A Phenomenologic-mathematical Model of Growth Dynamics

Starting point of the modelling procedure are measured courses of the body length increase of man (inverse problem) reaching from the time of conception up to the end of adolescence. First assumption: The whole growth process can be subdivided into independent partial processes for succeeding time periods of the individual's development each of them producess a more or less marked growth spurt. 2. Superposition of these partial processes means addition of the portions of body length which are generated by the spurts yielding in this manner the measured course of body length increase. 3. There is no change in dynamics for producing the several growth spurts, and this dynamics will be described by the differential equation of the logistic law of growth. These steps will be interpreted in control-theoretical terms. In this sense growth is a follow-up control process which is governed by the genetically fixed “biological program of growth” in form of a step function of reference values.     

Phenomenologic-mathematical modeling of the human-body-length growth through the analysis of growth periods and their quantitative-analytical registration

The body height growth (of masculine beings) was modelled in a phenomenologic-mathematical manner by partitioning the time course of measured growth curve in parts every of which corresponds to a separated growth period. This partitioning was reached in a natural way so that a superposition of the single spurts yields the whole measured course. Every growth batch will be described in its time course by one term of inverse tangent function. The biological meaning and an explanation of the succession of the growth spurt as an effect of control circuits need further exploratory work. For detailed statements on acceleration phenomena concerning the body height growth this analysis gives possibilities for comparing the single growth spurts of the mean growth process of two populations in question. For measured values given by BROCK (1954) and SALZLER (1967) there are five growth periods in the time intervall reaching from time of conception until the end of the first year. Comparing the mathematical functions of the corresponding growth spurts for these two groups one can conclude that the second spurt (fetal spurt) is responsible for an increase of birth body height and the fourth for an increase of body height in the suckling age of the latter group against the former one.     

Evolution of human growth spurts

This study investigates subadult growth spurts in a large sample of anthropoid primates, including humans. Analyses of body mass growth curves show that humans are not unique in the expression of female and male body mass growth spurts. Subadult growth spurts are observed in both New World and Old World anthropoid primates and are more common in males than in females. Allometric analyses of growth spurts indicate that many aspects of primate growth spurts are strongly correlated with species size. Small species tend not to exhibit growth spurts. Although male and female scaling patterns for velocity and size measures are comparable, scaling relations of variables that measure the timing of growth spurts differ by sex. These patterns can he related to sexual differences in life histories. Scaling analyses further show that humans do not depart substantially from patterns that describe other anthropoid primates. Thus, in relative terms, human growth spurts are not exceptional compared to this sample of primates. The long absolute delay in the initiation of the human growth spurt may be of substantial evolutionary importance and serves to distinguish humans from other primates. In essence, humans exhibit growth spurts that are comparable to other primates in many respects. However, human growth spurts are shifted to very late absolute ages. © 1996 Wiley-Liss, Inc.     

Kinetics of a bacterial culture growth: validity of the affinity rule in biological systems.

The kinetic study of a process is usually performed by measuring a convenient intensive property, P, as a function of time. The "affinity rule" states that, when a given process takes place under different external constraints (e.g., different temperatures, pressures, pH values, etc.), the various P versus time curves are related by an affinity transformation parallel to the time axis: in other words the P versus log time curves are parallel and can be superimposed by translation. The validity of the rule has been extensively tested in chemical and physiochemical processes, but there is no evidence as yet that it extends to biological systems. The present paper shows that the rule is indeed valid for the kinetics of growth of an Escherichia coli culture at various temperatures and pH values. More extended experiments are necessary to prove or disprove the general validity of the rule in biological systems, but its practical interest is evident: whenever it is valid it will be possible, from a very small number of measurements, to predict the complete behavior of the system in a number of various external conditions     

Monitoring the growth dynamics of somatic traits based on a semi-longitudinal study

Possibilities of conducting longitudinal human growth studies are very limited, since it is necessary to monitor the probands for a long time. Another problem can be a loss of data currency, and the small size of the final sample. The solution can be a follow-up semi-longitudinal observation. This research is drawn up as a short longitudinal monitoring of 1925 children (990 boys, 935 girls), aged 6-15 years, at 20 elementary schools in four regions of the Czech Republic, which has been conducted at the same time.Data of repeatedly examined probands of a wide age range were acquired in a short time period. With the help of a linear regression model with mixed effect, the growth velocity curves of 12 somatic traits have been obtained. The timing, intensity and duration of separate growth spurts have been observed, as well as the mutual location of both points of growth velocity, local maxima and minima, and points of the maximal acceleration and deceleration.The results demonstrate that the velocity of characters with variable growth dynamics (skin-fold thicknesses, circumferences of limbs) - contrary to characters with regular growth velocity - have a higher number of partial growth spurts and an opposite course. In the period of separate growth velocity, peaks of somatic characters with regular growth dynamics reach points of partial local minima. In comparison to previous longitudinal studies of body height growth dynamics, the shift of both the beginning and the peak of boys’ and girls’ pubertal spurt, to a lower age can be found.     

Analysis of differential growth of the right and the left leg

In spite of well documented standards for length and annual growth rates of the femur and tibia, there is little information on short term longitudinal bone growth. We investigated differential growth dynamics of the lower leg in 10 children, aged 6:3 to 14:2 years, by knemometry, a novel and non-invasive technique of accurate lower leg length measurement with a technical error of 0.09 to 0.16 mm. Mini growth spurts were detectable in 7 of the children and occurred synchroneously in both legs. Approximately half of the variance of the weekly lower leg length increments could be attributed to synchrony of leg length increments, but a significant amount of residual variance remained which exceeded the technical error of the measurements. Run-analysis of the individual series of right vs. left differences of the weekly lower leg length increments provided evidence for alternating periods of overgrowth of one leg compared to the contralateral side in 5 out of the 10 children. We concluded that there is suggestive evidence of partial independence of lower leg growth in the short term.     

The evolution of the axonal transport toolkit

Neurons are highly polarized cells that critically depend on long‐range, bidirectional transport between the cell body and synapse for their function. This continual and highly coordinated trafficking process, which takes place via the axon, has fascinated researchers since the early 20th century. Ramon y Cajal first proposed the existence of axonal trafficking of biological material after observing that dissociation of the axon from the cell body led to neuronal degeneration. Since these first indirect observations, the field has come a long way in its understanding of this fundamental process. However, these advances in our knowledge have been aided by breakthroughs in other scientific disciplines, as well as the parallel development of novel tools, techniques and model systems. In this review, we summarize the evolution of tools used to study axonal transport and discuss how their deployment has refined our understanding of this process. We also highlight innovative tools currently being developed and how their addition to the available axonal transport toolkit might help to address key outstanding questions.     

Evaluation of a method for determining the length of sperm whales (Physeter catodon) from their vocalizations

The click vocalizations of sperm whales often contain several regularly-spaced, discrete pulses of sound. Norris & Harvey (1972) hypothesized that these were caused as a single pulse of sound produced at the front of the whale's head bounced between reflective air sacs at either end of the spermaceti organ. Thus the interval between pulses will be twice the travel time for sound along the length of the spermaceti organ. It should therefore be possible to determine spermaceti organ length and thence total body length by measuring the interval between these pulses. Several workers have used an equation relating inter-pulse interval (IPI) to body length to estimate sperm whale body lengths acoustically.
In this paper, aspects of this technique are examined in some detail. In particular, variability in IPIs and trends in IPI with time and depth are investigated. Most importantly, for the first time IPIs in the vocalizations of whales of known lengths have been measured.
Variability in IPIs in the clicks of a single whale is acceptably low though there is a tendency for low and high values to occur in runs. There is no clear trend for IPI to alter significantly with the whale's depth or with the time since leaving the surface.
IPIs are positively correlated with body length though not as predicted by the equations used by previous workers. Some likely errors in these equations are discussed. A new empirically derived relationship between IPI and body length has been calculated, though more data are desirable to obtain a more accurate and reliable equation.     

Scatter factor-dependent branching morphogenesis: structural and histological features

Branching morphogenesis is a multi-step process that controls the formation of polarised tubules starting from hollow cysts. Its execution entails a series of rate-limiting events which include reversible disruption of cell polarity, dismantling of intercellular contacts, acquisition of a motile phenotype, stimulation of cell proliferation, and final re-establishment of cell polarity for creation of the definitive structures. Branching morphogenesis takes place physiologically during development, accounting for the establishment of organs endowed with a ramified architecture such as glands, the respiratory tract and the vasculartree. In cancer, aberrant implementation of branching morphogenesis leads to deregulated proliferation, protection from apoptosis and enhanced migratory/invasive properties, which together exacerbate the aggressive features of neoplastic cells. Under both physiological and pathological conditions, branching morphogenesis is mainly accomplished by a family of growth factors known as scatter factors. In this review, we will summarise the current knowledge on the biological and functional roles of scatter factors during branching morphogenesis, with a special emphasis on the phenotypic (structural and histological) consequences of scatter factor activity in different tissues.     

A Critical Study of the Auxin Theory of Growth Regulation in the Mesocotyl of Avena sativa

A method of growing Avena seedlings is described, which allowsthem to be handled individually in darkness. Mesocotyls of seedlinge from which the tip of the coleoptileis repeatedly removed are as long as those of control plantsnot so decapitated. Mesocotyls of seedlings which are deseeded on the 3rd day ofgrowth, followed by decapitation of the cleoptile tip on the4th day, are, at 7 days old, as long as those of controls notso decapitated. When deseeded plants are decapitated, regeneration of auxinproduction occurs at the tip of the coleoptile stump. Where a reduction in the length of the mesocotyl results fromdecapitation, a wound reaction is probably concerned in additionto any auxin changes. Removal of the coleoptilar node causes a sharp decrease in thefinal length of the mesocotyl. Heating intact seedlings at 40° C. for 3 hours causes areduction in the length of the mesocotyl but not of the coleoptile.The effect of heating is not reversed by subsequent treatmentat low temperature, which instead appears to augment these effects. When seedlings are exposed to the action of KCN, iodoacetate,or anaerobic conditions, and illuminated while so exposed, perceptionof light takes place, resulting in a reduction in the lengthof the mesocotyl. Perception of light takes place in seedlings germinated at normaltemperatures, but maintained at low temprature during illuminationand also in seedlings grown for 6 weeks at 2° C. withoutany previous growth at normal temperature. Light perception takes place in embryos excised from dry grainand grown on a culture medium. No difference in free amino-acid content is apparent betweendark grown and illuminated seedlings. The effects of illumination survive a period of drying downand become apparent upon subsequent germination of the grainin darkness. The drying process itself causes an additionalreduction in mesocotyl length. It is concluded that auxin itself is not the primary reactantin the perception process, and that the growth of the mesocotylis probably controlled by the coleoptilar node and plumulargrowing point, rather than by auxin diffusing downward fromthe tip of the coleoptile.     

In vitro liberation of charged gold atoms: autometallographic tracing of gold ions released by macrophages grown on metallic gold surfaces

The present study demonstrates that cultured macrophages are able to liberate gold ions from metallic gold surfaces, a process suggested to be called “dissolucytosis”, in a way analogous to the release taking place when metallic implants are placed in a body. Using the ultra-sensitive autometallographic (AMG) technique, we demonstrate that murine macrophages grown on a surface of metallic gold liberate gold ions. Ultra-structural AMG reveals that the gold ions are located in an ultra-thin membrane-like structure, “the dissolution membrane”, intervened between the macrophages and the metal surface. The presence of AMG silver enhanced gold nanoparticles in the dissolution membrane proves that the release of charged gold atoms takes place extracellularly. The dissolution membrane is most likely secreted and chemically controlled by the “dissolucytes”, here macrophages, and the membrane is essential for the dissolution of metal implants and particles, which cannot be phagocytosed. Our findings support the notion that whenever a metallic gold surface is attacked by dissolucytes, gold ions are liberated and taken up by surrounding cells. As gold ions can suppress the inflammatory process, it is reasonable to expect that when dissolucytosis takes place in the living organism the liberated gold ions will cause local immunosuppression.     

A new estimator of significance of correlation in time series data.

Many expression array experiments monitor gene activity as an organism goes through some biological process. It is desirable to find genes with similar expression patterns in the resulting time series data. We propose a new simulation approach that assesses the statistical significance of similarity scores between expression patterns. The simulation takes into account the dependence between columns of data.     

Optimum design of a series of continuous stirred tank reactors containing immobilised growing cells

The optimum design of a series of continuously operated stirred-tank reactors containing immobilised growing cells is described. Optimal design is defined as the minimal total holding time over the reactor series to achieve a certain degree of conversion. The analysis is made under the assumptions that there is a constant and equal concentration of immobilised biomass in all bioreactors along the series, no diffusion limitation takes place, all growth of the immobilised biomass will lead to an increase in suspended biomass, and that maintenance of the immobilised cells can be neglected. It is shown that the use of more than three bioreactors in series is likely to be de trop.     

Incorporating movement into models of grey seal population dynamics

1. One of the most difficult problems in developing spatially explicit models of population dynamics is the validation and parameterization of the movement process. We show how movement models derived from capture-recapture analysis can be improved by incorporating them into a spatially explicit metapopulation model that is fitted to a time series of abundance data. 2. We applied multisite capture-recapture analysis techniques to photo-identification data collected from female grey seals at the four main breeding colonies in the North Sea between 1999 and 2001. The best-fitting movement models were then incorporated into state-space metapopulation models that explicitly accounted for demographic and observational stochasticity. 3. These metapopulation models were fitted to a 20-year time series of pup production data for each colony using a Bayesian approach. The best-fitting model, based on the Akaike Information Criterion (AIC), had only a single movement parameter, whose confidence interval was 82% less than that obtained from the capture-recapture study, but there was some support for a model that included an effect of distance between colonies. 4. The state-space modelling provided improved estimates of other demographic parameters. 5. The incorporation of movement, and the way in which it was modelled, affected both local and regional dynamics. These differences were most evident as colonies approached their carrying capacities, suggesting that our ability to discriminate between models should improve as the length of the grey seal time series increases.     

Early post-mortem changes and stages of decomposition in exposed cadavers

Decomposition of an exposed cadaver is a continuous process, beginning at the moment of death and ending when the body is reduced to a dried skeleton. Traditional estimates of the period of time since death or post-mortem interval have been based on a series of grossly observable changes to the body, including livor mortis, algor mortis, rigor mortis and similar phenomena. These changes will be described briefly and their relative significance discussed. More recently, insects, mites and other arthropods have been increasingly used by law enforcement to provide an estimate of the post-mortem interval. Although the process of decomposition is continuous, it is useful to divide this into a series of five stages: Fresh, Bloated, Decay, Postdecay and Skeletal. Here these stages are characterized by physical parameters and related assemblages of arthropods, to provide a framework for consideration of the decomposition process and acarine relationships to the body.     

Comparative quantitative studies of mental and physical development of children up to age 3

Biomathematical-methodical aspects are exposed of quantitative recording of mean growth courses which will be taken as basis for comparisons between different sample curves. In the paper the body length growth process of children in the age period from 0 to 3 years is considered. There are samples of children growing up under different social conditions and data of corresponding samples collected about 20 years ago. After remarks on the correlation between physical and psychical development of infants several possibilities for representing mean body length growth curves are discussed. The advantages of empirical regression are explained as the best suited method for a modelfree data evaluation. The nonparametric location trend test of Cox and Stuart is used for statistical proving of global difference or parallelism in the course of 2 mean growth curves. Level differences in the global sense between 2 compared curves may be tested by constructing a Scheffé confidence region for a properly defined constrast. Local level differences can be proved by the t-test for those pairs of corresponding mean values for which the conditions of applying this test are fulfilled. The calculation of a curve-related normal belt as a succession of 95%-tolerance regions (without confidence probability) is demonstrated by an example.     

Critical temperatures and a critical chain length in saturated diacylphosphatidylcholines: calorimetric, ultrasonic and Monte Carlo simulation study of chain-melting/ordering in aqueous lipid dispersions

Chain-ordering/melting transition in a series of saturated diacylphosphatidylcholines (PCs) in aqueous dispersions have been studied experimentally (calorimetric and ultrasonic techniques) and theoretically (an Ising-like lattice model). The shape of the calorimetric curves was compared with the theoretical data and interpreted in terms of the lateral interactions and critical temperatures determined for each lipid studied. A critical chain length has been found (between 16 and 17 C-atoms per chain) which subdivides PCs into two classes with different phase behavior. In shorter lipids, the transition takes place above their critical temperatures meaning that this is an intrinsically continuous transition. In longer lipids, the transition occurs below the critical temperatures of the lipids, meaning that the transition is intrinsically discontinuous (first-order). This conclusion was supported independently by the ultrasonic relaxation sensitive to density fluctuations. Interestingly, it is this length that is the most abundant among the saturated chains in biological membranes.     

A plastic interval timer synchronizes pubertal development of summer- and fall-born hamsters

Summer and fall decreases in day length induce reproductive regression in adult hamsters and delay reproductive maturation of their young. The following year pubertal development is triggered by an interval timer (IT) that renders animals refractory to inhibitory short day lengths after approximately 25 wk. Timing of gonadal and somatic development was examined among offspring born to Siberian hamsters in early-August vs. late-September day lengths. Pubertal maturation was delayed in both groups until late winter. Gonadal growth occurred at significantly later ages among August- vs. September-born males as did late-winter spurts in ponderal growth of both sexes. Timing of reproductive and somatic development depended on postnatal rather than prenatal photoperiod exposure and was unrelated to the circadian entrainment status of dams. When developmental patterns were assessed in relation to time of year, group differences were largely eliminated. Because the IT triggers these developmental events, its duration must be plastic. This plasticity facilitates a relative synchronization or entrainment of developmental milestones in hamsters born into different late-summer/early-fall photoperiods.