Quantitative evaluation of the allometric transformation of of biological structures

Detection and quantification of allometry is a crucial problem in understanding morphological changes, both for systematic and morphogenetic purposes. A section of S.A.M. (Shape Analytical Morphometry) software system was used for this attempt. It consists of the following steps: a) boundary detection; b) starting point detection; c) size normalization; d) extraction of the fundamental shape by Kth order polynomials; e) finding of symmetry evaluator (S.A.E.) by means of a second degree equation. This last procedure gives an arc-chord complex that expresses a vector for allometry where intercept value was for application point, first degree coefficient was for direction and second degree coefficient was for modulus and versus. The main parameters, isometry fraction and allometry fraction may be understood referring them to morphogenetic models.     

Effect of asymmetry of concentration-response curves on the results obtained by the receptorial responsiveness method (RRM): an in silico study

The receptorial responsiveness method (RRM) was proposed to estimate changes in the concentration of an agonist in the microenvironment of its receptor. Usually, this is done by providing the equieffective concentration of another agonist for the same receptor or for a largely overlapping postreceptorial signaling ("test agonist"). The RRM is a special nonlinear regression algorithm to analyze a concentration-response (E/c) curve that represents the simultaneous actions of a single agonist concentration to be estimated and of increasing concentrations of the test agonist. The aim of this study was to explore whether asymmetry of the E/c curve to be analyzed influences the reliability of the RRM. For this purpose, computer simulation was performed by constructing symmetric and asymmetric E/c curves using the operational model of agonism, and then these curves were analyzed with the RRM. To perform the RRM, 2 types of equations were used: one involving the Hill equation, the simplest model of the E/c relationship, and one containing the Richards equation, an advanced model properly handling E/c curve asymmetry. Results of this study indicate that E/c curve asymmetry does not significantly influence the accuracy of the estimates provided by the RRM. Thus, when using the RRM, it is not necessary to replace the Hill equation with the Richards equation to obtain useful estimates. Furthermore, it was found that estimation of a high concentration of a high-efficacy agonist can fail when the RRM is performed with a low-efficacy test agonist in a system characterized by a small operational slope factor.     

Mathematical description of stress relaxation of bovine femoral cortical bone

In 1993 we proposed an empirical formula for describing the relaxation modulus of cortical bone based on the results of stress relaxation experiments performed for 1 x 10(5) sec: [E(t) = E0{A exp[ -(t/tau1)beta] + (1 - A) exp(-t/tau2)}, (0 < A, beta <1 and tau1 < tau2) where E0 is the initial value of the relaxation modulus, A is the portion of the first term, tau1 and tau2 are characteristic relaxation times, and beta is a shape factor [Sasaki et al., J. Biomechanics 26 (1993), 1369]. Although the relaxation properties of bone under various external conditions were described well by the above equation, recent experimental results have indicated some limitations in its application. In order to construct an empirical formula for the relaxation modulus of cortical bone that has a high degree of completeness, stress relaxation experiments were performed for 6 x 10(5) seconds. The second term in the equation was determined as an apparently linear portion in a log E(t) vs t plot at t>1 x 10(4) sec. The same plot for experiments performed for 6 x 10(5) seconds revealed that the linear portion corresponding to the second term was in fact a curve with a large radius of curvature. On the basis of this fact, we proposed a second improved empirical equation E(t) = E0{A exp [ -(t/tau1)beta] + (1 - A) exp[-(t/tau2)gamma]}, (0相似文献   

Steady-state kinetic studies of the negative co-operativity and flip-flop mechanism for Escherichia coli alkaline phosphatase.

1. A study of variations in experimental error of velocity measurement with substrate concentration for alkaline phosphatase reveals that the standard error is not constant or strictly proportional to velocity, but obeys a more complex dependence. 2. By using an approach based on error estimates at each individual substrate concentration, we show that the double-reciprocal plots in general are curved, necessitating a high-degree rate equation. The curves are analysed according to a recent classification of possible curve shapes for the 3:3 function, which is shown to be the lowest-degree rate equation satisfying the experimental data. 4. Other workers have supposed the enzyme to follow Michaelis-Menten kinetics, and it is shown that this assumption is approximately true at low temperatures in the absence of phosphate. 5. A study of the effects of phosphate concentration, pH and temperature on the kinetics shows that there is a gradual alteration in curve shape with these experimental variables, resulting in an apparent reduction in degree under certain special conditions, and particularly at low temperature. 6. It is shown that the steady-state kinetics do not require a flip-flop or half-of-sites reactivity mechanism as claimed, and a mechanism is proposed, a rate equation calculated and an analysis attempted. 7. An analysis of the product-inhibition effects for a linked two-sited Uni Bi enzyme is given. Alterations of asymptotic double-reciprocal slopes and limiting (1/nu) intercepts with products is discussed, and it is shown how the theory of product inhibition can be extended to complex kinetic situations to extract information as to molecular mechanism. 8. Deviations from Michaelis-Menten kinetics are expressed in terms of the magnitude of the appropriate Sylvester resultants.     

A new method to characterize saturation functions by their first four moments

The calculation of the first four moments of saturation functions is proposed as a method to describe the properties of enzymes or receptors models. The values of these moments in the case of the Langmuir or Michaelis-Menten equation and the Hill equation are reviewed. They have been calculated for the second degree Adair equation and in the case of binding site heterogeneity. A method for generalization to cases of greater complexity is also proposed. The advantage of this method over the classical ones—graphical representations and derivation of coefficients like n_H, $\text{[L]0.9}\text{[L]0.1}$…—is essentially that the moments are defined by one single value independently of any particular model for the whole of the saturation curve.     

The probability of obtaining complex kinetic curves for enzyme mechanisms with cubic terms in the pseudo-steady state rate equations

A number of details required for the classification of 3 : 3 double reciprocal plots are provided. It is shown that the ν(S) plot for a 3 : 3 function can have at most four inflexions and at most two inflexions adjacent to a turning point. Using this information, a classification of 3 : 3 ν(S) plots into ten main varieties with several subclasses is reported. The problem of defining the probability with which a given mechanism can give rise to specific curve shape features is considered. Applying this technique, the probability with which four simple enzyme mechanisms can give rise to 3 : 3 curve shapes is computed. It is shown that a 3 : 3 saturation function can have no turning points, at most two inflexions and at most one inflexion in double reciprocal space. The probability with which the available 3 : 3 shapes can arise is also computed. It is concluded that, with realistic values for rate constants, chemically reasonable enzyme mechanisms leading to rate equations of degree n : n can generate most of the kinetic profiles available to a rational function of degree n : n with positive coefficients. The probability of obtaining specific curve shapes is not so characteristic of the particular mechanism for 3:3 rate equations as it is for 2:2 rate equations. The probability of obtaining highly complex curves with several turning points or inflexions is rather lower for the enzyme mechanisms than with general 3 : 3 rational functions. There is a high probability that 3 : 3 mechanisms will generate kinetic curves that are geometrically similar to those possible for degree 2 : 2 but this is not so for binding isotherms. Hence differentiating 3 : 3 from 2 : 2 rate equations from experimental kinetic data is more likely to be successful by non-linear regression to the whole data set than by demonstrating a specific 3 : 3 feature. Binding curves, on the other hand, for three or more sites should give Scatchard plots with inflexions, features not possible with second degree equations which are conic sections in this space.     

Patterns of fluctuating asymmetry in flowers: Implications for sexual selection in plants

Characters in animals used in signalling and subjected to strong directional selection often demonstrate (i) an elevated level of fluctuating asymmetry (small random deviations from bilateral symmetry) and (ii) a negative relationship between the degree of individual fluctuating asymmetry and the size of a given character. We tested these two predictions in plants since flowers are subjected to strong directional selection and are involved in signalling to pollinators, whereas leaves are supposed not to be directly involved in signalling. The overall level of fluctuating asymmetry in a number of plant species with bilaterally or radially symmetric flowers was not generally higher in floral traits than in leaves. The level of fluctuating asymmetry in plants was sometimes significantly consistent within individuals. The absolute degree of individual fluctuating asymmetry in floral traits was generally negatively related to the size of the trait, while there was a positive relationship for leaves. The degree of individual fluctuating asymmetry in floral traits was marginally negatively related to the degree of individual fluctuating asymmetry in leaf traits. These patterns of fluctuating asymmetry in plants suggest that (i) the degree of asymmetry in flowers signals different aspects of quality than does the degree of asymmetry in leaves, and that (ii) fluctuating asymmetry in flowers often reflects the phenotypic quality of individual plants.     

Asymmetry of Mouth-Opening of a Small Herbivorous Cichlid Fish Telmatochromis temporalis in Lake Tanganyika

Direction of mouth-opening of a small herbivorous Tanganyikan cichlid, Telmatochromis temporalis, was studied. Each sample fish opened its mouth either rightward or leftward in some degree. The directions of mouth-opening were independent of the body curve directions, and the asymmetry will be due to asymmetric mouth morph individually specific. The degree of the mouth asymmetry was not related to body size, suggesting the asymmetry being not acquired characters. No fish opened the mouth in lateral symmetry, indicating that the asymmetry is different from "fluctuating asymmetry". This fish took algae on rock surface usually using right or left side of its mouth. However, strong relations between directions of mouth-openings and frequencies of mouth side used in foraging were not found, and the biological role of the asymmetry, if any, is not clear now.     

Semi-log model for interpreting the results of swabbing surfaces naturally contaminated

Two mathematical models for depicting microbial depletions during six consecutive swabbings of refrigerated tank wall and teat skin were tested. Although a second degree polynomial equation gave a better adjustment of the data, a first degree equation was preferred to calculate the total numbers of micro-organisms possibly retrieved from surfaces by swabbing. This model was used for estimating the level of milk contamination by teat skin.     

Semi-log model for interpreting the results of swabbing surfaces naturally contaminated

Two mathematical models for depicting microbial depletions during six consecutive swabbings of refrigerated tank wall and teat skin were tested. Although a second degree polynomial equation gave a better adjustment of the data, a first degree equation was preferred to calculate the total numbers of micro-organisms possibly retrieved from surfaces by swabbing. This model was used for estimating the level of milk contamination by teat skin.     

Postcranial robusticity in Homo. II: Humeral bilateral asymmetry and bone plasticity

The analysis of humeral asymmetry in Recent human skeletal samples and an extant tennis-player sample documents minimal asymmetry in bone length, little asymmetry in distal humeral articular breadth, but pronounced and variable asymmetry in mid- and distal diaphyseal crosssectional geometric parameters. More specifically, skeletal samples of normal modern Euroamericans, prehistoric and early historic Amerindians, and prehistoric Japanese show moderate (ca. 5–14%) median asymmetry in diaphyseal cross-sectional areas and polar second moments of area, whereas the tennis-player sample, with pronounced unilateral physical activity, exhibits median asymmetries of 28–57% in the same parameters. A sample of Neandertals with nonpathological upper limbs exhibits similarly low articular asymmetry but pronounced diaphyseal asymmetries, averaging 24–57%. In addition, three Neandertals with actual or possible post-traumatic upper limb alterations have the same low articular asymmetry but extremely high diaphyseal asymmetries, averaging 112–215%. These data support those from experimental work on animals, exercise programs of humans, and human clinical contexts in establishing the high degree of diaphyseal plasticity possible for humans, past and present, under changing biomechanical loading conditions. This lends support to activity-related functional interpretations of changing human diaphyseal morphology and robusticity during the Pleistocene. © 1994 Wiley-Liss, Inc.     

The mathematics of gnomonic seashells

Parametric Cartesian vector-valued functions are constructed for the purpose of systematically describing various features of spiral shell geometry. The underlying geometrical hypothesis is that molluscan shell shapes can usually, to at least a good first approximation, be developed by rotating a generating curve about a fixed axis whilst simultaneously diminishing it by an “equiangular spiral” scale factor. A first-order symmetry equation is derived; then variational calculus is used to construct energy functionals which establish that Hooke's law is inherent in the formalism and that naturally occurring shell geometries are analogous to those of elastic spiral “clock springs”. The biological requirement that shelly structures must exist in a three-dimensional space is shown to be a sufficiently powerful mathematical constraint to ensure the existence of geometrical artifacts which can, perhaps, be likened to the conservation laws, pseudoforces, and fields of classical physics.     

人类股骨断面面积与形状的不对称性——基于三维激光扫描的形态测量分析

人类股骨横断面面积、形状及其左右侧差异记载的人类演化、人群差异及生存活动的重要信息一直为古人类学研究所关注。多年来, 对股骨断面的研究通常采用破坏性地切割或者制作模型的方法。本文利用三维激光表面扫描技术, 无损、快捷、方便地获取了20对现代中国人左右侧股骨外轮廓的三维数据, 采用CAD软件及几何形态测量方法对两侧股骨断面轮廓的大小及形状进行了对比和分析。初步研究结果发现: 两侧股骨的横断面相对面积差异极其显著, 绝对面积差异不显著, 不对称方式表现为波动不对称性, 而不是偏向不对称性; 个体之间两侧股骨横断面外轮廓形状的波动不对称性极其显著, 偏向不对称性虽有差异但不显著; 平均形状和面积分析结果似乎表明股骨稍有偏左侧优势。虽然本文所采用的标本量有限, 所得出的结论需要更多标本的进一步验证, 但是, 本文的研究结果提示利用三维激光扫描技术获取股骨横断面外轮廓数据, 并采用形态测量方法分析确实能够揭示出一些以往研究方法不能发现的重要信息, 这种研究骨骼不对称性的新方法值得进一步的应用。     

Diagnostic differences in mandibular P4 shape between Neandertals and anatomically modern humans

This study uses elliptical Fourier analysis to quantify shape differences observed in the P(4) crown of Neandertals and anatomically modern humans. Previously, P(4) shape was assessed qualitatively, and results suggested marked differences between Neandertals and anatomically modern humans (Bailey [2002] New Anat. 269:148-156). The goal of this study was to investigate the P(4) shape in more detail, quantifying it in order to determine its utility for taxonomic classification and phylogenetic analysis. A comparison of mean shapes confirms that the mesiolingual portion of the P(4) is truncated in Neandertals, and that this produces a distinctively asymmetrical P(4). A randomization test confirms that the shape difference between Neandertals and anatomically modern humans is significant. Principal component and discriminant function analyses indicate that the relative size of the lingual portion of the tooth also affects tooth shape, with the lingual portion of the Neandertal P(4) being narrower than that of anatomically modern humans. Classification of P(4) crown shapes using discriminant functions analysis is far from perfect. While 86.4% of the teeth were correctly classified, classification was much better for anatomically modern humans (98.1%) than it was for Neandertals (65%). Fortunately, crown shape is but one of several diagnostic characters of the P(4) crown. P(4) crown asymmetry can be added to the growing list of dental morphological characters distinguishing Neandertals from anatomically modern humans. Moreover, based on a comparison of mean tooth shapes in fossil and recent humans, symmetry, rather than asymmetry, appears to be the primitive state, and the high frequency of P(4) asymmetry is likely derived in Neandertals.     

Characteristics of the development of postural asymmetry in rats as affected by the opioids met-enkephalin and the kappa-agonist bremazocine

It has been found that bremazocine and met-enkephalin induce postural asymmetry in spinal rats under subarachnoidal and intravenous administration. Intravenous administration of bremazocine to intact animals--even if after it (an hour later) their spinal cord is sectioned--produces no asymmetry, i. e. the spinal cord section is necessary for asymmetry development. The magnitude of postural asymmetry and the side of limb flexion are not constant for each animal, but they change in time. Though, on the average, the percent of asymmetric animals and the ratio of left and right flexions in each group of animals are practically constant. When the spinal cord is sectioned at the T1-T4 level, the bremazocine and metenkephalin induce mainly the right-leg flexion: when the section is made at the T5-T9 level, the left-leg is bent, i. e. the flexion side depends on the level of the section. It is suggested that the ability of opioids to induce postural asymmetry is based on lateralization of opioid receptors in the rat spinal cord.     

Determination of fatigue in the electrically stimulated quadriceps muscle and relative effect of ischaemia

The creation of muscle fatigue using surface electrical stimulation represents a highly reproducible phenomenon in spinal cord injured patients. The torque output was recorded as a function of time. The fatigue curves recorded over 110s exhibited three main parts: first, a plateau of short duration, followed by a more or less steep slope and then a second plateau which was maintained for a long time. This phenomenon was fitted using an exponential equation which had been developed and four parameters introduced that outlined to the muscle behaviour. A set of fatigue indices was defined to characterize the asymptotic value, the slope, the coordinates of the inflexion point, the time constant and the vertical amplitude of the curve recorded. Two populations were studied; a group of 11 thoracic level of injury paraplegic patients and a group of 10 able-bodied control subjects. The computed coefficients of determination, r², were of very high values (0.99). Therefore, fatigue indices gave reliable information. Torque output did not differ between the two populations until 25 s had elapsed, but from 30s onwards it was markedly lower in paraplegics. The residual torque output was 21.1 ± 10.6% in the paraplegic group while it was 58.5 ± 8.9% in the control group. The effect of blood supply in the production of fatigue was also studied by repeating the same test using a tourniquet at the groin level. The residual torque became 14.7 ± 2.3% in the paraplegic group and 42.9 ± 6.3% in the control group. This test permitted the determination at a gross level of the different metabolic phases and therefore the recruitment of the different populations of muscle fibres within the quadriceps. Fast fatiguable fibres (type FF) produced the maximum output during the first phase, then fast resistant (type FR) explained the slope, and slow fibres (type S) were responsible for the second plateau. The effects of the tourniquet were obvious on the fatigue indices in both populations. In the spinal cord injured patients, there appeared to be a lack of slow fibres, probably due to disuse. Fatigue appeared to be independent from blood flow in paraplegics.     

A method for characterizing the biodiversity in bat pinnae as a basis for engineering analysis

A quantitative analysis of the interspecific variability between beamforming baffle shapes in the biosonar system of bats is presented. The data set analyzed consisted of 100 outer ear (pinna) shapes from at least 59 species. A vector-space representation suitable for principal component analysis (PCA) was constructed by virtue of a transform of the pinna surfaces into cylindrical coordinates. The central axis of the cylindrical transform was found by minimizing a potential function. The shapes were aligned by means of their respective axes and their center of gravity. The average pinna of the sample was a symmetrical, obliquely truncated horn. The first seven eigenvalues accounted already for two-thirds of the variability around the mean, which indicates that most of the biodiversity in the bat pinna can be understood in a more low-dimensional space. The first three principal components show that most of the variability of the bat pinna sample is in terms of opening angle, left-right asymmetry, and selective changes in width at the top or the bottom of the pinna. The beampattern effects of these individual components have been characterized. These insights could be used to design bioinspired beamforming devices from the diversity in biosonar.