THE ANALYSIS OF THE GROWTH OF THE NORMAL WHITE MOUSE INTO ITS CONSTITUENT PROCESSES

1. The several growth-cycles which are distinguishable in the growth of an animal or plant are mutually independent in that they do not share a common catalyser. 2. The growth of the white mouse has been shown to consist of three autocatalytic processes and one "linear process" of weight-accretion. The parameters of these processes have been evaluated for one strain and generation of mice. 3. The first and most extensive autocatalytic process is asymmetrical, being defined by an equation of the type: See PDF for Equation The second and third cycles, which are more rapid and do not begin to affect the growth of the animal until a later stage of development, are symmetrical, being defined by equations of the type: See PDF for Equation 4. The amplitude of the first autocatalytic growth-cycle in the mouse is almost the same in males and females, but the moment of maximum growth-velocity in the female anticipates that in the male, the velocity constant is smaller in the female, and the asymmetry estimated by the magnitude of the constant B, is greater in the female than in the male. 5. The amplitude of the second cycle is almost the same in males and females, but data are as yet lacking which would enable us to ascertain whether the velocity-constant and moments of maximum growth-velocity in this cycle differ in the two sexes or not. 6. The amplitude of the third cycle is much less in the female than in the male, and this difference of amplitude almost wholly accounts for the difference of adult weight in the two sexes. The velocity-constant of the third cycle is, however, greater in the female than in the male. Maximum growth velocity due to this cycle is attained at very nearly the same age in both sexes. 7. The origin of asymmetry in autocatalytic growth-processes is discussed. It is pointed out that asymmetry might originate in a progressive diminution of the velocity-constant. If this is the origin of the asymmetry of the first growth-cycle in the mouse, then it is shown that the velocity constant of autocatalysis in this cycle must be very nearly proportional to the nucleo-cytoplasmic ratio, as estimated by the chemical method of Le Breton and Schaeffer. 8. It is pointed out that no reliable measure of senescent loss of weight is available at present. It is shown that removal or decay of those conditions which initially maintain the separability of the growth-cycles which collectively constitute the growth of the white mouse would necessarily result in loss of weight.     

THE RATE OF GROWTH OF THE DOMESTIC FOWL

This paper points out the fact that the growth period of the domestic fowl is analogous to that of the mammal, being composed of three, or perhaps four, cycles; two of these cycles are postembryonic with maxima at about 8 and 18 weeks varying somewhat with the breed and two or at least one, are embryonic with maxima at 11 to 12 and 15 to 16 days of age. Hatching occurs during the first part of the second or third cycle resembling in this respect the guinea pig rather than the mouse. The velocity curves of each of these cycles are similar to and can be represented by the equation of an autocatalytic monomolecular reaction.     

THE RATE OF OVULATION IN THE DOMESTIC FOWL DURING THE PULLET YEAR

The rate of ovulation of the domestic fowl may be expressed by the equation of an autocatalytic chemical reaction. This is not surprising in view of the fact that the rate of growth may also be expressed by such an equation, and that the rate of ovulation is probably an index of the growth of the eggs. This brings the phenomenon of ovulation in the hen under the general subject of growth, and substantiates the generality and the probability of the hypothesis that growth, or at any rate the limiting factor of growth, is an autocatalytic reaction.     

THE RATE OF GROWTH OF THE DAIRY COW : EXTRAUTERINE GROWTH IN WEIGHT.

The growth period of the Jersey and Holstein cows is made up of at least three cycles, two extrauterine cycles with maxima at about 5 and 20 months of age, and one intrauterine cycle, the maximum of which has not yet been determined. The equation of an autocatalytic monomolecular reaction was found to give very good results when applied to the cycle having its maximum at about 5 months of age. The values obtained from this equation when applied to the cycle having the maximum at about 20 months of age were higher than the observed values probably due to the retarding effect of pregnancy and lactation on growth.     

温度对萼花臂尾轮虫卵的发育、种群增长和生产量的影响

1981—1983年,在不同的培养温度下,观察了萼花臂尾轮虫(Brachionus calyciflorus)卵的发育时间、种群的增长并用3种不同方法测算生产量。在5—30℃的培养温度下,轮虫卵的发育时间(D)随温度(T)升高而缩短,其曲线迴归方程为: LnD=2.0539+0.1097LnT-0.3046(LnT)2 在10,15,20,25℃的培养温度下,从休眠卵孵化出来的孤雌生殖雌体,其繁殖的种群增长曲线都呈“S”形,或称逻辑斯蒂曲线(Logistic curve)。不同的温度,种群达到高峰所需的时间有所不同,温度高者短,低者长;容纳量(carrying capacity)却随温度增加而有所增加。用线性和指数方法计算轮虫种群的生产量所得的结果相似;而与世代时间方法计算所获得的结果相比,差距很大。这种差距随着温度增加而增加。根据本文的研究结果和文献中报道的数据,获得了在0.6—35.2℃温度范围内,卵的发育时间(D)与温度(T)之间的迴归方程: LnD=2.1869-0.1919LnT-0.2218(LnT)2       

ON THE NATURE OF THE EQUATION FOR GROWTH PROCESSES

An analysis of the growth curves of a cladoceran for one adult instar at each of two temperatures is made by comparing the apparent gains or losses in time when the animals are transferred from one of these temperatures to the other during the course of the developmental period. Since the curves for the two temperatures when brought together at their end-point do not coincide, the equation used to describe growth must have at least two velocity constants unequally affected by changes in temperature.     

Competition between Primary Nucleation and Autocatalysis in Amyloid Fibril Self-Assembly

Kinetic measurements of the self-assembly of proteins into amyloid fibrils are often used to make inferences about molecular mechanisms. In particular, the lag time—the quiescent period before aggregates are detected—is often found to scale with the protein concentration as a power law, whose exponent has been used to infer the presence or absence of autocatalytic growth processes such as fibril fragmentation. Here we show that experimental data for lag time versus protein concentration can show signs of kinks: clear changes in scaling exponent, indicating changes in the dominant molecular mechanism determining the lag time. Classical models for the kinetics of fibril assembly suggest that at least two mechanisms are at play during the lag time: primary nucleation and autocatalytic growth. Using computer simulations and theoretical calculations, we investigate whether the competition between these two processes can account for the kinks which we observe in our and others’ experimental data. We derive theoretical conditions for the crossover between nucleation-dominated and growth-dominated regimes, and analyze their dependence on system volume and autocatalysis mechanism. Comparing these predictions to the data, we find that the experimentally observed kinks cannot be explained by a simple crossover between nucleation-dominated and autocatalytic growth regimes. Our results show that existing kinetic models fail to explain detailed features of lag time versus concentration curves, suggesting that new mechanistic understanding is needed. More broadly, our work demonstrates that care is needed in interpreting lag-time scaling exponents from protein assembly data.     

The autocatalytic growth model

Summary Because of the important role which the autocatalytic or logistic equation has played in determining the direction of a good deal of research both in demography and in the study of individual growth phenomena, a critical and comparative evaluation of those leading ideas inRobertson's (1923) book which pertain to this equation and of some of the criticisms levelled against it seemed to be of interest. The present paper shows that, contrary to common belief,Robertson did not really assume that the autocatalytic reactions to which he compared growth processes, took place in closed systems (viz., cells). On the other hand, he does not seem to have found a satisfactory representation of how the growth phenomena of the individual cells in an organism might interact to yield the overall growth of the organism as a whole. Nor is the manner in which he made his equation account for the openness of the individual cells free from possible criticism. An alternative equation is here proposed, which will be discussed in another paper. The properties of the solutions of this equation are such that the autocatalytic theory might never have gained a foothold if this, more realistic, equation would have been the object of the initial studies.This research was in part supported by NIH training grant GM-678.     

Growth velocities of branched actin networks

The growth of an actin network against an obstacle that stimulates branching locally is studied using several variants of a kinetic rate model based on the orientation-dependent number density of filaments. The model emphasizes the effects of branching and capping on the density of free filament ends. The variants differ in their treatment of side versus end branching and dimensionality, and assume that new branches are generated by existing branches (autocatalytic behavior) or independently of existing branches (nucleation behavior). In autocatalytic models, the network growth velocity is rigorously independent of the opposing force exerted by the obstacle, and the network density is proportional to the force. The dependence of the growth velocity on the branching and capping rates is evaluated by a numerical solution of the rate equations. In side-branching models, the growth velocity drops gradually to zero with decreasing branching rate, while in end-branching models the drop is abrupt. As the capping rate goes to zero, it is found that the behavior of the velocity is sensitive to the thickness of the branching region. Experiments are proposed for using these results to shed light on the nature of the branching process.     

ON THE RELATION BETWEEN TOXICITY,RESISTANCE, AND TIME OF SURVIVAL,AND ON RELATED PHENOMENA

1. A relation between toxicity, resistance, and time of survival has been derived on the basis of the assumption that the time is a function of a parameter which is the difference between the toxicity and the resistance. Toxicity and resistance act like forces which can maintain an equilibrium-like (or stationary) state. If the equilibrium is upset, the time at which the event (death) occurs is proportional to the logarithm of the difference between toxicity and resistance. 2. It was found that if values proportional to the resistance are calculated with the proposed equation and the percentage mortality plotted against them (instead of against the time as is usual) symmetrical curves are obtained even though the corresponding mortality-time curves are asymmetrical. Assuming that the resistance varies like an error, that is, according to probability rules, theoretical mortality-time curves, similar to the experimental curves, can be constructed from the proposed equations. 3. In the case of a toxic agent acting on a unicellular organism suspended in solution, the toxicity is proportional to the adsorbed amount of the agent, as calculated with the aid of the Langmuir equation. In small concentration ranges the toxicity can be taken as approximately proportional to the concentration. 4. The variation of the temperature affects mainly the constant a which is a function of the temperature similar to that of the velocity constant of a chemical reaction (Arrhenius'' law). 5. The proposed equation has been tested in four different combinations of the variables, concentration, resistance, time, and temperature. The agreement with the experiments is satisfactory. 6. Any noxious agent acting on a unicellular organism may be characterized by three constants: r, the resistance, which is the threshold value at which the agent is still fatally toxic for the organism; a, the reciprocal of the rate constant determining the specific rate (that is, the time corresponding to a difference of 1 between the toxicity and the resistance); and finally the constant γ of the function representing the relation between toxicity and concentration.     

THE NATURE OF THE GROWTH RATE

1. The growth rate of organisms may be considered as a chemical reaction which gives the mature organism as its end-product. The organism grows at a definite rate which is, at any moment, proportional to the amount of growth yet to be made. 2. Shoots of young pear trees measured at weekly intervals during the growing season showed a rate similar to that of an autocatalytic reaction. 3. Young walnut trees showed distinct cycles of growth in a single season, but the growth in each cycle proceeded at a rate corresponding to an autocatalytic reaction. 4. The growth rate follows a definite, quantitative course though judged by different criteria. Data are presented for maize in which green weight, dry weight, and height of the plant are used. Data for cattle show that either weight or height of the animal may be used as a criterion.     

Inactive proteinases in silkmoth moulting gel

The moulting gel of silkmoths lacks proteolytic activity but contains an inactive form of the proteinases which are later found in the moulting fluid. These inactive enzymes are activatable in vitro by dilution, activation proceeding most rapidly at low ionic strength. Activation proceeds as a first-order process and is not autocatalytic. Approximately the full amount of proteinases ultimately found in moulting fluid are already present in the gel. Moulting gel does not inhibit the active proteinases of moulting fluid; moreover, the proteolytic activity elicited by dilution of the moulting gel does not disappear upon reconcentration. These observations suggest that the proteinases in moulting gel are not inhibited by a stable, dissociable inhibitor; they may be present either as compartmentalized active enzymes or as proenzymes. Several possible mechanisms for the in vivo activation at the time of gel to fluid transformation are discussed.     

Transport theory for growing cell populations

The partial differential equation that describes the growth of cell populations whose maturation rate is random is developed. The equation resembles that used in classical transport theory but mitotic boundary conditions and the restriction of the maturation rate to non-negative values brings out new features and new problems. This is a generalization of a previously published formulation in which cells could make transitions at random between only two maturation velocities: a characteristic velocity and zero. Growth rates, cycle time distributions and pulsed labeled mitotic curves are calculated for a simple choice of parameters. A numerical algorithm that is suited to the solution of the transport equation is given.     

OBSERVATIONS ON THE DISTRIBUTION,EMERGENCE AND BEHAVIOUR OF CENTRAL AFRICAN CHAOBORIDAE

SUMMARY

The distribution of four species of Chaoboras over selected parts of Zimbabwe is given. The effect of temperature on the duration of the larval life cycle is discussed in relation to the generation time and the lunar periodicity of the adult emergence period. There were apparently two generations of larvae present in the habitat at any one time, although these generations were not distinct due to the variations in the time taken by the larvae to complete development at any temperature. The emergence was synchronized to the lunar cycle, but the actual moon phase at which emergence occurred was variable, as the two populations under observation both changed from new moon emergences to full moon emergences during the study. Some observations on the behaviour of adult Chaoboras edulis are given.     

THE TIME CURVE OF FACET DETERMINATION IN AN ULTRABAR STOCK OF DROSOPHILA MELANOGASTER

By a dissection of the data obtained by Driver on the effective periods at different temperatures in males and females of an ultrabar stock of Drosophila melanogaster it has been found that a symmetrical sigmoid curve satisfactorily describes the time course of the facet-determining reaction. Consequently the differences between members of the bar series in regard to this reaction do not represent merely developmental arrests of the process at some greater or lesser distance from a common upper asymptote, but the termination of the process is approached asymptotically. The velocity constant/temperature relation shows a discontinuity in the neighborhood of 21° which may be causally related to the change in the position of the effective period from the second to the third instar. The velocity constant apparently does not conform to the well known Arrhenius equation in its relation to temperature.     

The notion of the internal and external limitations of monotonic growth functions. A reformulation of the logistic equation

The boundary value (plateau) of non-periodic growth functions constitutes one of the parameters of various usual models such as the logistic equation. Its double interpretation involves either a limit of an internal or endogenous nature or an external environment-dependent limit. Using the autocatalytic model of structured cell populations (Buis, model II, 2003), a reformulation of the logistic equation is put forward and illustrated in the case of three cell classes (juvenile, mature, senescing). The agonistic component corresponds exactly to the only active fraction of the population (non-senescing mature cells), whereas the antagonistic component is interpreted in terms of an external limit (available substrate or source). The occurrence and properties of an external limit are investigated using the same autocatalytic model with two major modifications: the absence of competition (non-limiting source) and the occurrence of a maximum number of mitoses per cell filiation (Lück and Lück, 1978). The analysis, which is carried out according to the principle of deterministic cell automata (L-systems), shows the flexibility of the model, which exhibits a diversity of kinetic properties: shifts from the sigmoidal form, number and position of growth rate extremums, number of phases of the temporal structure. These characteristics correspond to the diversity of the experimental growth curves where the singularities of the growth rate gradient are often not accounted for satisfactorily by the usual global models.     

THE RATE OF KILLING OF CLADOCERANS AT HIGHER TEMPERATURES

In spite of obvious possible sources of disturbance, the "velocity of killing" of organisms at supranormal temperatures, properly determined, tends to adhere to the Arrhenius equation for relation to temperature. Over certain ranges of temperature the relationship between log velocity of killing and 1/T° abs. is linear. Interpreted as due to the thermal denaturing of protein, it is possible that differences between the temperature characteristics for the killing process in closely related forms may be suggestive in regard to the mechanism of the denaturing. The temperature limits within which the linear relationships appear may be classed among those temperature levels which are critical temperatures for protoplasmic organization.     

Kinetics ofd-aspartic acid release from rat cortical synaptosomes

A kinetic study has been made of the release ofd-aspartate from rat cortical synaptosomes following pre-loading with labelled D-aspartate, and the results compared to a previous study of the release of the acidic amino acids glutamate plus aspartate following pre-loading with labeledl-glutamate. Qualitatively, the results of the two studies are similar. The D-aspartate taken up during the preload period appears to be totally releasable. However, release is greatly increased by depolarizing media. The increased rate of release induced by increasing [K]_o is independent of the [Ca]_o, while veratrine-induced release is inhibited by [Ca]_o. Release is from more than a single compartment, since plots of the log₁₀ of the synaptosomal D-aspartate content (calculated from the label content) as a function of the incubation time are non-linear for all incubation solutions. In the previous study which utilizedl-glutamate pre-loading, the results were consistent with either a model consisting of two passive compartments (that is, synaptosomal content T as a function of time is given by Ae^–Kat+Be^–Kbt, in which A and B are compartment sizes, Ka and Kb are exchange constants, and t is incubation time) or a model consisting of one passive compartment (Ae^–Kat) and one saturated carrier compartment (T-Kbt, in which T=total content at zero time and Kb=maximal velocity). The present results withd-aspartate also give excellent fits to these models. However, there are some quantitative differences in the estimates of the compartment sizes and exchange constants, which are obtained by optimizing the fit of the data to the equation for each model. Although most of these quantitative differences appear to be minor, one difference between the two studies is of potential significance in interpretation of the results. In the glutamate study, all depolarizing media were found to reduce the exchange constant for the carrier mechanism, while in the present study, depolarizing media were found to increase the exchange constant, with the exception of veratrine-containing medium without calcium.     

A simple equation for describing the temperature dependent growth of free-floating macrophytes

Temperature is one of the most important factors determining growth rates of free-floating macrophytes in the field. To analyse and predict temperature dependent growth rates of these pleustophytes, modelling may play an important role. Several equations have been published for describing temperature responses of macrophytes and algae. But they are often complex or are only applicable in a limited range of temperatures. In this paper, we present a simple three-parameter equation for describing the temperature dependent growth rates of pleustophytes. The equation that we developed is tested using results from laboratory growth experiments conducted with three different species of pleustophytes (Lemna minor, Salvinia molesta and Azolla filiculoides). The equation is simple and demonstrates reliable fits (adjusted R² reaching from 0.89 to 0.95). Additionally, our equation primarily uses parameters of biological significance, resulting in estimates of useful cardinal temperatures (minimum and maximum).