Methods for Non Invasive Determination of Growth

The oldest and easiest method to record growth is to use rulers. This is still an appropriate method for easy and rapid investigation of growth processes within plant populations (Walter and Schurr 1999; Christ et al. 2006).

First descriptions of spatially resolved growth patterns within plant organs date back to the approach of Sachs (1887) for roots and Avery (1933) for leaves. In both cases, ink dots were applied to the organ surfaces and their divergence (increase in distance between dots over time) was recorded. Methods without application of external marks were published decades later (root: Brumfield 1942; leaf: Schmundt et al. 1998). In linearly organized growth zones of leaves of monocotyledonous plants (Ben-Haj-Salah and Tardieu 1995; Beemster et al. 1996) or roots (Goodwin and Stepka 1945; Silk and Erickson 1979), the distribution of cell expansion rate can be quantified elegantly via a so-called "kinematic analysis":

On the basis of the premise that each cell is displaced in a linear way from the end of the cell division zone to the zone of fully differentiated tissue, a plot of average cell length versus distance from the distal end of the meristematic zone can be used to calculate cell elongation along the direction of this line of cells (cell file). First, the velocity distribution along the cell file is calculated by determining, how fast each point along the cell file is displaced away from the meristematic zone. For the elongation zone, this is done by multiplying cell length at each position with "cell flux" (which equals the ratio of the velocity of the root tip and cell length at the end of the growth zone). "Cell flux" is the reciprocal time that is needed to add one new cell to the cell file at the apical interface of the growth zone or to remove one full grown cell at the basal end of the growth zone from the end of the cell file. The elongation rate (or strain rate) is then given by the first derivative of the velocity distribution. For a more detailed explanation of these considerations see Silk et al. (1989).

Cell division rates can also be calculated in such organs based on determination of cell lengths at different positions and on determination of root tip velocity. These measurement parameters are used in the continuity equation (Silk and Erickson 1979; Silk 1984; Beemster and Baskin 1998) to calculate the production of cells and cell division rates within cell files.

Methods with high temporal resolution were initiated in the 1970s when electronic devices began to be applied on a wider scale (Hsiao et al. 1970). Linear Variable Displacement Transducers (LVDTs) register position changes of the leaf tip via a thread that is attached to it, that is kept under tension and that regulates an electric resistance or the inductance of a solenoid. This principle was first applied by Sachs (1887) more than a century ago, when he recorded the diel time series of shoot axis growth rate, but it fell into oblivion for a long time. Herein the term diel is used to depict variations occurring throughout 24 h in a repetitive way. Diel is a synonym of the more commonly found term diurnal that can also depict processes that are only active during the day, but not at night.

Methods providing a combination of high spatial and temporal resolution were elaborated when digital image processing became available (Schmundt et al. 1998; Van der Weele et al. 2003). Again, a pioneering study demonstrating the essential principles on which modern methods are based was leading the way some decades ahead of time: The distribution of growth activity in a maize root growth zone was analyzed throughout 12 h by Erickson and Sax (1956) by continually photographing the ink-dotted root growth zone with a slit camera and a slowly moving film. The transformation of successive temporal events into the x-axis of the image resulted in a so-called "streak image": A group of divergent trajectories was recorded and the inclination of each trajectory depicts the velocity of the cellular element on which the respective ink dot was situated. The difference of the velocity of neighbor ing elements, normalized by the distance of the elements equals the relative growth rate of the respective length element (Fig. 1). This method was further applied in at least one physiological study (Hejnowicz and Erickson 1968), but fell into oblivion thereafter.

On the basis of the same principle (extended into two dimensions) of so-called "optical flow", digital image sequence processing methods have been established during the last decade (Schmundt et al. 1998; Van der Weele et al. 2003). Images of root growth zones were recorded at time intervals of less than a minute, rendering results for growth distributions in almost cellular resolution (Walter et al. 2002b; Nagel et al. 2006). For leaves, the two-dimensional analysis of divergence of natural patterns like vein crossings or trichomes in image sequences rendered similar distributions of relative (elemental) growth rates (Schmundt et al. 1998; Walter et al. 2002a; Wiese et al. 2007; Fig. 1). Typical intervals between images were two to five minutes. Investigated leaves and roots were illuminated with near-infrared LEDs and were visualized with CCD-cameras that were equipped with appropriate near-infrared filters. Image recording in the near-infrared range has the advantage of achieving constant image brightness throughout day and night. Wavelengths of about 900 nm do not affect any known sensory systems ofplants and are not heating up leaves.

Calculation of spatio-temporal growth rate distributions was performed by optimized, custom-made image sequence processing algorithms (Scharr 2004) that are based on the above-mentioned principle of optical flow and that use a so-called structure-tensor approach to calculate motion from orientation in stacks of images (Bigun and Granlund 1987; Haufiecker and Spies 1999).

Fig. 1 Calculation of velocity and relative growth rate (RGR) from image sequences of ► roots and leaves. Root panels: Original images of a Zea mays root that was marked with ink dots and that was photographed every 15 min are arranged next to each other (left; grid indicates 1 mm). The black lines in the middle panel depict in the way of streak photographs, how the ink dots were displaced with the extending root. The inclination of each line towards the time-axis corresponds to the velocity of the ink dot. For clarity, those velocities are indicated additionally as colored vectors (arrows) in the middle of each line. Colors are coded via a "rainbow" look-up-table shown in the leaf growth panel (lower right): blue stands for low values, red for high values. The right hand root growth panel finally shows the differences of two neighboring velocities divided by the average distance between two neighboring dots throughout the investigated time period. Those differences equal the relative (elemental) growth rate of each segment situated between two neighboring ink dots. They are plotted versus the distance of the corresponding dots from the root tip. Leaf panels: Original images of a Nicotiana tabacum leaf, taken at t = 0 h and t = 24 h (left images). Images in the middle show color-coded distributions of velocity components in x- (top) and y- (bottom) directions (equation given above top panel) that are projected onto the original image at t = 0. The right hand panel finally shows the divergence of this velocity distribution projected onto the original image at t = 0 which corresponds to the distribution of relative (elemental) growth rates. All calculations follow the same principles as explained for the one-dimensional case of the root, but are performed in two dimensions (x- and y-direction)

Image sequence processing-based methods for determination of growth rates provide both high temporal and spatial resolution. Yet, since smoothing and regularization procedures are a necessary and intrinsic feature of those methods, it has to be pointed out that it is impossible to achieve maximally high spatial and temporal resolution at the same time. Depending on the question to be answered, the focus has to be put either on maximal temporal or on maximal spatial resolution or one has to take deductions of both dimensions into account. Calculation of velocities (and growth rates) takes into account information from spatial regions of about 10 x 10 pixels and from temporal neighborhoods of about 10-20 image frames. The maximal spatiotemporal resolution that was achieved up to now was reached in a study of root gravitropic curvature processes in Arabidopsis thaliana (Chavarria-Krauser et al. 2008). On the basis of the calculation of growth differences in immediate vicinities along the root growth zone, two distinct centers of curvature located about 100 ^m apart from each other were identified within the root growth zone which was about 600 ^m long. It was shown that the curvature activity within those centers was initiated with a time lag: While the more apical center of curvature reacted towards gravistimulation within minutes, the basal center commenced curvature about 60 minutes past gravistimulus. Pixel resolution of the acquired images was 1.4 ^m; images were recorded every 30 s.

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