Philippa Kaur

Direct injection method for ethylene and acetylene δ13C analyses by GC-C-IRMSFollowing the direct injection approach of classical ISARA12 with a few modifications, ARA samples with high ethylene yield ( > 500 ppmv) in 10% v/v acetylene were manually injected into a Thermo Scientific Trace GC Ultra-Isolink with an Agilent HP-PLOT/Q  capillary GC column (30 m, i.d. = 0.32 mm, f.t. = 20 μm) and a combustion reactor connected to a Thermo Scientific Delta V Plus isotope ratio mass spectrometer (GC-C-IRMS; Fig. 1a). Modifications include the replacement of silver ferrules in the GC oven with Valcon polymide (graphite reinforced polymer) ferrules to limit memory effects from acetylene. The combustion reactor was oxidized with pure oxygen for 1 h before each run and brief (15 min) seed oxidations were performed between measurement batches (i.e., required every ~ 6–8 ethylene injections, ~ 4–6 acetylene injections) to regenerate reactor oxidation capacity and minimize drift of δ13C values. See Supplementary Table S1a online for additional instrument settings.Ethylene Pre-Concentration (EPCon) methodARA samples with  More

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Overall frameworkCells in our model are arranged along independent radial files, with each cell in one of either the proliferation, enlargement-only, wall thickening, or mature zones, depending on the distance of the cell’s centre from the inside edge of the phloem and the time of year. Only cells that contribute to the formation of xylem tracheids are treated explicitly. A daily timestep is used, on which cells in the proliferation and enlargement-only zones can enlarge in the radial direction if these zones are non-dormant, and on which secondary-wall thickening can occur in the wall thickening zone. Cells in the proliferation zone divide periclinally if they reach a threshold radial length. Cell-size control at division is intermediate between a critical size and a critical increment22. Mother cells divide asymmetrically, with the subsequent relative growth rates of the daughters inversely proportional to their relative sizes. Size at division and asymmetry of division are computed with added statistical noise22, and therefore the model is run for an ensemble of independent radial files with perturbed initial conditions.Equations and parametersCell enlargement and divisionCells in the proliferation and enlargement-only zones, when not dormant, enlarge in the radial direction at a rate dependent on temperature and relative sibling birth size. A Boltzmann-Arrhenius approach is used for the temperature dependence30:$$mu={mu }_{0}{e}^{frac{{E}_{a}}{k}left(frac{1}{{T}_{0}}-frac{1}{T}right)}$$
(1)
where μ is the relative rate of radial cell growth at temperature T (μm μm−1 day−1), μ0 is μ at temperature T0 (=283.15 K), Ea is the effective activation energy for cell enlargement, k is the Boltzmann constant (i.e. 8.617 x 10−5 eV K−1), and T is temperature (K). μ0 was calibrated to an observed mean radial file length at the end of the elongation period dataset23 (Table 1; see “Observations”), and Ea was calibrated to an observed temperature dependence of annual ring width dataset31 (Table 1; Supplementary Fig. 4; see “Observations”).Table 1 Model parameters calibrated to observationsFull size tableRadial length of an individual cell then increases according to:$${{Delta }}{L}_{r}={L}_{r}({e}^{epsilon mu }-1)$$
(2)
where ΔLr is the radial increment of the cell (μm day−1), Lr is the radial length of the cell (μm), and ϵ is the cell’s growth dependence on relative birth size, given by22:$$epsilon=1-{g}_{asym}{alpha }_{b}$$
(3)
where gasym is the strength of the dependence of relative growth rate on asymmetric division (Table 2; unitless), and αb is the degree of asymmetry relative to the cell’s sister22 (scalar):$${alpha }_{b}=frac{{L}_{r}{,}_{b}-{L}_{r}{,}_{b}^{sis}}{{L}_{r}{,}_{b}+{L}_{r}{,}_{b}^{sis}}$$
(4)
where Lr,b is the radial length of the cell at birth (μm) and ({L}_{r}{,}_{b}^{sis}) is the radial length of its sister at birth (μm), which are calculated stochastically22:$${L}_{r}{,}_{b}={L}_{r}{,}_{d}(0.5-{Z}_{a})$$
(5)
$${L}_{r}{,}_{b}^{sis}={L}_{r}{,}_{d}(0.5+{Z}_{a})$$
(6)
where Lr,d is the length of the mother cell when it divides (μm) and Za is Gaussian noise with mean zero and standard deviation σa (Table 2; −0.49 ≤Za≤ 0.49 for numerical stability).Table 2 Parameters used in the model that are taken directly from literatureFull size tableLength at division is derived as22:$${L}_{r}{,}_{d}=f{L}_{r}{,}_{b}+{chi }_{b}(2-f+Z)$$
(7)
where f is the mode of cell-size regulation (Table 2; unitless), χb is the mean cell birth size (Table 3; μm), and Z is Gaussian noise with mean zero and standard deviation σ (Table 2).Table 3 Parameters used in the model that are calculated from observationsFull size tableThe first cell in each radial file is an initial, which produces phloem mother cells outwards and xylem mother cells inwards. It grows and divides as other cells in the proliferation zone, but on division one of the daughters is stochastically assigned to phloem or xylem, the other remaining as the initial. The probability of the daughter being on the phloem side is fphloem (Table 3).Cell-wall growthBoth primary and secondary cell-wall growth are influenced by temperature, carbohydrate concentration, and lumen volume. A Michaelis-Menten equation is used to relate the rate of wall growth to the concentration of carbohydrates in the cytoplasm:$${{Delta }}M=frac{{{Delta }}{M}_{max}theta }{theta+{K}_{m}}$$
(8)
where ΔM is the rate of cell-wall growth (mg cell−1 day−1), ΔMmax is the carbohydrate-saturated rate of wall growth (mg cell−1 day−1), θ is the concentration of carbohydrates in the cell’s cytoplasm (mg ml−1), and Km is the effective Michaelis constant (mg ml−1; Table 1).The maximum rate of cell-wall growth, ΔMmax, is assumed to depend linearly on lumen volume (a proxy for the amount of machinery for wall growth), and on temperature as in Eq. (1):$${{Delta }}{M}_{max}=omega {V}_{l}{e}^{frac{{E}_{aw}}{k}left(frac{1}{{T}_{0}}-frac{1}{T}right)}$$
(9)
where ω is the normalised rate of cell-wall mass growth (i.e. the rate at T0; Table 1; mg ml−1 day−1), Vl is the cell lumen volume (ml cell−1), and Eaw is the effective activation energy for wall building (eV; Table 1). ω and Km were calibrated to an observed distribution of carbohydrates23 (see next section). Eaw was calibrated to an observed temperature dependence of maximum density31 (Table 1; see “Observations”).Lumen volume is given by:$${V}_{l}={V}_{c}-{V}_{w}$$
(10)
where Vc is total cell volume (ml cell−1) and Vw is total wall volume (ml cell−1). Cells are assumed cuboid and therefore Vc is given by:$${V}_{c}={L}_{a}{L}_{t}{L}_{r}/1{0}^{12}$$
(11)
where La is axial length (μm; Table 2) and Lt is tangential length (μm; Table 3). Vw is given by:$${V}_{w}=M/rho$$
(12)
where M is wall mass (mg cell−1) and ρ is wall-mass density (Table 2; mg[DM] ml−1).Cells in the proliferation and enlargement-only zones only have primary cell walls. ΔMmax (Eq. (9)) is therefore given the following limit:$${{Delta }}{M}_{max}=min ({{Delta }}{M}_{max},rho {V}_{{w}_{p}}-M)$$
(13)
where ({V}_{{w}_{p}}) is the required primary wall volume:$${V}_{{w}_{p}}={V}_{c}-({L}_{a}-2{W}_{p})({L}_{t}-2{W}_{p})({L}_{r}-2{W}_{p})/1{0}^{12}$$
(14)
where Wp is primary cell-wall thickness (Table 3; μm).Carbohydrate distributionThe distribution of carbohydrates across each radial file is calculated independently from the balance of diffusion from the phloem and the uptake into primary and secondary cell walls. The carbohydrate concentration in the phloem is prescribed at the mean value observed across the three observational dates in23, as described below in “Observations”, and the resulting concentration in the cytoplasm of the furthest living cell from the phloem is solved numerically. The inside wall of this cell is assumed to be impermeable to carbohydrates and therefore provides the inner boundary to the solution. It is assumed that the rate of diffusion across each file is rapid relative to the rate of cell-wall building, and therefore concentrations are assumed to be in equilibrium on each day. Carbohydrate diffusion between living cells is assumed to be proportional to the concentration gradient:$${q}_{i}=({theta }_{i-1}-{theta }_{i})/eta$$
(15)
where qi is the rate of carbohydrate diffusion from cell i − 1 to cell i (mg day−1) and η is the resistance to flow between cells (calibrated to the observed distribution of carbohydrates23, see next section; Table 1; day ml−1).As it is assumed that carbohydrates cannot diffuse between radial files, at equilibrium the flux into a given cell must equal the rate of wall growth in that cell plus the wall growth in all cells further along the radial file away from the phloem. From this it can be shown that the equilibrium carbohydrate concentration in the furthest living cell from the phloem in each radial file is given by:$${theta }_{n}={theta }_{p}-eta mathop{sum }limits_{i=1}^{n}mathop{sum }limits_{j=i}^{n}{{Delta }}{M}_{j}$$
(16)
where θp is the concentration of carbohydrates in the phloem (Table 3; mg ml−1) and n is the number of living cells in the file (phloem mother cells are ignored for simplicity). The rate of wall growth in each cell depends on the concentration of carbohydrates (Eq. (8)), and therefore θn must be found that results in an equilibrium flow across the radial file. This is done using Brent’s method41 as implemented in the “ZBRENT” function42.Zone widthsThe widths of the proliferation, enlargement-only, and secondary wall thickening zones vary through the year, and are fitted to observations on three dates23 (see Supplementary Fig. 2 and “Observations”). Linear responses to daylength were found, which are therefore used to determine widths for the observational period and later days:$${z}_{k}={a}_{k}+{b}_{k}{{{{{{{rm{dl}}}}}}}};{{mathrm{DOY}}}ge 185$$
(17)
where zk is the distance of the inner edge of the zone from the inner edge of the phloem (μm), k is proliferation (p), secondary wall thickening (t), or enlargement-only (e), ak and bk are constants (Table 3), dl is daylength (s), and DOY is day-of-year. The proliferation zone width on earlier days when non-dormant was fixed at its DOY 185 width (assuming this to be its maximum, and that it would reach its maximum very soon after cambial dormancy is broken in the spring). During dormancy, the proliferation zone width is fixed at its value on DOY 231 (the first day of dormancy23). The enlargement-only zone width prior to DOY 185, the first observational day, is assumed to be a linear extension of the rate of change after DOY 185. The wall-thickening zone width plays little role prior to DOY 185 at the focal site, and so was set to its Eq. (17) value each earlier day. On all days the condition zt≥ze≥zp is imposed, and zone widths cannot exceed their values at 24 h daylength (necessary for sites north of the Arctic circle). Supplementary Figure 2 shows the resulting progression of zone widths through the year, together with the observed values.DormancyProliferation was observed to be finished by DOY 23123, and so the proliferation and enlargement-only zones are assumed to enter dormancy then. Release from dormancy in the spring is calculated using an empirical thermal time/chilling model33. It was necessary to adjust the asymptote and temperature threshold of the published model because the heat sum on the day of release calculated from observations in Sweden (see “Observations”) was much lower than reported for Sitka spruce buds in Britain in the original work:$${{{{{{{{rm{dd}}}}}}}}}_{req}=15+4401.8{e}^{-0.042{{{{{{{rm{cd}}}}}}}}}$$
(18)
where ddreq is the required sum of degree-days (°C) from DOY 32 for dormancy release and cd is the chill-day sum from DOY 306. The degree-day sum is the sum of daily mean temperatures above 0 °C, and the chill-day sum is the number of days with mean temperatures below 0 °C. Dormancy can only be released during the first half of the year.Simulation protocolsEach simulation consisted of an ensemble of 100 independent radial files. Each radial file was initialised by producing a file of 100 cells with radial lengths χb(1+Za), allowing these to divide once, ignoring the second daughter from each division, and then limiting the remaining daughters to only those falling inside the proliferation zone on DOY 1. Values for ϵ (the relative growth of daughter cells) and Lr,d (the radial length at division) were derived for each cell. The main simulations were conducted at the observation site in boreal Sweden (64.35°N, 19.77°E) over 1951–1995 to capture the growth period of the observed trees23. Results are mostly presented for 1995 when the observations were made. Simulations for calibration of the effective activation energies (i.e. Ea and Eaw) were performed at 68.26°N, 19.63°E in Arctic Sweden over 1901–200431. Daily mean temperatures for both sites were derived from the appropriate gridbox in a 6 h 1/2 degree global-gridded dataset43.ObservationsObservations of cellular characteristics and carbohydrate concentrations23 were used to derive a number of model parameters, and to test model output (model calibration and testing were performed using different outputs). According to the published study we used, samples were cut from three 44 yr old Scots pine trees growing in Sweden (64°21’ N; 19°46’ E) at different times during the growing season. 30 μm thick longitudinal tangential sections of the cambial region were made, and the radial distributions of soluble carbohydrates measured using microanalytical techniques23. Cell sizes, wall thicknesses, and positions in their Fig. 123, an image of transverse sections on three sampling dates, were digitised using “WebPlotDigitizer”44. These, together with the numbers of cells in each zone and their sizes given in the text of that paper, were used to estimate zone widths, which were then regressed against daylength to give the parameters for Eq. (17) (Table 3), mean cell size in the proliferation zone on the first sampling date (used to derive χb; Table 3), mean cell tangential length (Table 3), and final ring width (used to calibrate μ0; Table 1). The thickness of the primary cell wall (Table 3) was derived by plotting cell-wall thickness against time and taking the low asymptote.The distributions of carbohydrates along the radial files on the last sampling date for “Tree 1” and “Tree 3” (results for “Tree 2” were not shown for this date) shown in Fig. 2 of the observational paper23 were calculated. The masses for each of sucrose, glucose, and fructose in each 30 μm section were digitised using the same method as for cell properties and then summed and converted to concentrations, with the results shown in Supplementary Figure 5. Mean observed carbohydrate concentrations and cell masses at four points were used to calibrate values for the η, ω, and Km parameters in Table 1. Calibration was performed by minimising the summed relative error across the observations.The calibration target for the effective activation energy for wall deposition (i.e. Eaw) was the observed relationship between maximum density and mean June-July-August temperature over 1901-2004 in northern Sweden31 (Supplementary Fig. 3), and for the effective activation energy for cell enlargement the relationship between ring width and temperature (i.e. Ea) target was the same study (Supplementary Fig. 4). These observations were made on living and subfossil Scots pine sample material from the Lake Tornesträsk area (68.21–68.31°N; 19.45–19.80°E; 350–450 m a.s.l.) using X-ray densitometry for maximum density, and standardised to remove non-climatic information31.Reporting summaryFurther information on research design is available in the Nature Portfolio Reporting Summary linked to this article. More

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