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.     

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.     

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.     

Quantitative mathematical evaluation of growth studies from the viewpoint of exogenously or genetically influenced variability

Firstly, the ideas are sketched which serve as the basis for the phenomenologic-mathematical kind of modeling of the body length growth process of man. For proving the biological relevance of the spurts analyzed by numerical procedures one has to consider the social and the biological circumstances in which the growth process takes place. An analysis of longitudinal data series of the body length of (monozygotic) twins will give further hints to the possible meaning of the growth spurts by way of separation of exogenous and of genetic determined endogenous agents on the growth process. The data available for our examinations cover the time interval of the praepubertal and the postpuberal development as well as the time interval in which the puberal growth spurt takes place. The way to proceed in evaluation these time series will be presented.     

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.     

Partial deletion of the long arm of chromosome 18

Summary A female infant with mental retardation and multiple somatic anomalies is described. The karyological analysis disclosed the partial deletion of the long arm of chromosome 18 in cells of probands peripheral blood culture. Repeated investigations of probands mothers peripheral blood cultures disclosed the presence of various chromosomal aberrations in 25–70% of cells.     

Age and serotonin effects on locomotion in marine trematode cercariae

The effect of serotonin solutions on the locomotor activity of cercariae with different swimming patterns, Cryptocotyle lingua and Himasthla elongate, was investigated during their lifespan using motion track analysis and a frame-by-frame count of behavioral elements. Serotonin caused a noticeable alteration of several locomotion parameters in both species studied, while the activity per se decreased significantly with age. In intermittently swimming C. lingua cercariae, serotonin induced an increase in the frequency of active swimming phases (spurts) without significant changes in the duration and velocity of the spurts themselves. In continuously swimming H. elongata cercariae, serotonin increased the number of stops during the first hour after the emission from the host mollusk under a constant average swimming velocity. Immunocytochemical visualization of serotonin revealed a decline in its level with age (time after emission) and different dynamics of this process in neurons located in the tail and body of C. lingua cercariae. The data are interpreted in the light of the modulatory role of serotonin known for other animals.     

Longitudinal changes in growth hormone secretory process irregularity assessed transpubertally in healthy boys

Clarifying the time evolution, and underlying neuroendocrine regulation, of hormone secretion during puberty is of pivotal importance both physiologically and clinically. We sought to determine whether clinical growth and elevated growth hormone (GH) release in pubertal boys are associated with shifts in the irregularity of GH secretory patterns. We studied GH release in 23 healthy boys longitudinally at approximately 4-mo intervals over a 6-yr period throughout puberty, by repetitive blood sampling at 20-min intervals for 24 h on each study date. To quantify serial irregularity in the GH profiles, we utilized approximate entropy (ApEn), a scale- and model-independent quantification of the extent of sequential "randomness." Complementary statistical analyses establish that on a per-subject basis, serum GH concentration-time series show greatest secretory disorderliness (maximal ApEn) in prepuberty and mid-to-late puberty, followed by a steep decline in ApEn to maximal orderliness in postpubertal adolescence (P < 0.0001, ANOVA). Pooling all subject comparisons, we observed a persistent positive correlation between ApEn and growth velocity (GrVel), Pearson r = 0.467 (P < < 10(-10)). Moreover, in general, ApEn(GH) preceded GrVel evolution, with a time frame lead of 4-8 mo providing the most pronounced correlations between ApEn and GrVel. In the setting of low postpubertal growth, per-subject ApEn values fell to approximately one-half of maximal ApEn values and, on average, were in the 13th percentile from minimal (P < < 10(-10)) for fully mature boys. Thus, in a longitudinal transpubertal analysis, greater irregularity in GH secretion corresponds to greater linear growth in boys, which culminates in highly regular GH secretory dynamics after sexual maturity. In addition to clinical utility, there may be added experimental merit in knowing that GH dynamics typically predict accelerated linear growth in 4-8 mo.     

Growth models and growth spurt in the human

Growth of man differs basically from that of all animals - perhaps except some species of primates - by demonstrating a puberal growth spurt. This behaviour is well known but was hardly ever analyzed in a mathematical manner. The growth spurt is indeed difficult to grasp and this all the more as it shows varying forms of appearance. This becomes evident by the investigation of height values for normal and growth-restricted children as is the case with genetic diseases. From these variants, PELZ and SAGER came to the conclusion of setting up differentiated forms of growth spurts with adequate definitions in mathematical formulation. In this contribution, the models of human height growth and height velocity as practiced at Zurich (working group PRADER), London (working group TANNER) and Rostock (PELZ, SAGER, EYERMANN) are recalled and scrutinized as to the applicability of the new definitions. After the somewhat difficult comparisons of the model structures meditations are focussed at the proposals for the definition of the duration and the intensity of the growth spurt leading to quite different conceptions. Relative agreement is present for the time of the onset of the spurt whilst larger differences appear for the end of the puberal phase. A complete coincidence can hardly be reached but at least some light is thrown on this intricate problem by analyzing the different points of view.     

Conformation spaces of proteins

We report a simple method for measuring the accessible conformational space explored by an ensemble of protein structures. The method is useful for diverse ensembles derived from molecular dynamics trajectories, molecular modeling, and molecular structure determinations. It can be used to examine a wide range of time scales. The central tactic we use, which has been previously employed, is to replace the true mechanical degrees of freedom of a molecular system with the conformationally effective degrees of freedom as measured by the root-mean squared cartesian distances among all pairs of conformations. Each protein conformation is treated as a point in a high dimensional euclidean space. In this article, we model this space in a novel way by representing it as an N-dimensional hypercube, describable with only two parameters: the number of dimensions and the edge length. To validate this approach, we provide a number of elementary test cases and then use the N-cube method for measuring the size and shape of conformational space covered by molecular dynamics trajectories spanning 10 orders of magnitude in time. These calculations were performed on a small protein, the villin headpiece subdomain, exploring both the native state and the misfolded/folding regime. Distinct features include single, vibrationally averaged, substate minima on the 0.1-1-ps time scale, thermally averaged conformational states that persist for 1-100 ps and transitions between these local minima on nanosecond time scales. Large-scale refolding modes appear to become uncorrelated on the microsecond time scale. Associated length scales for these events are 0.2 A for the vibrational minima; 0.5 A for the conformational minima; and 1-2 A for the nanosecond events. We find that the conformational space that is dynamically accessible during folding of villin has enough volume for approximately 10(9) minima of the variety that persist for picoseconds. Molecular dynamics trajectories of the native protein and experimentally derived solution ensembles suggest the native state to be composed of approximately 10(2) of these thermally accessible minima. Thus, based on random exploration of accessible folding space alone, protein folding for a small protein is predicted to be a milliseconds time scale event. This time can be compared with the experimental folding time for villin of 10-100 micros. One possible explanation for the 10-100-fold discrepancy is that the slope of the "folding funnel" increases the rate 1-2 orders of magnitude above random exploration of substates.     

The induction of periodic and chaotic activity in a molluscan neurone

During prolonged exposure to extracellular 4-aminopyridine (4 AP) the periodic activity of the somatic membrane of an identified molluscan neurone passes from a repetitive regular discharge of >90 mV amplitude action potentials, through double discharges to <50 mV amplitude oscillations. Return to standard saline causes the growth of parabolic amplitude-modulated oscillations that develop, through chaotic amplitude-modulated oscillations, into regular oscillations. These effects are interpreted in terms of the actions of 4 AP on the dynamics of the membrane excitation equations.Emma and Leslie Reid scholar     

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.     

Self-organization of mobile populations in cyclic competition

The formation of out-of-equilibrium patterns is a characteristic feature of spatially extended, biodiverse, ecological systems. Intriguing examples are provided by cyclic competition of species, as metaphorically described by the ‘rock-paper-scissors’ game. Both experimentally and theoretically, such non-transitive interactions have been found to induce self-organization of static individuals into noisy, irregular clusters. However, a profound understanding and characterization of such patterns is still lacking. Here, we theoretically investigate the influence of individuals’ mobility on the spatial structures emerging in rock-paper-scissors games. We devise a quantitative approach to analyze the spatial patterns self-forming in the course of the stochastic time evolution. For a paradigmatic model originally introduced by May and Leonard, within an interacting particle approach, we demonstrate that the system's behavior—in the proper continuum limit—is aptly captured by a set of stochastic partial differential equations. The system's stochastic dynamics is shown to lead to the emergence of entangled rotating spiral waves. While the spirals’ wavelength and spreading velocity is demonstrated to be accurately predicted by a (deterministic) complex Ginzburg-Landau equation, their entanglement results from the inherent stochastic nature of the system. These findings and our methods have important applications for understanding the formation of noisy patterns, e.g. in ecological and evolutionary contexts, and are also of relevance for the kinetics of (bio)-chemical reactions.     

A New Lanternshark <Emphasis Type="Italic">Etmopterus splendidus</Emphasis> from the East China Sea and Java Sea

A new species of the lanternshark Etmopterus splendidus is described. This new species is distinguished from the congeners by the combination of the following characters: distance from snout tip to 1st dorsal spine much less than distance from the spine to upper caudal origin; caudal fin short, much less than head length; dermal denticles on lateral side of trunk with very small, erect thornlike, conical crowns, those on trunk arranged in regular longitudinal rows, and distinctly arranged on interdorsal area and on lateral trunk of interspace between 2nd dorsal and caudal, but not arranged in regular longitudinal rows on dorsal surface of interorbital and o abdomen; color in life purplish-black above and with inconspicuous bluish-black flank marks and three other bluish-black marks at base of caudal fin and along its axis; shape of flank marks narrow anterior to, but broader posterior to pelvic fins.     

Structural basis of hierarchical multiple substates of a protein. II: Monte Carlo simulation of native thermal fluctuations and energy minimization

Conformational fluctuations in a globular protein, bovine pancreatic trypsin inhibitor, in the time range between picoseconds and nanoseconds are studied by a Monte Carlo simulation method. Multiple energy minima are derived from sampled conformations by minimizing their energy. They are distributed in clusters in the conformational space. A hierarchical structure is observed in the simulated dynamics. In the time range between 10(-14) and 10(-10) seconds dynamics is well represented by a superposition of vibrational motions within an energy well with transitions among minima within each cluster. Transitions among clusters take place in the time range of nanoseconds or longer.     

Growth-Promoting Therapies May Be Useful In Short Stature Patients With Nonspecific Skeletal Abnormalities Caused By Acan Heterozygous Mutations: Six Chinese Cases And Literature Review

ObjectiveThere are numerous reasons for short stature, including mutations in osteochondral development genes. ACAN, one such osteochondral development gene in which heterozygous mutations can cause short stature, has attracted attention from researchers in recent years. Therefore, we analyzed six cases of short stature with heterozygous ACAN mutations and performed a literature review.MethodsClinical information and blood samples from 6 probands and their family members were collected after consent forms were signed. Gene mutations in the probands were detected by whole-exome sequencing. Then, we searched the literature, performed statistical analyses, and summarized the characteristics of all reported cases.ResultsWe identified six novel mutations in ACAN: c.1411C>T, c.1817C>A, c.1762C>T, c.2266G>C, c.7469G>A, and c.1733-1G>A. In the literature, more than 200 affected individuals have been diagnosed genetically with a similar condition (height standard deviation score &lsqb;SDS] -3.14 ± 1.15). Among affected individuals receiving growth-promoting treatment, their height before and after treatment was SDS -2.92 ± 1.07 versus SDS -2.14 ± 1.23 (P<.001). As of July 1, 2019, a total of 57 heterozygous ACAN mutations causing nonsyndromic short stature had been reported, including the six novel mutations found in our study. Approximately half of these mutations can lead to protein truncation.ConclusionsThis study used clinical and genetic means to examine the relationship between the ACAN gene and short stature. To some extent, clear diagnosis is difficult, since most of these affected individuals’ characteristics are not prominent. Growth-promoting therapies may be beneficial for increasing the height of affected patients.Abbreviations: AI = aromatase inhibitor; ECM = extracellular matrix; GnRHa = gonadotropin-releasing hormone analogue; IQR = interquartile range; MIM = Mendelian Inheritance in Man; PGHD = partial growth hormone deficiency; rhGH = recombinant human growth hormone; SDS = standard deviation score; SGA = small for gestational age; SGHD = severe growth hormone deficiency     

Palatal growth inMacaca nemestrina

A longitudinal study of the palatal growth of 80 male and 81 femaleMacaca nemestrina reveals that male growth rates are greater than female growth rates. In addition, both sexes demonstrate a similar pattern of palatal growth although growth rate differences between sexes probably reflect the larger canine/P₃ apparatus and overall body size of males. Growth of the premaxillary and postmaxillary palatal segments appear to be independent of one another. Palatal growth spurts, obvious in males, exist for two palatal length dimensions. The maxillary tuberosity growth center is postulated to account for more size dimorphism between sexes than the premaxilla growth center.     

Minimal models of growth and decline of microbial populations

Dynamics of growth and decline of microbial populations were analysed and respective models were developed in this investigation. Analysis of the dynamics was based on general considerations concerning the main properties of microorganisms and their interactions with the environment which was supposed to be affected by the activity of the population. Those considerations were expressed mathematically by differential equations or systems of the equations containing minimal sets of parameters characterizing those properties. It has been found that: (1) the factors leading to the decline of the population have to be considered separately, namely, accumulation of metabolites (toxins) in the medium and the exhaustion of resources; the latter have to be separated again into renewable (‘building materials’) and non-renewable (sources of energy); (2) decline of the population is caused by the exhaustion of sources of energy but no decline is predicted by the model because of the exhaustion of renewable resources; (3) the model determined by the accumulation of metabolites (toxins) in the medium does not suggest the existence of a separate ‘stationary phase’; (4) in the model determined by the exhaustion of energy resources the ‘stationary’ and ‘decline’ phases are quite discernible; and (5) there is no symmetry in microbial population dynamics, the decline being slower than the rise. Mathematical models are expected to be useful in getting insight into the process of control of the dynamics of microbial populations. The models are in agreement with the experimental data.     

Clinical and molecular diagnosis of Miller-Dieker syndrome.

We report results of clinical, cytogenetic, and molecular studies in 27 patients with Miller-Dieker syndrome (MDS) from 25 families. All had severe type I lissencephaly with grossly normal cerebellum and a distinctive facial appearance consisting of prominent forehead, bitemporal hollowing, short nose with upturned nares, protuberant upper lip, thin vermilion border, and small jaw. Several other abnormalities, especially growth deficiency, were frequent but not constant. Chromosome analysis showed deletion of band 17p13 in 14 of 25 MDS probands. RFLP and somatic cell hybrid studies using probes from the 17p13.3 region including pYNZ22 (D17S5), pYNH37 (D17S28), and p144-D6 (D17S34) detected deletions in 19 of 25 probands tested including seven in whom chromosome analysis was normal. When the cytogenetic and molecular data are combined, deletions were detected in 21 of 25 probands. Parental origin of de novo deletions was determined in 11 patients. Paternal origin occurred in seven and maternal origin in four. Our demonstration of cytogenetic or molecular deletions in 21 of 25 MDS probands proves that deletion of a "critical region" comprising two or more genetic loci within band 17p13.3 is the cause of the MDS phenotype. We suspect that the remaining patients have smaller deletions involving the proposed critical region which are not detected with currently available probes.