Non-Destructive Estimation of Root Pressure Using Sap Flow, Stem

Annals of Botany 111: 271–282, 2013 doi:10.1093/aob/mcs249, available online at www.aob.oxfordjournals.org

Non-destructive estimation of root pressure using sap ﬂow, stem diameter measurements and mechanistic modelling

Tom De Swaef*, Jochen Hanssens, Annelies Cornelis and Kathy Steppe Faculty of Bioscience Engineering, Department of Applied Ecology and Environmental Biology, Laboratory of Plant Ecology, Ghent University, Coupure links 653, B-9000 Ghent, Belgium * For correspondence. E-mail [email protected]

Received: 20 August 2012 Returned for revision: 24 September 2012 Accepted: 8 October 2012 Published electronically: 4 December 2012

† Background Upward water movement in plants via the xylem is generally attributed to the cohesion–tension theory, as a response to transpiration. Under certain environmental conditions, root pressure can also contribute Downloaded from to upward xylem water flow. Although the occurrence of root pressure is widely recognized, ambiguity exists about the exact mechanism behind root pressure, the main influencing factors and the consequences of root pressure. In horticultural crops, such as tomato (Solanum lycopersicum), root pressure is thought to cause cells to burst, and to have an important impact on the marketable yield. Despite the challenges of root pressure research, progress in this area is limited, probably because of difficulties with direct measurement of root pressure, prompt- ing the need for indirect and non-destructive measurement techniques. http://aob.oxfordjournals.org/ † Methods A new approach to allow non-destructive and non-invasive estimation of root pressure is presented, using continuous measurements of sap flow and stem diameter variation in tomato combined with a mechanistic flow and storage model, based on cohesion–tension principles. † Key Results Transpiration-driven sap flow rates are typically inversely related to stem diameter changes; however, this inverse relationship was no longer valid under conditions of low transpiration. This decoupling between sap flow rates and stem diameter variations was mathematically related to root pressure. † Conclusions Root pressure can be estimated in a non-destructive, repeatable manner, using only external plant sensors and a mechanistic model. at University of Ghent on January 25, 2013 Key words: Root pressure, stem diameter, diameter change, tomato, sap flow, Solanum lycopersicum, mechanistic model, cohesion–tension, water relations.

INTRODUCTION near the tracheary elements and allows root pressure to build up under conditions of low transpiration (Steudle and The process of water uptake and transpiration is generally Peterson, 1998). Under these conditions, water flow is coupled explained by the cohesion–tension (C–T) theory (Dixon and to solute flow, whereas interactions between solute and water Joly, 1894; Meinzer et al., 2001). According to this theory, the flows are of minor importance in a transpiring plant because ascent of water is a passive process ultimately driven by the the hydrostatic gradient will usually be the dominating force evaporation of water from leaves, which creates a water potential (Pickard, 2003). difference between the soil and the dry air (Steudle, 2001). Although this theory is still widely accepted, it has evoked some controversy (Meinzer et al., 2001; Angeles et al., 2004; Phenomena attributed to root pressure in horticulture Zimmermann et al., 2004) because of the meta-stable state of The best known phenomenon attributed to root pressure is xylem water and the measuring methodologies of water poten- guttation: due to a positive pressure in the xylem, as a result tial. Canny (1995), for instance, proposed a mechanism of of root pressure, excess water is pushed out of the leaf ends tissue pressure supporting the water column, in addition to via hydathodes (Kramer and Boyer, 1995). If plants are C–T. Many others have reported the phenomenon of root pres- unable to dispose of this excess water, cells might leak or sure as a feature in water transport, in addition to C–T (e.g. burst. Several physiological disorders are attributed to exces- Klepper and Kaufmann, 1966; Pickard 1981; Sperry et al., sive root pressure such as watery fruits in tomato (Dorais 1987; Tyree et al., 1987; Clearwater et al., 2007). In the et al., 2001) and glassiness in lettuce (Maaswinkel and absence of transpiration as the driving force of water flow Welles, 1986). In addition, bursting of cells allows pathogens across the soil–plant–atmosphere continuum (SPAC), root such as Botrytis and Mycosphaerella to infect the damaged pressure could serve as the auxiliary engine for water supply tissue and spread around in the plant. Many studies have to shoots under conditions of low transpiration (Steudle, demonstrated that the water relations in tomato (Solanum lyco- 2001). At present, it is widely believed that root pressure persicum L.) have crucial implications for fruit production and arises from active loading of solutes into the xylem and subse- fruit quality (e.g. Mitchell et al., 1991; Johnson et al., 1992; quent osmotic uptake of water (Kramer and Boyer, 1995). Dorais et al., 2001; De Swaef et al., 2012), but few deal More specifically, the endodermis retains solutes in a zone with the effects of root pressure. However, current efforts to # The Author 2012. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved. For Permissions, please email: [email protected] 272 De Swaef et al. — Stem diameter variations and root pressure reduce energy use in horticulture have led to modified glass- Continuous measurements house climate conditions (i.e. more humid) that might Heat balance sensors (Model SGA13-WS, Dynamax Inc., promote the occurrence of excess root pressure (Heuvelink Houston, TX, USA; accuracy approx. 10 %) were used to et al., 2008). measure sap flow (F ) below the lowest leaf on three Beside the above-mentioned disorders, root pressure is H2O plants and were installed according to the operation manual expected to play a beneficial role in the distribution of (van Bavel and van Bavel, 1990). At the start of this experi- calcium to the leaves of cabbage and lettuce (Palzkill and ment, all plants were approx. 8 m long and the sensors were Tibbitts, 1977), root-to-shoot water transport in trees during installed at about 0.5 m from the roots. spring (e.g. Sperry et al., 1987; Clearwater et al., 2007) and The sensors were thermally insulated by wrapping them in in refilling embolized xylem vessels (e.g. Tyree et al., 1987; several layers of aluminium and bubble foil. Stem diameter Zwieniecki and Holbrook, 2009). Moreover, Clearwater (D) variations were measured just below the sap flow sensors et al. (2007) recently uncovered a relationship between the using linear variable displacement transducers (LVDTs; rootstock ability to build up root pressure and the scion model 2.5 DF, Solartron Metrology, Bognor Regis, UK; accur- vigour for kiwi. acy approx. 1 mm). The LVDT sensors were attached to the The above-mentioned physiological effects attributed to root stem by custom-made stainless steel holders. Tests with a pressure indicate the need to investigate this intriguing phe- Downloaded from 12 mm aluminium rod showed that no temperature correction nomenon further. Currently, a ‘bottle-neck’ in root pressure re- was required (Steppe and Lemeur, 2004). Absolute stem diam- search is the lack of a system that allows continuous and eter was measured once before the start of the experiment non-destructive measurements, especially for herbaceous using an electronic calliper. plants. Clearwater et al. (2007) measured root pressure using Relative humidity (RH) of the air was measured with an pressure transducers that were installed inside the xylem of aspirated capacitive sensor (HMP50, Vaisala, Helsinki, http://aob.oxfordjournals.org/ kiwi roots. To our knowledge, this is the only existing non- Finland). Air temperature (T) was measured using a copper– destructive continuous method to measure root pressure. constantan thermocouple (Type T, Omega, Amstelveen, The However, the application of this method on herbaceous Netherlands). Both sensors were installed at 1.5 m height plants with limited root and stem diameters such as tomato and were shielded from direct radiation. Vapour pressure may be difficult, if not impossible, because this method deficit (VPD) was calculated from RH and T according to requires installation of the system 10–15 mm inside the Jones (1992). xylem. Other methods are mainly destructive, such as install- Data from all sensors were logged (CR1000, Campbell ing manometers on excised stems (Grossenbacher, 1938)or Scientific Inc., Logan, UT, USA) at 30 s intervals and averaged root pressure probes in excised roots (Steudle et al., 1993). at University of Ghent on January 25, 2013 every 5 min. To allow non-destructive and non-invasive estimation of root pressure, we present a new approach using continuous measurements of sap flow and stem diameter variations in Plant material and experimental set-up for validation of the tomato combined with a mechanistic flow and storage technique (expt 2) model, based on C–T principles. Estimated values of root pressure, under conditions of low transpiration rates, were Tomato plants (S. lycopersicum L. ‘Admiro’) were grown in compared with destructive measurements using a manometer a greenhouse compartment measuring 2 × 2.5 × 4 m at the installed on an excised stem. faculty of Bioscience Engineering, Ghent, Belgium (51803’N, 3843’E). Plants were sown on 4 September 2011 and transplanted on rockwool substrate (Master, Grodan, Hedehusene, Denmark) on 21 November 2011. To generate high night-time RH, an air humidifier (type MATERIALS AND METHODS Boneco 7135, Plaston, Widnau, Switzerland) was switched on between 1600 and 0900 h. The above-mentioned sap flow Plant material and experimental set-up for the development and LVDT sensors were installed on one plant. For three meas- of the technique (expt 1) urement periods (31 January–3 February 2012; 14–16 Tomato plants (Solanum lycopersicum ‘Admiro’) were grown February 2012; 21–25 February 2012), root pressure was con- in a greenhouse compartment measuring 16 × 12 × 5m at tinuously recorded using a manometer (type 401002, Jumo the Research Centre Hoogstraten, Belgium (51827′N, Midas C08, Fulda, Germany) installed on two excised stems 4847’E). Plants were sown on 5 November 2009, grafted on on 30 January, 13 February and 20 February 2012, respective- the rootstock Emperador and planted on rockwool substrate ly. As such, carbon starvation was not expected to affect root (Master, Grodan, Hedehusene, Denmark) on 5 January 2010. pressure in these experiments (Grossenbacher, 1938). Plants were provided with a nutrient solution of approx. 2.6 dS m21 (i.e. osmotic potential of approx. –0.08 MPa) using Modelling, simulations, calibrations a drip irrigation system, based on sums of solar radiation, to attain a daily drainage of approx. 30–50 %. Leaves under In this study, the principles of a mechanistic flow and the lowest ripe truss were removed and the lowest part of the storage model, originally developed for trees (Steppe et al., stem was horizontal, as is common practice in tomato. Three 2006), were used. These equations allow simulation of D, plants were continuously monitored during six consecutive stem water potential in the xylem (Cx), and total (Cs), days, starting on 17 September 2010. osmotic (Cp,s) and hydrostatic potential in the surrounding De Swaef et al. — Stem diameter variations and root pressure 273

storage tissues (Cp,s). The model uses FH2O as an input vari- estimation of the initial Cp,s: able, which is directly linked to Cx via the ﬂow resistance concept (van den Honert, 1948): < TC()0 C ()=−0 (8) p,s MM = − ( ) sucrose Cx Cm FH2ORx 1 where C(0) is the initial sugar concentration in the storage 21 where Cm isthewater potential in the growing medium (MPa) and tissue (g g ). Rx is the hydraulic resistance between the growing medium A summary of the model equations, used in the present and the point of interest in the plant stem (MPa h g21). The study, is presented in Fig. 1A. model simulates variations in water content of the storage tissue Model development, simulations, calibrations and identiﬁa- (Ws) as a result of the water potential gradient driving radial bility analyses were conducted with PhytoSim (Phyto-IT water transport between the xylem and the storage tissue: BVBA, Mariakerke, Belgium), a software developed for plant modelling and simulation. For model calibration, the dW C − C s = x s (2) simplex method, originally developed by Nelder and Mead dt r (1965) and available in PhytoSim, was used to minimize the

weighted sum of squared errors for the variable D. Downloaded from where r is the hydraulic resistance between xylem and storage Identifiability analysis was done as described by De Pauw 21 (MPa h g ). et al. (2008). The relationship between Ws and D is defined by: D2 − a2 p L r Methodology 1 H2O W = (3) http://aob.oxfordjournals.org/ s 4 Four steps are involved in the presented approach for non- destructive estimation of root pressure: where a is the proportion of inelastic tissue (dimensionless), L Step 1: measurement of sap flow and stem diameter varia- is the length of the stem element (m) and rH O is the density of tions; and Step 2: forward simulation and calibration. 23 2 water (g m ). Assuming a fixed volume of inelastic tissue, Using the model, described in Fig. 1A, Cx and D were variations in Ws and D are related as follows: simulated for three plants. Estimation of the parameters Cm and Rx was done based on previous measurements of Cx,as dD 2 dW = s (4) described by Begg and Turner (1970), on enclosed leaves dt p L r H2OD dt using the pressure chamber (PMS Instruments Co., Corvallis, at University of Ghent on January 25, 2013

OR, USA; n ¼ 28; data not shown) and concurrent FH2O. Water transport in and out of the surrounding tissues of the These were inserted in eqn (1) and both parameters could be stem induces changes in Cp,s.IfCp,s is smaller than the thresh- estimated independently. Parameter f (cell wall extensibility) old pressure at which wall yielding occurs (G), then variations was assumed to be very small (1 × 1025 MPa21 h21) and in D only reflect reversible swelling/shrinking: other model parameters were adopted from a previous modelling study on tomato (De Swaef and Steppe, 2010) or estimated dC 1 dW p,s = s (5) via model calibration based on daytime D measurements dt Ws dt between 1000 h and 2000 h on the first day (Table 1). Parameter S (rate of change of sugar concentration in the where 1 is the elastic modulus of the storage tissue (MPa). storage tissue) was recalibrated daily (Table 2). If Cp,s is larger than G, then irreversible radial growth Step 3: inverse simulation. occurs in addition to shrinkage/swelling (Steppe et al., 2006): After the forward simulation, the model equations were rearranged in such a way that the measured D was the input vari- dCp,s 1 dWs able (Fig. 1B). Cx was then simulated based on these D data, = − 1 wCp,s − G (6) dt Ws dt using the model parameter values estimated in step 2. Step 4: comparison of step 2 and step 3. where f is the cell wall extensibility of the storage tissue The night-time difference between Cx simulated in step 2, 21 21 (MPa h ). and Cx simulated in step 3 resulted in a positive pressure com- In accordance with De Schepper and Steppe (2010), Cp,s ponent (Pr). Differences following a drop to zero in Pr were was calculated using the van ‘t Hoff equation (Jones, 1992): small and inconsistent, and were therefore attributed to simpli- fications inherent to models. These differences were filtered < TMs out and set to zero. Cp,s =− (7) MMsucrose Ws RESULTS where < is the universal gas constant (8.31 MPa g mol21 21 K ), T the temperature (K), Ms the sugar content of the Figure 2 shows photosynthetically active radiation (PAR; storage tissue (g) and MMsucrose the molar mass of sucrose Fig. 2A), air temperature (T; Fig. 2B) and vapour pressure 21 (342.3g mol ). Cs is calculated as the sum of Cp,s and deficit (VPD; Fig. 2C) in the direct vicinity of the monitored Cp,s. Initial Cp,s is determined by assuming equilibrium plants for a period of six consecutive days starting on 17 between Cx and Cs at the start of the simulation period and September 2010. Pre-dawn VPD in the glasshouse 274 De Swaef et al. — Stem diameter variations and root pressure

(A) Original model (B) Rearranged model

Ψ Ψ πLρ D x = m − FH ORx dW H O dD 2 s = 2 dt 2 dt ℜTM Ψ s π , = − s MM W sucrose s ℜTM Ψ s π , = − Ψ Ψ Ψ s MM W s = p,s + π ,s sucrose s Ψ = Ψ + Ψ dW Ψ − Ψ s p,s π ,s s = x s dt r dW Ψ = Ψ + r s dM x s dt s = S dt

dW dMs dD 2 s = S = dt π ρ Downloaded from dt L H OD dt 2 ε = ε DΨ ε ε Ψ 0 p,s = 0D p,s

dΨ ε dW dΨ ε dW p,s = s − εφ(Ψ − Γ ) (if Ψ > Γ ) p,s = s − εφ(Ψ − Γ ) (if Ψ > Γ ) dt dt p,s p,s dt dt p,s p,s Ws Ws Ψ Ψ http://aob.oxfordjournals.org/ d p,s ε dW d p,s ε dW = s (if Ψ < Γ )= s (if Ψ < Γ) dt dt p,s dt dt p,s Ws Ws

F IG. 1. Scheme of the original model, used for simulation and calibration in step 2 of the method (A), and the rearranged model, used for simulation in step 3 of C ¼ C ¼ F ¼ the method (B). Rearranged equations are circled. x total water potential in xylem compartment; m total water potential in growing medium; H2O water ﬂow in xylem compartment; Rx ¼ hydraulic resistance between growing medium and xylem compartment; Cp,s ¼ osmotic potential of storage compartment; <¼universal gas constant; T ¼ air temperature; Ms ¼ content of osmotically active compounds in storage compartment; Ws ¼ water content in storage compartment; MMsucrose ¼ molar mass of sucrose; Cs ¼ total water potential in storage compartment; Cp,s ¼ hydrostatic water potential in storage compartment; r ¼ S ¼ D ¼ 1 ¼ hydraulic resistance between storage and xylem compartment; rate of change of sugar content in the storage tissues; stem diameter; bulk elastic at University of Ghent on January 25, 2013 modulus in relation to reversible dimensional changes; 10 ¼ proportionality parameter; f ¼ cell wall extensibility; G ¼ threshold hydrostatic water potential at which wall yielding occurs.

TABLE 1. Model parameter values for the three plants in expt 1

Parameter Plant 1 Plant 2 Plant 3 Source

21 Rx (MPa h g )0.0035 0.0035 0.0035 Initial calibration Cm (MPa) –0.1–0.1–0.1 Initial calibration f (MPa21 h21)1× 1025 1 × 1025 1 × 1025 Assumption r (MPa h g21)0.10.10.1 De Swaef and Steppe (2010) G (MPa) 0.30.30.3 De Swaef and Steppe (2010) a (dimensionless) 0.8137 0.8137 0.8137 De Swaef and Steppe (2010) C(0) (g g21)0.11 0.11 0.11 Liu et al. (2007) 21 10 (m ) 1770 5782 3209 Model calibration (step 2) S (g h21) see Table 2 Model calibration (step 2)

Initial calibration was done via measurements of stem water potential (n ¼ 28 in total) before the experiment. Model calibration was done on measurements of stem diameter every 5 min between 1000 and 2000 h on 17 September 2010 (n ¼ 120 per plant). Parameter S was recalibrated daily via measurements of stem diameter every 5 min between 1000 and 2000 h (n ¼ 120 per plant per day). Rx ¼ hydraulic resistance between growing medium and xylem compartment; Cm ¼ total water potential in growing medium; f ¼ cell wall extensibility; r ¼ hydraulic resistance between storage and xylem compartment; G ¼ threshold hydrostatic water potential at which wall yielding occurs; a ¼ proportion of inelastic tissue to the total stem diameter; 10 ¼ proportionality parameter; S ¼ rate of change of sugar content in the storage tissues; C(0) ¼ initial sugar concentration in the storage tissues; compartment approximated zero for the ﬁrst 5 d, as a result of the interplant similarity of the response to prevailing environ- high RH (Fig. 2C). On the last day of the period, pre-dawn mental conditions as previously reported by De Swaef et al. VPD remained a little higher compared with the previous 5 d. (2009). Step 1: sap ﬂow and stem diameter variations measurements. Step 2: forward simulation and calibration.

Figure 3 displays sap ﬂow (FH2O) and stem diameter vari- Using the model, described in Fig. 1A, Cx (Fig. 4A–C) and ation (D) measurements for 6 d for three plants. Proﬁles of D (Fig. 4D–F) were simulated for all plants. The simulation of both FH2O and D corresponded well for all plants, indicating D corresponded well with the measurements during the day, De Swaef et al. — Stem diameter variations and root pressure 275

TABLE 2. The optimized parameter value of S (rate of change of Step 4: comparison of step 2 and step 3. 21 sugar content in the storage tissue) in g h in each time frame The night-time difference between Cx simulated in step 2, and for every plant for expt 1 and Cx simulated in step 3 (Fig. 5A, C and E) resulted in a positive pressure component (Pr, Fig. 5B, D and F) for the Time (h) nights following day 1, 2, 3 and 4. 0–24 24–48 48–72 72–96 96–120 120–144 Manometer measurements of root pressure Plant 1 –0.0009 –0.0011 –0.0009 0.0045 –0.0017 –0.0017 Plant 2 0.0005 –0.0047 0.0055 0.0135 0.0008 –0.0057 The approach described above was validated in an extra ex- ...... Plant 3 –0 0029 –0 0029 0 0010 0 0010 –0 0007 –0 0063 periment on tomato plants in which RH of the air was manipu- lated to be high during the night. Figure 6A–C shows PAR and VPD for three measurement periods (A, 31 January–3 February 2012; B, 14–16 February 2012; C, 21–25 February 2012). The same model was used for the forward A simulation using sap ﬂow as input variable (Fig. 6D–F). Downloaded from 1500 Figure 6G–I shows comparison between measured and simulated D for the forward simulation. Parameter values are given )

–1 in Table 3. s

–2 The resulting estimates of root pressure were then compared 1000 with actual measurements of root pressure on excised shoots

(Fig. 7). http://aob.oxfordjournals.org/

PAR ( μ mol m PAR 500 DISCUSSION Model parameter values

0 Parameters Cm (substrate water potential) and Rx (hydraulic resistance between soil and stem) were estimated in advance 30 using destructive measurements of stem water potential (Cx) B (data not shown). Such an initial model calibration has at University of Ghent on January 25, 2013 proven its importance to allow unambiguous estimation of 20 the model parameters Cm and Rx (De Pauw et al., 2008;

T (°C) Steppe et al., 2008a). Different estimates for Rx in expt 1 (0.0035 MPa h g21) and 2 (0.0025 MPa h g21) and an earlier study on tomato (0.0057 MPa h g21; De Swaef and 10 C Steppe, 2010) may result from plant age, root development, cultivar and presence/absence of a rootstock. Parameter values for r (radial hydraulic resistance), G (threshold hydro- 1 static water potential at which wall yielding occurs) and a (proportion of inelastic tissue in the total stem diameter) VPD (kPa) were adopted from an earlier modelling study on tomato (De 0 Swaef and Steppe, 2010), and C(0) (initial sugar concentration 024487296 120 144 in the storage tissue) was taken from Liu et al. (2007). Cell Time (h) wall extensibility (f) is known to decrease as the tissue ages (Liu et al., 2007). Because the measured stem element F IG. 2. (A) Photosynthetically active radiation (PAR), (B) air temperature (T ) was rather old, it can be assumed that f was close to zero and (C) vapour pressure deficit of the air (VPD) for a period of 6 d starting on 25 21 21 17 September 2010 at midnight. The shaded bands indicate night-time. (1 × 10 MPa h ). For expt 2, f was set to 0.001 MPa21 h21, which is an acceptable value for young but differed explicitly during the nights following day 1, 2, 3 tomato stems (De Swaef and Steppe, 2010). The subset of and 4 (Fig. 4D–F), reaching a maximal discrepancy at the parameters 10 (proportionality constant for the elastic end of the night. During the night following day 5, this dis- modulus) and S (rate of change of sugar concentration in the crepancy was not visible. storage tissue) was found to be identifiable. Consequently, Step 3: inverse simulation. these parameters could be estimated independently using auto- In step 3, Cx was simulated (Fig. 5A, C, E) based on D data mated calibration in which the sum of squared errors between (Fig. 3D–F), using the model parameter values estimated in daytime (between 1000 and 2000 h) simulations and measure- step 2 and the model equations presented in Fig. 1B. This ments of D was minimized. For 10, this was done once on the shows an increase in Cx, during the nights following day 1, first day and the resulting parameter value was used from then 2, 3 and 4 which is not visible in Cx simulated in step 2. In onwards. Differences in estimated values for 10 between dif- the night following day 5, Cx simulations for step 2 and 3 ferent plants originate from differences in elasticity, which is were not different. affected by the stem tissue age (10 increases with age for 276 De Swaef et al. — Stem diameter variations and root pressure

150 AD

) 100 –1

10·75

Sap flow (g h Sap flow 50 Stem diameter (mm)

0 10·70 150 BEDownloaded from

) 100 –1 10·80 http://aob.oxfordjournals.org/

Sap flow (g h Sap flow 50 Stem diameter (mm)

10·75 0

150 at University of Ghent on January 25, 2013 CF

11·35 ) 100 –1

Sap flow (g h Sap flow 50 Stem diameter (mm) 11·30

0 0 24487296120 144 0 24 48 72 96 120 144 Time (h) Time (h)

F IG. 3. Measurements of sap ﬂow (FH2O) of plants 1, 2 and 3 (A, B, C, respectively) and stem diameter (D) of plants 1, 2 and 3 (D, E, F, respectively) for a period of 6 d starting on 17 September 2010 at midnight. The shaded bands indicate night-time. expt 2). Parameter S is determined by loading and unloading Parameters S and f predominantly determine the simulated mechanisms in the plant, and is therefore inﬂuenced by overall stem growth rate and could not be estimated independent- factors such as climatic conditions and crop load. The value ly. Therefore, we opted to attribute a plausible value to param- of S can be negative or positive, as the sugar content in the eter f(1 × 1025 MPa21 h21 in expt 1 and 0.001 MPa21 h21 storage tissue can decrease or increase. Because climatic con- in expt 2) and to estimate parameter S automatically. The ditions were variable among the different days in expt 1, par- strong correlation between both parameters is, however, of ameter S could not be considered constant for the entire period, limited importance in our approach of root pressure estimation: but was recalibrated every day (Table 2). In expt 2, parameter a test with different values of f (and corresponding optimized S was kept constant for each measurement period, because the values for S) showed no difference in estimated root pressure climate was similar for the different days within each period. (data not shown). De Swaef et al. — Stem diameter variations and root pressure 277

0·0 10·80 AD Measurement –0·1 Forward simulation 10·78

–0·2 10·76 –0·3 (MPa) x

Ψ 10·74 –0·4 Stem diameter (mm) 10·72 –0·5

–0·6 10·70

0·0 BEDownloaded from

–0·1 10·82

–0·2 10·80 http://aob.oxfordjournals.org/ –0·3 (MPa) x

Ψ 10·78 –0·4 Stem diameter (mm) 10·76 –0·5

–0·6 10·74

0·0 at University of Ghent on January 25, 2013 CF

–0·1 11·36

–0·2 11·34 –0·3 (MPa) x

Ψ 11·32 –0·4 Stem diameter (mm) 11·30 –0·5

–0·6 11·28 024487296 120 144 0 24 48 72 96 120 144 Time (h) Time (h)

F IG. 4. Simulation results of the original model, outlined in Fig. 1A, of xylem water potential (Cx) for plants 1, 2 and 3 (A, B, C, respectively) and comparison between simulation results and measurements of stem diameter (D) for the respective plants (D, E, F). All data presented describe a period of 6 d starting on 17 September 2010 at midnight. The shaded bands indicate night-time.

Parameters 10 and Rx predominantly determine the diurnal General discussion of the method amplitude of variations in D, and could also not be estimated Daytime F and D, shown in Fig. 3, demonstrated inverse independently from each other. The correlation between both H2O dynamics in accordance with previous results (De Swaef and parameters could, however, be broken, because R was esti- x Steppe, 2010). Because F results from a water potential mated using previous measurements of stem water potential. H2O gradient (DC) between the substrate and the stem xylem, The independent estimation of R is needed, because the x higher F rates typically correspond to more negative C value of R has an important effect on the estimated values H2O x x values under well-watered conditions [eqn (1)]. Due to the of root pressure. 278 De Swaef et al. — Stem diameter variations and root pressure

A Forward simulation between xylem and surrounding tissues and is therefore inﬂu- Inverse simulation enced instantaneously by variations in transpiration. Models 0·0 that are based on the C–T theory, such as our original model (Fig. 1A), can simulate these transpiration-driven varia- –0·2 tions well (Fig. 4). However, if a mechanism other than tran- (MPa) x

Ψ spiration affects Cx, Cs or the radial hydraulic resistance –0·4 between xylem and surrounding tissues, the response of D cannot longer be simulated accurately, because this affecting mechanism is not included in the model. B As such, Cx could increase under conditions of low transpir- C 0·2 ation as a direct result of root pressure. An increase in x the- (MPa) oretically will promote water transport from the xylem towards r P the surrounding tissues, ultimately enhancing D growth. Our D 0 measurements show such a night-time increase (Fig. 3D–F), that could not be explained by the original model, based on

C C–T. The simulations conducted with the model, displayed Downloaded from 0·0 in Fig. 1A, showed a linear D growth, whereas the measurements of D showed an explicit increase in the second half of the night (Fig. 4D–F), except for the night following day –0·2 (MPa)

x 5. During the second part of the ﬁrst nights, the microclimatic

Ψ conditions were very humid (Fig. 2C), favouring the build-up http://aob.oxfordjournals.org/ –0·4 of root pressure. Therefore, we suggest that the deviating D pattern, which was observed between measurements and model simulations, was caused by root pressure. In the night D following day 5, VPD remained slightly higher, enabling 0·2 enough transpiration to prevent the build-up of root pressure. (MPa) r Root pressure always started to build up at night when VPD P 0 approximated zero (Figs 2C and 5). Interestingly, estimated root pressure continued during a signiﬁcant part of the day, es- E pecially on day 5 (Figs 5 and 8). When investigating this day in at University of Ghent on January 25, 2013 detail, root pressure continued to increase until 1000 h, and 0·0 remained constant until 1200 h, whereas sunrise was at 0630 h. Only when the sap ﬂow rate rose sharply at 1200 h –0·2 did root pressure disappear. Apparently, water was highly (MPa) x available in this period to meet the low rates of transpiration Ψ –0·4 between 0630 and 1200 h. The abundant water in the leaves may have contributed to transpiration, postponing the effects at the stem level. In contrast, root pressure in the 2012 experi- F ment always declined at sunrise (Fig. 7). Because transpiration increased faster after sunrise (Fig. 6D–F), compared with 0·2

(MPa) 2010, root pressure probably disappeared immediately. r

P Therefore, further research should take into account these con- 0 tributions from the leaves using continuous measurements of 024487296 120 144 leaf thickness (Burquez, 1987) or leaf patch clamp pressure Time (h) probes (Zimmermann et al., 2008; Lee et al., 2012). F IG. 5. Comparison between xylem water potential (Cx) simulated in step 2, In addition toCx, both sugar content of the storage tissues and based on the original model equations, and step 3, based on the rearranged stem age are known to affect D variations (De Swaef and Steppe, model equations, for plants 1, 2 and 3 (A, C, E, respectively), together with 2010). However, it is unlikely that these features have played an pressure component (P ) in the xylem, which is the mathematical difference r important role in the reported night-time D pattern. First, it is un- between Cx simulated in step 2 and 3 (B, D, F). All data presented describe a period of 6 d starting on 17 September 2010 at midnight. Shaded bands in- likely that the night-time diameter increase could have evolved dicate night-time. from an increased sugar content of the storage tissues, because sugar loading generally decreases during the night and plants time lag between transpiration and root water uptake, water seem to maintain a constant sugar supply to the sinks (Geiger from surrounding tissues is drawn into the xylem when tran- et al., 2000; Komor, 2000). Secondly, stem ageing is a gradual spiration increases. These surrounding tissues are replenished process, which could be taken into account in the model by when transpiration again decreases. This alternate withdrawal assigning a time-dependent function to the cell wall extensibil- and replenishment of water in the tissues surrounding the ity (f) (e.g. Liu et al., 2007; De Swaef and Steppe, 2010). xylem causes D to vary (Ge´nard et al., 2001; Zweifel et al., However, because our work focuses on a period at the end of 2001; Steppe et al., 2006, 2012; De Swaef and Steppe, the growing season and measurements were done on an older 2010). This radial transport is the physical result of DC part of the stem, f was assumed to be close to zero (1 × De Swaef et al. — Stem diameter variations and root pressure 279

3·0 ABC 300 PAR 2·5

) VPD –1 s 2·0 VPD (kPa) –2 200 1·5

1·0 100 PAR ( μ mol m PAR 0·5

0 0 DEF 100 ) Downloaded from

–1 80

40 Sap flow (g h Sap flow

20 http://aob.oxfordjournals.org/

0 GHI 10·00 Measurement 9·95 Forward simulation

9·90 at University of Ghent on January 25, 2013

9·85 Stem diamter (mm) 9·80

9·75 0244872 0 24 48 0 24 48 72 96 Time (h) Time (h) Time (h)

F IG. 6. Photosynthetically active radiation (PAR) and vapour pressure deﬁcit (VPD) for three measurement periods in experiment 2, (A) 31 January–3 February 2012, (B) 14– 16 February 2012, and (C) 21–25 February 2012, and corresponding sap ﬂow rates for a young tomato plant (D–F). Comparison between stem diameter measurements and simulations using the original model outlined in Fig. 1A for the respective periods (G–I). Shaded bands indicate night-time.

TABLE 3. Model parameters for the three periods in expt 2

Parameter Period 1 Period 2 Period 3 Source

21 Rx (MPa h g )0.0025 0.0025 0.0025 Initial calibration Cm (MPa) -0.1–0.1–0.1 Initial calibration f (MPa21 h21)0.001 0.001 0.001 Assumption r (MPa h g21)0.10.10.1 De Swaef and Steppe (2010) G (MPa) 0.30.30.3 De Swaef and Steppe (2010) a (dimensionless) 0.8137 0.8137 0.8137 De Swaef and Steppe (2010) C(0) (g g21)0.11 0.11 0.11 Liu et al. (2007) 21 10 (m ) 478 690 770 Model calibration (step 2) S (g h21)0.000817 –0.000355 0.0035 Model calibration (step 2)

Initial calibration was done via measurements of stem water potential (n ¼ 48 in total) before the experiment. Model calibration was done on measurements of stem diameter every 5 min between 1000 and 2000 h on the ﬁrst day of each period (n ¼ 120 per plant).

1025 MPa21 h21), and it was unnecessary to include this The magnitude of the destructively measured root pressure dependency in the model. Furthermore, stem ageing is a using a manometer installed on excised tomato stems agreed process that limits D growth (Steppe et al., 2008a, 2008b), well with the model-based estimations (Fig. 7). However, de- whereas the measured D in this study showed a sudden increase. structively measured root pressure showed a decrease during 280 De Swaef et al. — Stem diameter variations and root pressure

0·20 ABC

0·15 Destructive measurement Model estimation 0·10 (MPa) r P

0·05

0 0244872 0 24 48 0 24 48 72 96 Time (h) Time (h) Time (h) Downloaded from F IG. 7. Comparison between destructively measured root pressure using a manometer and estimations using the model approach for three measurement periods in experiment 2, (A) 31 January–3 February 2012, (B) 14–16 February 2012, and (C) 21–25 February 2012. Destructively measured data are the mean of two plants. Shaded bands indicate night-time.

the night, presumably as a result of decreasing substrate tem- 150 0·2 perature, whereas estimated root pressure in intact leafed http://aob.oxfordjournals.org/ plants showed an increasing pattern towards the end of the night. It is therefore hard to relate diurnal dynamics of destruc- 0·0 )

–1 100 tively measured root pressure to diurnal dynamics of transpir- Ψ x ing plants: because the excised stems did not transpire during (MPa) the day, root pressure enhanced during the day because of the Sap flow –0·2 higher temperature in the greenhouse, whereas root pressure is Ψ 50 x not allowed to develop in transpiring plants. Sap flow (g h –0·4 at University of Ghent on January 25, 2013

Critical considerations 0 –0·6 Concurrent with the root pressure-induced night-time in- 96 100 104 108 112 116 120 crease in D, it might be expected that FH2O must increase. Time (h) This was not always visible in our FH O data (Fig. 3A–C), 2 F IG. 8. Diurnal profile of simulated xylem water potential and measurement but could be clarified by the model calculations. The measured of sap flow of plant 2 on 21 September 2010. The vertical dashed line indicates night-time diameter increase corresponded with a calculated where sap flow rose sharply. Shaded bands indicate night-time. maximum water mass inflow of approx. 250 mg h21 for an 8 m long tomato stem, which is 400 times smaller compared with daytime FH2O rates. Because of the low VPD at the end climate control, potentially unfavourable conditions could be of these nights, plant water loss via transpiration could be avoided using an intelligently managed compromise between neglected. Therefore, nearly all of the upward pushed water energy saving and optimal growing conditions. flow in the xylem was stored in the plant itself and thus In our study, no instant visible effects of excess root pres- resulted in the observed increase in D. However, the sensitivity sure were noticeable, probably indicating that root pressure of the heat balance sensors used in our study did not always had not yet reached a harmful level. Because some important allow detection of these low amounts of water flow (van physiological problems in horticulture are currently attributed Bavel and van Bavel, 1990). to excess root pressure, a critical level at which root pressure becomes undesired should be determined. To date, the main problem for investigating this critical level, as well as the en- Significance vironmental factors driving root pressure, is the lack of appro- In the last decades, the reduction of energy use has become priate systems for determining root pressure. Therefore, our an important issue in glasshouse cultivation. This has led to a non-destructive technique could allow root pressure to be esti- modified crop management and new energy-efficient climate mated continuously, while imposing a wide range of growing strategies that may create conditions favouring the build up conditions. of root pressure. Because the occurrence of excessive root Recently, Clearwater et al. (2007) unravelled a correlation pressure may cause considerable damage to the harvestable between the rootstock affinity to build up root pressure and product (Dorais et al., 2001), our approach could be of the scion vigour after grafting in kiwi. For tomato, it is direct significance to growers, as an indicator when root known in practice that rootstocks have an important effect pressure-associated problems might occur. Because these on scion vigour and on the occurrence of root pressure-related new energy-efficient technologies allow better glasshouse problems. Our approach could be used to select rootstocks De Swaef et al. — Stem diameter variations and root pressure 281 quantitatively with a different affinity for root pressure. As Dorais M, Papadopoulos AP, Gosselin A. 2001. Greenhouse tomato fruit such, better combinations of rootstocks and productive grafts quality. Horticultural Reviews 26: 239–319. Geiger DR, Servaites JC, Fuchs MA. 2000. Role of starch in carbon trans- could be made. location and partitioning at the plant level. Australian Journal of Plant Because our model and method rely on physiologically Physiology 27: 571–582. sound mechanisms which are valid for a broad range of vascu- Geńard M, Fishman S, Vercambre G, et al. 2001. A biophysical model of lar plants, our approach is perfectly applicable for many other stem and root diameter variations in woody plants. Plant Physiology plant species. Our technique to estimate root pressure in a con- 126: 188–202. Grossenbacher KA. 1938. Diurnal fluctuation in root pressure. Plant tinuous and non-destructive way is therefore a potential break- Physiology 13: 669–676. through for fundamental research in plant water relations. As Heuvelink E, Bakker MJ, Marcelis LFM, Raaphorst M. 2008. Climate and the role of root pressure in general plant functioning is still yield in a closed greenhouse. Acta Horticulturae 801: 1083–1092. not well understood, many plant physiological research van den Honert TH. 1948. Water transport in plants as a catenary process. topics such as cavitation or nutrient translocation could Faraday Society Discussions 3: 146–153. Johnson RW, Dixon MA, Lee DR. 1992. Water relations of the tomato during benefit from using this approach. fruit growth. Plant, Cell and Environment 15: 947–953. Jones HG. 1992. Plants and microclimate. A quantitative approach to environmental plant physiology, 2nd edn. Cambridge: Cambridge University

Conclusions Press. Downloaded from Klepper B, Kaufmann M. 1966. Removal of salt from xylem sap by leaves The combination of continuous measurements of FH2O and and stems of guttating plants. Plant Physiology 41: 1743–1747. D and the mechanistic water flow and storage model allowed Komor E. 2000. Source physiology and assimilate transport: the interaction of elucidation of the effects on D of mechanisms other than the sucrose metabolism, starch storage and phloem export in source leaves C–T theory, such as root pressure, which is as yet difficult and the effects on sugar status in phloem. Australian Journal of Plant Physiology 27: 497–505. to measure. Therefore, the presented method could have im- http://aob.oxfordjournals.org/ Kramer PJ, Boyer JS. 1995. Water relations of plants and soils. New York: portant contributions both in practice and in future root pres- Academic Press. sure research. As such we believe that our approach can Lee KM, Driever SM, Heuvelink E, et al. 2012. Evaluation of diel patterns of contribute to a future solution of the ‘riddle of root pressure’. relative changes in cell turgor of tomato plants using leaf patch clamp pressure probes. Physiologia Plantarum 146: 439–447. Liu HF, Geńard M, Guichard S, Bertin N. 2007. Model-assisted analysis of ACKNOWLEDGEMENTS tomato fruit growth in relation to carbon and water fluxes. Journal of Experimental Botany 58: 3567–3580. We thank Philip Deman and Geert Favyts for their technical Maaswinkel RHM, Welles GWH. 1986. Factors influencing glassiness in support, the Research Centre of Hoogstraten (PCH) for the lettuce. Netherlands Journal of Agricultural Science 34: 57–65. greenhouse infrastructure, and the Special Research Fund Meinzer FC, Clearwater MJ, Goldstein G. 2001. Water transport in trees: at University of Ghent on January 25, 2013 current perspectives, new insights and some controversies. (BOF) of Ghent University for the funding to the first author. 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