Regulation of solute flux through plasmodesmata in the root meristem.

Plasmodesmata permit solutes to move between cells nonspecifically and without having to cross a membrane. This symplastic connectivity, while straightforward to observe using fluorescent tracers, has proven difficult to quantify. We use fluorescence recovery after photobleaching, combined with a mathematical model of symplastic diffusion, to assay plasmodesmata-mediated permeability in the Arabidopsis (Arabidopsis thaliana) root meristem in wild-type and transgenic lines, and under selected chemical treatments. The permeability measured for the wild type is nearly 10-times greater than previously reported. Plamodesmal permeability remains constant in seedlings treated with auxin (30 mM indoleacetic acid for 2 and 24 h; 100 nm indoleacetic acid for 2 h); however, permeability is diminished in two lines previously reported to have impaired plasmodesmal function as well as in wild-type seedlings treated for 24 h with 0.6 mM tryptophan. Moreover, plasmodesmal permeability is strongly altered by applied hydrogen peroxide within 2 h of treatment, being approximately doubled at a low concentration (0.6 mM) and nearly eliminated at a higher one (6 mM). These results reveal that the plasmodesmata in the root meristem carry a substantial flux of small molecules and that this flux is subject to rapid regulation.


INTRODUCTION
other words, the flux of a small solute through plasmodesmata is governed by the effective size of the molecule and the concentration gradient between adjacent cells. While the size-exclusion limit is a useful number, it provides only a binary (yes or no) measure of molecular movement. A complete picture requires information about the magnitude of the molecular flux, that is, the number of molecules moving through the channel per unit time.
A flux may be observed qualitatively using a variety of techniques, including electrical coupling, the movement of microinjected dyes, and the photobleaching of dyes (Tucker et al., 1989;Robards and Lucas, 1990;Schulz, 1999). However, only a handful of studies have attempted to quantify the molecular flux, either through an individual plasmodesma or across a given cell wall (Tucker et al., 1989;Goodwin et al., 1990). These studies used microinjection, and so suffer from the drawback that they might trigger changes in the plasmodesmal conductivity because of a wound response (Radford and White, 2001). A second limitation of published studies is that experimental and theoretical challenges have encouraged a focus on large cells in simple tissuesfor example, filamentous stamenal hairs or aquatic leaves just two cell layers thick. To our knowledge, plasmodesmal flux has never been quantified in a fully three-dimensional tissue, such as a meristem.
In this paper we present an assay based on fluorescence recovery after photobleaching to quantify the plasmodesmal permeability in the root meristem of Arabidopsis thaliana. The protocol avoids possible complications due to microinjection by application of carboxyfluorescein diacetate (CF-DA), which is membrane-permeable and non-fluorescent.
Once in the cytoplasm, the acetate groups are cleaved by endogenous esterases to yield fluorescent CF, which is not membrane permeable (Zhu et al., 1998). We show that dye fluxes are much larger -by as much as an order of magnitude -as compared with fluxes measured in non-meristematic cells, and we validate the protocol by confirming that dye fluxes are decreased in transgenic lines with known impairment in plasmodesmal function. Furthermore, we assay several chemical treatments that might regulate plasmodesmal gating: the aromatic amino acid, tryptophan; the growth regulator, auxin; and the reactive oxygen species, hydrogen peroxide.

Plasmodesmal permeability from tissue-scale analysis
We load dye into the cells of the meristem by incubating the roots of intact seedlings in the di-acetate derivative of CF for 7 min. The seedlings are then transferred to dye-free growth medium and moved to the stage of a confocal fluorescence microscope for photobleaching and recovery. The observed recovery of fluorescence intensity is used to obtain an effective diffusion constant D and an effective permeability P, as outlined below.
Photobleaching single cells was challenging because of the rapidity of dye recovery and the difficulty of deriving an accurate permeability value from the bleaching geometry of cells in the root. Although we do use a single-cell method for verification (see Plasmodesmal permeability from cell-scale analysis below), we found that a more robust and reproducible method for obtaining a diffusion coefficient was by photobleaching dye in a large block of cells.
The root is bleached in a 50 μm long zone (~6 cell lengths) spanning the width of the root, and located about 200 μm from the quiescent center (Fig. 1). The bleach penetrated all visible layers of the root, not just the epidermis, and retained a length of approximately 50 µm at all depths ( Fig. S1). Image intensity is averaged across the width of the root, allowing us to approximate fluorescence recovery as a diffusion problem in one dimension. The diffusion coefficient we measure in this way combines the effects of diffusion within the cytoplasm and transport through plasmodesmata, so we refer to it as an "effective" diffusion coefficient.
To find the effective diffusion coefficient, we compare the recovery data with an approximate mathematical model of the experiment. Following photobleaching, the intensity profile I(x,t) is well-described by the steady-state solution, I ss (x), minus a diffusing mass of bleached dye with a Gaussian profile, as where I SS is the steady-state intensity that would be achieved if diffusion ran to completion, and the rightmost term is the solution to the diffusion equation on an infinite line with an initially Gaussian distribution. The constant B characterizes the depth of the bleach, x 0 is the location of the center of the bleach, t 0 is the effective starting time, and D is the effective diffusion coefficient.
We first find a preliminary location for the center of the bleach, x′ 0 , using a parabolic curve fit to I(x) at early post-bleach times. Then, to find t 0 , the intensity at the center of the bleach is fit to Eqn. 1 with x = x′ 0 , namely To eliminate the unknown function I SS (x) from our analysis, we subtract intensity data at two consecutive times, t 1 and t 2 , and fit the difference to where t 0 is obtained as described above, and t 1 and t 2 are known from the image acquisition times. Best results are achieved when the intensities vary rapidly, so we generally choose times within 15 seconds from the end of the bleach. In cases where the diffusion was relatively slow (specifically, for high concentrations of H 2 O 2 ), we averaged over longer times. The curve fit to Eqn.
(3) yields values for B, D, and an improved value for the bleach center, x 0 . The value for x 0 is used to validate the original choice for the intensity minimum, and D is the desired diffusion coefficient. Using this approach, values for an effective diffusion constant were recovered with good reproducibility (see below).
Having found the effective diffusion coefficient, D, we can convert this to a plasmodesma-mediated wall permeability, P. In general, the flux of a solute diffusing through the plasmodesmata is given by where J is the flux (moles crossing a unit area of wall per unit time) from cell 1 to 2, c 1 and c 2 are the solute concentrations adjacent to the open ends of the plasmodesmata, and P is a diffusive permeability, which will depend on the solute under consideration. Since our protocol does not resolve the concentration at the walls, we instead track the average solute concentration of an entire cell. In this case, the appropriate version of Fick's law is where C 1 and C 2 are the average concentration in cell 1 and 2, L is the mean cell length, and D is our effective diffusion coefficient.
As mentioned above, our value for D incorporates the effects of both the plasmodesmal permeability and the diffusion of solute within the cytoplasm. The relationship between P and D can be calculated for a single file of cells as where L is the mean cell length and D cyt is the diffusion coefficient of dye in the cytoplasm. The numerator (D/L) is the permeability estimate in the case where the cytoplasm is well-mixed, and the denominator is a correction due to the cytoplasmic dye gradient that accompanies diffusion (Kramer, 2002). Thus, a value for permeability can be obtained from the effective diffusion constant for the bulk tissue (measured above), the mean cell length in the region, and the cytoplasmic diffusion constant. For mean cell length, we measured the average length of cortex cells in the region used for bleaching (see Table III). In some experiments below, treatments lasted only two hours, and for those we used the control ("wild type") cell length because meristematic cell growth is approximately 5% h -1 (Beemster and Baskin, 1998) and hence can undergo little change within that interval. Our value obtained for the wild type agrees with previous results (Beemster and Baskin, 1998). We take the diffusion constant for CF in the cytoplasm, D cyt , as 162 μm 2 /s, which is one-third of its aqueous value (Paine et al., 1975;Kramer et al., 2007). The permeability thus obtained (see Fig. 4B) is almost an order of magnitude greater than previous reports (Goodwin et al., 1990).

Plasmodesmal permeability from cell-scale analysis
To validate the results from tissue-scale photobleaching, we developed an alternative method based on photobleaching single cells. Single cell bleaches were challenging because dye moved rapidly between cells (< 1 s), and because dye movement in three dimensions was difficult to model. We achieved satisfactory single-cell results for epidermal cells only. To minimize photobleaching of adjacent cells, the bleaching region was limited to a circular spot, approximately 10 μm 2 and centered within the target cell. Since the vacuole was relatively dark, by necessity the bleaching region overlay the nucleus. The nucleus is in diffusive communication with the cytoplasm, and bleached dye moved quickly (< 1 s) between compartments.
Rather than monitoring brightness recovery, we measured intensity during the bleaching process itself. We built a time course by taking the first post-bleach frame from a series of progressively longer bleaches (Fig. 3), effectively tracking the rate of brightness loss. In the Supplemental Information, we derive the following equation for the rate of change of intensity of a bleached nucleus during an ongoing bleach where n 1 and n 2 are the intensities of the bleached nucleus and an adjacent nucleus respectively, P is the cell wall permeability between epidermal cells, A is the cell wall area, V is the volume of the cell, τ is a time scale characterizing the strength of the bleach, and b is a constant. The first term on the right represents the diffusive movement of dye from the adjacent unbleached cells into the bleached cell, the second term represents the loss of dye due to bleaching, and the constant term b is an approximate correction to allow for the fact that the nuclear brightness will in general be different from the cytoplasmic brightness.
With measurements of n 1 , n 2 , and dn 1 /dt, we find the coefficients in Eqn. 7 using linear regression. This gives values for τ, b, and the ratio PA/V. The wall area A, and cell volume V, are measured from a corresponding z-stack of the bleached cell. We found the resulting value for plasmodesmal permeability of a single epidermal cell wall to be P = 3.3 ± 0.8 µm/s (SEM, n = 4). This is approximately half that obtained from the tissue-scale bleach protocol. Insofar as the single cell analysis involves the epidermis and the tissue-scale analysis involves multiple cells layers, their agreement within a factor of two gives us confidence in these measurements of permeability.

Analysis of lines with reduced plasmodesmal conductivity
To validate further our measurements of diffusion and resulting permeability, we applied the bulk bleaching protocol to plant lines where plasmodesmata are reported to be perturbed. GFP introduced into leaf epidermal cells by bombardment undergoes reduced cell-to-cell movement as compared with wild type. We find that permeability in this line was about one-half that of wild type (Fig. 4).
Second, we assayed permeability in radially swollen6 (rsw6), a line isolated on the basis of temperature-dependent root swelling and reported to have defective organization of cortical microtubules (Bannigan et al., 2006). The roots of rsw6 are similar to wild type at temperatures below about 22˚C and express the root swelling phenotype at higher temperatures. Following incubation of rsw6 at 30˚C for 6 h, dye movement in the epidermis and cortex is qualitatively reduced compared to wild type (Bannigan, 2003). Consistent with these observations we measured a substantial decrease in permeability for rsw6 under the same conditions (Fig. 4).
Thus, in two distinct genetic backgrounds, our assay quantifies a reduced plasmodesmal permeability consistent with previous, qualitative reports.

Alteration of plasmodesmal permeability
Having established a means to quantify plasmodesmal permeability, we used it to probe several situations where permeability might be expected to change. In an earlier study of Egeria densa leaves, microinjection of various aromatic amino acids at 10 mM significantly reduced plasmodesmal permeability to small molecules, implying a level of specific regulation (Erwee and Goodwin, 1984). Therefore, we first assayed the effects of the aromatic amino acid, tryptophan. To determine relevant concentrations, we transferred untreated seedlings to plates containing tryptophan and measured root elongation rate over the next three days ( Fig 5A). On 0.3 mM tryptophan, root elongation rate did not differ significantly from the control but on 0.4 mM, elongation rate decreased to below 20% of the control. Thus, for permeability assays, we chose 0.3 mM as a "low" concentration of tryptophan, and 0.6 mM as a "high" value.
For tissue-scale permeability assays, six-day-old seedlings were transferred to plates containing the indicated concentration and assayed after 2 hours (Table I) and after 24 hours of treatment (Table II). At either time, the low concentration (0.3 mM) had no significant effect on permeability. The high concentration (0.6 mM) reduced permeability at 24 hours by about 30%; and at 2 hours, permeability tended to be decreased although the effect was not significant.
We next assayed the effect of the plant hormone auxin (indoleacetic acid, IAA). We chose a "low" concentration of 30 nM IAA, which inhibits root elongation rate by approximately 50%, and a high concentration of 100 nM IAA, which stops growth almost completely (Rahman et al., 2007). After 2 hours of treatment, permeability did not significantly differ from the control on either concentration (Table I). We also assayed roots after treatment with 30 nM IAA for 24 hours and again, permeability did not significantly differ from control (Table II). We did not assay a 24 hour treatment with 100 nM IAA because the complete inhibition of growth seems non-physiological. These results suggest that flux through plasmodesmata is generally insensitive to increasing auxin levels.
For the controls in Tables I and II, permeability for the 2 h treatment was higher than that of the 24 h treatment and the difference was significant (see Fig. 4). For treatments, seedlings are transferred from one (control) plate to another (treatment) plate. Although lasting only a few minutes per treatment, transfer involves exposure to air, horizontal placement, and mechanical stress, any of which might have led to an increase in plasmodesmal flux. By 24 h, this effect had apparently subsided, in that recorded permeability values matched those of seedlings never transferred between plates. That this relatively mild transfer treatment significantly altered flux through plasmodesmata underscores the sensitivity of our assay.
Curiously, the production of reactive oxygen species has been associated with both an  5B). Root elongation rate was similar to controls on 0.6 mM H 2 O 2 , but was reduced to negligible levels on 1 mM H 2 O 2 . We chose 0.6 mM hydrogen peroxide as the "low" concentration, and 6 mM as the "high" concentration. To assay plasmodesmal permeability, we transferred sevenday-old seedlings to treatment plates for two hours. Strikingly, treatment with the low concentration of hydrogen peroxide increased plasmodesmal permeability by factor of two, whereas the high concentration nearly abolished it (Fig. 4).
To our knowledge, these results are the first reported quantitative changes in solute flux through plasmodesmata on a two-hour time scale. This implies an active regulation of symplastic connectivity.
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DISCUSSION
The observed plasmodesmal fluxes between cells of the A. thaliana root meristem are unexpectedly rapid. In fact, in our initial attempts to monitor the fluorescence recovery of single bleached cells, we acquired images at one frame per 5 seconds and missed the recovery process entirely. This is one reason we turned instead to a protocol in which a large volume of the root meristem is bleached. The large cytoplasmic volume slows down the time scale of diffusive recovery, and the involvement of hundreds of cells reduces the impact of cell-to-cell heterogeneity. Our results indicate that adjacent meristem cells will equilibrate small solutes in just a few seconds.
Although our results rely principally on tissue-scale bleaches, we did perform some single-cell bleaches for validation purposes. The permeability value measured for the transverse walls of single epidermal cells (3.3 µm/s) is two to three times smaller than values measured in the tissue as a whole (6 to 8.5 µm/s). Since the intensity data collected for single cells are for epidermis whereas those for the tissue-scale analysis are dominated by the large cross-sectional area of cortical cells, the difference could reflect a difference in permeability between epidermis and cortex. Indeed, in the A. thaliana root meristem, plasmodesmal frequency in transverse walls of cortical cells is about twice as high as that in the epidermis (Zhu et al., 1998), a finding that plausibly accounts for the two-fold difference we report for permeability.
To our knowledge, plasmodesmal permeability has been reported explicitly in only one previous paper (Goodwin et al., 1990). These authors tracked the movement of dye microinjected into leaf epidermal cells of E. densa and reported a permeability of 1.1 μm/sec for CF, and ten times less for fluorescein conjugated to single amino acids. Our bulk permeability values for the A. thaliana meristem are nearly an order of magnitude larger. We suggest that the difference is due in part to the non-invasive nature of our method, whereby a puncture-wound response was avoided. The difference could also reflect programmed permeability decreases coincident with differentiation, as previously observed using CF in roots (Duckett et al., 1994) and GFP in embryos (Kim and Zambryski, 2005).
Although obtained for fairly unusual tissues such as aquatic leaves or stamen hairs, earlier measurements of dye permeability and diffusion have been influential whenever a value for the transport capacity of the symplast has been needed. For example, Bret-Harte and Silk (1994) used results from a study of diffusion in stamen hairs (Tucker et al., 1989)  symplasmic pathway in the maize root apex cannot transport enough sucrose to sustain measured rates of dry mass deposition. However, with the permeability values reported here, symplastic transport would be sufficient.
Our assay also revealed that hydrogen peroxide increases or decreases plasmodesmal flux based on concentration (Fig. 4 A, B). This bi-phasic regulation is suggestive of two recent reports that have implicated reactive oxygen species in the regulation of plasmodesmal function, but in a contradictory way. Both reports featured A. thaliana loss-of-function mutants. The first mutation is increased size exclusion 1 (ise1), which occurs in a mitochondrial RNA helicase (Stonebloom et al., 2009), and the other is GFP arrested trafficking 1 (gat1), which occurs in an m-type, plastid-localized thioredoxin (Benitez-Alfonso et al., 2009). In both mutants, roots accumulate reactive oxygen species; however, the symplastic permeability phenotypes are opposite, increasing in ise1 and decreasing in gat1. Based on our results, we hypothesize that the opposite permeability phenotypes of the two mutants is explained by the degree to which reactive oxygen species accumulate, with a large increase in gat1 and a small increase in ise1.

Also consistent with our results, Benabdellah et al. (2009) found in Phaseolus vulgaris
roots that hydrogen peroxide exerts bi-phasic effects on bulk hydraulic conductivity, increasing it at low concentrations (below about 1 mM) and decreasing it at higher concentrations. Although their results did not distinguish contributions from symplastic and apoplastic pathways, taken together with ours, it suggests that the movement of small molecules including water is generally promoted by modest increase of reactive oxygen species and restricted by a larger increase. A speculative explanation for this response is that low levels of peroxide signal a state of stress that can be ameliorated by increased exchange of water and nutrients, while higher levels signal a dangerous state, such as pathogen invasion, where cell isolation is beneficial.
We also tested the effects of several other exogenous chemical treatments on plasmodesmal permeability. The aromatic amino acid, tryptophan, slows dye movement significantly at 0.6 mM after 24 hours, consistent with earlier qualitative work (Erwee and Goodwin, 1984). Since tryptophan concentration in plant tissues is between 0.1 and 1 mM tryptophan, IAA itself does not regulate plasmodesmatal permeability at physiologically relevant levels, both at 2 hour and 24 hour treatment times.
Since auxin does not gate plasmodesmata, we wondered whether the large permeabilities reported here would allow auxin to cross cell walls fast enough to short-circuit polar auxin transport. In fact, the permeabilities measured here are still consistent with auxin transport, according to a straightforward mathematical argument. In the simplest model of polar auxin transport, one considers a single, uniform file of non-vacuolated cells. The equation for the speed of auxin transport, v, through this cell file is where D cyt is the cytoplasmic diffusion coefficient of auxin, L is the cell length, p is the contribution to the cell wall permeability from the polar distribution of PIN carriers, and q is the contribution to cell wall permeability from any nonpolar auxin carriers as well as from open plasmodesmata (Mitchison, 1980a;Kramer, 2002).
To assess the impact of open plasmodesmata on auxin transport, we need to assign approximate values to the variables in Eq. 8. The PIN permeability will be approximately equal to the auxin transport speed, which in most tissues is about 1 cm/h (Kramer, 2004), so we set p = 1 cm/h = 2.8 μm/s. The cytoplasmic diffusion coefficient of auxin is perhaps one-third of its aqueous value, D cyt = 220 μm 2 /s (Paine et al., 1975). Assuming that open plasmodesmata make the largest contribution to q, we can use a typical permeability reported here, q = 10 μm/s. For a file of cells 10 μm in length, Eq. 8 gives v = p/1.5 = 1.8 μm/s, a reduction below p of 34%; however, for a file of 100 µm long cells, we have v = p/6.1 = 0.45 μm/s, a reduction below p by 84%. Therefore, the plasmodesmal permeability can be several times larger than the PIN permeability and still cause only a modest reduction of auxin transport speed, at least for smaller cells.
Competition between plasmodesmata and PIN proteins is made explicit in Eq. 8 through the dimensionless quantity q(L/D cyt ). To see the importance of this quantity, recall that polar auxin transport is believed to rely on diffusion to move auxin within the cell. Thus, one expects a maximum in the cytoplasmic auxin concentration at the upstream end of the cell and an auxin minimum adjacent to the PIN efflux proteins (Fig. 6). The ratio, D cyt /L, characterizes the diffusion of auxin through the cytoplasm from the auxin maximum to the auxin minimum (the "forward" flux) while the permeability q characterizes the flux of auxin through the cell wall back to the previous minimum (the "backward" flux). The ratio of reverse to forward fluxes is thus q(L/D cyt ). This ratio is 0.45 for a file of 10 μm cells and 4.5 for 100 μm cells. This might be one reason why cell enlargement coincides with a gradual restriction of flux through plasmodesmata, because otherwise polar auxin transport would be impractical in elongated cells.
Our method for quantifying plasmodesmal flux takes advantage of the small size, relative transparency, and lack of autofluorescent chlorophyll in the A. thaliana root, features that allow for easy dye loading and manipulation. However, the method could be applied to other tissues with appropriate modifications. It should also be straightforward to use this technique with larger fluorescent molecules and proteins, and thereby quantify plasmodesmal permeability for probes of different sizes and structure. Care must be taken to ensure that the rates of probe synthesis and degradation are low compared to the time scale of diffusion through the plasmodesmata; these requirements are met for ester-loaded CF in the root meristem. Using this method, we have

Plant growth and treatments
Arabidopsis thaliana L. (Heynh) seeds were surface sterilized, rinsed, and planted on agar plates containing 1% Bacto-agar (Difco) and 1% sucrose in a modified Hoagland's medium placed vertically in constant, yellow light (ca. 100 μmol m -2 s -1 ) at 22°C, as described previously (Bannigan et al., 2006). All material was in the Columbia background. For experimental treatments, seedlings were grown for 5 to 7 days before transfer to fresh agar plates containing the compound of interest and then returned to the growth chamber for the indicated interval (usually between 2 to 24 h). For hydrogen peroxide, agar plates were prepared with the required concentration 1 hour prior to transfer to ensure maximum activity of the compound. Assays of root elongation rate were done as described previously (Rahman et al., 2007).

Dye loading and confocal microscopy
Whole seedlings were removed from agar plates and roots were incubated in 30 mg/mL carboxyfluorescein-diacetate in growth medium for 7 minutes. Excess dye solution was removed with tissue paper. To avoid CF being generated during recovery from photobleaching, the root was rinsed once with growth medium, and then surrounded by fresh growth medium for imaging.
A cover slip was applied to reduce movement during imaging, and the root was immediately imaged on a confocal fluorescence microscope (either a Nikon Eclipse TE-2000S or a Zeiss LSM 510) with a 40X objective. Tissue-scale diffusion was measured by bleaching a 50 μm long segment of the root meristem, approximately 200 μm behind the quiescent center, for 35-40 s.
The focal plane is centered within the root cortex, as optical sections closer to the stele are too dim to monitor. The confocal pinhole is opened to give a focal depth of about 10 μm. Setting a thick focal plane allows us to reduce the laser intensity and thereby limit bleaching affects. Also, averaging over a thicker volume reduces the effects of micron-scale fluctuations in brightness.
The image acquisition rate during brightness recovery was typically one frame per 1.5 s, which includes an exposure time of 0.7-0.8 seconds per image. The mathematical details of the analysis used to determine the diffusion coefficient D and the wall permeability P are described in the main text.
To image the geometry of the bleach during measurements of tissue-scale diffusion, we first treated a wild-type root with 6 mM hydrogen peroxide for 2 h, sufficient to reduce plasmodesmal permeability to negligible levels (Fig. 4A,B). The root was then placed on the confocal as described above and subjected to a 35 to 40 s bleach. We collected a z-stack of the meristem immediately following the bleach and used ImageJ (v1.38x, http://rsbweb.nih.gov/ij/) to project an image of the x-z plane (Fig. S1).
For single-cell bleaches, the roots were loaded with CF and imaged with the confocal as above. Procedural details of the bleaches used to measure permeability are provided in the main text, and further mathematical analysis is described in the Online Supplement.
To measure cell length, seven-day-old roots were immersed in 1.0 μM FM4-64 for 5 minutes to stain the cell membranes. Roots were rinsed in growth medium and then imaged on a Nikon Eclipse TE-2000S confocal microscope with a 40X objective. All cell length measurements were made in the same region as used for bleaching. The values of average cell length used to convert the effective diffusion constant to a permeability (according to Eqn. 6) are given in Table III.

Data analysis
Images were analyzed using ImageJ and curve fits were performed using KaleidaGraph (v3.6.4; Synergy Software). For tissue-scale analysis, several frames were averaged and the midpoint time taken as t n . Standard errors for the permeability shown here (Table I; Table II     Symbols are data, solid lines are a guide to the eye. Note rapid bleaching within the target nucleus (n 1 ) and the more gradual spread of bleached dye to the adjacent nucleus (n 2 ). For each nucleus, intensity is normalized to the pre-bleach value. permeabilities. The rsw6 line was either exposed to the restrictive temperature for 6 h (rsw6) or maintained at the permissive temperature (rsw6-NC). The cell lengths used to calculate permeability are shown in Table III; for the 2 h treatments, the wild-type cell length was used.
For treatment with hydrogen peroxide, wild-type seedlings were grown for 7 days, then transferred to agar plates containing growth medium alone (2 h plate control) or with hydrogen peroxide for 2 hours before assay. n ≥ 17 for all treatments. Equivalence of means between wild type and mutants or 2 hr plate control rejected at (*) p < 0.05 or (**) p < 0.01; equivalence of means between 2 hr plate control and peroxide treatments rejected at (a) p < 0.05 or (b) p < 0.001.     Table III). Control data are for undisturbed seedlings (same data shown in Fig. 4 A, B).
a. Equivalence to the control mean rejected at p < 0.05 by t test.   The region marked by the red box is bleached for about 30 s. Recovery images are cropped (yellow box) to exclude the edges of the root, and intensity is averaged perpendicular to the root's long axis. This produces a one-dimensional intensity profile, used for analysis. (B) The intensity profile (AU, arbitrary units) before the bleach (black), at 4 s after the bleach (blue), and at 13.3 s after the bleach (green). The difference between blue and green data sets is plotted in Figure 2. 2 min, is sufficient to allow essentially complete recovery. Concatenated, the images approximate the progress of a single bleach. Bar = 20 μm. (B) Intensity versus time for a single-cell bleach. Symbols are data, solid lines are a guide to the eye. Note rapid bleaching within the target nucleus (n 1 ) and the more gradual spread of bleached dye to the adjacent nucleus (n 2 ). For each nucleus, intensity is normalized to the pre-bleach value.  line was either exposed to the restrictive temperature for 6 h (rsw6) or maintained at the permissive temperature (rsw6-NC). The cell lengths used to calculate permeability are shown in Table III; for the 2 h treatments, the wild-type cell length value was used. For treatment with hydrogen peroxide, wild-type seedlings were grown for 7 days, then transferred to agar plates containing growth medium alone (2 h plate control) or with hydrogen peroxide for 2 hours before assay. n ≥ 17 for all treatments. Equivalence of means between wild type and mutants or 2 hr plate control rejected at (*) p < 0.05 or (**) p < 0.01; equivalence of means between 2 hr plate control and peroxide treatments rejected at (a) p < 0.05 or (b) p < 0.001. Four day old wild type roots were transferred to media containing different concentrations of either tryptophan or hydrogen peroxide. Roots were measured measured at daily intervals over the next three days. Symbols plot the mean daily growth rate ± SEM (when larger than the symbol) of three replicate experiments.