Estimation of parameters in large offspring number models and ratios of coalescence times

The ratio of singletons to the total number of segregating sites is used to estimate a reproduction parameter in a population model of large offspring numbers without having to jointly estimate the mutation rate. For neutral genetic variation, the ratio of singletons to the total number of segregating sites is equivalent to the ratio of total length of external branches to the total length of the gene genealogy. A multinomial maximum likelihood method that takes into account more frequency classes than just the singletons is developed to estimate the parameter of another large offspring number model. The performance of these methods with regard to sample size, mutation rate, and bias, is investigated by simulation. The expected value of the ratio of the total length of external branches to the total length of the whole tree is, using simulation, shown to decrease for the Kingman coalescent as sample size increases, but can increase or decrease, depending on parameter values, for Λ coalescents. Considering ratios of tree statistics, as opposed to considering lengths of various subtrees separately, can yield better insight into the dynamics of gene genealogies.     

Morphogenesis of helical fibers in haplotaxids

There are two different muscle fiber types in haplotaxids. The pseudo-circomyarian type is typical of Haplotaxis gordioides and the flattened circomyarian type of Pelodrilus leruthi. The mechanisms of growth in fiber size and in fiber number of the two fiber types in the hindmost region of adult specimens have been studied ultrastructurally. The increase in length and girth of the muscle fiber is always the result of the insertion of new myofilaments in the peripheral zones of the muscle cells. The increase in the number of fibers seems to be due to division of differentiated muscle cells.     

Torsion of tendon fibers upon hydration and temperature shifts

Hydration of an isolated rat tail tendon fiber was found to cause its torsion. A similar effect was observed upon changing the specimen temperature in the 12–38°C range. The direction and the angle of rotation of the distal end of the fiber did not depend on its length (12–80 mm). Rather, they depended on the prevalence of clockwise-or counterclockwise-driving collagen units, the distribution of which in the tendon fiber was apparently probabilistic. The phenomenon of collagen bundle rotation is considered in the context of the mechanism of mechanoreceptor stimulation by temperature shifts.     

Contribution of biomechanics to management of ligament and tendon injuries

The contribution of biomechanics to the advancement of management of ligament and tendon injuries has been significant. Thanks to Professor Y.C. Fung's writing and guidance, our field of research has done fundamental work on anatomy and biology of ligaments and tendons, developed methods to accurately determine mechanical properties, identified various experimental factors which could change the outcome measurements as well as examined biological factors that change tissue properties in-vivo. Professor Fung also gave us his quasi-linear viscoelastic theory for soft tissues so that the time and history dependent properties of ligaments and tendons could be properly described. We have further adopted Professor Fung's eight steps on methods of approach for biomechanical investigation to understand as well as enhance the treatment of ligament and tendon injuries during work or sports related activities. Examples on how to better treat the tears of the medial collateral ligament of the knee, as well as how to improve reconstruction procedures for the anterior cruciate ligament are presented in detail. Currently the use of functional tissue engineering for ligament and tendon healing is a topic of great interest. Here the use of biological scaffolds, such as porcine small intestinal submucosa, has shown promise. For the last 35 to 40 years, the field of biomechanics has made great strides in the treatment of ligament and tendon injuries, and many patients have benefited. The future is even brighter because of what has been done properly in the past. Exciting advances can be made in the field of tissue engineering through novel in-vitro culture and bioscaffold fabrication techniques. Recent technology can also allow the collection of in-vivo data so that ligament and tendon injuries can be better understood. Yet, solving new and more complex problems must still follow the stepwise methods of approach as taught by Professor Fung.     

Identification of helical polyribosomes in sections of mature skeletal muscle fibers

Summary The localization and configurations of ribosomes in mature white skeletal muscle fibers of the rat were investigated. Differential visualization of ribosomes and glycogen granules was obtained by fixation with glutaraldehyde only and staining of the sections with uranyl acetate. Ribosomes are then electron dense and glycogen granules electron transparent. Their identity was ascertained by selective extractions of ribonucleic acid and polysaccharide.The vast majority of the ribosomes is not membrane-bound. They are located intermyofibrillarly (predominantly at the level of the I-bands), beneath the sarcolemma, and in the paranuclear cones of sarcoplasm. Occasionally short stretches of granular reticulum occur, often as characteristic double walled vesicles with ribosomes on the inner membrane only.Three main types of polysomal configurations are observed: rosettes of 4 to 6 ribosomes, helical arrays, and whorls of up to about 25 probably membrane-bound ribosomes. The average number of ribosomes in the extended helical configurations is estimated to be about 60. It is argued that these helices represent the polysomes instrumental in the synthesis of the large subunits of myosin. It is emphasized that helical polyribosomes are by no means typical of striated muscle, but probably represent a common configuration of large free polysomes.With the technical assistance of Tineke J. Hoogenboezem.     

Development and evaluation of multiple tendon injury models in the mouse

The mouse has proven to be an advantageous animal model system in basic science research focused on aiding in development and evaluation of potential treatments; however, the small size of mouse tendons makes consistent and reproducible injury models and subsequent biomechanical evaluation challenging for studying tendon healing. In this study, we investigated the feasibility and reproducibility of multiple mouse tendon injury models. Our hypothesis was that incisional (using a blade) and excisional (using a biopsy punch) injuries would result in consistent differences in tendon material properties. At 16 weeks of age, 17 C57BL/6 mice underwent surgery to create defects in the flexor digitorum longus, Achilles, or patellar tendon. Each animal received 1-2 full-thickness, central-width incisional or excisional injuries per limb; at least one tendon per limb remained uninjured. The injuries were distributed such that each tendon type had comparable numbers of uninjured, incisionally injured, and excisionally injured specimens. Three weeks after injury, all animals were euthanized and tendons were harvested for mechanical testing. As hypothesized, differences were detected for all three different tendon types at three weeks post-injury. While all models created injuries that produced predictable outcomes, the patellar tendon model was the most consistent in terms of number and size of significant differences in injured tendons compared to native properties, as well as in the overall variance in the data. This finding provides support for its use in fundamental tendon healing studies; however, future work may use any of these models, based on their appropriateness for the specific question under study.     

Collagen fibrils and elastic fibers in rat-tail tendon: an electron microscopic investigation

Earlier studies by the authors showed that the collagen fibrils in rat-tail tendon have a bi-modal distribution of fibril diameters from a time shortly after birth through to the onset of maturity at about 3–4 months. Present work has extended those observations for rats up to the age of 2 years. Histograms of the fibril diameter distributions for mature tail tendon and direct electron microscope observations show that the fibrils break down as the tendon ages. Further work on the constant diameter subfibrils of diameter 140 Å described previously, has confirmed that these are part of the elastic fibers present in tendon at all ages. It has been shown that there is relatively little variation in the collagen fibril diameter distribution as a function of the position of the specimen in the tail, and as the measured percentage of the area taken by the collagen fibrils present at any particular point. Estimation of the fibrillar collagen content of rat-tail tendon as a function of age indicates that it increases steadily from birth and reaches a maximum at the onset of maturity, beyond which the fibrillar collagen content appears to remain constant.     

Cytoplasm-to-myonucleus ratios and succinate dehydrogenase activities in adult rat slow and fast muscle fibers

The relationship between myonuclear number, cellular size, succinate dehydrogenase activity, and myosin type was examined in single fiber segments (n = 54; 9 ± 3 mm long) mechanically dissected from soleus and plantaris muscles of adult rats. One end of each fiber segment was stained for DNA before quantitative photometric analysis of succinate dehydrogenase activity; the other end was double immunolabelled with fast and slow myosin heavy chain monoclonal antibodies. Mean ± S.D. cytoplasmic volume/myonucleus ratio was higher in fast and slow plantaris fibers (112 ± 69 vs. 34 ± 21 x 10 ³µm ³) than fast and slow soleus fibers (40 ± 20 vs. 30 ± 14 x 10 ³µm ³), respectively. Slow fibers always had small volumes/myonucleus, regardless of fiber diameter, succinate dehydrogenase activity, or muscle of origin. In contrast, smaller diameter (<70 µm) fast soleus and plantaris fibers with high succinate dehydrogenase activity appeared to have low volumes/myonucleus while larger diameter (>70 µm) fast fibers with low succinate dehydrogenase activity always had large volume/myonucleus. Slow soleus fibers had significantly greater numbers of myonuclei/mm than did either fast soleus or fast plantaris fibers (116 ± 51 vs. 55 ± 22 and 44 ± 23), respectively. These data suggest that the myonuclear domain is more limited in slow than fast fibers and in the fibers with a high, compared to a low, oxidative metabolic capability.     

Theoretical analysis of an implantable force transducer for tendon and ligament structures.

A mathematical model was developed for an implantable force transducer to be inserted within the midsubstance of a ligament or tendon. The model was generated by performing both equilibrium and strain-displacement analyses on a metallic, curved beam structure placed within a parallel-fibered tissue. The analysis permitted the transverse pressure acting between the device and fibers to be calculated along with peak device strain and sensitivity (ratio of strain output to axial tissue force). Transducer pressure and transducer strain were expressed in terms of nondimensionalized design factors. A parametric analysis of the key design factors was then performed. The transverse pressure was shown to vary little for large changes in these factors whereas device strain changed markedly. The analysis was verified by a bench test on an example device. Such a model permits a proposed design to be evaluated without having to conduct costly experiments.     

Immunohistochemical characterization of elastic system fibers in rat molar periodontal ligament.

Among elastic system fibers, oxytalan fibers are known as a ubiquitous component of the periodontal ligament, but the localization and role of elastin-containing fibers, i.e., elastic and elaunin fibers, has yet to be clarified. In this study, we immunohistochemically investigated the localization of elastin and fibrillin, major proteins of elastin-containing fibers in the periodontal ligament of rat lower first molars. At the light microscope level, distribution of elastin-positive fibers was not uniform but often concentrated in the vicinity of blood vessels in the apical region of the ligament. In contrast, fibrillin-positive fibers were more widely distributed throughout the ligament, and the pattern of their distribution was comparable to the reported distribution of oxytalan fibers. At the ultrastructural level, assemblies or bundles of abundant fibrillin-containing microfibrils were intermingled with a small amount of elastin. This observation indicated that elastin-positive fibers observed under the light microscope were elaunin fibers. No mature elastic fibers, however, were found in the ligament. These results show that the major components of elastic system fibers in the periodontal ligament of the rat mandibular first molar were oxytalan and elaunin fibers, suggesting that the elastic system fibers play a role in the mechanical protection of the vascular system.     

Collagen fibril morphology and organization: implications for force transmission in ligament and tendon.

Connective tissue mechanical behavior is primarily determined by the composition and organization of collagen. In ligaments and tendons, type I collagen is the principal structural element of the extracellular matrix, which acts to transmit force between bones or bone and muscle, respectively. Therefore, characterization of collagen fibril morphology and organization in fetal and skeletally mature animals is essential to understanding how tissues develop and obtain their mechanical attributes. In this study, tendons and ligaments from fetal rat, bovine, and feline, and mature rat were examined with scanning electron microscopy. At early fetal developmental stages, collagen fibrils show fibril overlap and interweaving, apparent fibril ends, and numerous bifurcating/fusing fibrils. Late in fetal development, collagen fibril ends are still present and fibril bundles (fibers) are clearly visible. Examination of collagen fibrils from skeletally mature tissues, reveals highly organized regions but still include fibril interweaving, and regions that are more randomly organized. Fibril bifurcations/fusions are still present in mature tissues but are less numerous than in fetal tissue. To address the continuity of fibrils in mature tissues, fibrils were examined in individual micrographs and consecutive overlaid micrographs. Extensive microscopic analysis of mature tendons and ligaments detected no fibril ends. These data strongly suggest that fibrils in mature ligament and tendon are either continuous or functionally continuous. Based upon this information and published data, we conclude that force within these tissues is directly transferred through collagen fibrils and not through an interfibrillar coupling, such as a proteoglycan bridge.     

Maternal rank and local resource competition do not predict birth sex ratios in wild baboons

We test two models of adaptive adjustment of birth sex ratios that are expected to apply to Cercopithecine primate species. It has been predicted that when maternal investment differentially influences the reproductive success of male and female offspring, females in good condition will bias investment in favour of the sex that gains the greatest fitness returns from additional investment. This hypothesis was subsequently amended to take into account the effects of local resource competition on maternal investment strategies of primate females. This body of theory has been applied to primates with contradictory results, prompting some to question the conclusion that primate females facultatively adjust birth sex ratios in an adaptive manner. Here, we present a meta-analysis of the relationship between maternal rank, birth sex ratios and local resource competition in 36 groups of wild savannah baboons, Papio cynocephalus. The results do not support predictions derived from either model of facultative sex ratio adjustment, and we conclude that there is currently no evidence that baboon birth sex ratios are adjusted in an adaptive manner.     

Phosphatidylinositol-dependent bond between alkaline phosphatase and collagen fibers in the periodontal ligament of rat molars

Alkaline phosphatase (ALP) is anchored to the outer leaflet of the lipid bilayer via phosphatidylinositol (PI) and ALP activity has been localized in the plasma membrane of numerous tissues. In the periodontal ligament ALP activity is found in the collagen fibers in addition to the plasma membrane of the osteoblasts and fibroblasts. In this study, we examined the distribution of ALP activity in the periodontal ligament of rat molars and also examined whether the bond between ALP and collagen fibers is dependent on PI by using phosphatidylinositol-specific phospholipase C (PI-PLC). ALP activity was distributed in the periodontal ligament. The activity mirrored the distribution of collagen fibers in the periodontal ligament. Cytochemical analysis also demonstrated that ALP activity was located not only in the plasma membrane of fibroblasts, but also in the collagen fiber bundles and fibrils in the periodontal ligament. After treatment with PI-PLC, the loss of ALP activity in the periodontal ligament was observed histochemically, and the loss of ALP activity in the fibroblasts as well as in the collagen fiber bundles and fibrils was observed cytochemically. These results strongly indicate that the bond between ALP and the collagen fibers is also dependent on PI.     

Patellar tendon and hamstring moment-arms and cross-sectional area in patients with anterior cruciate ligament reconstruction and controls

The purpose of this study was to examine the moment-arm and cross-sectional area (CSA) of the patellar tendon (PT) and the hamstrings after anterior cruciate ligament (ACL) reconstruction. The right knee of five males who underwent ACL reconstruction with a PT graft and five age-matched controls was scanned using magnetic resonance image scans. Based on three-dimensional (3D) solids of the PT, CSAs and moment-arms of semitendinous (ST), biceps femoris (BF) long head and semimembranosus (SM) were estimated. Analysis of variance indicated no significant group differences in muscle moment-arms (p>0.05). 3D moment-arms of PT, ST and BF were significantly lower than the corresponding 2D values (p < 0.05). The ACL group displayed a significantly higher maximum BF CSA, a lower ST CSA (p < 0.05) but similar PT and SM CSAs compared with controls. It is concluded that any alterations in PT properties 1 year after harvesting do not affect knee muscle moment-arms compared with age-matched controls. Moment-arm estimation differed between 3D and 2D data, although it did not affect comparisons between ACL reconstruction group and controls. Design of rehabilitation programmes should take into consideration a potential alteration in hamstring morphology following surgery with a PT graft.     

Collagen fibrillogenesis in tendon development: current models and regulation of fibril assembly

Tendons are collagen-based fibrous tissues that connect and transmit forces from muscle to bone. These tissues, which are high in collagen type I content, have been studied extensively to understand collagen fibrillogenesis. Although the mechanisms have not been fully elucidated, our understanding has continued to progress. Here, we review two prevailing models of collagen fibrillogenesis and discuss the regulation of the process by candidate cellular and extracellular matrix molecules. Although numerous molecules have been implicated in the regulation of collagen fibrillogenesis, we focus on those that have been suggested to be particularly relevant to collagen type I fibril formation during tendon development, including members of the collagen and small leucine-rich proteoglycan families, as well as other molecules, including scleraxis, cartilage oligomeric matrix protein, and cytoskeletal proteins.     

Influence of sensor size on the accuracy of in-vivo ligament and tendon force measurements.

In-vivo tendon forces are commonly measured using transducers, which detect tension in the tendon fibers. A poorly understood source of measurement errors is the difference in stress distribution within the tendon between experimental and transducer calibration conditions. The objective of this study was to investigate this source of error, and to determine whether these errors could be minimized by proper selection of transducer size. The study was conducted using the infrapatellar ligament (patellar tendon) of New Zealand White rabbits. Tendon force was measured with two different size implantable force transducers (IFTs), one Wide and one Narrow, and by a strain gaged load cell in series with the tendon. Tests were conducted at five different loading conditions selected to produce five different stress distributions within the tendon. One loading condition corresponded to a typical post-experiment calibration, and the data from that condition were used to develop a calibration equation for the transducer. The errors that resulted from using this calibration were determined by comparing the tendon force measured by the in-series load cell with the force predicted from the IFT output using the calibration equation. Changes in stress distribution produced measurement errors up to 64 N with the Narrow IFT but only 24 N with the Wide IFT. We found the measurement error was dependent on sensor width. Our results support the hypothesis that measurement errors can be caused by differences in tendon stress distribution between calibration and experimental conditions. We further showed that these errors can be minimized by using an IFT, which samples the tension in a large percentage of the tendon fibers. Information from this study can be used for selection of an appropriately sized implantable force transducer for measuring tendon and ligament force.