| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
|
First published online July 9, 2004; 10.1104/pp.104.040881 Plant Physiology 135:1822-1837 (2004) © 2004 American Society of Plant Biologists Root-Gel Interactions and the Root Waving Behavior of Arabidopsis1,[w]Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts, 02138
Arabidopsis roots grown on inclined agarose gels exhibit a sinusoidal growth pattern known as root waving. While root waving has been attributed to both intrinsic factors (e.g. circumnutation) and growth responses to external signals such as gravity, the potential for physical interactions between the root and its substrate to influence the development of this complex phenotype has been generally ignored. Using a rotating stage microscope and time-lapse digital imaging, we show that (1) root tip mobility is impeded by the gel surface, (2) this impedance causes root tip deflections by amplifying curvature in the elongation zone in a way that is distinctly nontropic, and (3) root tip impedance is augmented by normal gravitropic pressure applied by the root tip against the gel surface. Thus, both lateral corrective bending near the root apex and root tip impedance could be due to different vector components of the same graviresponse. Furthermore, we speculate that coupling between root twisting and bending is a mechanical effect resulting from root tip impedance.
The roots of Arabidopsis, grown on dense agarose gels, exhibit a gradient of growth behaviors that depend on the pitch of the gel's surface (Okada and Shimura, 1990  ; Simmons et al., 1995b; Buer et al., 2000; Migliaccio and Piconese, 2001). Generally, when the gel pitch is vertical ( = 90°), the roots grow relatively straight; when the pitch is horizontal ( = 0°), the roots form regular coils; and when the pitch is of intermediate angle ( = 30°–60°), the roots grow in an oscillatory pattern commonly referred to as root waving. Root growth trajectories vary among ecotypes (Rutherford and Masson, 1996; Hashimoto, 2002). They are sensitive to exogenous or endogenous ethylene in the head space above the roots and to the concentration of Suc in the gel (Buer et al., 2003) and they depend on the kind and concentration of media salts, on the type and concentration of gel, and on the way the plates are sealed (Buer et al., 2000). Some genetic lesions are known to alter the gel pitch-dependence of the phenotype. The roots of one mutant produce tightly piled oscillations when the gel is shifted from vertical to 45° (Okada and Shimura, 1990). A similar phenotype is observed in the presence of exogenous ethylene (Buer et al., 2003). Another mutant (Okada and Shimura, 1990) will form coils at a gel pitch of 45°, as does the reduced gravitropism (rgr1) mutant of Simmons et al. (1995a).
In addition to the straight/waving/coiling phenotypes observed at different gel pitches, the roots also tend to toward the right as they grow (Migliaccio and Piconese, 2001
The central question in the study of root waving is why the root should coherently wave or coil. Why is the relatively straight growth of the root at 90° not matched by equally straight growth at 45°? And why at 0°, in the absence of any effectual lateral gravitropic bias, does the root not simply meander? While the overall downward trajectory of the root is clearly a gravitropic effect, as corroborated by studies of auxin-deficient or gravitropism-impaired mutants (Okada and Shimura, 1990 ; Simmons et al., 1995a; Rutherford and Masson, 1996; Mullen et al., 1998b; Rosen et al., 1999; Migliaccio and Piconese, 2001; Massa and Gilroy, 2003), why the root should turn at all—that is, what causes root tip deflection?—is still debated. A variety of deflecting forces have been proposed, including thigmotropism (Okada and Shimura, 1990), circumnutation (Simmons et al., 1995b; Rutherford and Masson, 1996; Migliaccio and Piconese, 2001), and, as mentioned above, the coupling that occasionally existed between root twisting, coiling and slanting. However, none of these studies has considered the direct physical effect that the gel could have on the growth of the root. Because the length and diameter of the root tip are small, the forces acting between the root and gel will be relatively large as compared to the bending and torsional moduli of the root (i.e. the degree of stress that must be applied to bend or twist the root a given amount; in roots, given their geometry, both of these moduli are likely to scale with the 4th power of radius). We hypothesize that root tip deflection—whether of the continuous sort as in coiling, or of the periodic sort as in waving—can be explained as the result of this physical interaction. If present, friction between the root tip and the gel surface (or root tip impedance), acting in opposition to the growth pressures produced by the root, could lead the more basal regions of the root to bend (Fig. 1A). Bending of this sort, i.e. exaggeration in root curvature due to root elongation, was previously observed by Simmons et al. (1995b), but not experimentally pursued.
Friction between the root tip and the gel would impede the normal movement of the root tip, an effect that would be enhanced by any force that drew the root tip against the gel surface, including gravitropism. This raises the intriguing possibility that both the production and correction of root tip deflections result from different aspects of the same graviresponse, parsed into its lateral and normal components (Fig. 1A). Lateral gravitropism, the more traditionally recognized component of the graviresponse in root waving studies, acts in the plane of the gel surface to maintain the root on a trajectory congruent with the downward slope of the gel surface. It will be strong—that is, it will contain more of the total bending differential imposed by the graviresponse—when the gel pitch is near vertical. Conversely, the remaining component of the graviresponse, normal gravitropism, acts to turn the root in a direction perpendicular to the plane of the gel surface. Normal gravitropic bending, and thus friction and root tip impedance, will be strongest when gel pitch is near horizontal. At a 90° pitch, then, root tip impedance will be minimal and lateral gravitropic corrections will be robust, leading to relatively straight growth along the downward slope of the gel. At a 0° pitch, on the other hand, root tip impedance will be at its maximum, while the lateral component of the graviresponse will be ineffectual, leading to bending in the root elongation zone from which the root cannot recover, i.e. coiling. At intermediate pitches, the normal and lateral components of the graviresponse will be of intermediate strength, leading to impedance-derived root tip deflections followed by lateral gravitropic corrections, and so on. This hypothesis, that gravitropism-derived root tip impedance is critical to the development of these phenotypes, is lent circumstantial support by the observation that roots will wave coherently when the gel is below the root (60° pitch), but not when the gel is above the root (120° pitch, Simmons et al., 1995b Evaluating this root tip impedance hypothesis requires not only a demonstration of the presence of root tip-gel surface interactions, but also evidence that it is gravitropism that generates this impedance. The former can be accomplished by direct observation of the evolution of the wavy root phenotype through time. This would represent a methodological break from previous studies, which have only documented already established patterns of growth. Depending on the behavior of the root tip and the elongation zone, the root-waving phenotype could emerge in one or a combination of at least three categorically different ways. In the first (Fig. 1B, follow-the-leader growth), the entire root follows the same trajectory as the root tip. A complex growth response would be required to generate the wavy-root shape in this way, and so seems unlikely to occur. In the second (Fig. 1C, wagging tail growth), the lateral and longitudinal movement of the root tip is unimpeded, and constrained only by the two-dimensional environment imposed by hydrostatic interactions with the gel surface. Here, root waving could be due to gravitropic overshoot or circumnutation. In the third (Fig. 1D, loaded beam growth), the lateral and longitudinal movement of the root tip is impeded by the gel surface, leading to growth-induced amplification of any curvature already present in the root. If root waving were found to emerge in this way, then it would probably preclude circumnutation as the primary deflective force.
Loaded beam growth and wagging tail growth can be critically distinguished in a number of ways. First, loaded beam growth will produce curvature anywhere in the root elongation zone up to where root hairs first begin to develop, whereas wagging tail growth will produce curvature only in the distal part of the root (first 500 µm) where tropic growth responses are most highly concentrated (Mullen et al., 1998a
In this study, these possibilities are distinguished using a rotating-stage zoom microscope that houses a sterile, gel-plated Arabidopsis seedling and permits digital time lapse imaging of the root while held at a fixed pitch. Our goal is to determine first if the root tip is impeded by the gel surface and second, using spectral analysis of rates of curvature development in different parts of the root elongation zone to see if deviations in root tip angle from the downward slope of the gel surface are attributable to that impedance. In a separate experiment, but using similar methods, we confirm the results of the asymmetric gel pitch experiment of Simmons et al. (1995b)
Growth Trajectories and Tip Movement
The growth of two roots was followed in detail over a period of 100 h at 0.33 to 0.5 h intervals, with one root grown at a gel surface temperature of 23°C and the other at a temperature of 28°C. In both cases, wavy growth commenced after the gels' pitch was changed from 90° to 45° (Fig. 2, A and B ), and root elongation rate (dc/dt) increased with time, with the root grown at 28°C growing slightly faster at the beginning of the experiment (Fig. 2, C and D). Both the distance from the tip to the root hairs dh and the distance from the tip to where the root stopped moving dm increased with time. Early in the 28°C experiment (between t = 10 and 20 h), dm was slightly higher than dh, indicating that the root was moving despite the presence of root hairs, but otherwise dm and dh were weakly correlated in both roots (Fig. 3
). Furthermore, dc/dt was well correlated with dh, suggesting that dc/dt was more closely aligned with the length of the elongation zone (that is, to the amount of root that is elongating) than with the root's relative elemental growth rate (compare with Beemster and Baskin, 1998
The final shape of the root did not match the trajectory of the root tip at either 23°C or 28°C (Fig. 2, A and B), immediately ruling out the follow-the-leader category of wavy root development (Fig. 1D). The root elongation rate-normalized difference between dc/dt and the rate of movement of the root tip (called the tip movement differential, or TMD) was positive in both roots (Fig. 4 ), implying a loaded beam mode of root waving. There were some negative excursions in TMD, indicating occasional wagging tail growth. TMD was nearly zero and relatively invariant prior to rotating the gel surface from a 90° to a 45° pitch, when it abruptly increased and thenceforth declined with time. TMD was greater at 28°C than at 23°C, but in both cases TMD varied periodically, suggesting periodic variation in root tip impedance.
Curvature Development Curvature developed differently in different parts of the root and in a basally progressive manner (Fig. 5 ). Gel pitch was initially set to 90°, allowing the root to grow straight along the downward slope of the gel (Fig. 5A). When rotated to a pitch of 45° (at t = 6.9 h for the 28° experiment), curvature developed behind the root tip with no lateral tip movement. Because the root tip was oriented along the downward slope of the gel surface prior to shifting the gel pitch to 45°, this initial curvature cannot be attributed to a lateral gravitropic correction. As the root grew, the bend continued to develop but at a position basal of the root tip, acting to turn the root tip away from the downward slope of the gel surface (Fig. 5B). Immediately subsequent to that, the root tip and the 0.5-mm region behind it bent slightly in the opposite direction (Fig. 5B). This new curvature then underwent additional bending with little lateral tip movement, again in a basally progressive manner (Fig. 5C). The process repeated itself in opposite directions, with bending at the root tip serving to correct deviations from the vertical, and the elongation of the root accentuating this curvature and thus imposing stimulus for future lateral gravitropic bending (Fig. 5, D–F; see Supplemental Video 1 at www.plantphysiol.org).
Because of the delay in the development of root curvature in the distal versus the more basal parts of the root elongation zone, curvature development (dk/dt) in the root elongation zone was measured (Fig. 6 ) separately for distal and basal zones (DZ and BZ, respectively). The DZ and BZ are arbitrarily delimited at a distance of 0.5 mm from the root tip, following the demarcations indicated by the work of Mullen et al. (1998a) , Massa and Gilroy (2003), and others. The angle between a tangent to the centerline of the root and the downward slope of the gel surface ( ) was measured (Fig. 6) at both the root tip ( ) and at a point 1 mm basal of the root tip ( ). Curvature developed at a higher rate in both the distal and basal zones at 28°C than it did at 23°C, and there was a clear visual synchronization between TMD and curvature development in the basal zone (dk/dtBZ) at 28°C. In both roots, curvature development in the distal zone (dk/dtDZ) appeared to be inversely in phase with at the root tip, and while both roots exhibited the same degree of variation in  variation in was much greater at 28°C. Furthermore, and dk/dtBZ were greater than and dk/dtDZ in both roots, supporting the presence of basally progressive and amplified curvature in the root.
Gel Surface Deformation Gel surface deformation by the root tip was quantified as the reflection diameter (RD) observed around the root tip. A large reflection diameter indicated a deeper deformation of the gel surface, and thus a larger applied force. This reflection was only observed at the tip. RD appeared to be in phase with TMD, especially at 28°C (Fig. 7 ), but was negligible at 23°C after approximately 70 h. RD was generally higher at 28°C than at 23°C, although the absence of a light level control made direct comparison of the two problematic. In both cases RD was periodic, suggesting that the force applied by the root tip to the gel surface was, as well.
Spectral Analysis
These signals were spectrally analyzed using the multiple-taper (MT) method of power spectral density estimation outlined by Thomson (1982)
The cross-spectral densities (CSDs) of select pairs of these signals were calculated to determine if they were correlated in magnitude and phase at different frequencies. If the CSD (a complex function) is statistically coherent at a given frequency (that is, its coherence is significantly greater than zero according to Student's t distribution), then it can be used to determine the phase shift between the signals at that frequency (Table I). The cross spectral density of curvature development in the distal zone and root tip deflection angle indicated that the two were negatively correlated and in phase, while a CSD of curvature development in the distal and basal zones indicated that the basal zone lagged by 2 to 3 h. Furthermore, change in root tip deflection angle with time was tightly in phase with curvature development in the basal zone.
While peak clustering in some signals might not be statistically distinguishable from noise on its own (as in the case of TMD and RD; Fig. 8), useful and statistically robust information can still be gleaned from CSDs of those signals with others of greater power (Thomson, 1982 ). TMD was found to be tightly in phase with excursions in dk/dtBZ (that is, with the absolute value of dk/dtBZ, or |dk/dtBZ|) for both roots, and also in phase with RD at 28°C.
Further evidence of friction between the root tip and gel surface was provided anecdotally by observations of a root grown at 23°C on an air dried 1.2% gel surface (Fig. 9 ; Supplemental Video 2). Dry air was delivered to the chamber, drying the gel, and causing the root tip to visibly stick its surface from t = 60 min to t = 80 min, after which the root's graviresponse releases the tip from sticking to the gel surface. Increased root twisting is observed as the root sticks to the gel before t = 80 min and then increases dramatically as the tip is freed after t = 80 min, suggesting that torsional energy, as well as bending energy, can be stored by the root when impeded by the gel surface.
Asymmetric Gel Surface Environments
An experiment confirming the results of Simmons et al. (1995b)
The Potential Importance of Root-Gel Interactions
The results presented here are meant to illustrate the potential importance of the root-gel interface for root waving. It should be noted at the outset that, although some roots are known to grow in a non-straight pattern or meander across the gel surface even at 90° (Rutherford and Masson, 1996
Temporal data are presented for only two root growth experiments, although the same qualitative behavior has been observed in all roots examined (data not shown). Nevertheless, because each experiment contains more than one oscillatory event, there is more statistical power than the limited number of discrete experiments would suggest. Thus, the study is not meant to cover root waving exhaustively—many studies have already established its presence and some of its characteristics (Okada and Shimura, 1990
The principle difficulty associated with the interpretation of root waving is the lack of a clear framework for understanding its behavior, and a general uncertainty as to which processes to include. Circumnutation (Simmons et al., 1995b
Previous studies showing high sensitivity to plate angle, ethylene concentration, and graviresponse impairment indicate a clear corrective role for gravitropism in root waving (Simmons et al., 1995b
The presence of root tip-gel interaction is documented by the positive values of TMD observed after the gel is rotated to a 45° pitch (Fig. 4), supporting the loaded beam hypothesis presented in Figure 1. At first glance, a positive TMD could be interpreted in one of two ways. Either the root tip is impeded by the gel, or the root elongation zone undergoes a complicated growth response that consistently gives the appearance of root tip immobility. The latter has some precedent; to maintain a constant hook shape and protect the emerging cotyledons and shoot apical meristem (Silk and Erickson, 1978 The physical interaction between the root tip and the gel is directly demonstrated by surface deformation around the root tip, as measured by reflection from the ring light (Fig. 7; Supplemental Video 1), showing that the root tip applies a force against the agar surface and sometimes causes it damage (see Supplemental Video 1). No significant gel surface deformations were observed at any time during the experiment except around the root tip (Fig. 7, Supplemental Video 1). Furthermore, TMD and RD data are tightly in phase at 28°C, indicating a strong relationship between root tip impedance and the force applied by the root tip against the gel surface. The presence of consistent gel surface deformation, at least at 28°C, indicates that root waving can occur even in the presence of perpetual positive pressure between the root tip and the gel. In fact, gel deformation tends to be largest when curvature development in the basal zone is at its greatest. This provides evidence against circumnutation or thigmotropism as the primary deflective force in root waving, since under those models root waving would require that the root tip be free to move (wagging tail growth), significantly reducing the positive pressure found between the gel and root tip just at the time that curvature developed in the root.
The immobility of the root tip should cause the entire elongating root to bend, up to the first root hairs, leading to a deflection in root tip direction. Curvature development in the distal zone is in phase with root tip deflection and appears to directly reflect the lateral component of the graviresponse (Table I). However, curvature development in the basal zone tends to lag curvature development in the distal zone by 2 to 3 h (Table I), a longer period of time than what is typically required to initiate gravitropic bending in Arabidopsis (Mullen et al., 1998a
If normal gravitropic bending enhances root tip impedance, as implied by the synchronization between TMD, RD, and dk/dtBZ, then inverting the gel surface should strongly reduce the intensity of root waving. This has been observed in previous work (Simmons et al., 1995b
Differences between the two experiments as a function of temperature are not statistically resolvable. However, the strong dependence of root growth on temperature has been repeatedly observed (compare with Silk, 1992
We suggest that root waving consists of the following sequence of events. When the gel is placed at an intermediate pitch, root tip impedance becomes strong relative to the capacity of the root to correct deflections in root tip angle, and curvature develops up to the point of first root hair development (it is significant that at both 23°C and 28°C this initial bend is to the right). As this curvature develops, the root tip is deflected, leading to an increase in the graviresponse, which causes the root tip to correct the deflection and bend the other way, but only in the distal part of the root tip. Root tip impedance then amplifies the distal curvature created by this lateral correction into greater curvature in the basal zone, leading to an opposite root tip deflection, another opposite graviresponse, and so on.
The same logic can be applied to root coiling. The gel surface is placed horizontally, and root tip impedance amplifies any preexisting curvature in the root elongation zone. The lateral component of the graviresponse is ineffectual at a horizontal pitch—or, in the case of graviresponse impaired mutants, minimal—and cannot correct the resulting deviation. In contrast, the normal component is at its strongest, leading to increased root tip impedance, root bending, and finally coiling. Root tip impedance could be important even without strong normal gravitropic bending, as evidenced by studies of graviresponse-impaired roots (Simmons et al., 1995a Circumnutation is an important growth phenomenon in plants but it seems to have little importance in explaining root waving. If circumnutation were strong enough to generate oscillations at a pitch of 45°, then it should also be strong enough to generate them at 135°. However, the mean curvature of roots grown at a 135° pitch is considerably lower than those grown at 45° (Fig. 10). Also, if circumnutation drove root tip deflections, then we would expect the roots to grow according to the wagging tail model, especially when the plate is inverted and there is little root tip impedance. The high degree of root tip immobility observed in this study does not bear out this prediction. While it is possible that internally derived oscillations could generate patterns similar to loaded beam growth via a complicated axial pattern of lateral growth differentials, we would then have to explain why the root tip remains immobile against the action of such strong internal forces, leading us back to root tip impedance as an important force in generating the root waving phenotype.
Although not explicitly treated in this work, much has been made of the role of root twisting in relation to root bending as an explanatory foundation for root waving (Okada and Shimura, 1990
The apparent importance of root tip impedance for root waving, as found and discussed here, leads naturally to speculation about how it could affect root bending asymmetry and the relation between bending and twisting. The initial turning tendency of Arabidopsis roots is to the right, but left and right only have meaning in the context of the gel surface. In animals, left-right asymmetry arises only when two axes—dorsal-ventral and anterior-posterior—are established. The analogous axes in this case are the basal-distal axis defined by the root's longitudinal axis and its direction of growth, and the up-down environment imposed by the gel surface. Thus, the initial turn must be somehow constrained by these axes of asymmetry to be internally biased to the right. It could be that the right handed bias in the initial turn is actually an emergent property of the left-twisting bias of the root. What determines this twisting bias is unclear. However, given that twisting is a whole-root phenomenon, the bias may emerge from the aggregate behavior of each cell in the root. During early cell expansion, the cell wall microtubules of epidermal root cells are known to be arranged in a right-handed helical manner (Liang et al., 1996
This left-twisting tendency could translate into a right-handed bend via the effects of root tip impedance. As the root tip is pushed along the resistive gel surface, the underlying tendency of the root to twist to the left could store torsional energy that is released only if the root turns to the right (a minimal energy configuration, one that is easily confirmed using a physical model such as a length of O-ring stock held against a rigid, frictional surface). Conversely, when the root is pushed forward in a left-handed turn, root tip impedance could cause the root to twist to the right and store torsional energy against its tendency to twist to the left. This differential in energy storage—where energy is stored in a left-handed turn and released in a right-handed turn—would explain why wavy roots turn more easily to the right than to the left, and why straight-growing and coiling roots have a right-handed bias. We present this only as a hypothesis, but it gains strength when we consider that the right-handed turning bias is only apparent when the gel is below the root (Fig. 10); that is, its emergence depends on the presence of root tip impedance. Not only the strength of root waving (Fig. 10), but also the slanting tendency of roots grown at a 60° pitch, disappears when the gel is shifted to a pitch of 120° (Simmons et al., 1995b
The coupling between root twisting and turning is not necessary to explain the fact of root waving or coiling, only their occasional lateral asymmetry. Indeed, the presence of ethylene in the headspace of the growth plate appears to remove any correlation between twisting and coiling, as well as the tendency of the root to slant to the right (Buer et al., 2000
Direct observation of the time-evolution of root waving yields considerable insight into the processes involved. The differential between root tip movement and root elongation rate suggests that the root tip is frictionally impeded, and direct observation of gel surface deformation by the root tip shows that the root tip presses against the gel surface. Furthermore, changes in root tip deflection angle, the tip movement differential, and gel surface deformation are all well correlated and in phase with major curvature development in regions just distal of sites of root hair development, suggesting that root tip deflection is due to root tip friction. The presence of surface deformations that are in phase with high values of the tip movement differential strongly suggests that much of the friction generated at the root tip is due to downward (or normal) gravitropic bending by the root tip against the gel surface, as supported by an experiment showing a reduction in mean root curvature at an oblique (135°) gel pitch. Root waving, and by extension root coiling, could be explicable solely in terms of gravitropism and root tip impedance by the gel surface.
Given that the roots in these experiments and others are grown on a physical medium, it is natural to assume that at least part of their behavior is explicable with adequate attention to what could result from these mechanical interactions. If a growing root tip is physically impeded, then either the root will cease to grow or it will bend (see especially Massa and Gilroy, 2003
Microscope Apparatus
Growth conditions were selected to best mimic those used in previous studies. Special note was taken of the results of Buer et al. (2000)
Images were recorded using a monocular video zoom microscope (VZM 450i, Edmund Industrial Optics, Barrington, NJ), mounted with a monochrome CCD camera (XC-73, Sony, Japan) and microscope-mounted ring light. Image capture and light control were managed by computer via custom electronics using the Windows Beta version 4.02 of Scion Image (Scion Corporation, Frederick, MD). Images were captured once every 20 to 30 min and stored as time-stamped TIFF files. Scale was determined using a transmission stage micrometer. Focus was manually controlled using a coarse-fine control knob mounted to the rotating arm, while the zoom was controlled via the microscope itself. Between images, the ring light was turned off and the roots were illuminated only by the overhead lights. At the time of image capture, the overhead lights were turned off, the ring light turned on and allowed to stabilize for at least 10 s, an image was captured, the ring light was turned off, and the overhead lights were turned back on. This avoided unwanted phototropic effects due to light from non-vertical sources.
The roots were grown at bath temperatures of 20°C and 25°C, corresponding to gel surface temperatures of 23°C and 28°C, respectively. Three Col-0 seeds per experiment (CS1092, Arabidopsis Biological Resource Center, www.arabidopsis.org) were plated on a 1-cm thick medium composed of 1.2% (w/v) Bacto-Agar (Difco Laboratories), 1.5% (w/v) Suc, and one-half strength Murashige and Skoog basal macro- and micronutrients and vitamins (M0654, M0529, M3900, Sigma-Aldrich, www.sigmaaldrich.com). Each dish was sealed with porous surgical tape (Buer et al., 2000 An additional experiment was performed on surgical-tape sealed plates in a germination chamber maintained at a constant temperature of 20°C, a constant light level of 85 µmol photons m–2 s–1, and with high humidity. Sterilized Col-0 seeds were plated on each of two plates. Both plates were stored in the dark at 4°C for 4 d, and then placed in the germination chamber at a 90° gel pitch until the seedlings had germinated and their roots had grown approximately 10 mm in length. Both plates were then shifted to a 45° pitch, and after 44 h, one of the plates was shifted to a 135° pitch. After an additional 44 h, the 135° plate was returned to a 45° pitch and both plates were permitted to grow for another 16 h. The roots of both plates were then photographed in detail using a camera-mounted stereomicroscope.
Each captured image was registered in TIF format (640 x 480 pixels, 8-bit grayscale depth). These images were then imported into CorelDraw v10 (Corel, Ottawa, Canada) and aligned to form a progressive composite. First (Fig. 12
), a single multi-node line, with approximately 100-µm node spacing, was drawn along the centerline of the root image composite from the radicle origin to the root tip. The data in this line was stored, and then the line was modified to fit the previous image in the series. This method of modifying previously drawn lines made it unnecessary to fully redraw the line for each image. An additional, straight line was drawn transversely across the root at the point on each image where root hairs first become visible. This method was time-consuming, but the lateral movement of wavy roots, and the visual artifacts they leave behind, such as gel surface damage and deformation, and root surface reflections, introduce problems that make it highly problematic to use traditional marker-based root growth measurements (Beemster and Baskin, 1998
The nodal data from these lines were exported into a single EPS file for the entire image series (a text file), from which the X-Y coordinates of the nodes in each line could be extracted for analysis. All analyses were performed using MATLAB version 6.5 (MathWorks, Natick, MA). The data were scaled to units of mm and translated so that the origin of each line (the point of radicle emergence) had coordinates [x,y] = [0 mm, 0 mm]. Because nodes were not regularly placed along the centerline, but instead spaced to assure an accurate representation of the root trajectory with varying nodal density depending on the curvature of the root, the centerlines' nodes were splined to a common spatial resolution of 20 µm, which was close enough to minimize quadratic error in arc length measurements. Each centerline (Fig. 12) was then rendered as a parametric vector function of root arc length, s (mm), and time, t (hr):
Arc length was measured from the root origin (s = 0 mm) to the root tip (s = c), where c is the root length (and a function of time). The rate of increase in root length, or the elongation rate of the root, is the first derivative of c with time, or dc/dt, and the position of the root tip is The distance between the root tip and the first appearance of root hairs, or dh (mm), was determined by calculating the intersection between r and the transverse line earlier drawn across the root to indicate root hair position. Another metric, dm (mm), which is the distance from the root tip to the point where the root ceases to change its position, was determined by first rendering r in terms of distance from the root tip [that is r* = r(c – s,t)] and then determining the magnitude of its derivative with time. The point along r* (i.e. c – s) where the rate of movement first exceeds 0.01 times the summed movement over the entire length of the root was assigned to dm. The size of the reflection of the ring light around the root tip caused by local deformation of the gel surface, or RD (mm), was measured as the transverse diameter of the reflection (Fig. 12A).
The tip movement differential, or TMD, is the growth rate-normalized difference between the rate of elongation of the root and the magnitude of the velocity of the root tip, or:
Positive values of TMD signify a relatively slow root tip, and negative values signifying a relatively fast root tip.
Root curvature k (mm–1) can be calculated from r, provided s is an accurate estimate of root arc length, as:
The angle
> 0 signifies a left turn in the frame of reference of the root, and < 0 signifies a right turn. This sign convention is also applied to k (even though curvature is a vector magnitude and thus conventionally non-negative), where a bend to the left indicates positive curvature.
The root elongation zone was arbitrarily split into two domains to tease apart root bending in its more basal and distal parts, following Mullen et al. (1998a)
Spectral analysis requires that the time series be evenly sampled in time. Because the degree of statistical significance assigned to the results does not depend on the sampling frequency but rather on the number of realizations of particular oscillations present in the time series, the re-sampling frequency is not critical, provided that it is sufficient to capture the major features. However, resampling requires a splining of the original time series and it is important that the resampling frequency be selected such that artifactual splining overshoot is introduced evenly throughout the resulting spectra. One way this can be done is to resample at twice or four times the underlying sampling frequency, but because the sampling rate was uneven in this study, an arbitrary resampling period of 1/ Some data series had central frequencies that were strongest at the oscillation frequency of the root (that is the frequency of one full oscillation of the root tip). Others (such as TMD and RD) oscillated at twice that frequency. To compare time series with common features, but which oscillated at different octaves, it was necessary to double the frequency of the more slowly oscillating series by detrending it and taking its absolute value, thereby converting negative excursions to positive ones. For example, dk/dt is compared against TMD as |dk/dt|. Each time series was linearly detrended. Because the root occasionally grew out of the field of view, there are occasionally missing data after t equals approximately 65 h in both experiments. Missing data were replaced with zeros prior to calculating their discrete Fourier transforms. Spectral analysis was only applied to data gathered after the gel surface had been rotated from 90° to 45°.
An estimate of the power spectral density (PSD) of
The background noise spectrum was assumed to be red noise, which is noise with some degree of temporal autocorrelation. Data without temporal autocorrelation is by definition white noise. The discrete red noise spectrum PRN(f) as a function of frequency f is given for a finite data series by the following relation (Mann and Lees, 1996
 is evaluated for f from 0 to the Nyquist frequency  to match the frequency distribution of the spectral estimate,  is a normalization coefficient, and  is the lag-one autocorrelation coefficient for the signal. An initial background spectral estimate was calculated for each spectrum by applying a 43-frequency bin median filter to the PSD (following the protocol described by Mann and Lees, 1996). Values of and were found by least-squares fit of Eq. (5) to the median filtered data (Mann and Lees, 1996). The statistical significance of any one peak was then calculated as the ratio of the power contained in that peak (i.e. the variance partitioned to that frequency) to the power contained at the frequency in the background noise estimate. This ratio was then compared to the  2 value at a given significance level with df = 6.
Cross-spectral densities (CSDs) of pairs of signals are also calculated using the MT method (Thomson, 1982
If the square-root of Coh2 is statistically significant (df = 6) against the Student's t distribution (determined as if Coh were a correlation coefficient), then the phase delay (
We thank Randol Villalobos Vega for assistance with experiment preparation, Prof. Tobias Baskin (University of Massachusetts, Amherst) and Prof. Jacques Dumais (Harvard University) for helpful comments and criticism on earlier versions of this manuscript, Marcy Rucker in the TeKrony laboratory and Joseph Chappell in the Agronomy Department of the University of Kentucky for facilities support, and two anonymous reviewers. Received February 11, 2004; returned for revision May 19, 2004; accepted May 20, 2004.
1 This work was supported by a NASA Gravitational Biology Life Sciences grant to Harvard University. 
2 Present address: Agronomy Department, University of Kentucky, Plant Sciences Building Room 343, 1405 Veterans Drive, Lexington, KY 40546–0312; matthew.thompson{at}uky.edu.
[w] The online version of this article contains Web-only data. Article, publication date, and citation information can be found at www.plantphysiol.org/cgi/doi/10.1104/pp.104.040881. * Corresponding author; e-mail matthew.thompson{at}uky.edu; fax 859–257–7125.
Baskin TI (2001) On the alignment of cellulose microfibrils by cortical microtubules: a review and a model. Protoplasma 215: 150–171[CrossRef][Web of Science][Medline]
Beemster GTS, Baskin TI (1998) Analysis of cell division and elongation underlying developmental acceleration of root growth in Arabidopsis thaliana. Plant Physiol 116: 1515–1526 Bowman J ed (1993) Arabidopsis: An Atlas of Morphology and Development. Springer-Verlag, New York
Buer CS, Masle J, Wasteneys GO (2000) Growth conditions modulate root-wave phenotypes in Arabidopsis. Plant Cell Physiol 41: 1164–1170
Buer CS, Wasteneys GO, Masle J (2003) Ethylene modulates root-wave responses in Arabidopsis. Plant Physiol 132: 1085–1096 Darwin C, Darwin F (1880) The Power of Movement in Plants. John Murray, London Furutani I, Watanabe Y, Prieto R, Masukawa M, Suzuki K, Naoi K, Thitamadee S, Shikanai T, Hashimoto T (2000) The SPIRAL genes are required for directional control of cell elongation in Arabidopsis thaliana. Development 127: 4443–4453[Abstract] Hashimoto T (2002) Molecular genetic analysis of left-right handedness in plants. Philos Trans of the R Soc Lond B Biol Sci 357: 799–808 Liang BM, Dennings AM, Sharp RE, Baskin TI (1996) Consistent handedness of microtubule helical arrays in maize and Arabidopsis primary roots. Protoplasma 190: 8–15[CrossRef] Mann ME, Lees JM (1996) Robust estimation of background noise and signal detection in climatic time series. Clim Change 33: 409–445 Marinelli B, Gomarasca S, Soave C (1997) A pleiotropic Arabidopsis thaliana mutant with inverted root chirality. Planta 202: 196–205[CrossRef][Web of Science][Medline] Massa GD, Gilroy S (2003) Touch modulates gravity sensing to regulate the growth of primary roots of Arabidopsis thaliana. Plant J 33: 435–445[CrossRef][Web of Science][Medline] Migliaccio F, Piconese S (2001) Spiralizations and tropisms in Arabidopsis. Trends Plant Sci 6: 561–565[Medline] Mullen JL, Ishikawa H, Evans ML (1998a) Analysis of changes in relative elemental growth rate patterns in the elongation zone of Arabidopsis roots upon gravistimulation. Planta 206: 598–603[CrossRef][Web of Science][Medline]
Mullen JL, Turk E, Johnson K, Wolverton C, Ishikawa H, Simmons C, Söll D, Evans ML (1998b) Root-growth behavior of the Arabidopsis mutant rgr1: roles of gravitropism and circumnutation in the waving/coiling phenomenon. Plant Physiol 118: 1139–1145 Okada K, Shimura K (1992) Mutational analysis of root gravitropism and phototropism of Arabidopsis thaliana seedlings. Aust J Plant Physiol 19: 439–448[Web of Science]
Okada K, Shimura Y (1990) Reversible root tip rotation in Arabidopsis seedlings induced by obstacle-touching stimulus. Science 250: 274–276 Rosen E, Chen R-J, Masson PH (1999) Root gravitropism: a complex response to a simple stimulus? Trends Plant Sci 4: 407–412[CrossRef][Web of Science][Medline] Rutherford R, Masson PH (1996) Arabidopsis thaliana sku mutant seedlings show exaggerated surface-dependent alteration in root growth vector. Plant Physiol 111: 987–998[Abstract] Silk WK (1992) Steady form from changing cells. Int J Plant Sci 153: S49–S58[CrossRef] Silk WK, Erickson RO (1978) Kinematics of hypocotyl curvature. Am J Bot 65: 310–319[CrossRef][Web of Science] Simmons C, Migliaccio F, Masson P, Caspar T, Söll D (1995a) A novel root gravitropism mutant of Arabidopsis thaliana exhibiting altered auxin physiology. Physiol Plant 93: 790–798[CrossRef][Medline]
Simmons C, Söll D, Migliaccio F (1995b) Circumnutation and gravitropism cause root waving in Arabidopsis thaliana. J Exp Bot 46: 143–150 Thitamadee S, Tuchihara K, Hashimoto T (2002) Microtubule basis for left-handed helical growth in Arabidopsis. Nature 417: 193–196[CrossRef][Medline] Thomson DJ (1982) Spectrum estimation and harmonic analysis. Proc IEEE 70: 1055–1096
van der Weele CM, Jiang HS, Palaniappan KK, Ivanov VB, Palaniappan K, Baskin TI (2003) A new algorithm for computational image analysis of deformable motion at high spatial and temporal resolution applied to root growth: roughly uniform elongation in the meristem and also, after an abrupt acceleration, in the elongation zone. Plant Physiol 132: 1138–1148 This article has been cited by other articles:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| ASPB Publications | PLANT PHYSIOLOGY® | THE PLANT CELL | |
|---|---|---|---|
TOP
ABSTRACT
RESULTS
h was selected for having a value near the image sampling periods of 20 or 30 min, and for not sharing any common roots with those numbers. The data were splined using a piecewise cubic hermite interpolating polynomial, or pchip, which provides a smooth spline with little overshoot. 
, hr) can be accurately calculated from the CSD as the inverse tangent of the ratio of the imaginary and real part of the CSD at f, divided by 2
