Modeling xylem and phloem water flows in trees according to cohesion theory and Münch hypothesis

Water and solute flows in the coupled system of xylem and phloem were modeled together with predictions for xylem and whole stem diameter changes. With the model we could produce water circulation between xylem and phloem as presented by the Münch hypothesis. Viscosity was modeled as an explicit function of solute concentration and this was found to vary the resistance of the phloem sap flow by many orders of magnitude in the possible physiological range of sap concentrations. Also, the sensitivity of the predicted phloem translocation to changes in the boundary conditions and parameters such as sugar loading, transpiration, and hydraulic conductivity were studied. The system was found to be quite sensitive to the sugar-loading rate, as too high sugar concentration, (approximately 7 MPa) would cause phloem translocation to be irreversibly hindered and soon totally blocked due to accumulation of sugar at the top of the phloem and the consequent rise in the viscosity of the phloem sap. Too low sugar loading rate, on the other hand, would not induce a sufficient axial water pressure gradient. The model also revealed the existence of Münch “counter flow”, i.e., xylem water flow in the absence of transpiration resulting from water circulation between the xylem and phloem. Modeled diameter changes of the stem were found to be compatible with actual stem diameter measurements from earlier studies. The diurnal diameter variation of the whole stem was approximately 0.1 mm of which the xylem constituted approximately one-third.     

Linking xylem diameter variations with sap flow measurements

Measurements of variation in the diameter of tree stems provide a rapid response, high resolution tool for detecting changes in water tension inside the xylem. Water movement inside the xylem is caused by changes in the water tension and theoretically, the sap flow rate should be directly proportional to the water tension gradient and, therefore, also linearly linked to the xylem diameter variations. The coefficient of proportionality describes the water conductivity and elasticity of the conducting tissue. Xylem diameter variation measurements could thus provide an alternative approach for estimating sap flow rates, but currently we lack means for calibration. On the other hand, xylem diameter variation measurements could also be used as a tool for studying xylem structure and function. If we knew both the water tension in the xylem and the sap flow rate, xylem conductivity and/or elasticity could be calculated from the slope of their relationship. In this study we measured diurnal xylem diameter variation simultaneously with sap flow rates (Granier-type thermal method) in six deciduous species (Acer rubrum L., Alnus glutinosa Miller, Betula lenta L., Fagus Sylvatica L. Quercus rubra L., and Tilia vulgaris L.) for 7–91 day periods during summers 2003, 2005 and 2006 and analyzed the relationship between these two measurements. We found that in all species xylem diameter variations and sap flow rate were linearly related in daily scale (daily average R ² = 0.61–0.87) but there was a significant variation in the daily slopes of the linear regressions. The largest variance in the slopes, however, was found between species, which is encouraging for finding a species specific calibration method for measuring sap flow rates using xylem diameter variations. At a daily timescale, xylem diameter variation and sap flow rate were related to each other via a hysteresis loop. The slopes during the morning and afternoon did not differ statistically significantly from each other, indicating no overall change in the conductivity. Because of the variance in the daily slopes, we tested three different data averaging methods to obtain calibration coefficients. The performance of the averaging methods depended on the source of variance in the data set and none of them performed best for all species. The best estimates of instantaneous sap flow rates were also given by different averaging methods than the best estimates of total daily water use. Using the linear relationship of sap flow rate and xylem diameter variations we calculated the conductance and specific conductivity of the soil–xylem–atmosphere water pathway. The conductance were of the order of magnitude 10⁻⁵ kg s⁻¹ MPa⁻¹ for all species, which compares well with measured water fluxes from broadleaved forests. Interestingly, because of the large sap wood area the conductance of Betula was approximately 10 times larger than in other species.     

Could rapid diameter changes be facilitated by a variable hydraulic conductance?

Adequate radial water transport between elastic bark tissue and xylem is crucial in trees, because it smoothens abrupt changes in xylem water potential, greatly reducing the likelihood of suffering dangerous levels of embolism. The radial hydraulic conductance involved is generally thought to be constant. Evidence collected about variable root and leaf hydraulic conductance led us to speculate that radial hydraulic conductance in stem/branches might also be variable and possibly modulated by putative aquaporins. We therefore correlated diameter changes in walnut (Juglans regia L.) with changes in water potential, altered by perfusion of twig samples with D-mannitol solutions having different osmotic potentials. Temperature and cycloheximide (CHX; a protein synthesis inhibitor) treatments were performed. The temperature response and diameter change inhibition found in CHX-treated twigs underpinned our hypothesis that radial hydraulic conductance is variable and likely mediated by a putative aquaporin abundance and/or activity. Our data demonstrate that radial water transport in stem/branches can take two routes in parallel: an apoplastic and a cell-to-cell route. The contribution of either route depends on the hydraulic demand and is closely linked to a boost of putative aquaporins, causing radial conductance to be variable. This variability should be considered when interpreting and modelling diameter changes.     

Impact of phloem girdling on leaf gas exchange and hydraulic conductance in hybrid aspen

We investigated phloem-xylem interactions in relation to leaf hydraulic capacity in hybrid aspen (Populus tremula L. × P. tremuloides Michx.) by using phloem girdling method. Removal of bark tissues (phloem girdling) at the branch base resulted in a substantial decline in stomatal conductance (g_S), net photosynthetic rate (P_N), and leaf hydraulic efficiency, and in increase of leaf water potential (Ψ_L). Although gS declined more than P_N (83 versus 78 %), the ratio of intercellular to ambient CO₂ concentrations (c_i/c_a) increased from 0.67 to 0.87 in three days after girdling. Girdling induced a decrease in leaf hydraulic conductance (K_L) on average by 43 % (P = 0.006). The changes in gS and leaf conductance to water vapour were co-ordinated with K_L only in girdled branches whereas intrinsic water-use efficiency was invariant to K_L. The declines in K_L with girdling were not accompanied by changes in potassium ion concentration ([K⁺]), electrical conductivity, or pH of xylem sap. The results suggest that phloem girdling at the branch base does not influence the recirculation of ions between the phloem and xylem in hybrid aspen and the decrease of K_L in response to the manipulation is not related to changes in [K⁺] and total ionic content of xylem sap.     

Comparative axial widening of phloem and xylem conduits in small woody plants

Key message

Along the stem axis phloem’s sieve elements increase in diameter basally at rates comparable to those of xylem conduits and in agreement with principles of hydraulic optimization.

Abstract

Plant physiology relies on the efficiency of the two long-distance transport systems of xylem and phloem. Xylem architecture comprises conduits of small dimensions towards the stem apex, where transpiration-induced tensions are the highest along the root-to-leaves hydraulic pathway, and widen basally to minimize the path length resistance to water flow. Instead, information on phloem anatomy and allometry is extremely scarce, although potentially relevant for the efficiency of sugar transportation. We measured the hydraulic diameter (Dh) of both xylem conduits and phloem sieve elements in parallel at different heights along the stem of a small tree of Picea abies, Fraxinus excelsior and Salix eleagnos. Dh increased from the stem apex to base in both xylem and phloem, with a higher scaling exponent (b) of sieve elements than that of tracheids in the conifer (0.19 vs. 0.14) and lower than that of vessels in the angiosperms (0.14–0.22 vs. 0.19–0.40). In addition, sieve elements were larger than tracheids in P. abies and narrower than angiosperms vessels at any height along the stem. In conclusion, axial conduit widening would seem to be a key feature of both xylem and phloem long-distance transport architectures.     

MRI of long-distance water transport: a comparison of the phloem and xylem flow characteristics and dynamics in poplar, castor bean, tomato and tobacco

We used dedicated magnetic resonance imaging (MRI) equipment and methods to study phloem and xylem transport in large potted plants. Quantitative flow profiles were obtained on a per-pixel basis, giving parameter maps of velocity, flow-conducting area and volume flow (flux). The diurnal xylem and phloem flow dynamics in poplar, castor bean, tomato and tobacco were compared. In poplar, clear diurnal differences in phloem flow profile were found, but phloem flux remained constant. In tomato, only small diurnal differences in flow profile were observed. In castor bean and tobacco, phloem flow remained unchanged. In all plants, xylem flow profiles showed large diurnal variation. Decreases in xylem flux were accompanied by a decrease in velocity and flow-conducting area. The diurnal changes in flow-conducting area of phloem and xylem could not be explained by pressure-dependent elastic changes in conduit diameter. The phloem to xylem flux ratio reflects what fraction of xylem water is used for phloem transport (Münch's counterflow). This ratio was large at night for poplar (0.19), castor bean (0.37) and tobacco (0.55), but low in tomato (0.04). The differences in phloem flow velocity between the four species, as well as within a diurnal cycle, were remarkably small (0.25-0.40 mm s(-1)). We hypothesize that upper and lower bounds for phloem flow velocity may exist: when phloem flow velocity is too high, parietal organelles may be stripped away from sieve tube walls; when sap flow is too slow or is highly variable, phloem-borne signalling could become unpredictable.     

Linking phloem function to structure: Analysis with a coupled xylem-phloem transport model

We carried out a theoretical analysis of phloem transport based on Münch hypothesis by developing a coupled xylem-phloem transport model. Results showed that the maximum sugar transport rate of the phloem was limited by solution viscosity and that transport requirements were strongly affected by prevailing xylem water potential. The minimum number of xylem and phloem conduits required to sustain transpiration and assimilation, respectively, were calculated. At its maximum sugar transport rate, the phloem functioned with a high turgor pressure difference between the sugar sources and sinks but the turgor pressure difference was reduced if additional parallel conduits were added or solute relays were introduced. Solute relays were shown to decrease the number of parallel sieve tubes needed for phloem transport, leading to a more uniform turgor pressure and allowing faster information transmission within the phloem. Because xylem water potential affected both xylem and phloem transport, the conductance of the two systems was found to be coupled such that large structural investments in the xylem reduced the need for investment in the phloem and vice versa.     

Seasonal development of phloem in scots pine stems

The formation of phloem was studied for two years in stems of 50 to 60 year old trees of Scots pine (Pinus sylvestris L.) growing in nature. The development of phloem of the current year begins 10 to 20 days before the xylem formation and is completed with the termination of shoot growth in the end of June. Observations over the seasonal activity of cambium producing sieve cells of phloem and duration of their differentiation as compared to the xylem derivatives of cambium have shown that the maxima of formation of phloem and xylem cells could coincide or not coincide by season, while the activities of their differentiation were always in antiphase. The sieve cells of early phloem were separated from those of late phloem by a layer of tannin-containing cells, which are formed simultaneously with the formation of late xylem cells by the cambium. Seasonal dynamics of accumulation of starch grain in structural elements of the phloem is related to the xylem development. The content of metabolites in differentiating and mature phloem elements, in the cambium zone, and in the xylem cells growing in the radial direction depended on cell specificity, stage of their development, and type of forming wood, early or late, which differ in the cell wall parameters and, hence, requirement of assimilates. Significant differences were described between the content of low molecular weigh carbohydrates, amino acids, organic acids, and phenol compounds using two methods of calculation: per dry weight and per cell.     

Seasonal development of phloem in Scots pine stems

The formation of phloem was studied for two years in stems of 50 to 60 year old trees of Scots pine (Pinus sylvestris L.) growing in nature. The development of phloem of the current year begins 10 to 20 days before the xylem formation and is completed with the termination of shoot growth in the end of June. Observations over the seasonal activity of cambium producing sieve-like cells of phloem and duration of their differentiation as compared to the xylem derivatives of cambium have shown that the maxima of formation of phloem and xylem cells could coincide or not coincide by season, while the activities of their differentiation were always at antiphase. The sieve-like cells of early phloem were separated from those of late phloem by a layer of tannin-containing cells, which are formed simultaneously with the formation of late xylem cells by the cambium. Seasonal dynamics of accumulation of starch grain in structural elements of the phloem is related to the xylem development. The content of metabolites in differentiating and mature phloem elements, in the cambium zone, and in the xylem cells growing in the radial direction depended on cell specificity, stage of their development, and type of forming wood, early or late, which differ in the cell wall parameters and, hence, requirement of assimilates. Significant differences were described between the content of low molecular weigh carbohydrates, amino acids, organic acids, and phenol compounds using two methods of calculation: per dry weight and per cell.     

Patterned cell determination in a plant tissue: the secondary phloem of trees

The secondary vascular tissues (xylem and phloem) of woody plants originate from a vascular cambium and develop as radially oriented files of cells. The secondary phloem is composed of three or four cell types, which are organised into characteristic recurrent cellular sequences within the radial cell files of this tissue. There is a gradient of auxin (indole acetic acid) across both the cambium and the immediately postmitotic cells within the xylem and phloem domains, and it is believed that this morphogen, probably in concert with other morphogenic factors, is closely associated with the determination and differentiation of the different cells types in each tissue. A hypothesis is developed that, in conjunction with the positional values conferred by the graded radial distribution of morphogen, cell divisions at particular positions within the cambium are sufficient to determine not only each of the phloem cell types but also their recurrent pattern of differentiation within each radial cell file.     

Modelling reveals endogenous osmotic adaptation of storage tissue water potential as an important driver determining different stem diameter variation patterns in the mangrove species Avicennia marina and Rhizophora stylosa

Background

Stem diameter variations are mainly determined by the radial water transport between xylem and storage tissues. This radial transport results from the water potential difference between these tissues, which is influenced by both hydraulic and carbon related processes. Measurements have shown that when subjected to the same environmental conditions, the co-occurring mangrove species Avicennia marina and Rhizophora stylosa unexpectedly show a totally different pattern in daily stem diameter variation.

Methods

Using in situ measurements of stem diameter variation, stem water potential and sap flow, a mechanistic flow and storage model based on the cohesion–tension theory was applied to assess the differences in osmotic storage water potential between Avicennia marina and Rhizophora stylosa.

Key results

Both species, subjected to the same environmental conditions, showed a resembling daily pattern in simulated osmotic storage water potential. However, the osmotic storage water potential of R. stylosa started to decrease slightly after that of A. marina in the morning and increased again slightly later in the evening. This small shift in osmotic storage water potential likely underlaid the marked differences in daily stem diameter variation pattern between the two species.

Conclusions

The results show that in addition to environmental dynamics, endogenous changes in the osmotic storage water potential must be taken into account in order to accurately predict stem diameter variations, and hence growth.     

New evidence for a role of vessel-associated cells and phloem in the rapid xylem refilling of cavitated stems of Laurus nobilis L.

Xylem recovery from embolism was studied in Laurus nobilis L. stems that were induced to cavitate by combining negative xylem pressure potentials (P_X = ?1.1 MPa) with positive air pressures (P_C) applied using a pressure collar. Xylem refilling was measured by recording the percentage loss of hydraulic conductance (PLC) with respect to the maximum 2 min, 20 min and 15 h after pressure release. Sodium orthovanadate (an inhibitor of many ATP‐ases) strongly inhibited xylem refilling while fusicoccin (a stimulator of the plasma membrane H⁺‐ATPase) promoted complete embolism reversal. So, the refilling process was interpreted to result from energy‐dependent mechanisms. Stem girdling induced progressively larger inhibition to refilling the nearer to the embolized stem segment phloem was removed. The starch content of wood parenchyma was estimated as percentages of ray and vasicentric cells with high starch content with respect to the total, before and after stem embolism was induced. A closely linear positive relationship was found to exist between recovery from PLC and starch hydrolysis. This, was especially evident in vasicentric cells. A mechanism for xylem refilling based upon starch to sugar conversion and transport into embolized conduits, assisted by phloem pressure‐driven radial mass flow is proposed.     

Distribution of vessel size,vessel density and xylem conducting efficiency within a crown of silver birch (<Emphasis Type="Italic">Betula pendula</Emphasis>)

Spatial patterns in vessel diameter, vessel density and xylem conducting efficiency within a crown were examined in closed-canopy trees of silver birch (Betula pendula). The variation in anatomical and hydraulic characteristics of branches was considered from three perspectives: vertically within a crown (lower, middle and upper crown), radially along main branches (proximal, middle and distal part), and with respect to branch orders (first-, second- and third-order branches). Hydraulically weighted mean diameter of vessels (D _h) and theoretical specific conductivity of the xylem (k _t) exhibited no vertical trend within the tree crown, whereas leaf-specific conductivity of the xylem (LSC_t) decreased acropetally. Variation in LSC_t was governed by sapwood area to leaf area ratio (Huber value) rather than by changes in xylem anatomy. The acropetal increase in soil-to-leaf conductance (G _T) within the birch canopy is attributable to longer path length within the lower-crown branches and higher hydraulic resistance of the shade leaves. D _h, k _t and LSC_t decreased, while vessel density (VD) and relative area of vessel lumina (VA) increased distally along main branches. A strong negative relationship between vessel diameter and VD implies a trade-off between hydraulic efficiency and mechanical stability of xylem. D _h and VD combined explained 85.4% of the total variation of k _t in the regression model applied to the whole data set. Xylem in fast-growing branches (primary branches) had greater area of vessel lumina per unit cross-sectional area of sapwood, resulting in a positive relationship between branch radial growth rate and k _t. D _h, k _t and LSC_t decreased, whereas VD increased with increasing branch order. This pattern promotes the hydraulic dominance of primary branches over the secondary branches and their dominance over tertiary branches. In this way crown architecture contributes to preferential water flow along the main axes, potentially providing better water supply for the branch apical bud and foliage located in the outer, better-insolated part of the crown.     

Stem anatomy and development of inter- and intraxylary phloem in Leptadenia pyrotechnica (Forssk.) Decne. (Asclepiadaceae)

Modification of external morphology and internal structure of plants is a key feature of their successful survival in extreme habitats. They adapt to arid habitats not only by modifying their leaves, but also show several modifications in their conducting system. Therefore, the present study is aimed to investigate the pattern of secondary growth in Leptadenia pyrotechnica (Forssk.) Decne., (Asclepiadaceae), one such species growing in Kachchh district, an arid region of Gujarat State. A single ring of vascular cambium, responsible for radial growth, divided bidirectionally and formed the secondary xylem centripetally and the phloem centrifugally. After a short period of secondary xylem differentiation, small arcs of cambium began to form secondary phloem centripetally instead of secondary xylem. After a short duration of such secondary phloem formation, these segments of cambium resumed their normal function to produce secondary xylem internally. Thus, the phloem strands became embedded within the secondary xylem and formed interxylary phloem islands. Such a recurrent behavior of the vascular cambium resulted in the formation of several patches of interxylary phloem islands. In thick stems the earlier formed non-conducting interxylary phloem showed heavy accumulation of callose on the sieve plates followed by their crushing in response to the addition of new sieve elements. Development of intraxylary phloem is also observed from the cells situated on the pith margin. As secondary growth progresses further, small arcs of internal cambium get initiated between the protoxylem and intraxylary phloem. In the secondary xylem, some of the vessels are exceptionally thick-walled, which may be associated with dry habitats in order to protect the vessel from collapsing during the dryer part of the year. The inter- and intraxylary phloem may also be an adaptive feature to prevent the sieve elements to become non-conducting during summer when the temperature is much higher.     

Interxylary phloem: Diversity and functions

Interxylary phloem is here defined as strands or bands of phloem embedded within the secondary xylem of a stem or root of a plant that has a single vascular cambium. In this definition, interxylary phloem differs from intraxylary phloem, bicollateral bundles, pith bundles, and successive cambia. The inclusive but variously applied terms included phloem and internal phloem must be rejected. Histological aspects of interxylary phloem are reviewed and original data are presented. Topics covered include duration of interxylary phloem; relationship in abundance between sieve tubes in external phloem and interxylary phloem; distinctions between interxylary and intraxylary phloem; presence of parenchyma, fibers, and crystals in the interxylary phloem strands; development of cambia within interxylary phloem strands; three-dimensionalization and longevity of phloem, systematic distribution of interxylary phloem; physiological significance; and habital correlations. No single physiological phenomenon seems to explain all instances of interxylary phloem occurrence, but rapidity and volume of photosynthate transport seem implicated in most instances.     

Seasonal development of phloem in Siberian larch stems

The seasonal development of phloem in the stems of Siberian larch (Larix sibirica Ldb.) was studied over two seasons on 50–60-year-old trees growing in a natural stand in the Siberian forest-steppe zone. Trees at the age of 20–25 years were used to study metabolites in differentiating and mature phloem elements, cambial zone, and radially growing xylem cells in the periods of early and late wood formation. The development of the current-year phloem in the stems of 50–60-year-old trees started, depending on climatic conditions, in the second-third decades of May, 10–20 days before the xylem formation, and ended together with the shoot growth cessation in late July. Monitoring of the seasonal activity of cambium producing phloem sieve cells and the duration of their differentiation compared to the xylem derivatives in the cambium demonstrated that the top production of phloem and xylem cells could coincide or not coincide during the season, while their differentiation activity was always in antiphase. Sieve cells in the early phloem are separated from those in the late phloem by a layer of tannin-containing cells, which are formed in the period when late xylem formation starts. The starch content in the structural elements of phloem depends on the state of annual xylem layer development. The content of low molecular weight carbohydrates, amino acids, organic acids, and phenols in phloem cells, cambial zone, and xylem derivatives of the cambium depends on the cell type and developmental stage as well as on the type of forming wood (early or late) differing by the cell wall parameters and, hence, by the requirement for assimilates. Significant differences in the dynamics of substances per dry weight and cell were observed during cell development.     

A closed‐form solution for steady‐state coupled phloem/xylem flow using the Lambert‐W function

A closed‐form solution for steady‐state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert‐W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time‐dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed‐form solution, and is expected to be useful as a component part of larger numerical models of entire plants.     

Water status of Hinoki cypress (<Emphasis Type="Italic">Chamaecyparis obtusa</Emphasis>) under reduced hydraulic conductance estimated from diurnal changes in trunk diameter

To estimate the water status of Hinoki cypress (Chamaecyparis obtusa) under reduced hydraulic conductance, we measured diurnal changes in the trunk diameter of two 20-year-old trees during a hot dry summer. One tree showed a greatly reduced water-transport area in its trunk cross-section and leaf specific hydraulic conductivity. Diurnal changes in trunk diameter were measured at the xylem surface using a strain-gauge method. At the start of the experiment, the diurnal changes in trunk diameter were similar in both trees with shrinking during the day and swelling at night. However, in the trunk of the tree with reduced hydraulic conductance, the maxima and minima decreased rapidly as days passed. These differences in trunk diameter changes might be caused by the differences in the leaf-specific hydraulic conductance.     

Dynamic studies of phloem and xylein flow in fully differentiated plants by fast nuclear-magnetic-resonance microimaging

A fast nuclear-magnetic-resonance imaging method was developed in order to measure simultaneously and quantitatively the water flow velocities in the xylem and the phloem of intact and transpiring plants. Due to technical improvements a temporal resolution of 7 min could be reached and flow measurements could be performed over a time course of 12-30 h. The novel method was applied to the hypocotyl of 35- to 40-day-old, leafy plants of Ricinus communis which were subjected to different light-dark regimes. The results showed that the xylem flow velocities and the xylem volume flow responded immediately to light on-off changes. Upon illumination the flow velocity and the volume flow increased as expected in respect to literature. In contrast, the phloem flow velocity did not change in response to the light-dark regimes. Interestingly, though, the volume flow in the phloem increased during darkness. These findings can be explained by assuming that the conducting area of the phloem becomes enlarged during the dark period due to opening of sieve pores.