Polar growth in pollen tubes is associated with spatially confined dynamic changes in cell mechanical properties

Cellular morphogenesis involves changes to cellular size and shape which in the case of walled cells implies the mechanical deformation of the extracellular matrix. So far, technical challenges have made quantitative mechanical measurements of this process at subcellular scale impossible. We used micro-indentation to investigate the dynamic changes in the cellular mechanical properties during the onset of spatially confined growth activities in plant cells. Pollen tubes are cellular protuberances that have a strictly unidirectional growth pattern. Micro-indentation of these cells revealed that the initial formation of a cylindrical protuberance is preceded by a local reduction in cellular stiffness. Similar cellular softening was observed before the onset of a rapid growth phase in cells with oscillating growth pattern. These findings provide the first quantitative cytomechanical data that confirm the important role of the mechanical properties of the cell wall for local cellular growth processes. They are consistent with a conceptual model that explains pollen tube oscillatory growth based on the relationship between turgor pressure and tensile resistance in the apical cell wall. To further confirm the significance of cell mechanics, we artificially manipulated the mechanical cell wall properties as well as the turgor pressure. We observed that these changes affected the oscillation profile and were able to induce oscillatory behavior in steadily growing tubes.     

Polymorphic aspects of male anthropoid canines

Interspecific variation in the architecture of male anthropoid maxillary canines is documented. Extant taxa are polymorphic, and most can be sorted into two major groupings based on quantitative measures of shape, distal edge sharpness, and interspecific changes in their linear dimensions (projection, mesiodistal length, and buccolingual breadth) relative to each other and to body mass (scaling). One group includes the great apes and ceboids; the other includes cercopithecoids and hylobatids. Statistically significant differences between these groups were found for canine shape, for trajectories of regressions for canine projection on canine length and canine breadth, and for canine projection and canine breadth relative to body mass. The data indicate that explantations of canine variation in male anthropoids must include a mechanical interpretation of form in addition to assessments of habitus, heritage, and body mass.     

Human body proportions explained on the basis of biomechanical principles

On the basis of theoretical biomechanics and of experiments, we investigated the mechanical requirements to which the body of a bipedally walking primate is subject, and the possibilities to meet these requirements with a minimum amount of energy. The least energy-consuming adaptation is clearly a body shape favourable for the preferred locomotion. Some characteristics of human body shape, in particular its proportions, could be identified as advantageous for fulfilling obvious biological roles or mechanical necessities. The characteristic length and the extended position of human hindlimbs make walking faster without additional input of energy. Mass distribution on the hindlimbs reduces the energy necessary for accelerating the swing limb after liftoff and for decelerating the swing limb before the heelstrike. Length and mass distribution in the forelimb gives it a pendulum length comparable to that of the hindlimb, so that both extremities swing at the same frequency. This swinging of the forelimbs counters in part the movements exerted by the moved hindlimbs on the trunk. The elongate and slim shape of the trunk provides great mass moments of inertia and that means stability against being flexed ventrally and dorsally by the forward and rearward movements of the heavy and long hindlimbs. Shoulder breadth in combination with the shallow shape of the thorax yield higher mass moments of inertia against the rotation of the trunk about a vertical axis than a cylindrical trunk shape. Further elongation of the hindlimbs is limited by the energy necessary for acceleration and deceleration, as well as for lifting them during the swing phase. In addition, the reaction forces exerted by the hindlimbs would expose the trunk to undue excursions if the proportions trunk length/limb length or trunk mass/limb mass would decrease. The above-noted kinetic requirements are partly in line, partly in conflict with the requirements of statics.     

Cell poking: quantitative analysis of indentation of thick viscoelastic layers.

A recently introduced device, the cell poker, measures the force required to indent the exposed surface of a cell adherent to a rigid substratum. The cell poker has provided phenomenological information about the viscoelastic properties of several different types of cells, about mechanical changes triggered by external stimuli, and about the role of the cytoskeleton in these mechanical functions. Except in special cases, however, it has not been possible to extract quantitative estimates of viscosity and elasticity moduli from cell poker measurements. This paper presents cell poker measurements of well characterized viscoelastic polymeric materials, polydimethylsiloxanes of different degrees of polymerization, in a simple shape, a flat, thick layer, which for our purposes can be treated as a half space. Analysis of the measurements in terms of a linear viscoelasticity theory yields viscosity values for three polymer samples in agreement with those determined by measurements on a macroscopic scale. Theoretical analysis further indicates that the measured limiting static elasticity of the layers may result from the tension generated at the interface between the polymer and water. This work demonstrates the possibility of obtaining quantitative viscoelastic material properties from cell poker measurements and represents the first step in extending these quantitative studies to more complicated structures including cells.     

Mechanics of the F-actin cytoskeleton

Dynamic regulation of the filamentous actin (F-actin) cytoskeleton is critical to numerous physical cellular processes, including cell adhesion, migration and division. Each of these processes require precise regulation of cell shape and mechanical force generation which, to a large degree, is regulated by the dynamic mechanical behaviors of a diverse assortment of F-actin networks and bundles. In this review, we review the current understanding of the mechanics of F-actin networks and identify areas of further research needed to establish physical models. We first review our understanding of the mechanical behaviors of F-actin networks reconstituted in vitro, with a focus on the nonlinear mechanical response and behavior of “active” F-actin networks. We then explore the types of mechanical response measured of cytoskeletal F-actin networks and bundles formed in living cells and identify how these measurements correspond to those performed on reconstituted F-actin networks formed in vitro. Together, these approaches identify the challenges and opportunities in the study of living cytoskeletal matter.     

Quantitative analysis of epithelial morphogenesis in Drosophila oogenesis: New insights based on morphometric analysis and mechanical modeling

The process of epithelial morphogenesis is ubiquitous in animal development, but much remains to be learned about the mechanisms that shape epithelial tissues. The follicle cell (FC) epithelium encapsulating the growing germline of Drosophila is an excellent system to study fundamental elements of epithelial development. During stages 8 to 10 of oogenesis, the FC epithelium transitions between simple geometries-cuboidal, columnar and squamous-and redistributes cell populations in processes described as posterior migration, squamous cell flattening and main body cell columnarization. Here we have carried out a quantitative morphometric analysis of these poorly understood events in order to establish the parameters of and delimit the potential processes that regulate the transitions. Our results compel a striking revision of accepted views of these phenomena, by showing that posterior migration does not involve FC movements, that there is no role for columnar cell apical constriction in FC morphogenesis, and that squamous cell flattening may be a compliant response to germline growth. We utilize mechanical modeling involving finite element computational technologies to demonstrate that time-varying viscoelastic properties and growth are sufficient to account for the bulk of the FC morphogenetic changes.     

The mechanical power requirements of avian flight

A major goal of flight research has been to establish the relationship between the mechanical power requirements of flight and flight speed. This relationship is central to our understanding of the ecology and evolution of bird flight behaviour. Current approaches to determining flight power have relied on a variety of indirect measurements and led to a controversy over the shape of the power-speed relationship and a lack of quantitative agreement between the different techniques. We have used a new approach to determine flight power at a range of speeds based on the performance of the pectoralis muscles. As such, our measurements provide a unique dataset for comparison with other methods. Here we show that in budgerigars (Melopsittacus undulatus) and zebra finches (Taenopygia guttata) power is modulated with flight speed, resulting in U-shaped power-speed relationship. Our measured muscle powers agreed well with a range of powers predicted using an aerodynamic model. Assessing the accuracy of mechanical power calculated using such models is essential as they are the basis for determining flight efficiency when compared to measurements of flight metabolic rate and for predicting minimum power and maximum range speeds, key determinants of optimal flight behaviour in the field.     

Morphology and Function of Lateral Hypaxial Musculature in Salamanders

SYNOPSIS. The lateral hypaxial musculature (LHM) of salamandersmay serve as a useful model for understanding the functionsof LHM in tetrapods more generally. Salamanders have betweentwo and four layers of LHM, arranged segmentally in myomeres.These layers produce three primary mechanical actions: theybend the body, pressurize the body, and produce or resist torsionabout the long axis of the body. The optimum muscle fiber anglefor forceful bending is 0° to the long axis, the optimumangle for pressurization is 90°, and the optimum angle fortorsion is 45°. For generating bending and torsional moments,lateral (superficial) muscle layers have greater mechanicaladvantage than medial (deep) layers. For increasing body pressure,by contrast, medial layers have greater mechanical advantage.A comparison of muscle fiber angles in aquatic and terrestrialsalamanders reveals that some aquatic salamanders have one musclelayer with a low fiber angle which may represent a specializationfor swimming. Overall, however, the fiber angles in the LHMof terrestrial and aquatic salamanders are surprisingly similar.In contrast, the pattern of fiber angles in caecilians is different,suggesting that these amphibians use their LHM differently.The fiber angle models and morphological observations presentedhere form a framework which may be useful in future studiesof lateral hypaxial musculature.     

Morphometrics within dog breeds are highly reproducible and dispute Rensch’s rule

Using 27 body measurements, we have identified 13 breed-defining metrics for 109 of 159 domestic dog breeds, most of which are recognized by the American Kennel Club (AKC). The data set included 1,155 dogs at least 1 year old (average 5.4 years), and for 53 breed populations, complete measurement data were collected from at least three males and three females. We demonstrate, first, that AKC breed standards are rigorously adhered to for most domestic breeds with little variation observed within breeds. Second, Rensch’s rule, which describes a scaling among taxa such that sexual dimorphism is greater among larger species if males are the larger sex, with less pronounced differences in male versus female body size in smaller species, is not maintained in domestic dog breeds because the proportional size difference between males and females of small and large breeds is essentially the same. Finally, principal components (PCs) analysis describes both the overall body size (PC1) and the shape (length versus width) of the skeleton (PC2). That the integrity of the data set is sufficiently rich to discern PCs has strong implications for mapping studies, suggesting that individual measurements may not be needed for genetic studies of morphologic traits, particularly in the case of breed-defining traits that are typically under strong selection. Rather, phenotypes derived from data sets such as these, collected at a fraction of the effort and cost, may be used to direct whole-genome association studies aimed at understanding the genetic basis of fixed morphologic phenotypes defining distinct dog breeds.

     

Morphometrics within dog breeds are highly reproducible and dispute Rensch’s rule

Using 27 body measurements, we have identified 13 breed-defining metrics for 109 of 159 domestic dog breeds, most of which are recognized by the American Kennel Club (AKC). The data set included 1,155 dogs at least 1 year old (average 5.4 years), and for 53 breed populations, complete measurement data were collected from at least three males and three females. We demonstrate, first, that AKC breed standards are rigorously adhered to for most domestic breeds with little variation observed within breeds. Second, Rensch’s rule, which describes a scaling among taxa such that sexual dimorphism is greater among larger species if males are the larger sex, with less pronounced differences in male versus female body size in smaller species, is not maintained in domestic dog breeds because the proportional size difference between males and females of small and large breeds is essentially the same. Finally, principal components (PCs) analysis describes both the overall body size (PC1) and the shape (length versus width) of the skeleton (PC2). That the integrity of the data set is sufficiently rich to discern PCs has strong implications for mapping studies, suggesting that individual measurements may not be needed for genetic studies of morphologic traits, particularly in the case of breed-defining traits that are typically under strong selection. Rather, phenotypes derived from data sets such as these, collected at a fraction of the effort and cost, may be used to direct whole-genome association studies aimed at understanding the genetic basis of fixed morphologic phenotypes defining distinct dog breeds.     

Covariation between forelimb muscle anatomy and bone shape in an Australian scratch-digging marsupial: Comparison of morphometric methods

The close association between muscle and bone is broadly intuitive; however, details of the covariation between the two has not been comprehensively studied. Without quantitative understanding of how muscle anatomy influences bone shape, it is difficult to draw conclusions of the significance of many morphological traits of the skeleton. In this study, we investigated these relationships in the Quenda (Isoodon fusciventer), a scratch-digging marsupial. We quantified the relationships between forelimb muscle anatomy and bone shape for animals representing a range of body masses (124–1,952 g) using two-block partial least square analyses. Muscle anatomy was quantified as muscle mass and physiological cross-sectional area (PCSA), and we used two morphometric methods to characterize bone shape: seven indices of linear bone proportions, and landmarks analysis. Bone shape was significantly correlated with body mass, reflecting allometric bone growth. Of the seven bone indices, only shoulder moment index (SMI) and ulna robustness index (URI) showed a significant covariation with muscle anatomy. Stronger relationships between muscle anatomy and forelimb bone shape were found using the landmark coordinates: muscle mass and PCSA were correlated with the geometric shape of the scapula, humerus, and third metacarpal, but to a lesser extent with shape of the ulna. Overall, our data show that landmark coordinates are more sensitive than bone indices to capturing shape changes evident throughout ontogeny, and is therefore a more appropriate method to investigate covariation with forelimb muscle anatomy. Single-species studies investigating ontogeny require refined methods to accurately develop understanding of the important relationships between muscle force generation and bone shape remodeling. Landmark analyses provide such a method.     

The effect of direct measurement versus cadaver estimates of anthropometry in the calculation of joint moments during above-knee prosthetic gait in pediatrics

Joint reaction forces, moments and powers are important in interpreting gait mechanics and compensatory strategies used by patients walking with above-knee prostheses. Segmental anthropometrics, required to calculate joint moments, are often estimated using data from cadaver studies. However, these values may not be accurate for patients following amputation as prostheses are composed of non-biologic material. The purpose of this study was to compare joint moments using anthropometrics calculated from cadaver studies versus direct measurements of the residual limb and prosthesis for children with an above-knee amputation. Gait data were collected for four subjects with above-knee prostheses walking at preferred and fast speeds. Joint moments were computed using anthropometrics from cadaver studies and direct measurements for each subject. The difference between these two methods primarily affected the inertia couple (Ialpha term) and the inertial effect due to gravity, which comprised a greater percentage of the total joint moment during swing as compared to stance. Peak hip and knee flexor and extensor moments during swing were significantly greater when calculated using cadaver data (p<0.05). These differences were greater while walking fast as compared to slow speeds. A significant difference was not found between these two methods for peak hip and knee moments during stance. A significant difference was found for peak ankle joint moments during stance, but the magnitude was not clinically important. These results support the use of direct measurements of anthropometry when examining above-knee prosthetic gait, particularly during swing.     

A new method for gravity correction of dynamometer data and determining passive elastic moments at the joint

Moments measured by a dynamometer in biomechanics testing often include the gravitational moment and the passive elastic moment in addition to the moment caused by muscle contraction. Gravitational moments result from the weight of body segments and dynamometer attachment, whereas passive elastic moments are caused by the passive elastic deformation of tissues crossing the joint being assessed. Gravitational moments are a major potential source of error in dynamometer measurements and must be corrected for, a procedure often called gravity correction. While several approaches to gravity correction have been presented in the literature, they generally assume that the gravitational moment can be adequately modeled as a simple sine or cosine function. With this approach, a single passive data point may be used to specify the model, assuming that passive elastic moments are negligible at that point. A new method is presented here for the gravity correction of dynamometer data. Gravitational moment is represented using a generalized sinusoid, which is fit to passive data obtained over the entire joint range of motion. The model also explicitly accounts for the presence of passive elastic moments. The model was tested for cases of hip flexion-extension, knee flexion-extension, and ankle plantar flexion-dorsiflexion, and provided good fits in all cases.     

Quantitative approaches to utilizing mutational analysis and disulfide crosslinking for modeling a transmembrane domain.

The transmembrane domain of chemoreceptor Trg from Escherichia coli contains four transmembrane segments in its native homodimer, two from each subunit. We had previously used mutational analysis and sulfhydryl cross-linking between introduced cysteines to obtain data relevant to the three-dimensional organization of this domain. In the current study we used Fourier analysis to assess these data quantitatively for periodicity along the sequences of the segments. The analyses provided a strong indication of alpha-helical periodicity in the first transmembrane segment and a substantial indication of that periodicity for the second segment. On this basis, we considered both segments as idealized alpha-helices and proceeded to model the transmembrane domain as a unit of four helices. For this modeling, we calculated helical crosslinking moments, parameters analogous to helical hydrophobic moments, as a quantitative way of condensing and utilizing a large body of crosslinking data. Crosslinking moments were used to define the relative separation and orientation of helical pairs, thus creating a quantitatively derived model for the transmembrane domain of Trg. Utilization of Fourier transforms to provide a quantitative indication of periodicity in data from analyses of transmembrane segments, in combination with helical crosslinking moments to position helical pairs should be useful in modeling other transmembrane domains.     

Polymorphic aspects of male anthropoid honing premolars.

A recent study has indicated that heritage may be an important component in explanations of interspecies variation in male anthropoid maxillary canines. To further test this hypothesis, comparative data for the maxillary canine's occlusal partner, the honing mandibular premolar, are presented. Relative to body mass, measurements of the honing premolar--length of the honing facet, mesiodistal length, and buccolingual breadth and shape (as expressed by the ratio of length to breadth)--show a similar but stronger heritage component than measurements of the maxillary canine. Results indicate that canine variation among male anthropoids has not yet been explained and that quantitative analyses of this issue will necessarily require a methodological approach which incorporates heritage as a factor.     

Changes in surface topologies of chondrocytes subjected to mechanical forces: an AFM analysis

The cartilage is composed of chondrocytes embedded in a matrix of collagen fibrils interspersed within a network of proteoglycans and is constantly exposed to biomechanical forces during normal joint movement. Characterization of the surface morphology, cytoskeletal structure, adherance and elastic properties of these mechanosensitive cells are crucial in understanding the effects of mechanical forces around a cell and how a cell responds to changes in its physical environment. In this work, we employed the atomic force microscope (AFM) to image cultured chondrocytes before and after subjecting them to mechanical forces in the presence or absence of interleukin-1β to mimic inflammatory conditions. Nanoscale imaging and quantitative measurements from AFM data revealed that there are distinct changes in cell-surface topology and cytoskeleton arrangement in the cells following treatment with mechanical forces, IL-1β or both. Our findings for the first time demonstrate that cultured chondrocytes are amenable to high-resolution AFM imaging and dynamic tensile forces may help overcome the effect of inflammatory factors on chondrocyte response.     

High throughput and quantitative enzymology in the genomic era

Accurate predictions from models based on physical principles are the ultimate metric of our biophysical understanding. Although there has been stunning progress toward structure prediction, quantitative prediction of enzyme function has remained challenging. Realizing this goal will require large numbers of quantitative measurements of rate and binding constants and the use of these ground-truth data sets to guide the development and testing of these quantitative models. Ground truth data more closely linked to the underlying physical forces are also desired. Here, we describe technological advances that enable both types of ground truth measurements. These advances allow classic models to be tested, provide novel mechanistic insights, and place us on the path toward a predictive understanding of enzyme structure and function.     

High-resolution analysis of neuronal growth cone morphology by comparative atomic force and optical microscopy

Neuronal growth cones are motile sensory structures at the tip of axons, transducing guidance information into directional movements towards target cells. The morphology and dynamics of neuronal growth cones have been well characterized with optical techniques; however, very little quantitative information is available on the three-dimensional structure and mechanical properties of distinct subregions. In the present study, we imaged the large Aplysia growth cones after chemical fixation with the atomic force microscope (AFM) and directly compared our data with images acquired by light microscopy methods. Constant force imaging in contact mode in combination with force-distant measurements revealed an average height of 200 nm for the peripheral (P) domain, 800 nm for the transition (T) zone, and 1200 nm for the central (C) domain, respectively. The AFM images show that the filopodial F-actin bundles are stiffer than surrounding F-actin networks. Enlarged filopodia tips are 60 nm higher than the corresponding shafts. Measurements of the mechanical properties of the specific growth cone regions with the AFM revealed that the T zone is stiffer than the P and the C domain. Direct comparison of AFM and optical data acquired by differential interference contrast and fluorescence microscopy revealed a good correlation between these imaging methods. However, the AFM provides height and volume information at higher resolution than fluorescence methods frequently used to estimate the volume of cellular compartments. These findings suggest that AFM measurements on live growth cones will provide a quantitative understanding of how proteins can move between different growth cone regions.     

Dynamic Time Warping compared to established methods for validation of musculoskeletal models

By means of Multi-Body musculoskeletal simulation, important variables such as internal joint forces and moments can be estimated which cannot be measured directly. Validation can ensued by qualitative or by quantitative methods. Especially when comparing time-dependent signals, many methods do not perform well and validation is often limited to qualitative approaches. The aim of the present study was to investigate the capabilities of the Dynamic Time Warping (DTW) algorithm for comparing time series, which can quantify phase as well as amplitude errors. We contrast the sensitivity of DTW with other established metrics: the Pearson correlation coefficient, cross-correlation, the metric according to Geers, RMSE and normalized RMSE.This study is based on two data sets, where one data set represents direct validation and the other represents indirect validation. Direct validation was performed in the context of clinical gait-analysis on trans-femoral amputees fitted with a 6 component force-moment sensor. Measured forces and moments from amputees' socket-prosthesis are compared to simulated forces and moments. Indirect validation was performed in the context of surface EMG measurements on a cohort of healthy subjects with measurements taken of seven muscles of the leg, which were compared to simulated muscle activations.Regarding direct validation, a positive linear relation between results of RMSE and nRMSE to DTW can be seen. For indirect validation, a negative linear relation exists between Pearson correlation and cross-correlation.We propose the DTW algorithm for use in both direct and indirect quantitative validation as it correlates well with methods that are most suitable for one of the tasks. However, in DV it should be used together with methods resulting in a dimensional error value, in order to be able to interpret results more comprehensible.