For the investigated root system, its components are classified as primary root, first-order lateral roots and nodules. The second-order laterals were not considered or modelled. When observing the soybean root from above (Fig. ), a regular branching pattern of the lateral roots was found; the radial angles of lateral emission, as defined by Jourdan and Rey (1997)
, are usually around 90°. This pattern is suggested to be the result of lateral formation opposite xylem poles (Bell and McCully, 1970
; Mallory et al., 1970
; Abadia-Fenoll et al., 1982
; Rolfe and Gresshoff, 1988
; Jourdan and Rey, 1997
Observation of soybean root branching pattern. From an overhead view (A), the radial angles of lateral root emission are usually around 90° (B), demonstrating a regular pattern.
To characterize lateral roots based on this emission pattern and collect their developmental data, a ‘RULD’ root mapping method (Han et al., 2007
) was developed. With the ‘RULD’ method, the first-order laterals are categorized into quadrants (right, R; up, U; left, L; down, D), according to the relative positions of their emission points to the obtuse angle composed by the two cotyledons (Fig. ). Then the lateral roots are further classified and identified by ‘regions’ (a 50-mm-long section on the primary root), ‘segments’ and ‘sites’ (Fig. ).
Fig. 2. ‘RULD’ mapping to characterize first-order lateral roots. For a growing soybean plant at early stages, its two cotyledons compose an obtuse angle in the horizontal plane. The lateral roots can be categorized as being in one of four quadrants (more ...)
Fig. 3. Identification of lateral root based on its formation sites. A region is defined as a 50mm-long primary root section. A segment is defined as a smaller area with four R-U-L-D quadrants in a region. Thus the formation site of each lateral root can be identified (more ...)
To capture nodule distribution information, a ‘nodulation section’ (Han et al., 2009
) is defined for each region of the primary root and for each first-order lateral root (Fig. ). The nodulation section covers the distance between the first and the last nodules in a particular primary-root region or on a lateral root. The relative locations of the first and the last nodules to the starting point of the primary or the lateral root are measured to position each nodulation section. The length of a nodulation section and its number of nodules are used to calculate the nodule density for this section.
Fig. 4. Definition of nodulation section. Each region of the primary root and each lateral root is defined to have its unique nodulation section. The positions of the first and the last nodules of a nodulation section determine its location in the root system. (more ...)
The empirical architectural data collected with the above measurement methods are then used to drive the root simulation. The primary root architecture is extended by the root tip, where potential positions for nodulation or lateral emission are also created. The root elongation has an appropriate rate to match the empirical length value, which defines the corresponding root tip location. There are three major rules for modelling the primary root elongation.
- When the root length indicates that the primary root has entered a section for future nodulation, the model starts checking whether the root tip should be marked as a potential nodule formation site. If the root tip location matched the positions of the first or last nodules (of this section) or if the root elongation since the last marked position is longer than the interval between two successive nodules, a potential site for nodule formation is made available.
- If the primary root elongation has covered an interval between two successive laterals, a potential site for lateral root emission is made available.
- If the current position of primary root tip does not match the conditions in (1) and (2), it has neither potential for nodulation nor for lateral emission.
The potential sites pre-set by rules (1) and (2) are only spatial markers; whether and when nodules or lateral roots will be formed there depend on other conditions derived from empirical data. The maximum number of nodules formed in each primary root region during each day is used to restrict further nodulation. At a potential nodulation site, a nodule will be formed if, and only if, the relevant maximum number of nodules is not exceeded. Whether a lateral root will be emitted from a potential formation site is determined by branching probabilities, while how soon the lateral will appear and how far it can elongate are controlled by the empirical daily growth rate. The apical zone around the root tip in the architectural model has no nodules attached and remains unbranched, as the maximum nodule number and the lateral growth rate for this area are both 0.
The architectural model was built with an L-system-based language ‘cpfg
’ in L-studio (Prusinkiewicz and Lindenmayer, 1990
; Hanan, 1997
; Prusinkiewicz, 2004
). In L-system plant models, a shoot organ is usually represented by a single module that not only contains its developmental information but also simulates its structure graphically. A number of such modules are then assembled into a string to represent the entire shoot architecture composed of different organs. The dynamics of plant development is supported by step-by-step application of a set of rules called ‘productions’. The productions are usually written as
where ‘predecessor’ is an original module while ‘successor’ is a module or a string of modules to replace the predecessor as long as the ‘condition’ is matched. At each simulation step, the modules in the current string are matched against the productions and only those with matched predecessor and condition are applied. If multiple productions have the same predecessor, they are checked sequentially and only the first one with matched condition is allowed to produce its successor. After all modules have been processed, the resulting string represents the structure of the plant at the end of the time step.
In this root study, the elongation information (such as overall root length already created) is recorded within a module representing the root tip, while the graphical role is played by a set of ‘sub-modules’ each with the same length (UNIT). The standard sub-modules here are similar to the elementary units used to model oil-palm root system (Jourdan and Rey, 1997
). During root elongation, a sub-module is added behind the root tip module at each simulation step, forming a string of sub-modules to make up root structure. For example, if ‘RT’ is used to represent root tip, ‘R’ to represent a sub-module, the initial structural string is ‘RT’ and the production is
then the string will become ‘R RT’ after one step and ‘R R RT’ after two steps. The sub-module length – UNIT – is definable by the modellers or users depending on specific requirements in specific cases. In this study, to allow the increment of root length to match conditions for setting potential nodulation or lateral formation sites, the value of UNIT should be smaller than the minimum interval between two successive nodules or laterals. For details of the time scale, see the next section. The algorithm for primary root elongation with sub-modules is illustrated in Fig. . Its implementation using the ‘cpfg
’ language is given in the text file in Supplementary data
(available online). Although all the sub-modules have the same length, their widths vary and increase with radial growth, capturing appropriate diameters at different stages of root development. The lateral root elongation is simulated in a similar way except that the second-order laterals are not taken into account. The simulation of root heading behaviours is supported by methods from the ROOTMAP model (Diggle, 1988
) and is representative only. Since the plants used for studying autoregulation of nodulation in this research are at their early developmental stages, the mortality of lateral root tips is not considered. A sample visualization of soybean root architecture with nodulation is given in Fig. and the video in Supplementary data
Fig. 5. Root elongation algorithm. At the beginning of each L-system time step during root elongation, the root tip module checks whether its current location has potential for future nodulation or lateral initiation. If it matches potential positions for nodule (more ...)
Fig. 6. A sample visualization of soybean root architecture with nodulation. The day-by-day developmental process leading to this root architecture is demonstrated in the video in Supplementary data (available online).
To evaluate the root reconstruction, growth data of a soybean hypernodulation genotype nts1116
(Carroll et al., 1985a
; mutated at V837 of the GmNARK
receptor kinase gene) are incorporated into the architectural model. nts1116
was shown to have severely reduced in vitro
kinase activity (Miyahara et al., 2008
), consistent with a 3x
elevated nodule number. The nts1116
plants were cultured in glasshouse conditions over a 16-d period, inoculated on the second day, with five plants sampled for destructive measurements every 2 d starting on the third day. The comparison of real-plant versus virtual-plant root systems, on lateral root branching and nodule distribution (Han et al., 2009
) as well as on root length, indicates a good fit between empirical data and simulation results (Fig. ).
Fig. 7. Comparison of empirical data with simulation results. The virtual-plant architecture, driven by empirical data, is compared with the real plant on the 16th day after sowing. For lateral root branching (A), the comparison classified by the R-U-L-D scheme (more ...)