THE RATE OF GROWTH OF THE DAIRY COW : IV. GROWTH AND SENESCENCE AS MEASURED BY THE RISE AND FALL OF MILK SECRETION WITH AGE.

Data are presented on the effect of age on milk secretion in the dairy cow. From the age when milk secretion usually begins (2 years) to the age when maximum body weight is reached (about 8 years) increase of milk secretion and increase of body weight with age follow the same exponential course, which is the course of a monomolecular reaction of chemistry. After this age, unlike body weight which remains practically constant, milk secretion declines exponentially, that is, the course of decline follows the course of decline of a monomolecular reaction. The whole course of milk secretion with age was therefore found to follow approximately the course of two simultaneous, consecutive, monomolecular reactions. This is taken to mean that growth and senescence go on simultaneously from the beginning to the end of life, and that each follows an exponential law with age; and therefore perhaps that the course of the two processes are limited by two consecutive chemical reactions.     

THE KINETICS OF SENESCENCE

The course of decline of vitality with age due to the process of senescence, when not complicated by the process of growth, follows a simple exponential law; that is the degree of vitality or of senescence (defining vitality as the reciprocal of senescence) at any moment is, regardless of age, a constant percentage of the degree of vitality or senescence of the preceding moment. This exponential law is the same as the law of monomolecular change in chemistry. During the actively growing period of life the index of vitality rises, due to the process of growth and the course of vitality in the case when the growing period is included in the vitality curve, follows a rising and falling course. This rising and falling course may often be represented by an equation containing two exponential terms which is practically the equation used to represent the course of accumulation and disappearance of a substance as the result of two simultaneous consecutive monomolecular chemical reactions.     

THE RATE OF GROWTH OF THE DAIRY COW : III. THE RELATION BETWEEN GROWTH IN WEIGHT AND INCREASE OF MILK SECRETION WITH AGE.

It is shown that from 2 years, the age when milk secretion usually begins, to 9 years, the age of maximum body weight, the increase of milk secretion with age follows the course of growth in body weight— both can be accurately represented by the equation of a monomolecular chemical reaction having a velocity constant of approximately the same numerical value. While increase in milk secretion and increase in body weight with age follow the same course, it is shown that increasing body weight contributes only about 20 per cent to increasing milk secretion with age. The fact that milk secretion and body weight follow the same course, even though they are largely independent of each other indicates that increase in body weight is a good measure of growth of the dairy cow; this fact also shows that the increase of milk secretion with age may be used as a measure of growth. The fact that milk secretion, like body weight, follows the course of a chemical reaction, adds further support to the theory that growth is limited by a chemical reaction.     

THE RATE OF SENESCENCE OF THE DOMESTIC FOWL AS MEASURED BY THE DECLINE IN EGG PRODUCTION WITH AGE

Data are presented showing that the course of decline of egg production with age in the domestic fowl from the time laying begins up to and including 8 years follows an exponential law, that is, each year''s egg production is a constant percentage of the preceding year''s production (88 per cent in the group of fowl studied). Since the exponential law is the same as the law of monomolecular change in chemistry, and since the course of egg production with age may be taken as an index of the course of senescence of organs, or tissues limiting egg production, it is suggested that this exponential law of egg production substantiates the idea that senescence is a physicochemical process the course of which is limited by a chemical reaction. It is shown that the exhaustion of the oocytes is not likely to be the factor limiting the course of egg production.     

A NOTE ON THE SIMILARITIES BETWEEN THE CURVES OF GROWTH AND OF REGENERATION

The curves of growth and of regeneration follow the same course, and can be represented by the same exponential equation. This is taken to substantiate the theory that growth and regeneration are essentially identical processes governed by the same laws. A common peculiarity of the curves of growth and of regeneration is that during a short period in the early stages of regeneration and of growth, the apparent observed speed of these processes seems to be relatively slow. As a result, the curve of the fitted equation cuts the time axis not at zero, the beginning of growth or regeneration, but somewhat later. Data on regeneration are cited indicating that the initial slow phase of regeneration is due to the time required for the formation of a cap of embryonic cells which serves as a basis for the more active later regeneration; in other words, to qualitative growth which cannot be expressed in terms of quantitative units. It is suggested that the apparent initial slow phase of growth of the individual from the fertilized egg is due to a similar qualitative growth. It is suggested that if the initial qualitative changes could be converted into some common unit with the subsequent quantitative changes, the apparent initial lag would disappear, and the exponential equation representing the course of these processes would then be the same as the equation used to represent the course of a monomolecular chemical reaction. Certain implications of this reasoning are discussed in the text.     

THE RATE OF GROWTH OF THE DAIRY COW : II. GROWTH IN WEIGHT AFTER THE AGE OF TWO YEARS.

An extensive amount of data is presented on the growth in weight of the dairy cow from 2 to 17 years of age, covering practically the entire duration of life. The data show that after the age of 2 years the rate of growth declines in a non-cyclic manner. The course of decline in growth follows the course of decline of a monomolecular chemical reaction; that is, the percentage decline in growth with age is constant.     

THE EFFECT OF GESTATION ON THE RATE OF DECLINE OF MILK SECRETION WITH THE ADVANCE OF THE PERIOD OF LACTATION

1. Data are presented showing that the course of decline of milk secretion with the advance of the period of lactation in farrow cows follows the course of decline of a monomolecular chemical reaction, that is each month''s milk production is a constant percentage of the production of the preceding month (94.77 per cent in the case of the cow under consideration), from which it is inferred that milk secretion is limited by a chemical reaction initiated at parturition, and declining with the decrease of the concentration of the limiting substance as it is transformed into milk. 2. Data are presented showing that the decline in milk secretion due to pregnancy is related to the increase in weight of gestating animals, from which it is inferred that growth of the fetus is in part, at least, responsible for the decline in the milk flow due to the demand of the fetus for nutrients to support its life processes.     

TIME RELATIONS OF GROWTH : III. GROWTH CONSTANTS DURING THE SELF-ACCELERATING PHASE OF GROWTH.

Growth curves consist, in all cases, of two major segments. The first major segment is, in the case of higher animals and plants, made up in turn of several (probably five) shorter segments during each of which growth takes place at a constant percentage rate. The transitions between the successive stages are abrupt, the abruptness being of the order of metamorphosis in cold blooded animals. It has been made clear in the first paper of this series that the time rate of growth following the major inflection declines at a constant percentage rate. The junction between the two major segments occurs at puberty in animals and flowering in plants. The two major segments are not symmetrical about the major inflection. The slope of the segment following the inflection is always less than the slope of the segment preceding the inflection. The major inflection does not occur in the center of the growth curve. The instantaneous rate of growth at the beginning of growth is of the order of 100–200 per cent per day (i.e. the body weight is doubled in from 7 to 17 hours). It may be mentioned that 2 months after conception the rate of growth in man is only 8 per cent per day. This is contrary to all the published statements. Thus, Minot concluded that growth begins at 1000 per cent per day; Jackson concluded that in man, growth during the 1st month takes place at 57.5 million per cent per month; during the 2nd month 990 per cent per month; during the 3rd month 390 per cent per month (8 per cent per day is only 240 per cent per month). The reason for the discrepancy between the values derived, by the method adopted by the writer, and the values given in the literature is explained by Fig. 1.     

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.     

CRYSTALLINE TRYPSIN : V. KINETICS OF THE DIGESTION OF PROTEINS WITH CRUDE AND CRYSTALLINE TRYPSIN

The rate of digestion, as determined by the increase in non-protein nitrogen or formol titration, of casein, gelatin, and hemoglobin with crystalline trypsin preparations increases nearly in proportion to the concentration of protein, but with crude pancreatic extract the rate of digestion becomes independent of the protein concentration in concentrations of more than 2.5 per cent. With both enzymes the rate of digestion of mixtures of 5 per cent casein and gelatin is greater than would be expected from the point of view of a compound between enzyme and substrate. The rate of digestion of 5 per cent casein in the presence of 5 per cent gelatin is exactly the same as that of 5 per cent casein alone. This result is obtained with both enzymes. The digestion of casein with crude trypsin follows the course of a monomolecular reaction quite closely while with purified trypsin the velocity constant decreases as the reaction proceeds. In the case of hemoglobin the monomolecular velocity constant decreases with both purified and crude enzyme. When the reaction is followed by changes in the viscosity of the solution the abnormal effect of changing substrate concentration disappears and the reaction is in fair agreement with the monomolecular equation. The results as a whole indicate that the abnormalities of the reaction are due to the occurrence of several consecutive reactions rather than to the formation of a substrate enzyme compound.     

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.     

THE INFLUENCE OF ALCOHOL UPON THE GROWTH OF SEEDLINGS

In this paper it is shown that if the dry seeds of the cantaloupe (Cucumis melo) are soaked for 3 hours in solutions of ethyl alcohol of concentration ranging from 2 to 16 per cent by volume, and then germinated and grown in distilled water in the dark, the total growth attained is greater by amounts ranging from 9 to 35 per cent than is that made by seeds treated in every way identically except that they are initially soaked in distilled water instead of alcohol. It is shown that this result is not due simply to differences in osmotic pressure in the different alcohol solutions. It is probably due to a simple selective action of the alcohol which eliminates the constitutionally weak and defective seeds.     

TIME RELATIONS OF GROWTH : II. THE EQUIVALENCE OF AGE IN MAMMALS ESTIMATED ON THE BASIS OF THEIR GROWTH CONSTANTS.

The numerical values of the growth constants given in the preceding paper of this series are utilized for determining equivalence of growth age and growth weight in several animal forms. The results are presented in the form of two age-equivalence tables and fifteen age-equivalence and weight-equivalence charts.     

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 NATURE OF THE FACTORS WHICH DETERMINE THE SEQUENCE OF GROWTH-CYCLES AND ITS RELATIONSHIP TO THE DIFFERENTIATION OF TISSUES

1. It has previously been shown by the author and many others that growth, in animals and plants, is an autocatalysed process. In animals it is usual to find that growth occurs in several superimposed autocatalytic cycles. In many cases, in plants and animals, especially if the cycle is one which occupies a large proportion of the growing period, it is found that the velocity-constant of the autocatalysed monomolecular formula falls off as growth proceeds, at first rapidly and later more slowly. 2. It has previously been shown by the author that the fall of the velocity-constant of growth, in the white mouse, is directly proportional to the fall of the nucleo-cytoplasmic ratio, determined by the chemical method of Le Breton and Schaeffer. If we assume this relationship to be generally applicable to the growth of animals and plants, then the following additional conclusions may be deduced, without calling in the aid of any other assumption:— 3. The increase of cytoplasm in any given cycle of growth is proportional to the concurrent increase of nuclear material. 4. The growth of cytoplasm takes place in accordance with a monomolecular formula in which the velocity-constant varies directly as the mass of the nucleus. If we superadd to these facts and deductions the hypothesis that each growth-cycle represents the growth of a separate group of cells within the animal, then the additional conclusions follow:— 5. That the cells which participate in the growth composing any cycle have initially lower nucleo-cytoplasmic ratios than the cells which participated in the preceding cycles. 6. That cells of large nucleo-cytoplasmic ratios in a multicellular animal inhibit the growth of cells which possess smaller ratios. 7. These conclusions collectively imply that the nucleus plays a predominant role in determining the development of the cell in which it resides.     

PHOTOCHEMISTRY OF VISUAL PURPLE : I. THE KINETICS OF THE DECOMPOSITION OF VISUAL PURPLE BY LIGHT.

1. Visual purple solutions are prepared under such conditions that the bleaching reaction is irreversible. 2. A method is described for the colorimetric estimation of very small quantities of visual purple. By this means the kinetics of the bleaching reaction are investigated. 3. The results show that the course of the decomposition follows that of a monomolecular reaction, without any measurable period of induction or after effect.     

THE RHEOLOGY OF THE BLOOD. V

A study has been made of those proteins which might offer exceptions to the law that the fluidity of a protein solution is a linear function of the volume concentration; viz., egg albumin, serum albumin, pseudoglobulin, euglobulin, gelatin, and sodium caseinogenate. Solutions of egg albumin below 20 per cent by weight obey the above law but somewhat below 30 per cent the fluidities begin to be too high, presumably due to the contribution to the fluidity made by the deformation of the particles as they come into contact, as the fluidity approaches zero. The fluidity of serum albumin solutions shows a similar behavior, being exceptional above 15 per cent in weight. Pseudoglobulin and euglobulin give fluidity-concentration curves (Fig. 4) which are linear up to about 2.5 per cent each in a total range of 20 and 14 per cent respectively. From this singular point both compounds show a second range which is linear. Pseudoglobulin is the only substance whose solutions seem to show a third linear range. We have also used the data of Chick and Martin for sodium caseinogenate and found evidence for two linear régimes. It is desirable at this time to call attention to the measurements of the flow of glycogen solutions by Botazzi and d''Errico (14) which in Fluidity and See PDF for Structure plasticity, page 207, are expressed in rhes. The data show two linear fluidity curves of different slopes. In this case it was definitely known that the data for each curve were measured with different viscometers which suggested the possibility of an error in viscometry entering in to confuse the issue. We have no suspicions as to the reliability of the data studied in this paper; we only wish to caution the readers that our hypotheses based on these data must be regarded with due reserve until confirmed. We have found a formula (11) based on the supposed linear relation between logarithmic fluidities and concentration which is convenient to use within the range, but close examination reveals that it does not reproduce the data for the higher concentrations at 25° nor does it permit extrapolation to pure water It is not realistic enough because it does not contemplate any change of régime in going from viscous to non-Newtonian or plastic flow. The formula does not apply to any other of the proteins studied in this paper nor to the great majority of proteins already reported as following the linear law. These are serious objections. We have therefore offered as an alternative a simple formula (24) according to which the fluidities are additive in the viscous régime. When the emulsoid particles approach close packing, they are deformed and this deformation contributes to the flow and the fluidity volume concentration curve is again linear. In fact, there may be one or more additional changes of régime.     

GROWTH OF THE EMBRYO OF GINKGO BILOBA UNDER EXPERIMENTAL CONDITIONS. III. GROWTH RATES OF ROOT AND SHOOT UPON MEDIA ABSORBED THROUGH THE COTYLEDONS

Ball , Ernest . (North Carolina State Coll., Raleigh.) Growth of the embryo of Ginkgo biloba under experimental conditions. III. Growth rates of root and shoot upon media absorbed through the cotyledons. Amer. Jour. Bot. 46(2) : 130-139. Illus. 1959.—Mature embryos of Ginkgo biloba were grown by inserting the cotyledons into agar medium containing one of the naturally-occurring sugars of the seed. These sugars were utilized at 1, 2, 4, 8 or 16% (w/v). Root growth was best on the sugar-mineral-water media and occurred at its maximum in media containing 4% sugar (ca. 0.25 M). The sugars may be listed as follows in order of decreasing effectiveness in root growth: glucose, sucrose, levulose, raffinose, galactose. Since very different growth rates of roots occurred on media of the same osmotic values when the latter were determined by the various sugars, it is suggested that the root utilized the entire sugar molecule as a unit whether it was mono-, di-, or trisaccharide. Such media were not effective in supporting shoot growth. Outstanding growth of shoots was obtained when either glutamine or coconut milk was placed in the culture medium. It is concluded that root growth can occur at a substantial rate by utilizing sugar and manufacturing organic nitrogen from nitrates. Shoot growth, in contrast, appears to require sources of organic nitrogen such as may be furnished by glutamine or coconut milk. These phenomena are thought to constitute fundamental differences between the metabolism of root and shoot of this embryo. Mannitol caused severe inhibition of growth of both root and shoot. It is probably toxic to this embryo. Indoleacetic acid caused severe inhibitions of growth of both root and shoot at all except the lowest concentrations utilized.     

Control of Leaf Growth and its Role in Determining Variation in Plant Growth Rate from an Ecological Perspective

Abstract: Plants vary widely in their relative growth rate (RGR), be it dependent on environmental conditions or due to their genetic background. In a comparison of the RGR of grasses growing under different environmental conditions, variation in RGR tends to correlate with that in the leaf elongation rate (LER). When different species or genotypes thereof are compared under identical growing conditions, variation in LER may or may not correlate with that in RGR, depending on the comparison. However, since RGR is described by an exponential equation, whereas LER is mainly a linear process, we conclude that any correlation between RGR and LER must be fortuitous. That is, exponential growth must be due to increases with time in plant traits such as 1) leaf dry mass per unit leaf length invested per unit time, and/or 2), i.e., the total LER of all the growing leaves at one point in time. The latter can be achieved as follows: 1) each subsequent leaf has a higher LER than the preceding one; 2) leaves appear at an increasing rate; 3) the duration of the process of leaf elongation increases for subsequent leaves. In this review, we only explore possible factors that account for changes in with time, in different genotypes and under different environmental conditions. Inherent variation in LER of individual leaves and variation due to environmental factors may reflect variation in the rate of cell division and/or in cell elongation.     

瓣结鱼的年龄和生长的研究

瓣结鱼全年均可形成新轮,新轮出现高峰期为４月。其生长特点是属于均匀生长类型,体长与鳞长呈直线关系,体长和体重指数关系,回归求得Ｂｅｒｔａｌａｎｆｆ个体生长方程参数Ｌ∞,Ｗ∞,Ｋ,Ｔ０分别为７０,４３,５９６１．５０,０．２２３１,０．０２２４,体重生长拐点年龄为４．９５龄,该拐点体重为１７６８．２３ｇ,瓣结鱼第１,２龄生长较为迅速。