RACCIA routine for species-specific parameterisation

The species-specific parameterisation of the HARLEY/TENHUNEN model and other Farquhar models with RACCIA is focused on the determination of three key parameters that are not rubisco-specific. Due to the - among higher plants - similar structure of the rubisco molecule and its highly conserved active sites (KELLOGG & JULIANO 1997), species-specific variations in rubisco kinetic parameters (K_M,C, K_M,O, ττττ^, ΓΓΓΓ*) are expected to be relatively small (BERNACCHI ET AL.2001). In vitro measured values for ττττ ^and ΓΓΓΓ* of many different species generally vary about

±20% around a mean value of 2560 (dimensionless) and 42 µmol/mol at 25°C for all species (EPRON ET AL.1995),and rather big (±10%) intra-specific variations were found under the same measurement conditions (PARRY ET AL. 1987). However, also single outlying measurements (-50% for ττττ and +100% for ΓΓΓΓ*) exist for Fagus sylvatica and Castanea sativa (EPRON ET AL. 1995). The in vivo derivation of ττττ ^and ΓΓΓΓ* from Nicotiana tabacum and Spinacia oleracea (VON

CAEMMERER ET AL. 1994) yielded ττττ-values of 2710 and 2975, which equals ΓΓΓΓ*-values of 38.8 and 35.3 µmol/mol at 25°C, when oxygen concentrati on O is assumed to equal 210000 µmol/mol (equation 29). These measurements are the only ones, where carboxylation dependent limitation of the assimilation rate is assured by the use of transgenic plants with low rubisco content.

The term K_M,C (1+210 / K_M,O) from the calculation of A_V (equation (24)) varies for the low number of measured species between 410 and 750, (MAKINO ET AL. 1988,HARLEY &TENHUNEN 1991,

VON CAEMMERER ET AL.1994,BERNACCHI ET AL.2001), though K_M,C and K_M,O are not expected to vary among higher plants (VON CAEMMERER ET AL. 1994). It has been argued that this variation might be due to the in vitro measurement method. The two newer measurements use transgenic Nicotiana tabacum plants that shall assure the rubisco limitation of assimilation for in vivo measurements and end up with 710 and 746 for the term mentioned above (VON

CAEMMERER ET AL. 1994, BERNACCHI ET AL. 2001).

Rubisco-specific parameters and their temperature dependencies may, thus, be considered as constant among higher plants, meaning that species-specific variations in assimilation rates that are not due to stomatal limitations prevailingly result from the quantities P , Vc , R , and αααα^. (33) h_s=rh- rh-1

1+ ^gaw

gsw

(34) Cs=Ca- 1.37_HCa-CiL

1.37+1.6^gaw

gsw

RACCIA and the appertaining photosynthesis measurements were designated to estimate the quantities P_ml, Vcmax, and R_d that are crucial for the calculation of leaf gas-exchange, because αααα is the most conservative parameter out of the four and may approximately be estimated to equal 0.06 mol CO₂/mol photons among C₃ species under most conditions (HARLEY & TENHUNEN

1991, EHLERINGER &BJÖRKMAN 1977).

While equations (24) and (26) are a common part of most so-called Farquhar models, different types of equations are employed to describe light dependence of electron transport rate J, temperature dependencies, and effects of stomatal regulation, if considered. The original Farquhar model (FARQUHAR & VON CAEMMERER 1982) for example employs a hyperbolic relationship instead of equation (29) to express the saturating relationship of electron transport rate J on irradiance I:

The factor 2.1 in this equation has to be changed under certain conditions. J_max stands here for the electron transport capacity, the maximum electron transport rate under saturating light conditions, and it is by definition of J and P_m equal to 4P_ml. RACCIA can be used to derive both quantities, when A/C_i-measurements are made at light saturation, because it then only uses the common equations (24) and (26).

Published values for J_max and Vcmax range from 17 to 372 µmol/(m²*s) and from 6 to 194 µmol/(m²*s) (WULLSCHLEGER 1993), which has due to the multiplication in equations (24) and (26) an immense impact on calculated species-specific photosynthesis rates. The effect of day respiration (R_d) is often smaller due to its additive consideration and rather low absolute values:

Published estimates of R_d at about 25°C according to the method of LAISK (1977) and BROOKS

&FARQUHAR (1985) lie prevailingly in the range from 0 to 0.8 µmol/(m²*s) (HÄUSLER ET AL.1996, HÄUSLER ET AL 1999,JACOB &LAWLOR 1993,HERPPICH ET AL.1998,BROOKS &FARQUHAR 1985, SUMBERG & LAISK 1995, LAISK &LORETO 1996,ATKIN ET AL.1997), but also higher values were measured (3.4 µmol/(m²*s) for Encelia farinosa, ZHANG ET AL.1995), partly with another method (1.1 µmol/(m²*s) for Pinus sylvestris, WANG ET AL.1996).

RACCIA first calculates R_d as the negative assimilation rate that would be measured at C_i = ΓΓΓΓ*, prolonging the linear initial slope of each A/C_i-curve towards lower values (see Fig. 57, BROOKS

&FARQUHAR 1985). The needed ΓΓΓΓ*-value is calculated from the temperature dependence of ΓΓΓΓ* and ττττ, which are connected by equation (27). The used temperature dependence has been found by JORDAN & OGREN (1984) on spinach and was confirmed by later measurements on spinach and wheat (BROOKS & FARQUHAR 1985), French bean (GHASHGHAIE & CORNIC 1994), potato (HÄUSLER ET AL. 1999), and Eucalyptus pauciflora (ATKIN ET AL. 2000), where it is expressed as a formula:

However, a different temperature dependence was found for Epilobium hirsutum at temperatures below 18°C (GHASHGHAIE &CORNIC 1994). A ΓΓΓΓ*-value of 38.8 µmol/mol at 25°C and 210,000 µmol/mol oxygen concentration in the air was derived from the measurements of

J= JmaxI I+2.1Jmax

(35)

(36) G^*= G^*₂₅+1.88_HT-298.16_L+0.036_HT-298.16_L²

VON CAEMMERER ET AL. (1994) and was applied considering equation (27) and correcting O for air pressure of the measurement.

The temperature dependent Michaelis-Menten constants for rubisco catalysed oxygenation and carboxylation, K_M,O and K_M,C , are calculated according to equation (28) based on the measurements of VON CAEMMERER ET AL. (1994) and the specific H_A-values of HARLEY &

TENHUNEN (1991), which are similar to those from BERNACCHI ET AL. (2001).

The data points below 350 µmol/mol CO₂-concentration inside the leaf intercellular spaces (C_i) are then used for a non-linear regression (based on the Levenberg-Marquardt method) of equation (24) on each curve, thereby assuming that Vc_max is limiting photosynthesis in that part of the curve, so that A = A_V (Fig. 57).

Similarly, equation (26) is fitted to the points above 350µmol/(m²*s), where Vcmax is not limiting and J_max is equal to J due to saturating irradiance (2000µmol/(m²*s)) during the measurement.

RACCIA then evaluates groups of A/Ci-curves that belong to the same leaf (or to the same group of leaves, if desired) and were measured at different temperatures. A non-linear regression of equation (30) is performed on the calculated Vcmax values of these A/C_i-curves versus temperature. An additional data point in the Vcmax versus temperature diagram results from complete enzyme inactivation of rubisco, which was shown to occur at 60°C (GEZELIUS

1975). At least three additional Vcmax values at different temperatures are necessary, because equation (30) is used to estimate four parameters.

The same equation for J_max is fitted to the J_max values of at least three A/Ci-curves at different temperatures again completed by a Zero-value, which was estimated from ARMOND ET AL. (1978)andNOLAN &SMILLIE (1976)to occurat 50°C. 4 data points were sometimes not enough for these approximations, especially when the measured values were close to each other, so that a completely different shape of the curve better fulfilled the requirements of the χ² merit function given by the sum of squared residuals. In this case, data points were weighted and an additional Zero-value at -30°C was added with 10% o f the weight of the measurement-derived data to assure that the functional relationship starts with low values at 0°C instead of very high ones.

500 1000 1500 2000 2500

CiHµmol ê Hm²*sL L 0

10 20 30 40 50 60 70

AHlomµê²m*sLL

2

AV

A_J

20 40 60 80 100

CiHµmolê Hm²*sL L -1.5

-1 -0.5 0 0.5 1 1.5 2

AHlomµêH²m*sLL

Γ*

R_d

Fig. 57: Determination of Vcmax and Jmax with non-linear approximations of equations (24) and (26) (left graph), and determination of Rd from the initial slope of the A/Ci-curve.

3.2 Results