Three-Dimensional Time-Lapse Analysis Reveals Multiscale Relationships in Maize Root Systems with Contrasting Architectures

Time-lapse 3D imaging, computer vision, and mathematical modeling were used to quantify the root system architectures of three maize genotypes as they grew in complexity from a few to many roots.

Abstract

Understanding how an organism’s phenotypic traits are conditioned by genetic and environmental variation is a central goal of biology. Root systems are one of the most important but poorly understood aspects of plants, largely due to the three-dimensional (3D), dynamic, and multiscale phenotyping challenge they pose. A critical gap in our knowledge is how root systems build in complexity from a single primary root to a network of thousands of roots that collectively compete for ephemeral, heterogeneous soil resources. We used time-lapse 3D imaging and mathematical modeling to assess root system architectures (RSAs) of two maize (Zea mays) inbred genotypes and their hybrid as they grew in complexity from a few to many roots. Genetically driven differences in root branching zone size and lateral branching densities along a single root, combined with differences in peak growth rate and the relative allocation of carbon resources to new versus existing roots, manifest as sharply distinct global RSAs over time. The 3D imaging of mature field-grown root crowns showed that several genetic differences in seedling architectures could persist throughout development and across environments. This approach connects individual and system-wide scales of root growth dynamics, which could eventually be used to predict genetic variation for complex RSAs and their functions.

INTRODUCTION

Variation in root system architecture (RSA) can have profoundly different effects on plant health and productivity in different environments (Fitter, 1987; Lynch, 1995). In the absence of sensing mechanisms that extend beyond the plant, roots form branched three-dimensional (3D) networks that blindly forage the soil, adapting their developmental programs to environmental stimuli such as locally encountered resource patches (Lambers et al., 2006; Hodge et al., 2009; Bao et al., 2014; Giehl and von Wirén, 2014). Thus, when and where a plant grows its roots largely determine its ability to obtain water and nutrients but are, in turn, constrained by genetically encoded developmental programs and environmental perception. Since a plant must allocate its limited carbon resources to the growth of either new or existing organs, trade-offs exist in root foraging patterns (Fitter et al., 2002; Lynch et al., 2005; Lynch, 2013; Chen et al., 2016), such as the frequency of lateral root branching and how much to invest in topsoil versus subsoil exploration. Genetic variation for these and other root traits is of broad scientific interest, because they provide the links to how root structure and function are related from single roots, to root systems, to ecosystems (Jackson et al., 1996; Lynch, 2013; Warren et al., 2015; Koebernick et al., 2017; Ma et al., 2018). Furthermore, understanding the mechanisms that govern root system architecture would provide a major new lever for crop improvement work (de Dorlodot et al., 2007; Topp et al., 2016; Morris et al., 2017), especially considering low-input agriculture and future climate scenarios (Lynch, 2007; Godfray et al., 2010; Tester and Langridge, 2010; Warren et al., 2015).

This is a difficult task. In maize (Zea mays), a 3D architecture develops that can eventually consist of tens of thousands of roots occupying more than 200 cubic feet of soil (Weaver and Bruner, 1926); a wild oat (Avena fatua) root system was estimated to be 4.5 miles long (Pavlychenko, 1937). The tools necessary to analyze such an overwhelmingly large and complex structure in situ are currently inadequate. Consequently, root system architecture of mature crop plants has not been described more accurately than Weaver and Bruner (1926) did with extreme labor and destructive harvesting in the early 1900s. Yet root systems begin with a single root. In annual grasses such as maize, additional seminal and nodal roots subsequently emerge (Weaver and Bruner, 1926). All of these root types grow exponentially in size and complexity from three simple processes local to the root tip: elongation, curvature, and lateral branching; hence, it is logical to assume that if biologically meaningful rules and conditions could be learned at this local scale, accurate extrapolations could be made across increasing global complexities (Fitter, 1987; Diggle, 1988; Pagès et al., 1989). While molecular mechanisms and genetic variation in single root growth have long been intensively studied (reviewed in Walter et al., 2009; Wachsman et al., 2015; Slovak et al., 2016), we cannot make meaningful predictions of 3D architectures from them. The key to this translation will be root growth and soil biophysical models that can simulate a wide range of root system architectures and environmental interactions (Dupuy et al., 2010; Dunbabin et al., 2013; Araya et al., 2016; Roose et al., 2016; Postma et al., 2017; Schlüter et al., 2018; Schnepf et al., 2018) and have benefited from recent advances in computing power. Some are now starting to be used to improve real-world predictions of root growth (Postma et al., 2014; Kalogiros et al., 2016; Zhao et al., 2017). However, realistic parameterization and constraint of these models are known to be inaccurate due to a paucity of empirical data. In particular, time-resolved data sets that can simultaneously capture entire 3D root systems, genetic patterns, and stochasticity in individual root growth, while controlling or measuring soil parameters, have been highlighted as a critical need (Kalogiros et al., 2016; Roose et al., 2016; Zhao et al., 2017; Landl et al., 2018; Schlüter et al., 2018; Schnepf et al., 2018).

Image-based phenotyping technologies that enable nondestructive measurement of root system architectures have been developing at a rapid pace in recent years (Lobet et al., 2013; Spalding and Miller, 2013; Downie et al., 2015; Piñeros et al., 2016); however (for many practical reasons), the vast majority artificially constrain root growth to two dimensions, thereby limiting an understanding of the actual 3D phenotype, especially in field environments. For example, branching angles are poorly estimated (Landl et al., 2018). Another important caveat of two-dimensional (2D) growth systems is that once architectures become large and complex enough for roots to occlude one another, the ability to track the growth of individual roots is greatly diminished and usually unfeasible if grown in soil because the topology is obscured. A recent optical imaging study quantifying lateral root development in millet and maize growing in hydroponic 2D rhizotrons reported an average of 2-d-per-plant processing time using a state-of-the-art semi-automated root tracing tool (Passot et al., 2018). Hence, intense interest in X-ray and magnetic resonance–based 3D imaging for root studies has been warranted (Mooney et al., 2012; Helliwell et al., 2013; Roose et al., 2016; Morris et al., 2017). Both techniques have the potential to image time-resolved root growth of complex architectures in at least some types of extracted or reconstituted field soil. Yet there are significant imaging and image processing challenges to the recovery of intact root systems, especially thin lateral roots (Mooney et al., 2012; Helliwell et al., 2013; Pfeifer et al., 2015; Rogers et al., 2016; Roose et al., 2016; Burr-Hersey et al., 2017; Schlüter et al., 2018). This is a critical problem to 3D root growth modeling applications for two main reasons: (1) lateral roots are biologically important (Pierret et al., 2005) and thus essential inputs for the models themselves and (2) gaps or other inconsistencies in the root topology within the time series hinder the analysis of individual root growth because the 3D model cannot be reliably segmented into its constituent root branches (Symonova et al., 2015). Furthermore, X-ray and magnetic resonance imaging (MRI) are greatly constrained by well-known imaging trade-offs: field of view, resolution/image quality, and scan time. A survey of the most recent work in this area (Flavel et al., 2012; Tracy et al., 2012; Pfeifer et al., 2015; Ahmed et al., 2016; Rogers et al., 2016; Burr-Hersey et al., 2017; Helliwell et al., 2017; Schlüter et al., 2018) reveals that very few data sets have been published in any one study, with root growth or plant age strongly limited by pot size (in the range of 2.5 to 11 cm in diameter; vividly referred to as the bonsai effect [Roose et al., 2016]). Although time-resolved data have been collected, only global or demographic data have been reported (Koebernick et al., 2014; van Dusschoten et al., 2016). Finally, with the exception of one or two example plants (van Dusschoten et al., 2016; Morris et al., 2017), maize and other large, rapidly growing species have been left out of these analyses (Schlüter et al., 2018). Simply put, the actual capability of X-ray– or MRI-based imaging to capture entire freely-grown 3D roots systems to measure individual roots over time has not yet been demonstrated, and significant challenges remain. Hence, the gap in our understanding of how complex root system architectures form, and the critical need for better root modeling inputs, also remain.

Here, we quantified the 3D architectures of freely-growing maize root systems in a gel-based environment. This optical imaging platform, along with a hydroponics-based variation, has produced the only large-scale genetic studies of 3D (Fang et al., 2009, 2013; Clark et al., 2011; Topp et al., 2013; Hufnagel et al., 2014; Uga et al., 2018), or pseudo-3D (Iyer-Pascuzzi et al., 2010; Zurek et al., 2015), root system architecture to date, including the identification of single nucleotide polymorphisms that corresponded to sorghum (Sorghum bicolor) yield increases in low-phosphorus field experiments (Hufnagel et al., 2014). The homogeneity of the medium is a feature for our analysis comparing genetic, not environmental, differences in local root growth patterns of two maize inbred genotypes with contrasting architectures. We automated the imaging to monitor the seedling root systems of inbred lines B73, Mo17, and their hybrid over 1 week of development. During this time, architectural complexity grew from ∼2 to ∼100 roots. Building on a previously developed software that aligns the 3D reconstruction for each time point and constructs a graph representation (Symonova et al., 2015), we computed the time function for each root and analyzed the growth patterns. Mathematical modeling of the time series revealed the key parameters that drive genotype-specific differences in root system architecture, including the timing of a sharp inflection point in relative growth rate and the propensity to allocate carbon to either new or existing roots. Importantly, 3D analysis of mature field-grown roots showed that these patterns could persist from gel to field and could thus be more influenced by genetics than by the environment. Our analysis approach will work equally well with any time-lapse imaging technology that produces voxel (essentially a 3D pixel) data, such as X-ray or MRI, and can facilitate the study of growth responses to resource patches, other roots, soil particles, or other heterogeneously distributed soil parameters at local and global levels. This work will enhance the development of empirically driven growth models that can accurately predict root growth and root–environment interactions as a function of genotype.

RESULTS

Plant roots have typically been studied individually in great detail, or as entire systems, but rarely both, especially as freely-growing 3D structures. In order to understand how local root growth patterns contribute to global architectures along both a real-time and a developmental time axis, we established a four-dimensional (4D) analysis pipeline (Supplemental Figure 1). We automated a 3D gel-based optical imaging system (Topp et al., 2013) for time lapse and paired it with DynamicRoots software (Symonova et al., 2015) and custom R code (see “Methods”, data and software release) to compute the dynamic traits of individual branches based on the time series of 3D shapes. Two historically agronomically important maize inbred genotypes with contrasting root system architectures, B73 (a stiff-stalk genotype) and Mo17 (a non-stiff-stalk genotype), and their hybrid were imaged every 4 h across 8 d of development (164 h total), from 4 to 11 days after germination (DAG). The plants typically had only a primary root and one or two seminal roots at the beginning of the experiments, but more than 100 root branches by the end, including nodal roots (Supplemental Movie 1 shows the 4D patterns), providing a wide spectrum of architectural complexity.

Global Root Trait Dynamics Reveals Fundamental Genetic Differences in Growth patterns

Phenotypic analysis of root system architecture in a panel of diverse maize inbred lines has shown complex genotype-specific patterns that change during early development (Zurek et al., 2015), but the underlying root growth dynamics leading to these differences is not understood. Using the automated imaging system, we were able to observe global-scale growth patterns on a well-resolved temporal scale of 4 h. To provide information about the size and shape of the root systems, we compared total root volumes, lengths, and numbers (Figure 1). Despite a highly controlled and homogeneous environment, the dynamic range of growth varied extensively among genetically identical plants, as evidenced by the large spread of data, providing a measure of stochasticity. Yet phenotypic separation of the two genotypes could be identified very early in the experiment along the values of the mean curve (Figures 1A to 1C; t tests for each time point in Supplemental Tables 1 to 3). The values for the hybrid genotype had the greatest intragenic variation, but the average values were largely intermediate to those of the parents, which is similar to previous findings (Hund et al., 2012). The total root volume and number of roots in the B73 samples were consistently greater than those of Mo17 at all time points, but initial differences in total root length disappeared by day 11 (Figure 1; Supplemental Table 2). Since analysis of dry root weights from day 11 also showed that B73, Mo17, and their hybrid all had similar root biomass (Supplemental Figure 2), we conclude that Mo17 and B73 fundamentally differ in how they allocate carbon resources for root foraging. B73 invests in relatively more, shorter, and cheaper roots (i.e., less biomass per unit of surface area), and Mo17 invests relatively more in the continued growth of extant roots, with their hybrid as intermediate.

Figure 1.

Global Root Trait Dynamics Reveals Fundamental Genetic Differences in Growth Patterns.

Time-course values of total root volume (A), total root length (B), and total root number (C). Each point represents an individual seedling at a specific time point, and the solid lines indicate mean values. Time course of growth rates and accelerations of the total root volume (D), total root length (E), and total root number (F). Points represent the mean value of growth rates. Vertical error bars represent the se. Bar plots show the accelerations. The gray bars represent nighttime.

To capture the underlying dynamics of these temporal relationships, we computed the rates of change (or velocities, the first derivative) and accelerations (changes in velocity, the second derivative) for the three global traits (Figures 1D to 1F). A sharp demarcation occurs in both inbred genotypes that separates increasing and decreasing growth rates for root volume and length. However, the inflection point is delayed in Mo17 relative to B73 (Figures 1D and 1E) and is slightly earlier in the hybrid. This transition is coupled to the rate of new root formation in B73 and the hybrid, but not in Mo17 (Figure 1F), suggesting a fundamentally different process for patterning root system architecture between the two genotypes that appears semi-dominant in the hybrid.

Despite the clear trend over the 1-week time interval, accelerations or decelerations between any two 4-h time intervals were generally smooth; no significant differences were found for rates of change in total root number for any genotype at this temporal resolution, and in only a single interval each in B73 and the hybrid for root volume. Rates of change for total root length were more variable in all genotypes, but not in a consistent pattern (Figures 1D to 1F; Supplemental Table 4). Diurnal patterns of growth in plant leaves and shoots (Walter et al., 2009) are well established, but evidence in grasses suggests that their roots do not change elongation patterns along day/night cycles (Iijima et al., 1998; Walter et al., 2002). We compared the growth rates during the 4 h before dark to the growth rate during the next 4 h in the dark for each genotype. All three genotypes had differences (P < 0.05) in day/night growth rates at some time points, but not others (Supplemental Table 4), providing no clear pattern of diurnal regulation. Instead, we found that growth rates were predominantly driven by developmental time, rather than diurnal real time (Figures 1D to 1F).

Seedling Root System Architecture Traits Can Persist in Field-Grown Mature Root Systems

We next investigated whether these genotype-specific seedling root growth properties found in seedlings grown in an artificial medium could persist into maturity in the field environment. We shovel extracted and washed root crowns from a field experiment in Missouri at anthesis, scanned them with X-rays, and measured identical 3D features from the reconstructed root models (Figure 2). Washed root crowns are a main focus of the current state-of-the-art techniques in field-based root analysis because, as the nexus of the entire root system, they are information rich, and become heavily lignified during development, which largely preserves their structure (Trachsel et al., 2011; Das et al., 2015; Schneider et al., 2015). In previous work, we showed that 3D X-ray scanning provided a benefit over 2D optical imaging for the genotypic discrimination of maize root crown phenotypes (Bray and Topp, 2018). Here, this technique also allowed us to compare precisely the same traits to one another in roots from seedlings and mature plants.

Figure 2.

Seedling Root Architectures Persist in Field-Grown Mature Root Systems.

Reconstructions (3D) of seedling root systems at 11 DAG (A) and mature root crowns at anthesis (B). Score and loading plots for the first two PCs of seedling root traits (C) and mature root crown traits (D). Each dot represents one plant.

Nearly every significant difference between gel-grown seedlings of B73 and Mo17 was also reflected in the field-grown mature roots (Figure 2; Supplemental Figure 3), including total root volumes, lengths, and numbers. In multivariate space, our analysis clearly delineated the two inbred genotypes, rather than growth stage or environment, with the first two principal components (PCs) explaining ∼75% of the total phenotypic variation in the combined data set (Figure 2C; Supplemental Table 5). As expected, the aboveground mean biomass of field-grown hybrids was much larger than that of either parent (Supplemental Figure 2), but while the first two PCs separated the hybrid from either parent in the field data (pink triangles in Figure 2C), extreme values were found only for total root volume and convex hull area. Although we could not directly correlate gel and field values due to our unbalanced data set, we compared the standardized distributions for each trait in both environments and found that solidity (a measure of the thoroughness of exploration), specific root length (a measure of root biomass allocation to relatively thinner or thicker roots), total root length, and total number of root tips persisted across growth stages and environments for all genotypes, while the persistence of convex hull volume and width-to-depth ratios was conditional on genotype and was not supported for root system volumes (Supplemental Figure 3; Supplemental Table 6). These results allow us to make two important points with implications for maize 3D root system architecture complexity: (1) we found a strong correspondence between several seedling and mature root traits driven by genotype-specific growth dynamics that were largely uninfluenced by environmental variation; and (2) at odds with well-cited literature (Mackay and Barber, 1984; Wissuwa et al., 2008; Gregory et al., 2009; Hargreaves et al., 2009; Wasson et al., 2012; Watt et al., 2013; Shrestha et al., 2014; Poorter et al., 2016), controlled environment analyses using artificial media can provide meaningful insight into root growth patterns throughout development and in field environments. Given our small sample size and analysis of only three maize genotypes, these observations are not meant to be conclusive but to underscore the influence of endogenous developmental mechanisms on RSA at any scale and to provide an example of how emerging high-information content root phenotyping tools can be used to re-evaluate conventional wisdom.

Modeling Global Growth Patterns Allows a Direct Comparison of Parameters That Control More Complex Patterns

Nonlinear models such as logistic growth functions can provide function-valued traits that integrate both real and developmental time to describe complex patterns of growth or architectural change (Barlow et al., 1991; Morris and Silk, 1992; Paine et al., 2012; Araya et al., 2016). After testing various nonlinear models for several fitting criteria (Supplemental Table 7), we chose a three-parameter logistic growth function to model the global trait dynamics (Figure 3; see “Methods”). Parameter α₁ describes the carrying capacity of the function, which reports the maximum values of the modeled growth curve. B73 had significantly higher α₁ values for total root volume and total number of root branches, reflecting the finding that B73 has a larger final volume and more branches than Mo17 (Figure 3). However, the α₁ values for total root length were not different, despite significantly larger values for B73 at each time point until hour 144. This result highlights the importance of capturing and integrating the time dimension through an appropriate model, rather than ad hoc analysis of individual time points, which can mislead. Parameter α₂ represents the maximum rate of change and is a direct measure of the trends seen in Figures 2D to 2F. It provides an explicit quantification of the different times at which the inflection points between increasing and decreasing growth trends were reached for a given trait. B73 and the hybrid begin slowing the rate at which root length and volume are added more than 24 h prior to Mo17 (Figures 3A and 3B), whereas differences in the time at which additions of new lateral roots slowed were much less pronounced (Figure 3C). Parameter α₃ captures the slope of the growth curve, and except for total root volume, the values between B73 and Mo17 were significantly different, reflecting the finding that the total number of branches and to a lesser extent total root length increased more sharply for B73. The overall growth trends for the hybrid were most similar to B73, although we note that the range of values was typically larger than that of either parent (reflected in the long axes of the violin plots in Figure 3), suggesting the hybrid is less constrained in its developmental program than the parental genotypes.

Figure 3.

Modeling Global Growth Patterns Allows a Direct Comparison of Parameters That Control More Complex Patterns.

Parameters (α_l, α₂, α₃) of the logistic growth models estimated for total root volume (A), total root length (B), and total number of branches (C). Violin plots and box plots were generated using the ggplot2 package with default settings for statistics in R. The significance levels of pairwise t tests were added. *P ≤ 0.05, **P ≤ 0.01,***P ≤ 0.001, ****P ≤ 0.0001. ns, not significant, P > 0.05.

Modeling of dense (4-h intervals) time-series data provided important insights into the growth dynamics underlying genotypic differences in root system architecture, but from a practical standpoint, we wanted to know whether similar answers could be derived from fewer data points. We conducted two types of sensitivity tests for each trait by progressively removing data from the analysis to generate pseudo time intervals and either (1) comparing the differences in modeled trait values for a single genotype (B73, Supplemental Figures 4 to 6) or (2) comparing the differences in statistical test results among B73, Mo17, and the hybrid (Supplemental Figures 7 to 9). Our estimates of the B73 total root volume modeling parameters would not have changed significantly if we would have imaged at any interval of 20 h or less, whereas 4- versus 24-h intervals gave statistically different results. Model estimates of total branch number hardly varied at pseudo time intervals from 4 to 24 h, with a few sporadic exceptions. However, total root length estimates were extremely labile, resulting in significant differences in the values between 4 h and nearly every other interval (Supplemental Figures 4 to 6). Despite this intra-genotypic variability, the computed statistical differences among B73, Mo17, and the hybrid were remarkably consistent at any time interval from 4 to 24 h for all three traits (Supplemental Figures 7 to 9). The results of this analysis suggest that much of the same information about root growth dynamics could be attained through less frequent phenotyping, which could translate to increases in sample throughput and more power to resolve subtle environmental or genetic differences.

Genetic Differences in Aggregate Local Growth Patterns Suggest Distinct Foraging Strategies

A key feature of our phenotyping pipeline is automated derivation of the time function and quantification of local growth. We computed the branch hierarchies for entire root systems, enabling us to know the precise topological relationships of all the roots in each 3D model (see “Methods”) and analyzed all of the individual branches as aggregate trait distributions during the time course. Demographic differences between genotypes that reflected fundamental growth patterns were apparent and supported by two-sample Kolmogorov–Smirnov (K-S) tests (Figure 4; Supplemental Figures 10 to 12). For each genotypic comparison at each time point, we computed the critical value of the D-statistic (D-critical; see “Methods”), above which we conclude the distributions differ between genotypes and vice versa (Figure 4). Analysis of root length distributions showed that while B73 had a higher proportion of longer branches than Mo17 at the earliest time points (<5 DAG), the proportion of shorter branches increased rapidly for B73 during the 5 to 7 DAG period (Figure 4A), resulting in statistically indistinguishable distributions between B73 and Mo17 during hours 28 to 44 and a significantly higher proportion of shorter branches for B73 through the rest of the experiment (Figure 4A; Supplemental Figure 10). This trend reflects the rapid proliferation of lateral roots captured in the global architecture and growth modeling analyses (Figures 1C, 1F, and 3C). However, the burst of new roots began tapering off by 8 DAG as B73 began shifting growth toward root elongation rather than formation. This change in carbon resource allocation is clearly seen by the steadily decreasing proportion of relatively shorter branches throughout the rest of the experiment (Figure 4A), although to a lesser extent than for Mo17 (Figure 4A; Supplemental Figure 10). The architecture of Mo17 was initially defined by shorter roots but then balanced elongation of existing roots with new root production throughout the time course, reflected in the steady root length distributions seen from 8 DAG. Growth patterns of the hybrid were also consistent, but there was a lesser or greater emphasis on new root production relative to B73 and Mo17, respectively, at nearly every time point (Figure 4A; Supplemental Figure 10).

Figure 4.

Genetic Differences in Aggregate Local Growth Patterns Suggest Distinct Foraging Strategies.

(A) Time course and K-S D-statistic of root length distribution. Relative (unitless) root length for each individual branch was normalized by the longest branch in the whole root system and recorded in 10 bins.

(B) Time course and K-S D-statistic of soil angle distribution. The soil angle (degrees) is the angle formed by the root branch and the horizontal level.

(C) Time course and K-S D-statistic of branching angle distribution. The branching angle (degrees) is the angle formed by the child branch and its parent branch. D-statistic and D-critical values were drawn with straight lines for visualization.

To study root curving, we computed the soil angle distribution, which compares root geometry relative to an extrinsic reference (the soil horizon), and branching angle distribution, which measures the intrinsic angle between a child and parent branch regardless of orientation to the soil horizon (also referred to as deflection index in modeling terms [Dunbabin et al., 2013]). As shown in Figure 4B and Supplemental Figure 11, B73 and Mo17 had similar soil angle distributions from hours 0 to 52. However, the proportion of shallow-angled branches quickly increased with the emergence of new branches in B73 (Figure 1C), peaking from 7 to 9 DAG and intermittently thereafter (Figure 4B; Supplemental Figure 11), whereas Mo17 was more consistent during the experiment, and the hybrid fluctuated around the parental values (Figure 4B; Supplemental Figure 11). Since most maize roots eventually orient to the vertical gravity vector over time, the production of new lateral roots and their angles relative to the parent branch (which is older and thus more likely to be vertically oriented) largely dictate the extent of horizontal soil exploration. In the earliest stages of maize root development, several embryonic (seminal) roots emerge from the seed, which is reflected in all three genotypes by the dominance of shallow root branching angles at the earliest time points (Figure 4C; Supplemental Figure 12). As root system architectures became more complex, branching angle distribution patterns were consistent, but the magnitudes depended on genotype (Figure 4C). The greater angles at every time point beyond hour 32 demonstrate that lateral roots grew further away from the parent branch in B73 relative to Mo17 and the hybrid (Figure 4C; Supplemental Figure 12). These results highlight fundamental differences in local growth patterns that have strong implications for root system architecture and thus plant fitness in different environments (Fitter et al., 2002; Hodge et al., 2009; Lynch, 2013; Postma et al., 2014).

Genetic Differences in Primary Root Development Reveal the Basis for Distinct Global Architectures

Primary roots have been used extensively to study multiscale relationships in molecular, cellular, and developmental patterning along a single root, but these insights have not translated to a predictive understanding of how complexity emerges at the root system scale (Petricka et al., 2012; Hill et al., 2013; Slovak et al., 2016), despite their inclusion in root system architecture models (Pagès et al., 1989). To understand these relationships more explicitly, we studied the genetic differences in developmental patterns along an individual root in situ of a 3D root system. For the final, most architecturally complex time point, we defined the primary root as the branch connected to the seed that had the most child branches and analyzed the patterns along this developmental axis. The positions of each lateral root were computed using the distance between the branching fork and the base of the primary root, divided by the primary root length (Figure 5A). B73 had more total lateral branches along the primary root than Mo17, but they also emerged much closer to the root tip. On average, B73 lateral roots were found along the upper 80% of the primary root, whereas Mo17 lateral roots were found along only the upper 60%. Since there was no significant difference in the primary root length between the two genotypes, B73 had both a higher lateral root branching density and a longer zone of branching. These data are congruent with the local and global root length and branching traits we measured previously. Thus, the global architectural trade-off of investment in new branches versus growth of existing branches (Figures 2 and 5) appears to be controlled by genetic differences in local developmental processes.

Figure 5.

In Situ 3D Analysis of Genetic Differences in Primary Root Development Reveals the Basis for Distinct Global Architectures.

(A) Computational dissection of primary root longitudinal and radial branching traits from maize root systems.

(B) Distribution of the first-order lateral root number on the primary root. The percent distance refers to the distance between the branching fork and the primary root base, divided by the primary root length.

(C) Distribution of the radial angles for lateral branching around the primary root. The radial angle is the angle (degrees) formed by the root branch and the adjacent branch along the longitudinal axis. For each genotype, each column represents an individual seedling, and mean values are given on the right.

Recent work has uncovered key links between water perception and the radial position of new lateral roots around their parent, with strong implications for 3D root system architecture (Bao et al., 2014; Orosa-Puente et al., 2018; Robbins and Dinneny, 2018). However, little is known about the inherent genetic variation of radial patterning outside of the well-studied 2D branching plane of Arabidopsis (Arabidopsis thaliana), whereas in maize and other monocots, lateral roots can emerge radially in 3D (Smith and De Smet, 2012). To quantify whether genotype-specific radial emergence patterns contributed to differences in global architecture in a homogeneously wet substrate, we leveraged our 3D data to compute radial angles for lateral branching around the primary root. Each lateral root was compared with the adjacent branch along the longitudinal axis, and the relative angle between them was recorded in 10 bins, 36° apart. The mean distributions of the radial angle had a near constant probability, suggesting that lateral roots overall emerged in all directions equally for B73, Mo17, and their hybrid (Figure 5B, mean values). However, the significant intra-plant variation across the experiment reveals substantial heterogeneity along any given primary root, suggesting that stochasticity (randomness) may play a significant role in maize radial branching patterns.

DISCUSSION

Here, we addressed a major knowledge gap spanning local- and global-scale root system architecture complexity. We conducted a comprehensive 3D analysis of the spatiotemporal dynamics of 38 maize seedling root systems representing three genotypes as they grew freely through several orders of magnitude in complexity and compared the results to samples from the field. Mathematical modeling revealed genetic differences in these patterns by simple function-values that integrated growth trends along both real and developmental timescales. For example, the parameter value α₂ not only quantifies the sharp inflection point between increasing and decreasing global root elongation rates for both B73 and Mo17 but also the differences in the timing of this event between the inbreds (79 and 98 h after first imaging for total root length, respectively). This difference mitigated the relatively faster growth of B73 (provided by α₃) such that total root length was equivalent by the end of the experiment (provided by α₁). We also analyzed the dynamics of root volume, numbers, soil, and lateral root deflection angles, which collectively can be used to parameterize growth models with realistic statistical distributions that are specific to genotype (Kalogiros et al., 2016; Roose et al., 2016; Zhao et al., 2017; Landl et al., 2018; Schlüter et al., 2018; Schnepf et al., 2018). Time-resolved 3D phenotyping applied to mapping populations or association panels could resolve the genetic basis of complex root system architecture formation, as it has for simpler root traits (Moore et al., 2013; Kwak et al., 2014). Unlike X-ray or MRI, 3D optical imaging has proven to be scalable to the population sizes needed for such studies (Fang et al., 2009, 2013; Clark et al., 2011; Topp et al., 2013; Hufnagel et al., 2014; Uga et al., 2018), and our model sensitivity analysis provides guidance on the imaging frequency at which these studies could be effectively conducted, depending on the traits of interest.

Critically, we recovered intact root systems at each time point, so that using computer vision, we could parse the global architectures into demographics of their constituent roots. From these, we learned how the maize inbreds differentially balanced their carbon investments in new root production relative to the maintenance of existing root growth over time. We also monitored the angular distance that each root grew relative to the soil, and of lateral roots to their parent branch, which was quite consistent for a given genotype during our experiment. Analysis along a single root axis showed that B73 makes lateral roots more frequently and more densely than Mo17. In sum, these features suggest genetically encoded differences in rhizoeconomic foraging strategy (Fitter et al., 2002; Lynch et al., 2005; Lynch, 2013; Chen et al., 2016). In this context, plants in the wild explore the soil while competing against other root systems for resources, or in the case of agriculture, to optimize resource capture at the plot level. However, the carbon economic cost of producing many or few, short or long, and thick or thin roots must also be considered, among other factors. Previous studies have posited that the ideotype of fewer but longer and deeper lateral roots acquires mobile resources such as nitrogen more efficiently, but the ideotype of shorter but denser lateral roots in the topsoil acquires immobile resources such as phosphorus more efficiently (Lynch, 2013). Our work shows the underlying features that cause B73 to develop a more densely packed root system, and Mo17 a more open and extensive system, which are in agreement with the known P efficiency of B73 and inefficiency of Mo17 (Kaeppler et al., 2000; Zhu et al., 2005). Corresponding 3D X-ray–based analysis of field-excavated mature root crowns showed that these architectural properties could be developmentally hardwired and environmentally stable.

Through computational dissection of spatiotemporal data, we have shown how genetic differences in developmental and local growth patterns measurable at the seedling level can be diagnostic of root system architecture at maturity. Despite a wide range of phenotypic variation within the root system of a single plant or among genetically identical plants, the overall patterns were strongly correlated with genotype. Considering the homogeneous conditions of the gel, we interpret this to mean that a significant amount of stochasticity is inherent to the development of RSA complexity, which can be incorporated into predictive growth models. Our multiscale approach can be extended to a wide variety of other research questions where local interactions, such as patchy nutrients or competing roots, can be studied in the context of their effects on global architecture. Furthermore, function-valued approaches are superior to simple summary statistics to quantify growth and environmental interactions (Stinchcombe et al., 2012). 3D imaging and computational analysis of root growth allows traits (e.g., radial angle) to be quantified at a global scale that are not accurate or even measurable via 2D phenotyping approaches, especially with complex root systems. Our methods transfer to any 3D voxel data, including to X-ray and MRI studies when those technologies have sufficiently matured (Mooney et al., 2012; van Dusschoten et al., 2016; Morris et al., 2017). Efforts are underway to develop improved imaging technologies and computational tools to close the gap between our current capabilities and the ideal of accurate and biologically relevant nondestructive imaging and evaluation of root system architecture in field soil. Nonetheless, our current work bridges local and global scales to meet the need of parameterizing multiscale models (Lynch et al., 1997; Bodner et al., 2013; Araya et al., 2016; Kalogiros et al., 2016; Postma et al., 2017; Zhao et al., 2017; Passot et al., 2018; Schnepf et al., 2018). Continued work toward accurate predictions of root growth and root–environment interactions at increasingly complex scales is critical for a realistic understanding of integrated plant biology and the enormous potential of root systems for the improvement of agriculture.

METHODS

Plant Materials and Growth Conditions

Two maize (Zea mays) inbred genotypes, B73 (n = 12) and Mo17 (n = 12), and their hybrid (n = 14) were used in this study. Seed preparation and growth conditions follow Zurek et al. (2015). The growth medium was made with a modified 1/2× Hoagland solution, pH 6.0, and solidified with gellan gum. The seeds were sterilized with 35% (v/v) hydrogen peroxide for 20 min and rinsed four times with reverse osmosis water. After imbibing in reverse osmosis water for 8 h at 29°C in the dark, the seeds were sterilized again with 35% hydrogen peroxide for 10 min and rinsed four times with sterile water. The seeds were germinated at 29°C in the dark until the radicle reached 1 to 2 cm in length (∼48 h). One seedling was planted into a glass growth cylinder sealed with generic plastic cling film; this constitutes a biological replicate. The cylinders were placed on a dark shelf at ambient conditions overnight for acclimation before moving them into a growth chamber starting at 4 DAG. The plants were illuminated with 315-W Ceramic Metal Halide bulbs (Philips), with a light intensity at the top of each jar of 700 µmol/m²/s. Humidity in the chamber was maintained at 50%, although the jars were sealed with generic plastic cling film. Temperatures were set to 28°C during the day and 24°C at night, with a 16/8-h day/night cycle.

Imaging System

The imaging system was set up in the growth chamber. It consists of a Stingray F-504C digital camera (Allied Vision Technologies), a LT360 turntable (LinearX), a near-infrared 850 nm light-emitting diode light (SOBL, Smart Vision Lights), an optical correction tank, and a personal computer. The schematic details of a nearly identical imaging system can be seen in Clark et al. (2011). The near-infrared light-emitting diode was used with a longpass 830 nm infrared camera filter (LP830-49, Midwest Optical Systems) to provide a high-contrast silhouette during the day and to avoid affecting plant growth during night. The light was turned on 10 s before each imaging course and was turned off immediately after the rotational sequence was taken. For each imaging course, 180 images were taken at 2° increments. A custom program written in LabVIEW was used to control the image acquisition and set up time-lapse imaging, which enabled the imaging system to take automatic rotational image sequences. Because of the nearly real-time imaging frequency, plants were imaged one-at-a-time during a week of growth, before the next plant was loaded into the system. In this study, all the plants were imaged every 4 h for a week, until day 11 after germination. For each plant, 41 or 42 image sets were captured.

Maize Field Experiment

The same maize inbreds and hybrids that were used in the gel were included in a field experiment at the University of Missouri Genetics Farm in Columbia and were planted on May 16, 2017. Six plants each were sampled from two rows after flowering (Trachsel et al., 2011) and washed root crowns were scanned on a North Star Imaging (NSI) X5000 X-ray Computed Tomography system at the Donald Danforth Plant Science Center in St. Louis. All the scans were performed at 70 kV and 1700 μA, collecting 1800 projections over 360° of rotation. Scanning resolution was 111 μm. The total scan time for each sample was 3 min. Projections were reconstructed into single 3D volumes using NSI efX-ct software, and each volume was exported as a 2D image stack for analysis. For the root segmentation, 2D image slices were thresholded using band thresholding to remove any soil that remained in the images. The two threshold values were determined by triangle algorithm and Otsu algorithm, respectively. Cleaned 3D root models were input into the RSA-GiA pipeline to calculate root trait values.

Quantification of RSA Traits

We used the RSA-GiA pipeline to generate the 3D reconstructions from 2D rotational images. The pipeline included three main steps: (1) cropping, to remove the above-gel parts from the images; (2) thresholding, to convert the images to binary images, in which roots were the foreground; and (3) reconstruction, to build the 3D models based on the visual hull algorithm built into RSA-GiA (Topp et al., 2013). To analyze a time series of 3D reconstructions, we used DynamicRoots. DynamicRoots is a software tool that is capable of computing structural and dynamic traits for growing roots (Symonova et al., 2015). It aligns all the models in a time series, decomposes the 3D root system into individual branches, and records the growth process. The primary output of DynamicRoots is a txt file that includes columns for different root traits at every observation time and rows for data from every branch. To analyze root growth patterns, we developed R functions for computing global root traits, root growth rate, root growth direction, and root distribution from DynamicRoots-generated files. Using the traits for each branch, the total volume, total length, and total number of branches were obtained for every time point. In order to avoid noise, branches shorter than 5 voxels at the last observation time were removed. The total root volume was the sum of the root volume of all individual roots. The total root length was the sum of the root length of all individual roots. The total number of branches was the sum of the numbers of individual roots. The growth rate was the difference of root traits between two subsequent time points. We defined the angle between branch and soil level as soil angle, and the angle between branch and its parent branch as branching angle.

Data Analysis

To compare the shape of root growth for different genotypes, we modeled the dynamic of global root traits. Linear, exponential, power law, monomolecular, three-parameter logistic, four-parameter logistic, and Gompertz models were tested. The basic functional forms for these models can be seen in Paine et al. (2012). We parameterized the three-parameter logistic model in the following way to facilitate descriptions of growth curves:

where y represents the global traits, that is, total root volume, total root length, and total root number; t is the time after the start of the imaging course; α₁ is the maximum growth capacity; α₂ is the inflection time point; and α₃ is the steepness.

To compare models, R squared (R²), root mean squared error, se, and Akaike Information Criterion of the regression were computed for each model as scores of model fitness. The best model was selected based on these scores and the number of regression parameters. Student’s t test was used to detect whether the means of the parameters among different genotypes were significantly different.

To understand whether overall root architectural patterns clustered more strongly by genotype, or maturity and growth environment, principal component analysis (PCA) was performed for all 3D features from both seedling and mature roots in all samples. PCA is a technique used to reduce dimensionality of the data, and here we performed PCA to visualize the data globally and look for patterns.

To investigate which seedling root system feature values persisted in mature root systems, Student’s t tests were performed for each 3D feature: (1) between genotypes within either the gel or field data sets and 2) between seedling and mature root samples for a given genotype. Since the features from the two stages had different scales, we standardized the data for seedling and mature roots separately by the following equation:

where x′ is the standardized data (Z-score), x is the raw data, M is the mean of the data set, and sd is the standard deviation of the data set.

Two-sample K-S tests were performed to detect whether the root trait distributions among different genotypes were significantly different. K-S is a nonparametric test that can be used to detect differences in both the location and shape of distributions of two samples. To compare the distributions of root length, soil angle, and branching angle among different genotypes, we performed K-S tests for each trait value at each time point. Both D-statistic and P-values were reported. We set the P-value at a 95% confidence level, and D-critical was calculated as follows:

where n₁ and n₂ are the sizes of first and second sample, respectively. If the D-statistic value is greater than the corresponding D-critical value, we accept the hypothesis that there is difference between the two distributions.

All the data analysis was perform using custom code written in R programing language (http://www.r-project.org/). The parameters for all growth models were estimated using linear (“lm” function) or nonlinear least squares regression (“nls” function). The PCA was computed using the function “prcomp”. The Student’s t test was computed using the function “t.test”. The K-S test was computed using the function “ks.test” in the R package “stats”.

Data and Software Availability

The visual hull algorithm for 3D reconstruction is available at https://github.com/Topp-Roots-Lab/3D_reconstruction (release v1.0). The DynamicRoots software is available at https://sourceforge.net/projects/dynamicroots/files (release February 17, 2015). The time series of 3D reconstructions, 3D features from RSA-GiA pipeline, DynamicRoots-generated files, analyzed results, and corresponding code are available at https://github.com/Topp-Roots-Lab/timeseries_analysis (release v1.0).

Supplemental Data

• Supplemental Figure 1. Workflow for 4D analysis of maize roots.

• Supplemental Figure 2. Comparisons of seedling root dry weight at 11 days after germination and shoot dry weight at anthesis between B73, Mo17, and their hybrid.

• Supplemental Figure 3. Comparisons of 3D traits from seedling and mature roots.

• Supplemental Figure 4. Comparison of the three parameters in the total root volume growth model at different intervals for genotype B73.

• Supplemental Figure 5. Comparison of the three parameters in the total root length growth model at different intervals for genotype B73.

• Supplemental Figure 6. Comparison of the three parameters in the total root number growth model at different intervals for genotype B73.

• Supplemental Figure 7. Comparison of the statistical differences in the total root volume growth model among B73, Mo17, and the hybrid at different intervals.

• Supplemental Figure 8. Comparison of the statistical differences in the total root length growth model among B73, Mo17, and the hybrid at different intervals.

• Supplemental Figure 9. Comparison of the statistical differences in the total root number growth model among B73, Mo17, and the hybrid at different intervals.

• Supplemental Figure 10. Comparisons of root length distribution among B73, Mo17, and the hybrid at each time point. CF represents cumulative frequency.

• Supplemental Figure 11. Comparisons of soil angle distribution among B73, Mo17, and the hybrid at each time point. CF represents cumulative frequency.

• Supplemental Figure 12. Comparisons of branching angle distribution among B73, Mo17, and the hybrid at each time point.

• Supplemental Table 1. t Tests of total root volume for each time point.

• Supplemental Table 2. t Tests of total root length for each time point.

• Supplemental Table 3. t Tests of total root number for each time point.

• Supplemental Table 4. Paired t test of day/night growth rates.

• Supplemental Table 5. Loadings of traits that contribute to each principal component.

• Supplemental Table 6. t Test of traits from seedling and mature roots for each genotypes.

• Supplemental Table 7. Comparison of different models for global root traits.

• Supplemental Movie 1. Representative time function of each genotype in the analysis.

Dive Curated Terms

The following phenotypic, genotypic, and functional terms are of significance to the work described in this paper:

• primary root AmiGo: PO:0020127

• root AmiGo: PO:0009005

• seed AmiGo: PO:0009010