Quantifying Shape Changes and Tissue Deformation in Leaf Development

The analysis of biological shapes has applications in many areas of biology, and tools exist to quantify organ shape and detect shape differences between species or among variants. However, such measurements do not provide any information about the mechanisms of shape generation. Quantitative data on growth patterns may provide insights into morphogenetic processes, but since growth is a complex process occurring in four dimensions, growth patterns alone cannot intuitively be linked to shape outcomes. Here, we present computational tools to quantify tissue deformation and surface shape changes over the course of leaf development, applied to the first leaf of Arabidopsis (Arabidopsis thaliana). The results show that the overall leaf shape does not change notably during the developmental stages analyzed, yet there is a clear upward radial deformation of the leaf tissue in early time points. This deformation pattern may provide an explanation for how the Arabidopsis leaf maintains a relatively constant shape despite spatial heterogeneities in growth. These findings highlight the importance of quantifying tissue deformation when investigating the control of leaf shape. More generally, experimental mapping of deformation patterns may help us to better understand the link between growth and shape in organ development.The analysis of biological shapes is a field of broad interest, with diverse applications ranging from medical imaging to comparative anatomy and botany (Lestrel, 2011). Within plant biology, the wide variation of leaf shapes among species has long intrigued evolutionary biologists, physiologists, and developmental biologists alike. Leaves typically develop into flat structures that maximize photosynthetic surface, with variations that may help to facilitate gas exchange, offset water loss, improve convective cooling, increase mechanical support, or reduce resistance to physical environmental forces, for example (for review, see Tsukaya, 2006; Cronk, 2009). The processes controlling leaf shape development, therefore, are important to plant survival and biomass accumulation and hence have important agricultural implications.Understanding how leaf shape is controlled typically involves studying shape variation among related species and in shape mutants and requires tools to quantify phenotypic differences. In recent years, several sophisticated semiautomatic methods have been developed to analyze leaf shapes in terms of their two-dimensional (2D) profiles. Analyses range from simple length and width measurements and allometric ratios to statistical analysis of outline coordinates (Langlade et al., 2005; Bylesjö et al., 2008; Weight et al., 2008; Backhaus et al., 2010).Leaf shape can also be quantified in terms of a three-dimensional (3D) surface, which can range from flat to curved or ruffled, as observed in nature and in many leaf shape mutants. Approaches to 3D shape analysis based on flattened and unflattened leaf dimensions in the proximodistal and mediolateral axes have been presented by Liu et al. (2010) and Wu et al. (2007). Kaminuma et al. (2004) developed a technique for obtaining coordinates of the leaf surface in vivo, from which they measured the angle of the surface across the leaf and fit curves along the leaf proximodistal and mediolateral axes to characterize blade epinasty.These existing methods for leaf shape analysis are very useful for detecting and quantitatively describing shape differences, but they do not provide information about the underlying mechanisms that give rise to those shape differences. For example, the correspondence between evenly spaced outline points (Langlade et al., 2005; Bylesjö et al., 2008; Weight et al., 2008; Backhaus et al., 2010) is arbitrary. Furthermore, existing work has not provided an analysis of leaf shape in terms of both 2D and 3D phenotypic features together, and with the exception of Kaminuma et al. (2004), the methods are destructive and cannot be used to measure changes in shape in vivo.Differences in shapes between two organs arise through differences in how the organs grow. It is impossible, however, to ascertain from differences in final organ shape what differences in growth gave rise to them, as the possible combinations of spatial and temporal alterations in growth patterns that could be responsible for the final shape are endless. By the same token, it can be difficult to conceptualize from growth patterns how the interconnected tissues will deform and, thus, how overall organ shape will change.To address this issue, Kennaway et al. (2011) recently proposed a simulation modeling framework to investigate how a shape may locally and globally deform under the control of spatially distributed growth- and polarity-regulating substances. This framework was used to hypothesize how growth and shape deformation may be controlled in flowers (Green et al., 2010; Sauret-Güeto et al., 2013) and leaves (Kuchen et al., 2012). However, to date, shape deformation patterns have not been quantified experimentally. Here, we use data collected for a study on leaf growth (Remmler and Rolland-Lagan, 2012) to develop a method for describing 3D surface shape and shape deformations during leaf development. In particular, we generate experimental maps of tissue deformation, which offer a new approach to investigating shape differences and uncovering the link between growth and shape during development.     

The Measurement of Dynamic Latent Variables in Longitudinal Aging Research: Quantifying Adult Development

Dynamic latent variables involve systematic intraindividual change over time. Although it seems natural to apply traditional measurement theory to dynamic latent variables, in fact this is often inappropriate. Traditional measurement theory is based on the idea of static latent variables and offers little guidance to the researcher who wishes to measure a dynamic latent variable with a high degree of accuracy and validity. It is the contention of this article that measurement of a dynamic latent variable must start from a clearly defined substantive theory about human development. Two approaches that take this perspective are presented; the longitudinal Guttman simplex (LGS), a measurement model for dynamic latent variables undergoing irreversible cumulative, unitary development; and latent transition analysis (LTA), a more general latent class measurement model.     

The Shape of the Female Fitness Curve for Cynoglossum officinale: Quantifying Seed Dispersal and Seedling Survival in the Field

Abstract: When hermaphroditic plants shift their sex allocation to produce more seeds and less pollen, it is frequently assumed that the female component of fitness is strictly proportional to the number of seeds produced. However, if producing more seeds results in more competition between seedlings, the female fitness gain curve levels off with high investments in seeds. The shape of this curve is relevant for sex allocation theory, but rarely have data been collected. For Cynoglossum officinale we described the relationship between the number of seeds produced on the mother plant and the number and weight of seedlings in September of the following year. As expected, around large plants of C. officinale more seedlings were retrieved after the germination period in March. The seedlings of large plants were dispersed over an area similar to that of small plants. As a result, seedlings around large plants had a significantly higher chance to have a neighbouring sibling within one dm². Survival and growth of single or grouped (density > 2) seedlings did not differ significantly. As a result, total dry weight of seedlings in September was a linear function of the number of seeds on the parent plant. Our data indicate a linear female fitness gain curve.     

Quantifying the Adaptive Cycle

The adaptive cycle was proposed as a conceptual model to portray patterns of change in complex systems. Despite the model having potential for elucidating change across systems, it has been used mainly as a metaphor, describing system dynamics qualitatively. We use a quantitative approach for testing premises (reorganisation, conservatism, adaptation) in the adaptive cycle, using Baltic Sea phytoplankton communities as an example of such complex system dynamics. Phytoplankton organizes in recurring spring and summer blooms, a well-established paradigm in planktology and succession theory, with characteristic temporal trajectories during blooms that may be consistent with adaptive cycle phases. We used long-term (1994–2011) data and multivariate analysis of community structure to assess key components of the adaptive cycle. Specifically, we tested predictions about: reorganisation: spring and summer blooms comprise distinct community states; conservatism: community trajectories during individual adaptive cycles are conservative; and adaptation: phytoplankton species during blooms change in the long term. All predictions were supported by our analyses. Results suggest that traditional ecological paradigms such as phytoplankton successional models have potential for moving the adaptive cycle from a metaphor to a framework that can improve our understanding how complex systems organize and reorganize following collapse. Quantifying reorganization, conservatism and adaptation provides opportunities to cope with the intricacies and uncertainties associated with fast ecological change, driven by shifting system controls. Ultimately, combining traditional ecological paradigms with heuristics of complex system dynamics using quantitative approaches may help refine ecological theory and improve our understanding of the resilience of ecosystems.     

Quantifying the extinction vortex

We developed a database of 10 wild vertebrate populations whose declines to extinction were monitored over at least 12 years. We quantitatively characterized the final declines of these well-monitored populations and tested key theoretical predictions about the process of extinction, obtaining two primary results. First, we found evidence of logarithmic scaling of time-to-extinction as a function of population size for each of the 10 populations. Second, two lines of evidence suggested that these extinction-bound populations collectively exhibited dynamics akin to those theoretically proposed to occur in extinction vortices. Specifically, retrospective analyses suggested that a population size of n individuals within a decade of extinction was somehow less valuable to persistence than the same population size was earlier. Likewise, both year-to-year rates of decline and year-to-year variability increased as the time-to-extinction decreased. Together, these results provide key empirical insights into extinction dynamics, an important topic that has received extensive theoretical attention.     

Quantifying the randomness of extinctions

Extinctions occur either randomly or in a more deterministic and predictable manner, with certain characteristics making some species more vulnerable to (local) extinction than others. Although the quantification of extinction randomness would better our understanding of the extinction causes and increase the predictability of future species losses, few quantification methods are currently available. To this purpose, we propose two indices based on a comparison of an a priori (expected) extinction series with an observed one. Whereas the first index requires data on the order of extinctions, the second index is only concerned with which species went extinct and which did not. Using a model for generating extinction data, we tested both indices successfully for accordance with the robustness prerequisites. Index outputs were furthermore unaffected by species richness, apart from decreased variation with rising species numbers. Because of its independence of non-extinct species and its focus on extinction sequences, the first randomness index seems especially useful for use in paleontological and paleo-ecological research. The second index is likely a good tool to study shorter term extinctions, for which the extinction order is often not known and for which the comparison with species that did persist is of greater interest. We use a real dataset to illustrate this. Finally, we discuss how it is possible to expand the use of this index toward identifying previously unknown extinction-promoting species characteristics, and toward a credible assessment of the extinction risk posed by global change.     

Quantifying the geometry of micropipets

Accurate knowledge of the internal diameter (id) of micropipet tips is important, because the ability to study many different aspects of biological membranes is a very sensitive function of tip size. The authors examined two methods used to characterize pipet tips: the digital manometric method (DMM) and bubble number method (BNM). For DMM, the authors compared the ability of Laplace's equation (model I) and a modified form of his equation (model II), which accounts for adhesion between the test fluid and glass Pressure measurements were made with a digital manometer, and ids at the tip were measured using scanning electron microscopy (SEM). The micropipet tips showed a slight asymmetry in id, with a approx 5% difference between maximum and minimum id. On average, model I overestimates the largest id by 2%. Model II overestimates the smaller id by 2%. For micropipet tips ranging from 1.00 to 5.00 μm, the corresponding uncertainties range from 20 to 100 nm. Making the normally hydrophilic glass surface hydrophobic strongly reduced threshold pressures when tested in water, but not 100% methanol. Compared to BNM, DMM was insensitive to changes in atmospheric pressure: BNM can be corrected for changes in atmospheric pressure. Convergence angle(s) can be determined from measurements of the pressure and the axial distance of the meniscus from the tip. The accuracy and precision of digital manometry approaches that of SEM. DMM should be particularly useful in selecting, micropipets for patch clamp studies of small vesicles (<10 μm), and may enable systematic selection of micropipets for many other experiments.     

Quantifying the community-level consequences of competition

Changes in plant community structure after changes in some aspect of the environment such as nutrients or grazing is often ascribed to changes in competitive relationships among the plants. However, very rarely is competition measured directly in such experiments. To distinguish between the direct effects of environmental treatments and changes in competitive relationships, it is necessary to quantify the influence of competition on community structure and compare the magnitude and direction of this influence between environments. We describe an experimental approach to accomplish this that is based on the classic yield-density experiment of agronomy. The approach is called the community-density experiment and requires experimental establishment of a gradient in total initial community density such that absolute densities of each species increase but initial relative abundances of each species stay constant along the gradient. We define various indices of the magnitude of community-level consequences of increasing density that can be compared among environments such as different fertilizer or grazing treatments. We also discuss various practical ways of achieving the experimental density gradient that are suitable for different kinds of communities. *** DIRECT SUPPORT *** A02DO006 00011     

Quantifying the Consistency of Scientific Databases

Science is a social process with far-reaching impact on our modern society. In recent years, for the first time we are able to scientifically study the science itself. This is enabled by massive amounts of data on scientific publications that is increasingly becoming available. The data is contained in several databases such as Web of Science or PubMed, maintained by various public and private entities. Unfortunately, these databases are not always consistent, which considerably hinders this study. Relying on the powerful framework of complex networks, we conduct a systematic analysis of the consistency among six major scientific databases. We found that identifying a single "best" database is far from easy. Nevertheless, our results indicate appreciable differences in mutual consistency of different databases, which we interpret as recipes for future bibliometric studies.     

Quantifying the cleanliness of glass capillaries

I used capillary rise methods to investigate the lumenal surface properties of quartz (fused silica, Amersil T-08), borosilicate (Corning 7800), and high-lead glass (Corning 0010) capillaries commonly used to make patch pipets. I calculated the capillary rise and contact angle for water and methanol from weight measurements. The capillary rise was compared with the theoretical maximum value calculated by assuming each fluid perfectly wetted the lumenal surface of the glass (i.e., zero contact angle, which reflects the absence of surface contamination). For borosilicate, high-lead, and quartz capillaries, the rise for water was substantially less than the theoretical maximum rise. Exposure of the borosilicate, lead, and quartz capillaries to several cleaning methods resulted in substantially better—but not perfect—agreement between the theoretical maximum rise and calculated capillary rise. By contrast, the capillary rise for methanol was almost identical in untreated and cleaned capillaries, but less than its theoretical maximum rise. The residual discrepancy between the observed and theoretical rise for water could not be improved on by trying a variety of cleaning procedures, but some cleaning methods were superior to others. The water solubility of the surface contaminants, deduced from the effectiveness of repeated rinsing, was different for each of the three types of capillaries examined: Corning 7800>quartz>Corning 0010. A surface film was also detected in quartz tubing with an internal filament. I conclude that these borosilicate, quartz, and high-lead glass capillaries have a film on the lumenal surface, which can be removed using appropriate cleaning methods. The surface contaminants may be unique to each type of capillary and may also be hydrophobic. Two simple methods are presented to quantitate the cleanliness of glass capillary tubing commonly used to make pipets for studies of biological membranes. It is not known if the surface film is of importance in electrophysiological studies of biological membranes.     

Aging of the erythrocyte

In contrast to situation found in other cell types, no linear dependence of product fluorescence vs time is observed when fluoresceine diacetate (FDA) is hydrolysed by erythrocytes and hemolysates. The rate of hydrolysis is increased by high concentrations of sucrose suggesting a positive effect of viscosity on the rate of the reaction. These peculiarities can be explained by assumption of a two-step hydrolysis of FDA. The FDA-hydrolytic activity decreases with increasing cell density (age).     

Quantifying the complexity of bat wing kinematics

Body motions (kinematics) of animals can be dimensionally complex, especially when flexible parts of the body interact with a surrounding fluid. In these systems, tracking motion completely can be difficult, and result in a large number of correlated measurements, with unclear contributions of each parameter to performance. Workers typically get around this by deciding a priori which variables are important (wing camber, stroke amplitude, etc.), and focusing only on those variables, but this constrains the ability of a study to uncover variables of influence. Here, we describe an application of proper orthogonal decomposition (POD) for assigning importances to kinematic variables, using dimensional complexity as a metric. We apply this method to bat flight kinematics, addressing three questions: (1) Does dimensional complexity of motion change with speed? (2) What body markers are optimal for capturing dimensional complexity? (3) What variables should a simplified reconstruction of bat flight include in order to maximally reconstruct actual dimensional complexity? We measured the motions of 17 kinematic markers (20 joint angles) on a bat (Cynopterus brachyotis) flying in a wind tunnel at nine speeds. Dimensional complexity did not change with flight speed, despite changes in the kinematics themselves, suggesting that the relative efficacy of a given number of dimensions for reconstructing kinematics is conserved across speeds. By looking at subsets of the full 17-marker set, we found that using more markers improved resolution of kinematic dimensional complexity, but that the benefit of adding markers diminished as the total number of markers increased. Dimensional complexity was highest when the hindlimb and several points along digits III and IV were tracked. Also, we uncovered three groups of joints that move together during flight by using POD to quantify correlations of motion. These groups describe 14/20 joint angles, and provide a framework for models of bat flight for experimental and modeling purposes.     

Quantifying the quality of coral bleaching predictions

Techniques that utilize sea surface temperature (SST) observations to predict coral reef bleaching are in common use and form the foundation for predicted global coral reef ecosystem demise within this century. Yet, quality assessments of these methods are typically qualitative or anecdotal. Quality is the correspondence of forecasts with observations and has standard quantitative measures. Here a forecast verification method, commonly used in meteorology, is presented and used to measure the quality of the degree heating weeks (DHW) technique as an exploration of insights that can be gleaned from this methodology. DHW values were calculated from NOAA Optimum Interpolation SST version 2 data and compared to a database of bleaching observations from 1990–2007. Quality is expressed with an objective measure, the Peirce Skill Score (PSS). The quality at varying DHW thresholds above which bleaching was projected to occur is calculated. By selecting the thresholds that maximize quality, the predictive technique is objectively optimized. This results in optimal threshold maps, showing reefs more prone and more resistant to bleaching. Optimization increases the quality of DHW as a predictor of bleaching from PSS = 0.55 to PSS = 0.83, in global average, but the optimal PSS and corresponding DHW values vary significantly from location to location. The coral reef research and management community are urged to adopt the simple, but rigorous tools of forecast verification routinely used in other disciplines so that bleaching forecasts can be quantitatively compared and their quality improved.     

Quantifying the Clinical Significance of Cannabis Withdrawal

Background and Aims

Questions over the clinical significance of cannabis withdrawal have hindered its inclusion as a discrete cannabis induced psychiatric condition in the Diagnostic and Statistical Manual of Mental Disorders (DSM IV). This study aims to quantify functional impairment to normal daily activities from cannabis withdrawal, and looks at the factors predicting functional impairment. In addition the study tests the influence of functional impairment from cannabis withdrawal on cannabis use during and after an abstinence attempt.

Methods and Results

A volunteer sample of 49 non-treatment seeking cannabis users who met DSM-IV criteria for dependence provided daily withdrawal-related functional impairment scores during a one-week baseline phase and two weeks of monitored abstinence from cannabis with a one month follow up. Functional impairment from withdrawal symptoms was strongly associated with symptom severity (p = 0.0001). Participants with more severe cannabis dependence before the abstinence attempt reported greater functional impairment from cannabis withdrawal (p = 0.03). Relapse to cannabis use during the abstinence period was associated with greater functional impairment from a subset of withdrawal symptoms in high dependence users. Higher levels of functional impairment during the abstinence attempt predicted higher levels of cannabis use at one month follow up (p = 0.001).

Conclusions

Cannabis withdrawal is clinically significant because it is associated with functional impairment to normal daily activities, as well as relapse to cannabis use. Sample size in the relapse group was small and the use of a non-treatment seeking population requires findings to be replicated in clinical samples. Tailoring treatments to target withdrawal symptoms contributing to functional impairment during a quit attempt may improve treatment outcomes.     

Quantifying the effects of melittin on liposomes

Melittin, the soluble peptide of bee venom, has been demonstrated to induce lysis of phospholipid liposomes. We have investigated the dependence of the lytic activity of melittin on lipid composition. The lysis of liposomes, measured by following their mass and dimensions when immobilised on a solid substrate, was close to zero when the negatively charged lipids phosphatidyl glycerol or phosphatidyl serine were used as the phospholipid component of the liposome. Whilst there was significant binding of melittin to the liposomes, there was little net change in their diameter with melittin binding reversed upon salt injection. For the zwitterionic phosphatidyl choline the lytic ability of melittin is dependent on the degree of acyl chain unsaturation, with melittin able to induce lysis of liposomes in the liquid crystalline state, whilst those in the gel state showed strong resistance to lysis. By directly measuring the dimensions and mass changes of liposomes on exposure to melittin using Dual Polarisation Interferometry, rather than following the florescence of entrapped dyes we attained further information about the initial stages of melittin binding to liposomes.