1 INTRODUCTION

During drought stress, the pressure of xylem sap can become negative enough to allow a local phase change from liquid to water vapour (Tyree & Zimmermann, 2002). If this phase change takes place, the water vapour, which becomes gradually mixed with gas, fills the entire water-conducting conduit and blocks the water transport by a process known as embolism (Hölttä et al., 2002; Wang et al., 2015b). There is growing evidence that embolism formation can be induced in sap-filled conduits that are directly connected to an embolised vessel via a joint interconduit wall (Brodersen & McElrone, 2013; Choat et al., 2016; Guan et al., 2021; Knipfer et al., 2015; Skelton et al., 2017). Although embolism formation in xylem conduits has been given considerable research attention, we lack a mechanistic understanding of how exactly embolism is formed, and how it propagates between vessels (Jansen & Schenk, 2015; Lens et al., 2022; Levionnois et al., 2020; Lintunen et al., 2022). It is known that bordered pits in interconduit walls play a major role in transport of liquids and gasses across conduits (Kaack et al., 2019, 2021; Park et al., 2019; Zhang et al., 2020), but there is a knowledge gap in predicting embolism resistance based on pit membrane characteristics and relevant physical parameters.

The mechanism behind embolism formation has traditionally been described as ‘air-seeding’, and the Young–Laplace equation has been used to predict the pressure difference that a gas bubble would require to penetrate a pore in a pit membrane by mass flow and then induce embolism (Tyree & Zimmermann, 2002). However, applying the Young–Laplace equation presents practical challenges when dealing with the complex gas-liquid interfaces and dynamic surface tension inside a three-dimensional pit membrane, which shows multiple pore constrictions in each pore pathway (Kaack et al., 2021; Yang et al., 2020). Embolism formation seems to be largely a pressure-driven process, with more negative pressure of xylem sap increasing the likelihood of embolism (Jansen & Schenk, 2015; Lens et al., 2022; Levionnois et al., 2020; Lintunen et al., 2022). However, there is evidence suggesting that embolism formation may not only be pressure-driven but also depends on the proximity to a gas source and local changes in gas pressure and gas concentration (Avila et al., 2022a; Choat et al., 2010; Guan et al., 2021; Torres-Ruiz et al., 2015).

The level of xylem embolism can be indirectly quantified by measuring the reduction of the hydraulic conductivity (K_h) when a xylem sample is submitted to a decreasing xylem water potential (Sperry, 1985). Although centrifuge methods have been employed to construct vulnerability curves in many studies (Cochard et al., 2013), it remains unclear how exactly embolism inside a centrifuge sample is generated, how vessel dimensions may affect embolism formation, and where embolism in stem segments is formed (Cai & Hacke, Zhang, et al., 2010). Different interpretations have been given to data obtained from centrifuge experiments with samples that have cut-open vessels longer than the actual sample, and to vulnerability curves generated with a flow-centrifuge and static-centrifuge (Choat et al., 2010; Jacobsen & Pratt, 2012; Lamarque et al., 2018; Sperry et al., 2012; Yin et al., 2019). Although Alder et al. (1997) did not find an effect on the loss of conductivity when varying the spin time from 3 to 60 min in a static-centrifuge, this issue requires more in-depth experiments.

Any hydraulic measurement is affected by temperature as it has an impact on conductance, modifying considerably the liquid viscosity, and also the cell membrane fluidity and permeability for symplastic transport (Burlett et al., 2022a; Cochard et al., 2000; Wang et al., 2014). Moreover, temperature has an influence on the gas solubility, and thus on the concentration of dissolved gas in xylem sap (Weiss, 1970). A potential link between the amount of gas dissolved in xylem sap and embolism formation has been suggested (Guan et al., 2021), but remains largely untested. If changes in the concentration of dissolved and undissolved gas are associated with embolism formation, embolism propagation may be dynamic because gas diffusion in xylem can be relatively slow, from seconds to many hours (Sorz & Hietz, 2006; Yang et al., 2023). Thus, based on this assumption, it would be reasonable to expect that both time and temperature affect embolism formation in flow-centrifuge experiments. Interestingly, Wang et al. (2014) reported the challenge of predicting K_h using linear regression at the end of a vulnerability curve, suggesting that ‘new embolism may have been occurring during the process’ (i.e., during the spin time in a flow-centrifuge at a fixed speed). Also, K_h measurements over long time periods (hours) have been reported to show a constantly decreasing trend, which has been explained by clogging or coating of intervessel pit membranes, wounding response, or another unknown phenomenon (De Baerdemaeker et al., 2019; Espino & Schenk, 2011). Therefore, it is important to test if any decline in K_h over time is caused by embolism propagation, related to a change in temperature, and/or caused by any other unknown aspect.

Moreover, there is rather contradictory information in literature about the distribution of embolised vessels along the axis of centrifuged samples (Table S1). While some studies have shown that the highest level of embolism occurs in the centre (Cai et al., 2010; Sperry et al., 2012; Tobin et al., 2013), others have reported that embolism occurred mainly near the sample ends (Cochard et al., 2010; Martin-StPaul et al., 2014; Yin et al., 2019). Theoretically, the most negative pressure occurs at the centre of the rotor, with the pressure increasing along the axis towards the outer sides of the sample (Alder et al., 1997; Cai & Tyree, 2010; Cai et al., 2010). Therefore, the amount of embolism formed in the stem should be proportional to the pressure that is applied to the centre (Cochard et al., 2010; Yin et al., 2019). Other researchers observed that the highest embolism levels occur at the water injection side of samples in a flow-centrifuge (López et al., 2018; Martin-StPaul et al., 2014; Yin et al., 2019). It has been suggested that tiny bubbles could enter cut-open conduits at stem ends, causing local embolism and therefore a gradient in loss of conductivity along a sample, with the greatest loss of conductivity at the basal and upstream part of centrifuge samples (Yin et al., 2019). There is also evidence suggesting that vessel dimensions play a role in embolism formation in a flow-centrifuge, with artificial embolism formation in conduits that are completely cut-open at stem ends (Lamarque et al., 2018). Although we do not fully understand the relationship between vessel dimensions and vulnerability to embolism in plants (Lens et al., 2022), vessel dimensions play a role in the movement of gas between vessels (Avila et al., 2022b; Salomón et al., 2021; Yang et al., 2023). It has been suggested that plant species with small vessel volumes may experience faster embolism spread compared to those with larger vessel volumes (Pereira et al., 2023). Therefore, vessel dimensions may affect embolism location in a sample used for flow-centrifuge experiments.

This study aims to elucidate fundamental mechanisms behind embolism propagation. In particular, we hypothesise that if gas movement between conduits is relatively slow and related to embolism formation and propagation, there would be a considerable time effect on K_h measurements for a constant centrifugal speed and temperature. This time effect may also affect temporal changes in embolism location in flow-centrifuge experiments. By modelling how time, temperature and vessel dimensions affect gas movement and gas solubility, we expect that there is a correlation between the gas concentration in a recently embolised water vapour-filled vessel and the loss of K_h of xylem. Finally, we speculate that vessel dimensions affect the speed of gas movement in stem xylem, and therefore the rate and location of embolism in samples that are subject to spinning in a flow-centrifuge.

2 MATERIAL AND METHODS

3 RESULTS

3.2 Experiment 2: The effect of water potential, time and temperature on xylem embolism propagation

At 22°C, K_h and ΔK_h values were largely pressure-driven, but changed logarithmically over time, increasing when Ψ was close to zero, but decreasing for low values of Ψ (Figures 1 and S2). The effect of time was visually most pronounced when plotting the relative values of ΔK_h against time (Figure 1). For water potentials between −0.4 and −0.9 MPa, ΔK_h increased over time for all three study species. For C. avellana and F. sylvatica, ΔK_h was stable, and around zero when Ψ was between −1.1 and −2.1 MPa, respectively. There were no stable ΔK_h values for P. avium within the 1 h of spinning. Values of Ψ that were lower than −1.4, −2.2, and −3.0 MPa, resulted in an overall decrease of ΔK_h for C. avellana, F. sylvatica, and P. avium, respectively.

After 1 h of spinning, ΔK_h decreased by a maximum of 40.6%, 42.3%, and 61.5%, or increased by a maximum of 10.0%, 5.8%, and 40.4% for C. avellana, F. sylvatica and P. avium, respectively. The magnitude of ΔK_h was variable, depending on the species and the Ψ applied. Overall, the more negative Ψ induced in the flow-centrifuge, the higher the values of ΔK_h, and the lower the absolute values of K_h at time zero.

Our results also showed a temperature effect on ΔK_h, mainly at 5°C (Figure 2). At this temperature and for Ψ values close to zero, we did not observe the same increasing pattern of ΔK_h as seen at 22°C. ΔK_h at 5°C tended to increase during the first 5 min, similar to the pattern at 22°C, but then decreased, and became negative after 15 min of spin time (except for one sample of P. avium), reaching values of −23, −24, and −8%, for C. avellana, F. sylvatica, and P. avium, respectively. Moreover, ΔK_h at 5°C presented a pattern similar to that observed at 22°C for more negative Ψ values. When centrifuging samples at 35°C, ΔK_h showed fairly similar temporal patterns to the ones observed at 22°C. Samples of P. avium reached +78.5 and −67.4% as the most positive and negative values of ΔK_h, respectively.

The asymptotic exponential fitting function demonstrated a significant estimation of K_h values (p-value < 0.05) when we considered the two most negative Ψ values applied (Figure S3). The fitting function's efficacy was evident through low RMSE values and R values close to 1, indicating its ability to estimate K_h values with minimal error. The standardised residuals of the fitting, when plotted against the predicted values, ranged between −2 and 2, and exhibited a random distribution in most cases (Figure S4). In some cases, notably in P. avium, the residuals were wavelike, resembling sinusoidal functions. Therefore, we could estimate the minimum value of hydraulic conductivity (K_min), and consequently the relative hydraulic conductivity (K_relative) with high precision for most of the treatments.

3.3 Experiment 3: Location of embolised vessels in centrifuged stem segments

The Percentage Loss of Conductivity (PLC) changed over time, and was not homogeneously distributed along the 27.4 cm stem sample when cuvettes were used (Figure 3). The PLC distribution demonstrated symmetry with respect to the centre of the sample, and was in line with the theoretical pressure profile induced by centrifugation. Across the species studied, PLC values were significantly higher in segments at the centre of the centrifuge sample (p-value < 0.001) than in segments near the stem ends. Moreover, the PLC in segments at the centre of the centrifuge sample increased with a long spin time (p-value < 0.05). This trend was most evident for C. avellana, with PLC increasing from 7.8% after 1 min of spin time, to 53% after 7.5 min of spinning. Interestingly, C. avellana showed 27.2% of PLC at both stem ends after 1 min of spin time. These PLC values gradually decreased over time, while the amount of embolism near the centre of the centrifuge sample increased.

A comparison between stem samples spun for 1 min with and without cuvettes revealed significant differences in the location of embolism (Figure 4). PLC levels were higher at the stem edges in samples of F. sylvatica and P. avium that were spun without cuvettes than those spun with cuvettes (p-value < 0.05). The stem edges of C. avellana, however, did not exhibit a difference between samples spun with or without cuvettes. Samples of all species spun without cuvettes displayed a homogeneous PLC distribution along the centrifuge sample, with no statistical differences between stem segments at the ends and the centre (p-value > 0.05).

3.4 Modelling the gas pressure in a recently embolised vessel in flow-centrifuge experiments

Once embolism had occurred near the centre of a centrifuge sample, the model predicted fast axial movement of gas along the 27.4 cm stem sample during the first minutes, but considerably slower gas diffusion rates after 1 h (Figure 5). One hour after embolism formation, the relative gas concentration in a recently embolised vessel (C_relative) reached values between 83.8% and 87.7%, 63.1% and 69.7%, and 79.6% and 84.5% for C. avellana, F. sylvatica and P. avium, respectively.

The axial gas diffusion rate was strongly affected by the temperature and the anatomical traits of the species (Figure S5), but minimally affected by Ψ (Figure 5). The higher the temperature, the smaller the changes in C_relative over time for all three species (Figure S5). Unlike temperature and xylem anatomy, Ψ changed C_relative by less than 1%. We noticed a slight difference between C. avellana and P. avium, but a larger difference between these two species and F. sylvatica. (Figure S6). For F. sylvatica, the axial gas diffusion was on average 20% slower than for C. avellana and P. avium.

We observed a strong and positive correlation between K_relative and C_relative (Figure 6). These correlations were significant (p < 0.05) for all conditions of temperature and Ψ, with RMSE and R values close to 1. The performance of the model was most accurate for P. avium at 35°C and a Ψ of −4.45 MPa, with an error up to 5.2% (Table S8). Nevertheless, the fitting function could not accurately estimate the loss of K_h in some cases, either underestimating or overestimating K_h, depending on the conditions. The decrease in K_h over time for C. avellana at 5° and 22°C was slower than the increase in C_relative. On the other hand, F. sylvatica at 22°C and 35°C showed underestimation of C_relative, with K_h decreasing faster than the increasing C_relative. For C. avellana at 35°C, F. sylvatica at 5°C, and P. avium at 5, 22, and 35°C, the correlation curves were close to the 1:1 line (Figure 6), showing that the increase in C_relative was strongly correlated to the decrease in K_relative.

4 DISCUSSION

Our results revealed that hydraulic conductivity (K_h) measurements in a flow-centrifuge are not stable at a fixed pressure and temperature over a spinning duration of 1 h. Since relative changes in hydraulic conductivity (ΔK_h) did not change randomly around zero over time, the variation observed cannot be considered as noise (Figures 1 and 2). As expected, experiment 2 (the effect of water potential, time and temperature on K_h) showed that pressure is highly important in determining the overall magnitude of K_h, with absolute K_h values taken at high water potentials being much higher than those measured at low water potentials (Figure S2). However, depending on the temperature, the xylem anatomy of the plant species studied, and the pressure applied, changes in K_h showed a particular behaviour over time. Therefore, assuming that decreases in K_h are related to increasing levels of embolism, we argue that embolism spread may represent a relatively slow process, and is not only pressure-driven. The main reason why we consider ΔK_h is that we aim to shed light on the relative changes in K_h over time to explore the driving mechanisms behind embolism spread. These ΔK_h values also enable us to compare the effects of the different treatments applied, and differences in xylem anatomy between species. As such, methodological issues related to vulnerability curves and how we quantify embolism resistance go beyond the purpose of this study, and are published separately (Silva et al., 2024).

Our findings presented strong evidence for a mechanistic relationship between K_h and embolism formation. While an increase in PLC over time at the centre of centrifuge samples (Figure 3) can explain the decrease in K_h in flow centrifuge measurements (Figures 1 and 2), experiment 1 (the effect of flow on K_h) showed that temporal variation in K_h cannot be driven only by a non-embolism related decline in K_h over time. We observed a small, but long-term decline in conductivity when there was a constant flow through a stem sample (Figure S1), which can be attributed to various processes (Sperry et al., 1988; Yin et al., 2019). Potential explanations include pit membrane clogging, wound response, a potential difference between the inlet and outlet flow, radial or background flow, or compression of intervessel pit membranes (De Baerdemaeker et al., 2019; Espino & Schenk, 2011). However, K_h changed minimally over time (−0.7%) when we only injected solution during measurements within the first hour of spinning. This 'natural' decline in K_h cannot explain the much higher changes in K_h observed in experiment 2, and is certainly not in line with our observations of increases in ΔK_h. Moreover, if nanobubbles included in the injected water of the centrifuge were to cause embolism, as suggested by Yin et al. (2019), we would only observe a decrease in K_h and higher levels of embolism at the injection side. However, this was not the case, even if the spin time was relatively long. As reviewed by Ingram et al. (2023), nanobubbles typically range from 100 to 200 nm in size, exceeding the dimensions needed to traverse the 5–50 nm pores in mesoporous pit membranes (Choat et al., 2003, 2004; Zhang et al., 2020). Consequently, nanobubbles exhibit limited propensity to migrate across segments when pit membranes are present. In fact, our experiment 3 (embolism location) demonstrated that the distribution of embolism displayed a nearly symmetrical distribution around the stem centre when cuvettes were used.

Since embolism removal is generally not considered to occur in a sample that is exposed to a negative pressure (Lamarque et al., 2018; Tyree & Sperry, 1988), the observed increase in K_h over time has been rarely reported in literature. Sperry et al. (1988) described this increase as a rearrangement and/or dissolution of embolism within xylem conduits, which mainly occurs under subatmospheric pressure (6 KPa). Thus, this rearrangement and/or dissolution of embolism can explain the increase in K_h when we applied a water potential close to zero or slightly negative pressures. Apart from rearrangement, the replacement of xylem sap with the flow-centrifuge solution may also modify the water flow through interconduit pit membranes and thus increase K_h, a phenomenon also known as the ‘ionic effect’ (Jansen et al., 2011). Interestingly, samples centrifuged at 5°C presented a much weaker increase in ΔK_h (Figure 2), suggesting that the temperature may also play an important role in the rearrangement and/or dissolution of embolism and eventually in embolism spreading. One explanation for this finding can be provided by Briggs (1950), who described that water under negative pressure loses much of its ability to support negative pressure between 0°C and 5°C, which may lead to an increase in embolism events. While the likelihood of homogeneous and heterogeneous cavitation is known to increase with increasing temperature (Caupin & Herbert, 2006; Herbert et al., 2006), embolism in xylem conduits is not known to be caused by cavitation (Hölttä et al., 2002). Overall, little is known about how temperature may affect xylem embolism resistance (Cochard et al., 2007; Lodge et al., 2018). Temperature may also affect gas solubility and oversaturation of xylem sap, or could affect the dynamic surface tension at gas-liquid interfaces (Schenk et al., 2016; Yang et al., 2020).

Experiment 3 shows that there are at least two different locations in centrifuge samples where embolism is formed, namely near the stem edges and in the centre. Over time, the amount of embolism near stem edges decreased, but increased near the centre. We speculate that the initial embolism levels near stem edges are caused by the axial proximity of the cut-open conduits to atmospheric gas, either dissolved gas in the liquid in the cuvettes, or gas outside the cuvettes. The comparison of spinning samples with and without cuvettes supports this speculation. This comparison, which is similar to comparing the static with the flow-centrifuge, demonstrated that embolism formation is faster and more pronounced near both stem ends when no cuvette is used. In the absence of cuvettes, cut-open vessels at the stem ends were exposed directly to atmospheric pressure, which quickly led these to be filled with gas at atmospheric pressure. However, the constant decrease in K_h over time observed in experiment 2 is likely associated with embolism spreading in the stem centre, as the most negative pressure in this area clearly increases the likelihood of new embolism events. Gas solubility increases slightly with decreasing negative liquid pressure (Lidon et al., 2018; Mercury et al., 2003), but the effect of temperature has a higher influence on gas solubility than pressure (Schenk et al., 2016). Our results also revealed that the speed of embolism formation and the location of embolism may vary according to the species studied. Therefore, we suggest that the disagreement between earlier studies on the location of embolised vessels in centrifuged stems is likely due to different species used in each study, as well as to the spin time, which proved to be essential in our observations, but was not reported or considered in earlier work (Cai & Hacke, Zhang, et al., 2010; Cochard et al., 2010; Martin-StPaul et al., 2014; Sperry et al., 2012; Tobin et al., 2013; Yin et al., 2019).

The observed difference in the speed of embolism propagation between species in our experiments may be related to the ability of the species to resist embolism formation, and is likely associated with the vessel anatomy, including vessel diameter, vessel length, and intervessel connectivity. However, more experiments with a larger number of species would be needed to test this hypothesis (Isasa et al., 2023; Lens et al., 2011, 2022). Interestingly, the vessel anatomy also affected our model of gas pressure in a recently embolised vessel in the centre of a centrifuge sample. While a higher value of the total intervessel pit membrane area (A_p) increases the axial gas transport rate in xylem sap (k_a), and the gas transport rate across the pit membranes (k_p), a larger vessel volume (V_v) also requires much more gas, and probably more time to achieve atmospheric pressure. Wide and long vessels can therefore be suggested to provide a longer, temporary 'buffer' against further embolism spread than narrow and short ones. If the gas concentration in a recently embolised vessel (C_relative) is related to the rate of embolism formation and propagation, it seems reasonable to expect that V_v and A_p could play a role in xylem embolism resistance. Notably, Pereira et al. (2023) unveiled a convex safety-efficiency trade-off, in which plants could display adaptability in modifying pit membrane thickness (T_PM) and A_p. Even minor alterations of these two parameters could have an exponential impact on the pressure difference and flow across bordered pit pairs.

Here, we modelled the transition of a water-vapoured filled conduit to a conduit filled with gas at atmospheric pressure, which was shown to correlate significantly with ΔK_h (Figure 6). This significant correlation provides evidence that the increase in C_relative and the decline of ΔK_h have the same time scale and order of magnitude, suggesting that a functional link between both processes is likely. Two different steps in the process of embolism spread may explain this functional link. Firstly, a recently embolised vessel that is water vapour filled provides likely a buffer for further embolism propagation because the low vapour pressure (ca. 3.2 kPa) will extract gas molecules from surrounding vessels, until it eventually reaches atmospheric pressure (Figure 7; Wang et al., 2015b). If a high gas concentration is necessary for embolism initiation, the temporal and local extraction of gas from surrounding, sap-filled vessels can be suggested to reduce the risk of new embolism events. Secondly, when sufficient gas has been accumulated in an embolised conduit, this gas reservoir becomes a gas source that may increase the likelihood to have embolism formation in a neighbouring, interconnected conduit (Guan et al., 2021). Thus, we assume that the amount of gas in a recently embolised conduit determines the likelihood of embolism spread in a neighbouring conduit, for instance through snap-off events and nanobubble formation (Schenk et al., 2015, 2017). Finally, this new conduit will again extract gas from neighbouring conduits, slowing down embolism spread temporarily.

The lack of a strong agreement between measured and modelled data in some samples may originate from limitations inherent to the flow-centrifuge method, as well as simplifications and assumptions made in our gas diffusion model, which focuses solely on the build-up of pressure within a single conduit due to gas diffusion, without considering the potential for artificially generating embolism events in neighbouring conduits. Correlating modelled data on gas concentration within a single, embolised conduit with experimental data on flow conductivity involves comparing two fundamentally different quantities, and this discrepancy underlines the shortcomings in the model's representation of the actual physical processes under study. Moreover, our non-propagating embolism model primarily considered passive axial diffusion as the sole mechanism for gas transport, which might have led to a slight underestimation of the rate of gas diffusion. In reality, the presence of flow, which we estimate to occur for a total of approximately 7.7 min within a 1-h spinning experiment, and radial gas diffusion may introduce additional exogenous gas into the xylem, thereby increasing the rate of gas diffusion to a recently embolised conduit. Also, models have typically considered vessels as cylindrical structures, which are connected to each other at their ends and have a homogeneous diameter (Pereira et al., 2022, 2023; Yang et al., 2023), and thus overestimated the average distance that water and gas molecules travel within a single conduit (Bouda et al., 2019). Further refinement of the model would thus be useful in future research. Moreover, minor changes in K_h due to pit membrane deformation, clogging by impurities, polar lipids, or nanobubbles, or variation in K_h under different pressures (Krieger et al., 2022), may not always reflect changes in the amount of embolism. These uncertainties may propagate a certain, minor degree of error, and may weaken our analyses, correlations, and interpretations. Nevertheless, fitting the data measured in models proved to be an appropriate strategy, and showed that the modelled data were not randomly generated, but likely reflect physical phenomena. Hence, experiments with flow-centrifuges provide a valid approach to investigate the driving mechanisms behind embolism, even if flow-centrifuge experiments do not entirely mimic functional, intact xylem operating in plants under natural field conditions, especially when it comes to time-based changes in gas pressure and concentration.

In conclusion, the modelled data suggest that embolism propagation may be affected by gas diffusion, which is driven by local differences in gas concentration. Our findings raise questions about the traditional assumption that embolism is exclusively pressure-driven, as suggested for instance by the x-axis of vulnerability curves (Silva et al., 2024). Embolism propagation proved to be dynamic, influenced by an interplay of pressure and temperature, and is likely related to key vessel traits. Our experiments showed that not only the amount of embolism may slightly change over time in a flow-centrifuge, but also its location within the sample. These findings significantly enhance our understanding of how hydraulic failure by embolism formation spreads within xylem.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.