroot cell extension and assimilate supply through the phloem. Key words: Phloem, sieve tube, aphid, root, barley, osmotic pressure, translocation     

Time-dependent Behavior of a Mathematical Model for Munch Translocation: Application to Recovery from Cold Inhibition

The time evolution of a Munch pressure-flow translocation system is calculated using a numerical computer method. Results are obtained for the time course of the system variables following application of a large resistance in the translocation path, intended to simulate a cold block. The resistance factor required to produce translocation inhibition indicates that even moderate inhibition is primarily due to sieve plate pore block-age, rather than to the viscosity increase. The calculated time for recovery from cold inhibition and the shape of the translocation recovery curve agree with experimental results. The time for translocation recovery and the level of velocity recovery depend on the rate of sucrose unloading in the sink; on the sucrose concentration in the sieve tube; on the position, length, and resistance factor of the cold block; and on the hydraulic conductivities.     

Water Flow Across the Sieve Tube Boundary: Estimating Turgor and Some Implications for Phloem Loading and Unloading. IV. Root Tips and Seed Coats

In the present paper, the theory developed in Part I of thisseries is applied to seed coats of Phaseolus vulgaris and somecombined data on root tips of Hordeum distichum and Hordeumvulgare. Because of the large back-pressures implied, it isconcluded that phloem transport into these primary sinks wouldbe physiologically impossible in the absence of a symplasticpathway for the unloading of water from sieve elements. In thiscase, unloading of water and sucrose will occur predominantlyas a pressure-driven flow of solution through plasmodesmata,although diffusion can contribute significantly to the plasmodesmatalsucrose flux. At least 20% of the plasmodesmata connecting sieveelements and adjacent cells must be unobstructed if large changesin turgor and osmotic pressure are to be avoided. Dependingon the membrane area available for water fluxes, it is possiblethat the difference in water potential across the sieve-tubeplasmalemma can lead to significant errors when axial turgorgradients are estimated from gradients of osmotic pressure andexternal water potential. The magnitude and even the sign ofthese errors is uncertain, but it is possible that sieve-tubeturgor pressures will be significantly underestimated in primarysinks Phloem, turgor, osmotic pressure, plasmodesmata, Munch hypothesis, Phloem unloading     

Phloem loading and unloading of sugars and amino acids

In terrestrial higher plants, phloem transport delivers most nutrients required for growth and storage processes. Some 90% of plant biomass, transported as sugars and amino nitrogen (N) compounds in a bulk flow of solution, is propelled though the phloem by osmotically generated hydrostatic pressure differences between source (net nutrient export) and sink (net nutrient import) ends of phloem paths. Source loading and sink unloading of sugars, amino N compounds and potassium largely account for phloem sap osmotic concentrations and hence pressure differences. A symplasmic component is characteristic of most loading and unloading pathways which, in some circumstances, may be interrupted by an apoplasmic step. Raffinose series sugars appear to be loaded symplasmically. However, sucrose, and probably certain amino acids, are loaded into minor veins from source leaf apoplasms by proton symporters localized to plasma membranes of their sieve element/companion cell (se/cc) complexes. Sucrose transporters, with complementary kinetic properties, are conceived to function as membrane transporter complexes that respond to alterations in source/sink balance. In contrast, symplasmic unloading is common for many sink types. Intervention of an apoplasmic step, distal from importing phloem, is reserved for special situations. Effluxers that release sucrose and amino acids to the surrounding apoplasm in phloem loading and unloading are yet to be cloned. The physiological behaviour of effluxers is consistent with facilitated membrane transport that can be energy coupled. Roles of sucrose and amino acid transporters in phloem unloading remain to be discovered along with mechanisms regulating symplasmic transport. The latter is hypothesized to exert significant control over phloem unloading and, in some circumstances, phloem loading.     

Gradients in water potential and turgor pressure along the translocation pathway during grain filling in normally watered and water-stressed wheat plants

The water relations parameters involved in assimilate flow into developing wheat (Triticum aestivum L.) grains were measured at several points from the flag leaf to the endosperm cavity in normally watered (Psi approximately -0.3 MPa) and water-stressed plants (Psi approximately -2 MPa). These included direct measurement of sieve tube turgor and several independent approaches to the measurement or calculation of water potentials in the peduncle, grain pericarp, and endosperm cavity. Sieve tube turgor measurements, osmotic concentrations, and Psi measurements using dextran microdrops showed good internal consistency (i.e. Psi = Psi(s) + Psi(p)) from 0 to -4 MPa. In normally watered plants, crease pericarp Psi and sieve tube turgor were almost 1 MPa lower than in the peduncle. This suggests a high hydraulic resistance in the sieve tubes connecting the two. However, observations concerning exudation rates indicated a low resistance. In water-stressed plants, peduncle Psi and crease pericarp Psi were similar. In both treatments, there was a variable, approximately 1-MPa drop in turgor pressure between the grain sieve tubes and vascular parenchyma cells. There was little between-treatment difference in endosperm cavity sucrose or osmotic concentrations or in the crease pericarp sucrose pool size. Our results re-emphasize the importance of the sieve tube unloading step in the control of assimilate import.     

Hydrodynamics and cell volume oscillations in the pollen tube apical region are integral components of the biomechanics of Nicotiana tabacum pollen tube growth

Pollen tube growth is localized at the apex and displays oscillatory dynamics. It is thought that a balance between intracellular turgor pressure (hydrostatic pressure, reflected by the cell volume) and cell wall loosening is a critical factor driving pollen tube growth. We previously demonstrated that water flows freely into and out of the pollen tube apical region dependent on the extracellular osmotic potential, that cell volume changes reflect changes in the intracellular pressure, and that cell volume changes differentially induce, increases or decreases in specific phospholipid signals. This article shows that manipulation of the extracellular osmotic potential rapidly induces modulations in pollen tube growth rate frequencies, demonstrating that changes in the intracellular pressure are sufficient to reset the pollen tube growth oscillator. This indicates a direct link between intracellular hydrostatic pressure and pollen tube growth. Altering hydrodynamic flow through the pollen tube by replacing extracellular H₂O with ²H₂O adversely affects both cell volume and growth rate oscillations and induces aberrant morphologies. Normal growth and cell morphology are rescued by replacing ²H₂O with H₂O. Further studies revealed that the cell volume oscillates in the pollen tube apical region. These cell volume oscillations were not from changes in cell shape at the tip and were detectable up to 30 μm distal to the tip (the longest length measured). Cell volume in the apical region oscillates with the same frequency as growth rate oscillations but surprisingly the cycles are phase-shifted by 180°. Raman microscopy yields evidence that hydrodynamic flow out of the apex may be part of the biomechanics that drive cellular expansion. The combined results suggest that hydrodynamic loading/unloading in the apical region induces cell volume oscillations and has a role in driving cell elongation and pollen tube growth.     

Water Flow Across the Sieve-Tube Boundary: Estimating Turgor and Some Implications for Phloem Loading and Unloading. III. Phloem in the Leaf

The theory described in Part I of this series is applied hereto the loading of water and sucrose into the sieve-element-companion-cell(se-cc) complexes of minor veins. It is concluded that symplasticphloem loading cannot account for large increases in osmoticpressure from mesophyll to se-cc complex or the dilution ofsieve tube sap which is evident in leaves. By contrast, loadingfrom the free space into a symplastically isolated se-cc complexcan account for both these observations. Within the se-cc complex,sucrose and water will be transported from the companion cellsto the sieve elements by a pressure-driven flow of solutionthrough the cytoplasmic annuli of plasmodesmata. The associatedchanges in turgor and osmotic pressure are small, and so these-cc complex can be regarded as a single compartment with respectto water potential. The assumption that this compartment isat water flux equilibrium will lead to significant overestimatesof turgor gradients. However, if the trans-membrane water potentialdifference and the external water potential are taken into account,the correlation of such gradients with sieve-element dimensionsand / or transport velocities provides one means of testingthe Munch hypothesis of phloem transport Phloem, turgor, osmotic pressure, plasmodesmata, Münch hypothesis, Phloem loading     

Revisiting the Münch pressure-flow hypothesis for long-distance transport of carbohydrates: modelling the dynamics of solute transport inside a semipermeable tube

A mathematical model of the Münch pressure-flow hypothesis for long-distance transport of carbohydrates via sieve tubes is constructed using the Navier-Stokes equation for the motion of a viscous fluid and the van't Hoff equation for osmotic pressure. Assuming spatial dimensions that are appropriate for a sieve tube and ensuring suitable initial profiles of the solute concentration and solution velocity lets the model become mathematically tractable and concise. In the steady-state case, it is shown via an analytical expression that the solute flux is diffusion-like with the apparent diffusivity coefficient being proportional to the local solute concentration and around seven orders of magnitude greater than a diffusivity coefficient for sucrose in water. It is also shown that, in the steady-state case, the hydraulic conductivity over one metre can be calculated explicitly from the tube radius and physical constants and so can be compared with experimentally determined values. In the time-dependent case, it is shown via numerical simulations that the solute (or water) can simultaneously travel in opposite directions at different locations along the tube and, similarly, change direction of travel over time at a particular location along the tube.     

Water Flow Across the Sieve-Tube Boundary: Estimating Turgor and Some Implications for Phloem Loading and Unloading. II. Phloem in the Stem

Confirming a previous analysis by Lang (1974), it is concludedthat in tree trunks, phloem turgor and turgor gradients maybe estimated from osmotic pressure and osmotic-pressure gradients,respectively. The present analysis is an improvement becauseit is based on observed osmotic-pressure gradients rather thansupposed turgor gradients, and allowance is made for sucroseunloading and gradients of external water potential. It is concludedthat the rate of sucrose unloading in tree trunks must be lessthan 50 nmol m^–2 S m^–1. In small plants, higherrates of unloading (100 nmol m m^–2 S m^–1) and steeperconcentration gradients will lead to larger errors, but turgorpressures can still be estimated with acceptable accuracy. Oneshould be more cautious when considering turgor gradients insmall plants, although it seems likely that reasonable estimateswill still be obtained. Assuming plasmodesmatal transport throughan unconstricted cytoplasmic annulus, it is concluded that thesieve elements and their associated cells will sustain verysimilar turgor and osmotic pressures. Convection and diffusioncan both contribute significantly to plasmodesmatal sucroseunloading. Similarly, the plasmodesmatal volume flux will reflecta combination of pressure flow and osmosis. Water fluxes acrossthe sieve element plasmalemma and through the plasmodesmatacan be in opposite directions. It may be possible to assessthe extent of hydraulic coupling between the sieve elementsand their associated cells from studies of phloem water relations Phloem, turgor, osmotic pressure, plasmodesmata, phloem unloading, Munch hypothesis     

The water relations of the root–soil interface

The difference in hydrostatic pressure between the xylem of the leaf and the soil depends, for a given transpiration rate, on the series of hydraulic resistances encountered along this pathway. Many studies have shown that the sum of the resistances in the plant and the soil is too small to account for the fall in water pressure between the leaf xylem and the soil, especially when plants are growing in sandy soils, which are prone to dry rapidly. A resistance at the root–soil interface, caused possibly by poor contact between the roots and the soil, has been proposed to account for the discrepancy. We explored the resistance in the pathway from soil to leaf using a technique that allows precise and continuous non-destructive measurement of the hydrostatic pressure in the leaf xylem. When the soil was leached with water, the fall in leaf water status as the soil dried was reasonably well described by a simple physical model without the need to invoke an interfacial resistance. However, when the soil was flushed with a nutrient solution with an osmotic pressure of 70kPa, the hydrostatic pressure in the leaf xylem fell several times faster than that in the soil. We suggest that solutes accumulated either in the root or just outside it, creating large osmotic pressures, which gave the appearance of an interfacial resistance.     

The structure of the phloem--still more questions than answers

Long-distance assimilate distribution in higher plants takes place in the enucleate sieve-tube system of the phloem. It is generally accepted that flow of assimilates is driven by an osmotically generated pressure differential, as proposed by Ernst Münch more than 80?years ago. In the period between 1960 and 1980, the pressure flow hypothesis was challenged when electron microscopic images suggested that sieve tubes contain obstructions that would prevent passive flow. This led to the proposal of alternative translocation mechanisms. However, most investigators came to the conclusion that obstructions in the sieve-tube path were due to preparation artifacts. New developments in bioimaging have vastly enhanced our ability to study the phloem. Unexpectedly, in vivo studies challenge the pressure-flow hypothesis once again. In this review we summarize current investigations of phloem structure and function and discuss their impact on our understanding of long-distance transport in the phloem.     

Distorted phytochrome action spectra in green plants

An evaluation was made of the extent which a Münch-type pressure flow mechanism (i.e., osmotically-generated pressure flow) might contribute to phloem transport in soybean. Estimates of sucrose concentrations in source (leaf) and sink (root) sieve tubes were obtained by a negativestaining procedure. Water potential measurements of the leaf and of the nutrient solution allowed calculation of the turgor pressures in source and sink sieve tubes. The turgor difference between source and sink sieve tubes was compared to that required to drive translocation at the observed velocity between the source and sink, as measured by [¹⁴C] photosynthate movement. Sieve-tube conductivity was calculated from the sieve-tube dimensions, assuming an essentially unobstructed pathway. In three experiments, the sucrose concentration was consistently higher in source sieve tubes (an average of 11.5%) than in sink sieve tubes (an average of 5.3%). The ratio of these values (2.3:1) agreed reasonably well with an earlier ratio for source/sink sieve tube concentrations of 1.8:1, obtained by quantitative microautoradiography. The resulting calculated turgor difference (an average of 4.1 bars) was adequate to drive a pressure flow mechanism at the observed translocation velocities (calculated to require a turgor difference of 1.2 to 4.6 bars). No other force need be presumed to be involved.This work was presented in part at a joint U.S.-Australian Conference on Transport and Transfer Processes in Plants, Canberra, Australia, December 15–20, 1975; see Fisher (1976)     

Osmosis and viscoelasticity both contribute to time-dependent behaviour of the intervertebral disc under compressive load: A caprine in vitro study

The mechanical behaviour of the intervertebral disc highly depends on the content and transport of interstitial fluid. It is unknown, however, to what extent the time-dependent behaviour can be attributed to osmosis. Here we investigate the effect of both mechanical and osmotic loading on water content, nucleus pressure and disc height. Eight goat intervertebral discs, immersed in physiological saline, were subjected to a compressive force with a pressure needle inserted in the nucleus. The loading protocol was: 10 N (6 h); 150 N (42 h); 10 N (24 h). Half-way the 150 N-phase (24 h), we eliminated the osmotic gradient by adding 26% poly-ethylene glycol to the surrounding fluid. For 62 additional discs, we determined the water content of both nucleus and annulus after 6, 24, 48, or 72 h. The compressive load was initially counterbalanced by the hydrostatic pressure in the nucleus. The load forced 4.3% of the water out of the nucleus, which reduced nucleus pressure by 44(±6)%. Reduction of the osmotic gradient disturbed the equilibrium disc height, and a significant loss of annulus water content was found. Remarkably, pressure and water content of the nucleus pulposus remained unchanged. This shows that annulus water content is important in the response to axial loading. After unloading, in the absence of an osmotic gradient, there was substantial viscoelastic recovery of 53(±11)% of the disc height, without a change in water content. However, for restoration of the nucleus pressure and for full restoration of disc height, restoration of the osmotic gradient was needed.     

Scaling phloem transport: water potential equilibrium and osmoregulatory flow

In this work, the common assumption that phloem sap is in water potential equilibrium with the surrounding apoplast was examined. With a dimensionless model of phloem translocation that scales with just two dimensionless parameters (R?and F?), a ‘map’ of phloem behaviour as a function of these parameters was produced, which shows that the water potential equilibrium assumption (R?F? >> 1) is valid for essentially all realistic values of the relevant scales. When in water potential equilibrium, a further parameter reduction is possible that limits model dependence to a single parameter (F?), which describes the ratio of the solution's osmotic strength to its axial pressure drop. Due to the locally autonomous nature of individual sieve element/companion cell complexes, it is argued that long‐distance integrative control is most efficient when F? is large (that is, when the pressure drop is relatively small), permitting the sieve tube to regulate solute loading in response to global changes in turgor. This mode of transport has been called ‘osmoregulatory flow.’ Limitations on the pressure drop within the transport phloem could require that sieve tubes be shorter than the long axis of the plant, and thus arranged in series and hydraulically isolated from one another.