Saurer et al. (1997) modified Eq. 2.2 to allow interpretation of observed variation in <5180 of cellulose (<518Oc) from three tree species. This expression incorporated a 'dampening factor' (/) to summarize the effects of deviation in leaf water enrichment from Eq. 2.2, and the exchange of oxygen atoms with local cellular water (i.e., full dampening when f — 0). The expression was (Saurer et al., 1997):
<518Oc = S18Os +/ ■ [e* + sk + (S18Ov - S18Os - ekKM] + ewc (2.5)
where <518Os and <518Ov are the isotopic composition of source water and atmospheric water vapor, respectively, and sK(: is the fractionation factor between carbonyl oxygen and water (27%o). Roden and Ehleringer (1999; and see also Roden and Ehleringer 2000; and Roden et al., 2000) suggested that <518Oc of wood should be a function of the isotopic composition of sucrose imported from the leaf, and of local water in the developing cell, such that:
<$18Oc = pex • (518Owm + £wc) + (1 - pex) • (¿18OwI + ewc) (2.6)
where pex is the proportion of oxygen that exchanges with local water, <518Owm is the isotopic composition of sink cell water, and 518Owi is the isotopic composition of leaf water. Equation 2.6 can be simplified by expressing compositions in terms of enrichments above source water, by assuming that sucrose exported from the source leaf is in full isotopic equilibrium with average leaf water enrichment (A18Ol, as demonstrated by Barbour, 1999), and by including the term px, the proportion of xylem-sourced water in the developing cell. Barbour and Farquhar (2000) presented the simplified form:
where A18Oc is the enrichment of lsO above source water. The oxygen isotope composition of whole leaf tissue ( A18Oi) has been found to be significantly less enriched than its cellulose, by 7.5%o for cotton leaves (Barbour and Farquhar, 2000), and by 9.1%o in wheat leaves (Barbour et al., 2000a).
Equation 2.7 may be rewritten to include the term £cp, the difference in enrichment between cellulose and whole leaf tissue by:
Note that £cp is equal to A18Oi — A18Oc, so that £cp is negative. However, a significant weakness in Eq. 2.8 is that £cp is likely to be variable over time. Cernusak et al (2002) have shown that A18Oi of Lupinus angustifolius leaves varied considerably over a diurnal period, suggesting that diurnal variation in AlsO of non-structural carbohydrates contributed significantly to the whole leaf AlsO. Substantial temporal variation in AlsO of non-structural carbohydrates is expected, based on the measured variation in AlsO of phloem sap sucrose (Barbour et al, 2000b; Cernusak et al, 2002).
Whole wood AlsO should be much less variable in time than leaf tissue, due to the lower concentrations of non-structural carbohydrates, and the slower rate of metabolic activity in these cells. However, because lignin can form a large portion of whole wood by weight (about 40%; Barbour et al, 2001), and its isotopic history is rather different (Schmidt et al, 2001), the contribution of lignin to whole wood AlsO should be considered separately. Enrichment of lignin above source water (A18Oiig) may be modeled in a similar form to Eq. 2.7 by including molecular oxygen as a source (Barbour etal, 2001):
A180lig = (1 - po2) x [A18Ol(1 - pfx ■ px) + £WC] + po2 x [(1 - pl°)
x (A18Oo2 - £o2) + pl° x (A18Ol(1 - px) + £„i)] (2.9)
where po2 is the proportion of oxygen atoms in lignin from molecular oxygen (at least initially), p^ is the proportion of oxygen atoms in lignin from leaf water but exchanged with sink cell water during lignin synthesis, p^ is the proportion of oxygen atoms in lignin from molecular oxygen but later exchanged with sink cell water, A18Oo2 is the enrichment of molecular oxygen over source water, so2 is the fractionation associated with monooxygenase reactions, and £wi is the fractionation associated with exchange of oxygen with water in polymerization intermediates (i.e., may differ from £wc). Parameters in Eq. 2.9 remain loosely constrained by theoretical limits of biochemical reactions at present.
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