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
Key words: Root pressure, stem diameter, diameter change, tomato, sap flow, Solanum lycopersicum, mechanistic model, cohesion– tension, water relations.
IN T RO DU C T IO N The process of water uptake and transpiration is generally explained by the cohesion – tension (C – T) theory (Dixon and Joly, 1894; Meinzer et al., 2001). According to this theory, the ascent of water is a passive process ultimately driven by the evaporation of water from leaves, which creates a water potential 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; Zimmermann et al., 2004) because of the meta-stable state of xylem water and the measuring methodologies of water potential. Canny (1995), for instance, proposed a mechanism of tissue pressure supporting the water column, in addition to C– T. Many others have reported the phenomenon of root pressure as a feature in water transport, in addition to C– T (e.g. Klepper and Kaufmann, 1966; Pickard 1981; Sperry et al., 1987; Tyree et al., 1987; Clearwater et al., 2007). In the absence of transpiration as the driving force of water flow across the soil – plant – atmosphere continuum (SPAC), root pressure could serve as the auxiliary engine for water supply to shoots under conditions of low transpiration (Steudle, 2001). At present, it is widely believed that root pressure arises from active loading of solutes into the xylem and subsequent osmotic uptake of water (Kramer and Boyer, 1995). More specifically, the endodermis retains solutes in a zone
near the tracheary elements and allows root pressure to build up under conditions of low transpiration (Steudle and Peterson, 1998). Under these conditions, water flow is coupled to solute flow, whereas interactions between solute and water flows are of minor importance in a transpiring plant because the hydrostatic gradient will usually be the dominating force (Pickard, 2003). Phenomena attributed to root pressure in horticulture
The best known phenomenon attributed to root pressure is guttation: due to a positive pressure in the xylem, as a result of root pressure, excess water is pushed out of the leaf ends via hydathodes (Kramer and Boyer, 1995). If plants are unable to dispose of this excess water, cells might leak or burst. Several physiological disorders are attributed to excessive root pressure such as watery fruits in tomato (Dorais et al., 2001) and glassiness in lettuce (Maaswinkel and Welles, 1986). In addition, bursting of cells allows pathogens such as Botrytis and Mycosphaerella to infect the damaged tissue and spread around in the plant. Many studies have demonstrated that the water relations in tomato (Solanum lycopersicum L.) have crucial implications for fruit production and fruit quality (e.g. Mitchell et al., 1991; Johnson et al., 1992; Dorais et al., 2001; De Swaef et al., 2012), but few deal with the effects of root pressure. However, current efforts to
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† 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 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, prompting the need for indirect and non-destructive measurement techniques. † 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.
272
De Swaef et al. — Stem diameter variations and root pressure
M AT E R IA L S A ND M E T HO DS Plant material and experimental set-up for the development of the technique (expt 1)
Tomato plants (Solanum lycopersicum ‘Admiro’) were grown in a greenhouse compartment measuring 16 × 12 × 5 m at the Research Centre Hoogstraten, Belgium (51827′ N, 4847’E). Plants were sown on 5 November 2009, grafted on the rootstock Emperador and planted on rockwool substrate (Master, Grodan, Hedehusene, Denmark) on 5 January 2010. Plants were provided with a nutrient solution of approx. 2.6 dS m21 (i.e. osmotic potential of approx. – 0.08 MPa) using a drip irrigation system, based on sums of solar radiation, to attain a daily drainage of approx. 30– 50 %. Leaves under the lowest ripe truss were removed and the lowest part of the stem was horizontal, as is common practice in tomato. Three plants were continuously monitored during six consecutive days, starting on 17 September 2010.
Continuous measurements
Heat balance sensors (Model SGA13-WS, Dynamax Inc., Houston, TX, USA; accuracy approx. 10 %) were used to measure sap flow (FH2 O ) below the lowest leaf on three plants and were installed according to the operation manual (van Bavel and van Bavel, 1990). At the start of this experiment, all plants were approx. 8 m long and the sensors were installed at about 0.5 m from the roots. The sensors were thermally insulated by wrapping them in several layers of aluminium and bubble foil. Stem diameter (D) variations were measured just below the sap flow sensors using linear variable displacement transducers (LVDTs; model 2.5 DF, Solartron Metrology, Bognor Regis, UK; accuracy approx. 1 mm). The LVDT sensors were attached to the stem by custom-made stainless steel holders. Tests with a 12 mm aluminium rod showed that no temperature correction was required (Steppe and Lemeur, 2004). Absolute stem diameter was measured once before the start of the experiment using an electronic calliper. Relative humidity (RH) of the air was measured with an aspirated capacitive sensor (HMP50, Vaisala, Helsinki, Finland). Air temperature (T) was measured using a copper – constantan thermocouple (Type T, Omega, Amstelveen, The Netherlands). Both sensors were installed at 1.5 m height and were shielded from direct radiation. Vapour pressure deficit (VPD) was calculated from RH and T according to Jones (1992). Data from all sensors were logged (CR1000, Campbell Scientific Inc., Logan, UT, USA) at 30 s intervals and averaged every 5 min. Plant material and experimental set-up for validation of the technique (expt 2)
Tomato plants (S. lycopersicum L. ‘Admiro’) were grown in a greenhouse compartment measuring 2 × 2.5 × 4 m at the 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 Boneco 7135, Plaston, Widnau, Switzerland) was switched on between 1600 and 0900 h. The above-mentioned sap flow and LVDT sensors were installed on one plant. For three measurement periods (31 January – 3 February 2012; 14– 16 February 2012; 21 – 25 February 2012), root pressure was continuously recorded using a manometer (type 401002, Jumo Midas C08, Fulda, Germany) installed on two excised stems on 30 January, 13 February and 20 February 2012, respectively. As such, carbon starvation was not expected to affect root pressure in these experiments (Grossenbacher, 1938). Modelling, simulations, calibrations
In this study, the principles of a mechanistic flow and storage model, originally developed for trees (Steppe et al., 2006), were used. These equations allow simulation of D, stem water potential in the xylem (Cx), and total (Cs), osmotic (Cp,s) and hydrostatic potential in the surrounding
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reduce energy use in horticulture have led to modified glasshouse climate conditions (i.e. more humid) that might promote the occurrence of excess root pressure (Heuvelink et al., 2008). Beside the above-mentioned disorders, root pressure is expected to play a beneficial role in the distribution of calcium to the leaves of cabbage and lettuce (Palzkill and Tibbitts, 1977), root-to-shoot water transport in trees during spring (e.g. Sperry et al., 1987; Clearwater et al., 2007) and in refilling embolized xylem vessels (e.g. Tyree et al., 1987; Zwieniecki and Holbrook, 2009). Moreover, Clearwater et al. (2007) recently uncovered a relationship between the rootstock ability to build up root pressure and the scion vigour for kiwi. The above-mentioned physiological effects attributed to root pressure indicate the need to investigate this intriguing phenomenon further. Currently, a ‘bottle-neck’ in root pressure research is the lack of a system that allows continuous and non-destructive measurements, especially for herbaceous plants. Clearwater et al. (2007) measured root pressure using pressure transducers that were installed inside the xylem of kiwi roots. To our knowledge, this is the only existing nondestructive continuous method to measure root pressure. However, the application of this method on herbaceous plants with limited root and stem diameters such as tomato may be difficult, if not impossible, because this method requires installation of the system 10 –15 mm inside the xylem. Other methods are mainly destructive, such as installing manometers on excised stems (Grossenbacher, 1938) or root pressure probes in excised roots (Steudle et al., 1993). 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 tomato combined with a mechanistic flow and storage model, based on C –T principles. Estimated values of root pressure, under conditions of low transpiration rates, were compared with destructive measurements using a manometer installed on an excised stem.
De Swaef et al. — Stem diameter variations and root pressure storage tissues (Cp,s). The model uses FH2 O as an input variable, which is directly linked to Cx via the flow resistance concept (van den Honert, 1948):
Cx = C m − F H 2 O R x
dWs Cx − Cs = dt r
(2)
where a is the proportion of inelastic tissue (dimensionless), L is the length of the stem element (m) and rH2 O is the density of water (g m23). Assuming a fixed volume of inelastic tissue, variations in Ws and D are related as follows: (4)
Water transport in and out of the surrounding tissues of the stem induces changes in Cp,s. If Cp,s is smaller than the threshold pressure at which wall yielding occurs (G), then variations in D only reflect reversible swelling/shrinking: dCp,s 1 dWs = dt Ws dt
(5)
where 1 is the elastic modulus of the storage tissue (MPa). If Cp,s is larger than G, then irreversible radial growth occurs in addition to shrinkage/swelling (Steppe et al., 2006): dCp,s 1 dWs = − 1 w Cp,s − G dt Ws dt
(6)
where f is the cell wall extensibility of the storage tissue (MPa21 h21). In accordance with De Schepper and Steppe (2010), Cp,s was calculated using the van ‘t Hoff equation (Jones, 1992):
Cp,s = −
< T Ms MMsucrose Ws
Cp,s (0) = −
(7)
where < is the universal gas constant (8.31 MPa g mol21 K21), T the temperature (K), Ms the sugar content of the storage tissue (g) and MMsucrose the molar mass of sucrose (342.3 g mol21). Cs is calculated as the sum of Cp,s and Cp,s. Initial Cp,s is determined by assuming equilibrium between Cx and Cs at the start of the simulation period and
< T C (0) MMsucrose
(8)
where C(0) is the initial sugar concentration in the storage tissue (g g21). A summary of the model equations, used in the present study, is presented in Fig. 1A. Model development, simulations, calibrations and identifiability analyses were conducted with PhytoSim (Phyto-IT BVBA, Mariakerke, Belgium), a software developed for plant modelling and simulation. For model calibration, the simplex method, originally developed by Nelder and Mead (1965) and available in PhytoSim, was used to minimize the weighted sum of squared errors for the variable D. Identifiability analysis was done as described by De Pauw et al. (2008). Methodology
Four steps are involved in the presented approach for nondestructive estimation of root pressure: Step 1: measurement of sap flow and stem diameter variations; and Step 2: forward simulation and calibration. Using the model, described in Fig. 1A, Cx and D were simulated for three plants. Estimation of the parameters Cm and Rx was done based on previous measurements of Cx, as described by Begg and Turner (1970), on enclosed leaves using the pressure chamber (PMS Instruments Co., Corvallis, OR, USA; n ¼ 28; data not shown) and concurrent FH2 O . These were inserted in eqn (1) and both parameters could be estimated independently. Parameter f (cell wall extensibility) was assumed to be very small (1 × 1025 MPa21 h21) and other model parameters were adopted from a previous modelling study on tomato (De Swaef and Steppe, 2010) or estimated via model calibration based on daytime D measurements between 1000 h and 2000 h on the first day (Table 1). Parameter S (rate of change of sugar concentration in the storage tissue) was recalibrated daily (Table 2). Step 3: inverse simulation. After the forward simulation, the model equations were rearranged in such a way that the measured D was the input variable (Fig. 1B). Cx was then simulated based on these D data, using the model parameter values estimated in step 2. Step 4: comparison of step 2 and step 3. The night-time difference between Cx simulated in step 2, and Cx simulated in step 3 resulted in a positive pressure component (Pr). Differences following a drop to zero in Pr were small and inconsistent, and were therefore attributed to simplifications inherent to models. These differences were filtered out and set to zero. R E S ULT S Figure 2 shows photosynthetically active radiation (PAR; Fig. 2A), air temperature (T; Fig. 2B) and vapour pressure deficit (VPD; Fig. 2C) in the direct vicinity of the monitored plants for a period of six consecutive days starting on 17 September 2010. Pre-dawn VPD in the glasshouse
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where r is the hydraulic resistance between xylem and storage (MPa h g21). The relationship between Ws and D is defined by: D2 1 − a2 p L rH2 O (3) Ws = 4
dD 2 dWs = dt p L r H2 O D dt
estimation of the initial Cp,s:
(1)
where Cm is the water potential in the growing medium (MPa) and Rx is the hydraulic resistance between the growing medium and the point of interest in the plant stem (MPa h g21). The model simulates variations in water content of the storage tissue (Ws) as a result of the water potential gradient driving radial water transport between the xylem and the storage tissue:
273
274
De Swaef et al. — Stem diameter variations and root pressure (A) Original model
(B) Rearranged model
Ψx = Ψm − FH ORx
dWs
2
Ψπ,s = −
dt
ℜTM s MMsucroseWs
Ψπ,s = −
Ψs = Ψp,s + Ψπ,s dW s
=
dt dMs dt
πLρH OD
dD dt
ℜTM s
Ψs = Ψp,s + Ψπ,s
Ψ x − Ψs r
=S
dWs dt
dMs =S dt
dWs dt
2
ε = ε0DΨp,s
ε = ε0DΨp,s dΨp,s dt dΨp,s dt
=
ε dWs − εφ(Ψp,s − Γ ) (if Ψp,s > Γ ) Ws dt
dΨp,s
=
ε dWs Ws dt
dΨp,s
(if Ψp,s < Γ )
dt dt
=
ε dWs − εφ(Ψp,s − Γ ) (if Ψp,s > Γ ) Ws dt
=
ε dWs Ws dt
(if Ψp,s < Γ)
F I G . 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 the method (B). Rearranged equations are circled. Cx ¼ total water potential in xylem compartment; Cm ¼ total water potential in growing medium; FH2O ¼ water flow in xylem compartment; Rx ¼ hydraulic resistance between growing medium and xylem compartment; Cp,s ¼ osmotic potential of storage compartment; < ¼ universal 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 hydraulic resistance between storage and xylem compartment; S ¼ rate of change of sugar content in the storage tissues; D ¼ stem diameter; 1 ¼ bulk elastic 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.
TA B L E 1. Model parameter values for the three plants in expt 1 Parameter Rx (MPa h g21) Cm (MPa) f (MPa21 h21) r (MPa h g21) G (MPa) a (dimensionless) C(0) (g g21) 10 (m21) S (g h21)
Plant 1
Plant 2
Plant 3
Source
0.0035 – 0.1 1 × 1025 0.1 0.3 0.8137 0.11 1770
0.0035 – 0.1 1 × 1025 0.1 0.3 0.8137 0.11 5782 see Table 2
0.0035 – 0.1 1 × 1025 0.1 0.3 0.8137 0.11 3209
Initial calibration Initial calibration Assumption De Swaef and Steppe (2010) De Swaef and Steppe (2010) De Swaef and Steppe (2010) Liu et al. (2007) Model calibration (step 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 high RH (Fig. 2C). On the last day of the period, pre-dawn VPD remained a little higher compared with the previous 5 d. Step 1: sap flow and stem diameter variations measurements. Figure 3 displays sap flow (FH2 O ) and stem diameter variation (D) measurements for 6 d for three plants. Profiles of both FH2 O and D corresponded well for all plants, indicating
the interplant similarity of the response to prevailing environmental conditions as previously reported by De Swaef et al. (2009). Step 2: forward simulation and calibration. Using the model, described in Fig. 1A, Cx (Fig. 4A– C) and D (Fig. 4D– F) were simulated for all plants. The simulation of D corresponded well with the measurements during the day,
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2 πLρH OD
2
MMsucroseWs
Ψx = Ψs + r
dD = dt
2
=
De Swaef et al. — Stem diameter variations and root pressure TA B L E 2. The optimized parameter value of S (rate of change of sugar content in the storage tissue) in g h21 in each time frame and for every plant for expt 1 Time (h)
Plant 1 Plant 2 Plant 3
0–24
24– 48
48–72
72–96
96–120
120 –144
–0.0009 0.0005 –0.0029
–0.0011 –0.0047 –0.0029
– 0.0009 0.0055 0.0010
0.0045 0.0135 0.0010
– 0.0017 0.0008 – 0.0007
– 0.0017 – 0.0057 – 0.0063
A
PAR (μmol m–2 s–1)
1000
500
Step 4: comparison of step 2 and step 3. The night-time difference between Cx simulated in step 2, 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 nights following day 1, 2, 3 and 4. Manometer measurements of root pressure
The approach described above was validated in an extra experiment on tomato plants in which RH of the air was manipulated 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 simulation using sap flow as input variable (Fig. 6D– F). Figure 6G – I shows comparison between measured and simulated D for the forward simulation. Parameter values are given in Table 3. The resulting estimates of root pressure were then compared with actual measurements of root pressure on excised shoots (Fig. 7). DISCUSSION Model parameter values
0
T (°C)
30
B
20
VPD (kPa)
10
C
1
0
0
24
48
72
96
120
144
Time (h) F I G . 2. (A) Photosynthetically active radiation (PAR), (B) air temperature (T ) and (C) vapour pressure deficit of the air (VPD) for a period of 6 d starting on 17 September 2010 at midnight. The shaded bands indicate night-time.
but differed explicitly during the nights following day 1, 2, 3 and 4 (Fig. 4D– F), reaching a maximal discrepancy at the end of the night. During the night following day 5, this discrepancy was not visible. Step 3: inverse simulation. In step 3, Cx was simulated (Fig. 5A, C, E) based on D data (Fig. 3D –F), using the model parameter values estimated in step 2 and the model equations presented in Fig. 1B. This shows an increase in Cx, during the nights following day 1, 2, 3 and 4 which is not visible in Cx simulated in step 2. In the night following day 5, Cx simulations for step 2 and 3 were not different.
Parameters Cm (substrate water potential) and Rx (hydraulic resistance between soil and stem) were estimated in advance using destructive measurements of stem water potential (Cx) (data not shown). Such an initial model calibration has proven its importance to allow unambiguous estimation of the model parameters Cm and Rx (De Pauw et al., 2008; 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 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 hydrostatic water potential at which wall yielding occurs) and a ( proportion of inelastic tissue in the total stem diameter) were adopted from an earlier modelling study on tomato (De Swaef and Steppe, 2010), and C(0) (initial sugar concentration in the storage tissue) was taken from Liu et al. (2007). Cell wall extensibility ( f ) is known to decrease as the tissue ages (Liu et al., 2007). Because the measured stem element was rather old, it can be assumed that f was close to zero (1 × 1025 MPa21 h21). For expt 2, f was set to 0.001 MPa21 h21, which is an acceptable value for young tomato stems (De Swaef and Steppe, 2010). The subset of parameters 10 ( proportionality constant for the elastic modulus) and S (rate of change of sugar concentration in the storage tissue) was found to be identifiable. Consequently, these parameters could be estimated independently using automated calibration in which the sum of squared errors between daytime (between 1000 and 2000 h) simulations and measurements of D was minimized. For 10, this was done once on the first day and the resulting parameter value was used from then onwards. Differences in estimated values for 10 between different plants originate from differences in elasticity, which is affected by the stem tissue age (10 increases with age for
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1500
275
276
De Swaef et al. — Stem diameter variations and root pressure A
D
Stem diameter (mm)
Sap flow (g h–1)
150
100
50
10·70
0 150
E
Stem diameter (mm)
B
100
50
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Sap flow (g h–1)
10·75
10·80
10·75 0 C
F
Stem diameter (mm)
Sap flow (g h–1)
150
100
50
11·35
11·30
0
0
24
48
72 Time (h)
96
120
144
0
24
48
72 Time (h)
96
120
144
F I G . 3. Measurements of sap flow (FH2 O ) 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 mechanisms in the plant, and is therefore influenced by factors such as climatic conditions and crop load. The value of S can be negative or positive, as the sugar content in the storage tissue can decrease or increase. Because climatic conditions were variable among the different days in expt 1, parameter S could not be considered constant for the entire period, but was recalibrated every day (Table 2). In expt 2, parameter S was kept constant for each measurement period, because the climate was similar for the different days within each period.
Parameters S and f predominantly determine the simulated overall stem growth rate and could not be estimated independently. Therefore, we opted to attribute a plausible value to parameter f(1 × 1025 MPa21 h21 in expt 1 and 0.001 MPa21 h21 in expt 2) and to estimate parameter S automatically. The strong correlation between both parameters is, however, of limited importance in our approach of root pressure estimation: a test with different values of f (and corresponding optimized values for S) showed no difference in estimated root pressure (data not shown).
De Swaef et al. — Stem diameter variations and root pressure 0·0
10·80
A
–0·1 Stem diameter (mm)
10·78
Ψx (MPa)
–0·2 –0·3 –0·4
0·0
10·74
E
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B
–0·1 Stem diameter (mm)
10·82
–0·2
Ψx (MPa)
10·76
10·70
–0·6
–0·3 –0·4
10·80
10·78
10·76
–0·5
10·74
–0·6 0·0
C
F
–0·1 Stem diameter (mm)
11·36
–0·2
Ψx (MPa)
Measurement Forward simulation
10·72
–0·5
–0·3 –0·4
11·34
11·32
11·30
–0·5 –0·6
D
277
0
24
48
72 Time (h)
96
120
144
11·28
0
24
48
72 Time (h)
96
120
144
F I G . 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 amplitude of variations in D, and could also not be estimated independently from each other. The correlation between both parameters could, however, be broken, because Rx was estimated using previous measurements of stem water potential. The independent estimation of Rx is needed, because the value of Rx has an important effect on the estimated values of root pressure.
General discussion of the method
Daytime FH2 O and D, shown in Fig. 3, demonstrated inverse dynamics in accordance with previous results (De Swaef and Steppe, 2010). Because FH2 O results from a water potential gradient (DC) between the substrate and the stem xylem, higher FH2 O rates typically correspond to more negative Cx values under well-watered conditions [eqn (1)]. Due to the
278
De Swaef et al. — Stem diameter variations and root pressure A
Forward simulation Inverse simulation
Ψx (MPa)
0·0 –0·2
Pr (MPa)
–0·4
B 0·2 0
Ψx (MPa)
0·0 –0·2
Pr (MPa)
–0·4
D 0·2 0 E
Ψx (MPa)
0·0 –0·2
Pr (MPa)
–0·4
F 0·2 0
0
24
48
72 Time (h)
96
120
144
F I G . 5. Comparison between xylem water potential (Cx) simulated in step 2, based on the original model equations, and step 3, based on the rearranged model equations, for plants 1, 2 and 3 (A, C, E, respectively), together with pressure component (Pr) in the xylem, which is the mathematical difference 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 indicate night-time.
time lag between transpiration and root water uptake, water from surrounding tissues is drawn into the xylem when transpiration increases. These surrounding tissues are replenished when transpiration again decreases. This alternate withdrawal and replenishment of water in the tissues surrounding the xylem causes D to vary (Ge´nard et al., 2001; Zweifel et al., 2001; Steppe et al., 2006, 2012; De Swaef and Steppe, 2010). This radial transport is the physical result of DC
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C
between xylem and surrounding tissues and is therefore influenced instantaneously by variations in transpiration. Models that are based on the C – T theory, such as our original model (Fig. 1A), can simulate these transpiration-driven variations well (Fig. 4). However, if a mechanism other than transpiration affects Cx, Cs or the radial hydraulic resistance between xylem and surrounding tissues, the response of D cannot longer be simulated accurately, because this affecting mechanism is not included in the model. As such, Cx could increase under conditions of low transpiration as a direct result of root pressure. An increase in Cx theoretically will promote water transport from the xylem towards the surrounding tissues, ultimately enhancing D growth. Our D measurements show such a night-time increase (Fig. 3D – F), that could not be explained by the original model, based on C– T. The simulations conducted with the model, displayed 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 5. During the second part of the first nights, the microclimatic conditions were very humid (Fig. 2C), favouring the build-up 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 following day 5, VPD remained slightly higher, enabling enough transpiration to prevent the build-up of root pressure. Root pressure always started to build up at night when VPD approximated zero (Figs 2C and 5). Interestingly, estimated root pressure continued during a significant part of the day, especially on day 5 (Figs 5 and 8). When investigating this day in detail, root pressure continued to increase until 1000 h, and remained constant until 1200 h, whereas sunrise was at 0630 h. Only when the sap flow rate rose sharply at 1200 h did root pressure disappear. Apparently, water was highly available in this period to meet the low rates of transpiration 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 experiment always declined at sunrise (Fig. 7). Because transpiration increased faster after sunrise (Fig. 6D – F), compared with 2010, root pressure probably disappeared immediately. Therefore, further research should take into account these contributions from the leaves using continuous measurements of leaf thickness (Burquez, 1987) or leaf patch clamp pressure probes (Zimmermann et al., 2008; Lee et al., 2012). In addition toCx, both sugar content of the storage tissues and stem age are known to affect D variations (De Swaef and Steppe, 2010). However, it is unlikely that these features have played an important role in the reported night-time D pattern. First, it is unlikely that the night-time diameter increase could have evolved from an increased sugar content of the storage tissues, because sugar loading generally decreases during the night and plants seem to maintain a constant sugar supply to the sinks (Geiger et al., 2000; Komor, 2000). Secondly, stem ageing is a gradual process, which could be taken into account in the model by assigning a time-dependent function to the cell wall extensibility ( f ) (e.g. Liu et al., 2007; De Swaef and Steppe, 2010). However, because our work focuses on a period at the end of the growing season and measurements were done on an older part of the stem, f was assumed to be close to zero (1 ×
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F I G . 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.
TA B L E 3. Model parameters for the three periods in expt 2 Parameter Rx (MPa h g21) Cm (MPa) f (MPa21 h21) r (MPa h g21) G (MPa) a (dimensionless) C(0) (g g21) 10 (m21) S (g h21)
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0.0025 -0.1 0.001 0.1 0.3 0.8137 0.11 478 0.000817
0.0025 – 0.1 0.001 0.1 0.3 0.8137 0.11 690 – 0.000355
0.0025 –0.1 0.001 0.1 0.3 0.8137 0.11 770 0.0035
Initial calibration Initial calibration Assumption De Swaef and Steppe (2010) De Swaef and Steppe (2010) De Swaef and Steppe (2010) Liu et al. (2007) Model calibration (step 2) 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 dependency in the model. Furthermore, stem ageing is a process that limits D growth (Steppe et al., 2008a, 2008b), whereas the measured D in this study showed a sudden increase.
The magnitude of the destructively measured root pressure using a manometer installed on excised tomato stems agreed well with the model-based estimations (Fig. 7). However, destructively measured root pressure showed a decrease during
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the night, presumably as a result of decreasing substrate temperature, whereas estimated root pressure in intact leafed plants showed an increasing pattern towards the end of the night. It is therefore hard to relate diurnal dynamics of destructively measured root pressure to diurnal dynamics of transpiring plants: because the excised stems did not transpire during the day, root pressure enhanced during the day because of the higher temperature in the greenhouse, whereas root pressure is not allowed to develop in transpiring plants.
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Concurrent with the root pressure-induced night-time increase in D, it might be expected that FH2 O must increase. This was not always visible in our FH2 O data (Fig. 3A– C), but could be clarified by the model calculations. The measured night-time diameter increase corresponded with a calculated maximum water mass inflow of approx. 250 mg h21 for an 8 m long tomato stem, which is 400 times smaller compared with daytime FH2 O rates. Because of the low VPD at the end of these nights, plant water loss via transpiration could be neglected. Therefore, nearly all of the upward pushed water flow in the xylem was stored in the plant itself and thus resulted in the observed increase in D. However, the sensitivity of the heat balance sensors used in our study did not always allow detection of these low amounts of water flow (van Bavel and van Bavel, 1990). Significance
In the last decades, the reduction of energy use has become an important issue in glasshouse cultivation. This has led to a modified crop management and new energy-efficient climate strategies that may create conditions favouring the build up of root pressure. Because the occurrence of excessive root pressure may cause considerable damage to the harvestable product (Dorais et al., 2001), our approach could be of direct significance to growers, as an indicator when root pressure-associated problems might occur. Because these new energy-efficient technologies allow better glasshouse
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Time (h) F I G . 8. Diurnal profile of simulated xylem water potential and measurement of sap flow of plant 2 on 21 September 2010. The vertical dashed line indicates where sap flow rose sharply. Shaded bands indicate night-time.
climate control, potentially unfavourable conditions could be avoided using an intelligently managed compromise between energy saving and optimal growing conditions. In our study, no instant visible effects of excess root pressure were noticeable, probably indicating that root pressure had not yet reached a harmful level. Because some important physiological problems in horticulture are currently attributed 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 environmental factors driving root pressure, is the lack of appropriate systems for determining root pressure. Therefore, our non-destructive technique could allow root pressure to be estimated continuously, while imposing a wide range of growing conditions. Recently, Clearwater et al. (2007) unravelled a correlation between the rootstock affinity to build up root pressure and the scion vigour after grafting in kiwi. For tomato, it is known in practice that rootstocks have an important effect on scion vigour and on the occurrence of root pressure-related problems. Our approach could be used to select rootstocks
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F I G . 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.
De Swaef et al. — Stem diameter variations and root pressure quantitatively with a different affinity for root pressure. As such, better combinations of rootstocks and productive grafts could be made. Because our model and method rely on physiologically sound mechanisms which are valid for a broad range of vascular plants, our approach is perfectly applicable for many other plant species. Our technique to estimate root pressure in a continuous and non-destructive way is therefore a potential breakthrough for fundamental research in plant water relations. As the role of root pressure in general plant functioning is still not well understood, many plant physiological research topics such as cavitation or nutrient translocation could benefit from using this approach.
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