Genetic Architecture of Maize Rind Strength Revealed by the Analysis of Divergently Selected Populations.

The strength of the stalk rind, measured as rind penetrometer resistance (RPR), is an important contributor to stalk lodging resistance. To enhance the genetic architecture of RPR, we combined selection mapping on populations developed by 15 cycles of divergent selection for high and low RPR with time-course transcriptomic and metabolic analyses of the stalks. Divergent selection significantly altered allele frequencies of 3,656 and 3,412 single- nucleotide polymorphisms (SNPs) in the high and low RPR populations, respectively. Surprisingly, only 110 (1.56%) SNPs under selection were common in both populations, while the majority (98.4%) were unique to each population. This result indicated that high and low RPR phenotypes are produced by biologically distinct mechanisms. Remarkably, regions harboring lignin and polysaccharide genes were preferentially selected in high and low RPR populations, respectively. The preferential selection was manifested as higher lignification and increased saccharification of the high and low RPR stalks, respectively. The evolution of distinct gene classes according to the direction of selection was unexpected in the context of parallel evolution and demonstrated that selection for a trait, albeit in different directions, does not necessarily act on the same genes. Tricin, a grass-specific monolignol that initiates the incorporation of lignin in the cell walls, emerged as a key determinant of RPR. Integration of selection mapping and transcriptomic analyses with published genetic studies of RPR identified several candidate genes including ZmMYB31, ZmNAC25, ZmMADS1, ZmEXPA2, ZmIAA41 and hk5. These findings provide a foundation for an enhanced understanding of RPR and the improvement of stalk lodging resistance.

Measurement accuracy and uncertainty in plant biomechanics.

All scientific measurements are affected to some degree by both systematic and random errors. The quantification of these errors supports correct interpretation of data, thus supporting scientific progress. Absence of information regarding reliability and accuracy can slow scientific progress, and can lead to a reproducibility crisis. Here we consider both measurement theory and plant biomechanics literature. Drawing from measurement theory literature, we review techniques for assessing both the accuracy and uncertainty of a measurement process. In our survey of plant biomechanics literature, we found that direct assessment of measurement accuracy and uncertainty is not yet common. The advantages and disadvantages of efforts to quantify measurement accuracy and uncertainty are discussed. We conclude with recommended best practices for improving the scientific rigor in plant biomechanics through attention to the issues of measurement accuracy and uncertainty.

A general review of the biomechanics of root anchorage.

With few exceptions, terrestrial plants are anchored to substrates by roots that experience bending and twisting forces resulting from gravity- and wind-induced forces. Mechanical failure occurs when these forces exceed the flexural or torsional tolerance limits of stems or roots, or when roots are dislodged from their substrate. The emphasis of this review is on the general principles of anchorage, how the mechanical failure of root anchorage can be averted, and recommendations for future research.

Preventing lodging in bioenergy crops: a biomechanical analysis of maize stalks suggests a new approach.

The hypothetical ideal for maize (Zea mays) bioenergy production would be a no-waste plant: high-yielding, with silage that is easily digestible for conversion to biofuel. However, increased digestibility is typically associated with low structural strength and a propensity for lodging. The solution to this dilemma may lie in our ability to optimize maize morphology using tools from structural engineering. To investigate how material (tissue) and geometric (morphological) factors influence stalk strength, detailed structural models of the maize stalk were created using finite-element software. Model geometry was obtained from high-resolution x-ray computed tomography (CT) scans, and scan intensity information was integrated into the models to infer inhomogeneous material properties. A sensitivity analysis was performed by systematically varying material properties over broad ranges, and by modifying stalk geometry. Computational models exhibited realistic stress and deformation patterns. In agreement with natural failure patterns, maximum stresses were predicted near the node. Maximum stresses were observed to be much more sensitive to changes in dimensions of the stalk cross section than they were to changes in material properties of stalk components. The average sensitivity to geometry was found to be more than 10-fold higher than the average sensitivity to material properties. These results suggest a new strategy for the breeding and development of bioenergy maize varieties in which tissue weaknesses are counterbalanced by relatively small increases (e.g. 5%) in stalk diameter that reduce structural stresses.

On measuring the bending strength of septate grass stems.

UNLABELLED: • PREMISE OF THE STUDY: Reliable testing methodologies are a fundamental tenet of scientific research. However, very little information is found in the literature explaining how to accurately measure the structural bending strength of plant stems. It was hypothesized that the most commonly employed loading configuration used in bending experiments (placement of loading anvil at an internodal region of the stem or stalk) may significantly alter test results and introduce errors in bending strength measurements of plant stems.• METHODS: Four types of mechanical tests were performed on bamboo (Phyllostachys aurea), giant reed (Arundo donax), and maize (Zea mays) to investigate how different loading configurations employed during three-point bending experiments affect test results of septate grass stems and to develop a testing protocol that provides reliable measures of stalk bending strength.• RESULTS: RESULTS confirmed the hypothesis that internodal-loaded three-point bending test can produce erroneous bending strength measurements. This testing methodology causes plant stems to break prematurely and produces failure types and patterns incongruent with stalks that broke in their natural (in situ) environment. In contrast, a modified test configuration produces natural failure patterns and more accurate measurements of bending strength.• CONCLUSION: Reliable measurements of stalk bending strength can be obtained by maximizing the span length of bending tests and placing the loading anvil at stronger and denser nodal tissues. These results are relevant to ecological and evolutionary plant biomechanics studies as well as agronomic breeding studies focused on measuring plant phenotypes such as stalk lodging strength, or on improving bending strength of septate plant stems.

The influence of water content on the longitudinal modulus of elasticity of maize stalk pith and rind tissues.

BACKGROUND: Modern computational modeling could provide the key to obtaining new insights into the mechanisms of maize stalk failure as well as suggesting new ways to improve stalk strength. However, a complete set of mechanical properties of maize tissues is required to enable computational modeling of maize stems. This study developed two compression test methods for obtaining the longitudinal modulus of elasticity of both rind and pith tissues, assessed the influence of water content on tissue properties, and investigated the relationship between rind modulus and pith modulus. These methods involved uniform 5-7 cm segments of maize stems which were scanned using a flatbed scanner then tested in compression using a universal testing machine in both intact and dissected (rind-only and pith-only) states. RESULTS: The modulus of elasticity of pith tissues was highest for fully turgid specimens and decreased as water was removed from the specimens. Water content was negatively correlated with the modulus of elasticity of the rind. Rind and pith tissues were found to be weakly correlated. The median ratio of rind modulus to pith modulus was found to be 17. Of the two methods investigated, the pith-only specimen preparation was found to be simple reliable while the rind-only method was found to be adversely affected by lateral bowing of the specimen. CONCLUSIONS: Researchers can use the information in this paper to improve computational models of maize stems in three ways: (1) by incorporating realistic values of the longitudinal modulus of elasticity of pith and rind tissues; (2) by selecting pith and rind properties that match empirically observed ratios; and (3) by incorporating appropriate dependencies between these material properties and water content. From an experimental perspective, the intact/pith-only experimental method outlined in this paper is simpler than previously reported methods and provides reliable estimates of both pith and rind modulus of elasticity values. Further research using this measurement method is recommended to more clearly understand the influence of water content and turgor pressure on tissue properties.

Maize stalk stiffness and strength are primarily determined by morphological factors.

The maize (Zea mays) stem is a biological structure that must balance both biotic and structural load bearing duties. These competing requirements are particularly relevant in the design of new bioenergy crops. Although increased stem digestibility is typically associated with a lower structural strength and higher propensity for lodging, with the right balance between structural and biological activities it may be possible to design crops that are high-yielding and have digestible biomass. This study investigates the hypothesis that geometric factors are much more influential in determining structural strength than tissue properties. To study these influences, both physical and in silico experiments were used. First, maize stems were tested in three-point bending. Specimen-specific finite element models were created based on x-ray computed tomography scans. Models were validated by comparison with experimental data. Sensitivity analyses were used to assess the influence of structural parameters such as geometric and material properties. As hypothesized, geometry was found to have a much stronger influence on structural stability than material properties. This information reinforces the notion that deficiencies in tissue strength could be offset by manipulation of stalk morphology, thus allowing the creation of stalks which are both resilient and digestible.

Sensitivity analysis on a network model of glymphatic flow.

Intracranial cerebrospinal and interstitial fluid (ISF) flow and solute transport have important clinical implications, but limited in vivo access to the brain interior leaves gaping holes in human understanding of the nature of these neurophysiological phenomena. Models can address some gaps, but only insofar as model inputs are accurate. We perform a sensitivity analysis using a Monte Carlo approach on a lumped-parameter network model of cerebrospinal and ISF in perivascular and extracellular spaces in the murine brain. We place bounds on model predictions given the uncertainty in input parameters. Péclet numbers for transport in penetrating perivascular spaces (PVSs) and within the parenchyma are separated by at least two orders of magnitude. Low permeability in penetrating PVSs requires unrealistically large driving pressure and/or results in poor perfusion and are deemed unlikely. The model is most sensitive to the permeability of penetrating PVSs, a parameter whose value is largely unknown, highlighting an important direction for future experiments. Until the value of the permeability of penetrating PVSs is more accurately measured, the uncertainty of any model that includes flow in penetrating PVSs is so large that absolute numbers have little meaning and practical application is limited.

Axial variation in flexural stiffness of plant stem segments: measurement methods and the influence of measurement uncertainty.

BACKGROUND: Flexural three-point bending tests are useful for characterizing the mechanical properties of plant stems. These tests can be performed with minimal sample preparation, thus allowing tests to be performed relatively quickly. The best-practice for such tests involves long spans with supports and load placed at nodes. This approach typically provides only one flexural stiffness measurement per specimen. However, by combining flexural tests with analytic equations, it is possible to solve for the mechanical characteristics of individual stem segments. RESULTS: A method is presented for using flexural tests to obtain estimates of flexural stiffness of individual segments. This method pairs physical test data with analytic models to obtain a system of equations. The solution of this system of equations provides values of flexural stiffness for individual stalk segments. Uncertainty in the solved values for flexural stiffness were found to be strongly dependent upon measurement errors. Row-wise scaling of the system of equations reduced the influence of measurement error. Of many possible test combinations, the most advantageous set of tests for performing these measurements were identified. Relationships between measurement uncertainty and solution uncertainty were provided for two different testing methods. CONCLUSIONS: The methods presented in this paper can be used to measure the axial variation in flexural stiffness of plant stem segments. However, care must be taken to account for the influence of measurement error as the individual segment method amplifies measurement error. An alternative method involving aggregate flexural stiffness values does not amplify measurement error, but provides lower spatial resolution.

The effect of probe geometry on rind puncture resistance testing of maize stalks.

BACKGROUND: Stalk lodging (breaking of plant stems prior to harvest) is a major impediment to increasing agricultural yields of grain crops. Rind puncture resistance is commonly used to predict the lodging resistance of several crop species. However, there exist no standard operating procedures or suggested protocols for conducting rind penetration experiments. In addition, experimental details of rind penetration tests such as the shape and size of the penetrating probe are rarely reported in the literature. This has prevented meta-analysis of results and has likewise prevented key findings of past studies from being replicated. As a first step towards establishing an agreed upon measurement standard for rind puncture resistance this study investigates the effect of the puncturing probe's geometry on test results. RESULTS: Results demonstrate that probe geometry has a significant impact on test results. In particular, results showed that a 2 mm diameter chamfered probe produced stronger correlations with stalk bending strength than a 1.5 mm diameter pointed probe. The chamfered probe was also more strongly correlated with geometric features of the stalk that are known to influence stalk lodging resistance (e.g., rind thickness, diameter and section modulus). In addition, several alternative rind penetration metrics were investigated, and some were found to be superior to the most common rind penetration metric of maximum load. CONCLUSIONS: There is a need in the agricultural and plant science community to create agreed-upon operating procedures and testing standards related to mechanical traits of plant stems. In particular, a standardized probe geometry and insertion rate for rind penetration studies are needed to enable greater interoperability and meta-analysis of results. Probe shape and size should be reported in any study conducting rind penetration tests as these factors significantly impact test results.

Integrated Puncture Score: force-displacement weighted rind penetration tests improve stalk lodging resistance estimations in maize.

BACKGROUND: Stalk lodging (breaking of agricultural plant stalks prior to harvest) is a multi-billion dollar a year problem. Rind penetration resistance tests have been used by plant scientists and breeders to estimate the stalk lodging resistance of maize for nearly a hundred years. However, the rind puncture method has two key limitations: (1) the predictive power of the test decreases significantly when measuring elite or pre-commercial hybrids, and (2) using rind penetration measurements as a breeding metric does not necessarily create stronger stalks. In this study, we present a new rind penetration method called the Integrated Puncture Score, which uses a modified rind penetration testing protocol and a physics-based model to provide a robust measure of stalk lodging resistance. RESULTS: Two datasets, one with a diverse array of maize hybrids and one with only elite hybrids, were evaluated by comparing traditional rind penetration testing and the Integrated Puncture Score method to measurements of stalk bending strength. When evaluating the diverse set of hybrids, both methods were good predictors of stalk bending strength (R2 values of 0.67). However, when evaluating elite hybrids, the Integrated Puncture Score had an R2 value of 0.74 whereas the traditional method had an R2 value of 0.48. Additionally, the Integrated Puncture Score was able to differentiate between the strongest and weakest hybrids in the elite hybrid data set whereas the traditional rind penetration method was not. Additional experiments revealed strong evidence in favor of the data aggregation steps utilized to compute the Integrated Puncture Score. CONCLUSIONS: This study presents a new method for evaluating rind penetration resistance that highly correlates with stalk bending strength and can possibly be used as a breeding index for assessing stalk lodging resistance. This research lays the foundation required to develop a field-based high-throughput phenotyping device for stalk lodging resistance.

Field-based mechanical phenotyping of cereal crops to assess lodging resistance.

Plant mechanical failure, also known as lodging, is the cause of significant and unpredictable yield losses in cereal crops. Lodging occurs in two distinct failure modes-stalk lodging and root lodging. Despite the prevalence and detrimental impact of lodging on crop yields, there is little consensus on how to phenotype plants in the field for lodging resistance and thus breed for mechanically resilient plants. This review provides an overview of field-based mechanical testing approaches to assess stalk and root lodging resistance. These approaches are placed in the context of future perspectives. Best practices and recommendations for acquiring field-based mechanical phenotypes of plants are also presented.

Maize brace roots provide stalk anchorage.

Mechanical failure, known as lodging, negatively impacts yield and grain quality in crops. Limiting crop loss from lodging requires an understanding of the plant traits that contribute to lodging-resistance. In maize, specialized aerial brace roots are reported to reduce root lodging. However, their direct contribution to plant biomechanics has not been measured. In this manuscript, we use a non-destructive field-based mechanical test on plants before and after the removal of brace roots. This precisely determines the contribution of brace roots to establish a rigid base (i.e. stalk anchorage) that limits plant deflection in maize. These measurements demonstrate that the more brace root whorls that contact the soil, the greater their overall contribution to anchorage, but that the contributions of each whorl to anchorage were not equal. Previous studies demonstrated that the number of nodes that produce brace roots is correlated with flowering time in maize. To determine if flowering time selection alters the brace root contribution to anchorage, a subset of the Hallauer's Tusón tropical population was analyzed. Despite significant variation in flowering time and anchorage, selection neither altered the number of brace root whorls in the soil nor the overall contribution of brace roots to anchorage. These results demonstrate that brace roots provide a rigid base in maize and that the contribution of brace roots to anchorage was not linearly related to flowering time.

Ranking vocal fold model parameters by their influence on modal frequencies.

The purpose of this study was to identify, using computational models, the vocal fold parameters which are most influential in determining the vibratory characteristics of the vocal folds. The sensitivities of vocal folds modal frequencies to variations model parameters were used to determine the most influential parameters. A detailed finite element model of the human vocal fold was created. The model was defined by eight geometric and six material parameters. The model included transitional boundary regions to idealize the complex physiological structure of real human subjects. Parameters were simultaneously varied over ranges representative of actual human vocal folds. Three separate statistical analysis techniques were used to identify the most and least sensitive model parameters with respect to modal frequency. The results from all three methods consistently suggest that a set of five parameters are most influential in determining the vibratory characteristics of the vocal folds.

Measuring the transverse Young's modulus of maize rind and pith tissues.

Wind-induced bending loads frequently cause failure of maize (corn) stalks. When failure occurs, it usually manifests as transverse buckling. Because this failure mode is closely related to transverse tissue stiffness, the purpose of this study was to develop a method for measuring the transverse Young's modulus of maize stalk rind and pith tissues. Short, disc-shaped stalk segments were used for this purpose. X-ray computed tomography was used to obtain the geometry of each specimen prior to testing. Each specimen was tested in two different configurations. Computed tomography data was used to create a specimen-specific finite element model of each test specimen. Data from the first testing configuration was used in conjunction with the finite element model to determine the Young's Modulus values for each specimen. The specimen-specific finite element models provided estimates of the stress states in the stem under transverse loading, and these stress states accurately predicted the location of failure in transverse test specimens. The entire testing method was validated using data from one test configuration to predict the structural response of each specimen during the second test configuration.

DARLING: a device for assessing resistance to lodging in grain crops.

BACKGROUND: Stalk lodging (breakage of plant stems prior to harvest) is a major problem for both farmers and plant breeders. A limiting factor in addressing this problem is the lack of a reliable method for phenotyping stalk strength. Previous methods of phenotyping stalk strength induce failure patterns different from those observed in natural lodging events. This paper describes a new device for field-based phenotyping of stalk strength called "DARLING" (device for assessing resistance to lodging in grains). The DARLING apparatus consists of a vertical arm which is connected to a horizontal footplate by a hinge. The operator places the device next to a stalk, aligns the stalk with a force sensor, steps on the footplate, and then pushes the vertical arm forward until the stalk breaks. Force and rotation are continuously recorded during the test and these quantities are used to calculate two quantities: stalk flexural stiffness and stalk bending strength. RESULTS: Field testing of DARLING was performed at multiple sites. Validation was based upon several factors. First, the device induces the characteristic "crease" or Brazier buckling failure patterns observed in naturally lodged stalks. Second, in agreement with prior research, flexural rigidity values attained using the DARLING apparatus are strongly correlated with bending strength measurements. Third, flexural stiffness and bending strength values obtained with DARLING are in agreement with laboratory-based stiffness and strength values for corn stalks. Finally, a paired specimen experimental design was used to determine that the flexural data obtained with DARLING is in agreement with laboratory-based flexural testing results of the same specimens. DARLING was also deployed in the field to assess phenotyping throughput (# of stalks phenotyped per hour). Over approximately 5000 tests, the average testing rate was found to be 210 stalks/h. CONCLUSIONS: The DARLING apparatus provides a quantitative assessment of stalk strength in a field setting. It induces the same failure patterns observed in natural lodging events. DARLING can also be used to perform non-destructive flexural tests. This technology has many applications, including breeding, genetic studies on stalk strength, longitudinal studies of stalk flexural stiffness, and risk assessment of lodging propensity.

Reducing the number of vocal fold mechanical tissue properties: evaluation of the incompressibility and planar displacement assumptions.

The incompressibility and planar displacement assumptions were used to reduce the number of independent tissue parameters required for the characterization of a structural model of the vocal folds. The influence of these simplifying assumptions on the vibratory properties of the model was investigated. The purpose was to provide estimates of the error introduced by these assumptions. The variability in human tissue properties was accounted for through systematic variation of several material parameters. The modal properties of a vocal fold structural model were computed with each assumption and, in turn, were relaxed to determine their respective effects. The results indicated that the incompressibility assumption introduces little error. Errors introduced by the planar displacement assumption were found to depend on the ratio of the longitudinal stiffness and the transverse stiffness. Criteria for determining the compatibility of tissue property values from independent studies are also presented.

Measuring the compressive modulus of elasticity of pith-filled plant stems.

BACKGROUND: The compressional modulus of elasticity is an important mechanical property for understanding stalk lodging, but this property is rarely available for thin-walled plant stems such as maize and sorghum because excised tissue samples from these plants are highly susceptible to buckling. The purpose of this study was to develop a testing protocol that provides accurate and reliable measurements of the compressive modulus of elasticity of the rind of pith-filled plant stems. The general approach was to relying upon standard methods and practices as much as possible, while developing new techniques as necessary. RESULTS: Two methods were developed for measuring the compressional modulus of elasticity of pith-filled node-node specimens. Both methods had an average repeatability of ± 4%. The use of natural plant morphology and architecture was used to avoid buckling failure. Both methods relied up on spherical compression platens to accommodate inaccuracies in sample preparation. The effect of sample position within the test fixture was quantified to ensure that sample placement did not introduce systematic errors. CONCLUSIONS: Reliable measurements of the compressive modulus of elasticity of pith-filled plant stems can be performed using the testing protocols presented in this study. Recommendations for future studies were also provided.

The generic modeling fallacy: Average biomechanical models often produce non-average results!

Computational biomechanics models constructed using nominal or average input parameters are often assumed to produce average results that are representative of a target population of interest. To investigate this assumption a stochastic Monte Carlo analysis of two common biomechanical models was conducted. Consistent discrepancies were found between the behavior of average models and the average behavior of the population from which the average models׳ input parameters were derived. More interestingly, broadly distributed sets of non-average input parameters were found to produce average or near average model behaviors. In other words, average models did not produce average results, and models that did produce average results possessed non-average input parameters. These findings have implications on the prevalent practice of employing average input parameters in computational models. To facilitate further discussion on the topic, the authors have termed this phenomenon the "Generic Modeling Fallacy". The mathematical explanation of the Generic Modeling Fallacy is presented and suggestions for avoiding it are provided. Analytical and empirical examples of the Generic Modeling Fallacy are also given.