If it could be shown that the determination of organ size in the animal body is not reached by an independent process, but that the magnitude of any one structure is determined by that of others, such evidence, if of a strictly quantitative nature, would tend to affirm the existence of a physical mechanism regulating the relative growth of body components. It is the object of this paper to present such evidence, and to describe a model from physical chemistry which lends a reasonable interpretation to the diversification observed in the ontogenetic and phylogenetic history of organ size.

There is no lack of data to support the proposition that the growth of parts tends to be a simple function of growth in the whole.

Donaldson (1898) and Donaldson with Shoemaker (1900) reported that in frogs of various sizes the lengths of femur, tibia, and foot exhibited constant specific relationships to the entire length of the animal. Such data may be expressed by the general equation

formula

where x and y represent the values of the structures compared, a is a constant descriptive of the relative initial sizes of x and y, and c is a correction for absolute magnitude.

Meek (1905) observed that the growth of body width in the flatfish bears the same straight-line relationship to total body length as that recorded by Donaldson.

Crozier (1912), and Crozier and Hecht (1914) investigated the correlation of weight, length, and other measurements in fishes. They observed that these relations could be expressed by the above equation. Crozier (1914) also showed that the same generalisation held true for the growth of a lamellibranch shell. Hecht (1916) compared eight species of fish from several different orders and concluded that in their external measurements the amphibia and pisces differed from the mammals since in the former the component parts all show an identical specific growth rate.

Some of these observations are of particular interest in that the value of the constant c approximates to zero, thereby simplifying the equation. A corresponding absence of this constant may be noted in the descriptions of “heterogonic growth.” Huxley (1924) made a quantitative study of the development of a chela in the fiddler crab, Uca pugnax. The enlargement of a chela is not an arithmetic but a logarithmic function of growth in the remainder of the body. If y represents chela weight and x the body weight this observation may be expressed thus :

formula

where a has the same significance as before and k is the “differential growth ratio” of the masses compared. It is apparent that when k equals unity the expression becomes, as in the previous paragraph, y = ax. Further investigations by Huxley (1927 a, b and c) have shown that this logarithmic relationship, “simple heterogony,” characterises the relative growth of mandible length to total length in certain insects, head width to abdomen width in ants, antler weight in relation to cleaned body weight in deer, and (so it is claimed) horn length to elytron length in the earwig, Forficula.

Pearsall (1927) has reported that in growing plants a similar relation obtains between stem weight and root weight in plants. The above equation accurately describes this relation in normal peas, etiolated peas, carrots, turnips and a dozen other cases. In the garden nasturtium the value of petiole length is associated with lamina diameter by the same equation.

Hersh (1928) has discovered that in the eye of Drosophila the numbers of facets in the dorsal (x) and ventral (y) lobes maintain a constant relation to each other such that y = xk and thus constitute another example of “heterogony” in growth relations as modified by temperature in the case of bar-eyed flies.

With reference to organogenesis in mammals, Robb (1928) has shown that if the logarithm of pituitary weight be plotted against the logarithm of cleaned body weight the points lie along a straight line. In other words, these data adhere to the equation y = axk. It is significant that the value of k remains constant throughout postnatal life in the rabbit. Moreover, k is identical in value for Flemish Giants (adult weight circa 6000 gm.), diminutive Polish (maximum weight about 1500 gm.), Flemish-Polish reciprocal hybrids—(about 3000 gm.), and other races of nondescript male rabbits of a lesser size than the latter. These data are reproduced in Fig. 1.

Fig. 1.

Weight of the pituitary body of the rabbit, in milligrams, against the “cleaned body weight “in hectograms (logarithmic plotting in both directions). Data represent individual observations; squares for Flemish Giants; triangles for Polish; and circles for their F1 hybrids.

Fig. 1.

Weight of the pituitary body of the rabbit, in milligrams, against the “cleaned body weight “in hectograms (logarithmic plotting in both directions). Data represent individual observations; squares for Flemish Giants; triangles for Polish; and circles for their F1 hybrids.

Owing to the storage of material in the intestinal tract of a rabbit all direct observations of the live body weight are subject to an error of 10 to 20 per cent. (Robb, 1928-29). As a more reliable basis of comparison I have used a “cleaned body weight,” obtained by subtracting from the live body weight the weight of stomach, intestine and contents. The error involved by thus neglecting the tissues of the alimentary tract is small (circa 4 per cent.) and approximately constant. It does not affect this study of relative organ size, but should be remembered in comparing these data with those of other investigators.

One hundred and fifty-two animals have been used for this study—sixty-seven Flemish Giants, forty-seven Polish, thirteen Flemish-Polish hybrids, and twenty-five rabbits of other genetic stocks which at maturity weigh between two and three thousand grams. These animals were all males and of selected ages from birth to senescence. This age distribution was such as to indicate for the entire post-natal life the gross relations of the endocrine organs in giant and pigmy rabbits.

The animals were bled to death after a brief administration of ether. With all possible dispatch the organs were dissected free of adipose and connective tissue and weighed in stoppered glass bottles, in the case of small structures, to tenths of a milligram.

The errors of dissection and weighing have been minimised by the fact that both were performed by a single individual—thus keeping the personal equation constant. The estimated error of each observation of adrenal weight is less than 2 per cent. ; for the thyroid, less than 3 per cent.; testes, 2 per cent. Errors of observation for thymus weight prior to its involution are of the same order of magnitude as for the testes. After the onset of degenerative changes, an irregular infiltration of adipose tissue invalidates the observed weight data. In this my histological studies confirm those of Marine, Manley and Baumann (1924).

This survey of pituitary bodies in Flemish Giant, hybrid, and pigmy rabbits led to the observations on growth in the adrenals, thyroid, thymus, and testes.

The logarithm of adrenal weight is a simple rectilinear function of the logarithm of cleaned body weight. This organ therefore exhibits simple heterogony throughout post-natal life.

The value of this function for the adrenal body shows racial difference, being very much greater in the Polish than in the Flemish (Fig. 2). No explanation of this fact is ventured. Drawings of serial sections were made with an Edinger projection apparatus (magnification 800) to ascertain the rôle of the cortex in the enlargement. Only four glands were measured, but these figures confirm the impression gained from other sectioned adrenals that no marked variation of medulla-cortex ratio distinguishes the organs of giant and pigmy races. The relative doubling of adrenal size to body weight characteristic of the small race is largely due (97 per cent.) to an excess of the adrenal cortex.

Fig. 2.

Organ weights in male rabbits. Mean values plotted against cleaned body weight, logarithmic scale both ways. Adrenal weight × 12.

Fig. 2.

Organ weights in male rabbits. Mean values plotted against cleaned body weight, logarithmic scale both ways. Adrenal weight × 12.

Since the cases presented hitherto have exhibited simple heterogony, the value of k has remained unaltered throughout post-natal development. Such simple instances may illustrate the presence of a general basic principle of tissue mass regulation, which principle may be obscured by the presence of other factors. The development of the thymus, thyroid and testes suggests that in the regulation of these tissues a second factor is involved.

Prior to its involution, the thymus of the large and of the small races is of a comparable size with reference to body weight. From birth to puberty the relation is unchanged. But at that time a disturbing factor alters the ratio. The nature of this disturbance has been elucidated by Jaffe (1924), who found that if the adrenal cortex be removed from the animal the thymus continues to enlarge, this being favoured by the secretion of the thyroid. One may therefore assume that, in the absence of the inhibition due to the adrenal cortex, the growth of the thymus would continue to show simple heterogony.

Table I.

The relative volume of cortex in the adrenal bodies of male Flemish Giant and Polish rabbits

The relative volume of cortex in the adrenal bodies of male Flemish Giant and Polish rabbits
The relative volume of cortex in the adrenal bodies of male Flemish Giant and Polish rabbits

The growth of the thyroid gland indicates a break similar to that of the thymus. With reference to body weight there is no difference in the quantity of thyroid tissue present in giant, dwarf, or hybrid rabbits. But when the cleaned body weight of a rabbit exceeds six hundred grams a new logarithmic ratio becomes effective. This is apparent in Table II. The cause of this “break” is unknown but its reality seems well attested by the coincident change in the amplitude of the percentage deviation.

Fig. 3.

Thymus weight in male rabbits. Above: mean values in relation to age, showing retardation at the fortieth day and involution at puberty. Below: Individual observations plotted against pituitary weight, logarithmic scale both ways. Puberty involution at A and B. Squares = Giants; circles = hybrids ; triangles = Polish.

Fig. 3.

Thymus weight in male rabbits. Above: mean values in relation to age, showing retardation at the fortieth day and involution at puberty. Below: Individual observations plotted against pituitary weight, logarithmic scale both ways. Puberty involution at A and B. Squares = Giants; circles = hybrids ; triangles = Polish.

Mühlmann (1927) is inclined to believe that the relatively large amount of thyroid present at birth is due to the sex hormone of the mother. In female rabbits at puberty a relative enlargement of the thyroid seems to exist. Therefore it would seem that thyroid weight tends to maintain a specific relationship to body weight but that this relation may be altered in the presence of some internal secretion.

Table II.

Dissection data and weights of organs in Flemish Giant male rabbits

Dissection data and weights of organs in Flemish Giant male rabbits
Dissection data and weights of organs in Flemish Giant male rabbits

The growth of the testis relative to body weight is directly plotted in Fig. 4. The curves are sigmoid and the Polish values are seen to be relatively much greater than those for the Flemish. But when plotted against adrenal weight it is found that the mass of Giant, hybrid and Polish testes may all be represented by the same straight line. Using the logarithms of testis weight against those of adrenal weight a linear relationship is unquestionable (Fig. 5).

Fig. 4.

Adrenal weight (above) and Testes weight (below) as percentages of cleaned body weight. Mean values, showing relative increase of both organs in the diminuitive Polish rabbits.

Fig. 4.

Adrenal weight (above) and Testes weight (below) as percentages of cleaned body weight. Mean values, showing relative increase of both organs in the diminuitive Polish rabbits.

Fig. 5.

Testes weight, mean values.

A. Polish testes in relation to whole pituitary weight.

B. Flemish Giant testes on pituitary.

C. Flemish Giant (squares), hybrid (circles), and Polish (triangles) testes plotted on adrenal weight.

D. Rat testes weight on adrenal weight. (Data from Donaldson 1924.) Logarithmic scale both ways.

Fig. 5.

Testes weight, mean values.

A. Polish testes in relation to whole pituitary weight.

B. Flemish Giant testes on pituitary.

C. Flemish Giant (squares), hybrid (circles), and Polish (triangles) testes plotted on adrenal weight.

D. Rat testes weight on adrenal weight. (Data from Donaldson 1924.) Logarithmic scale both ways.

Curiously enough, the relationship of testis weight to adrenal weight exhibits a sharp break. This occurs as a function of age at about the fortieth day of post-natal existence. This event is coincident with a sharp, though temporary, reduction of body growth velocity characteristic of Flemish, hybrid, and Polish rabbits of both sexes (Robb 1928-29). At the same time the testis-pituitary relationship—hitherto rectilinear—likewise shows a sharp change of angle, expressing a new value for k, and thymus growth shows a marked retardation. These coincidences point to the initiation of some new process at this time.

From Donaldson’s (1924) data on the rat I have selected tissues representing each of these three groups :

  1. Organs with an early rapid growth, e.g. the eyeballs.

  2. Organs with nearly uniform growth, e.g. liver, thyroid, suprarenals, hypo-physis and skeleton.

  3. Organs with a sinuous curve of growth, e.g. testes (Fig. 5).

The data have been plotted in Fig. 6. The rectilinear correlations need no further demonstration.

Fig. 6.

Weight of organs and the fresh skeleton in the rat, data from Donaldson (1924), plotted against the live body weight (horizontal values), to show the post-natal rectilinear relationship. Logarithmic spacing both ways.

E. Weight of eyeballs in mg. (× 2).

T. Weight of thyroid in mg.

A. Weight of adrenal bodies in mg. ×12.

S. Weight of fresh skeleton in gm.

L. Weight of liver in gm.

H. Weight of hypophysis in mg.

Fig. 6.

Weight of organs and the fresh skeleton in the rat, data from Donaldson (1924), plotted against the live body weight (horizontal values), to show the post-natal rectilinear relationship. Logarithmic spacing both ways.

E. Weight of eyeballs in mg. (× 2).

T. Weight of thyroid in mg.

A. Weight of adrenal bodies in mg. ×12.

S. Weight of fresh skeleton in gm.

L. Weight of liver in gm.

H. Weight of hypophysis in mg.

These facts tend to establish the proposition that the growth of the whole determines the relative size of its parts. That conception of the growth curve which leads to its interpretation as the summation of the growth of component organs cannot be justified. An investigation of the growth of parts has enlarged the evidence leading to the conclusion that the growth of the organism (and thus of its component tissues) is determined by some general process.

Table III.

Dissection data and weight of organs in Flemish-Polish hybrid males

Dissection data and weight of organs in Flemish-Polish hybrid males
Dissection data and weight of organs in Flemish-Polish hybrid males
Table IV.

Dissection data and weights of organs in Polish male rabbits

Dissection data and weights of organs in Polish male rabbits
Dissection data and weights of organs in Polish male rabbits

A Physico-Chemical analogy

It has been shown that during a more or less extended period of growth certain tissues maintain a precise logarithmic relationship of mass with reference to that of the body as a whole.

The fundamental problem here involved is the nature of that mechanism which brings about the harmony observed in the relative growth of parts. It has been supposed that the growth characteristic of each organ may be determined by specific master reactions. But since, as observed in different varieties of the rabbit, a certain organ may exhibit quite different velocities of growth while maintaining a specific relationship to the growth of other parts, this supposition requires the further premise that numerous local growth velocities have “by chance” exhibited the persistent conformity observed. This leads to absurdity, as Castle has shown (1924).

The existence of these rectilinear logarithmic relations between the weights of tissues may be described by a very simple analogy.

It is known that, other factors being constant, the amount of growth exhibited by a plant tends to be proportional to the available amount of raw materials essential for growth.

Let us postulate that the differences observed in the relative growths of organs are due to differences in the amounts of materials available for each. There remains to be explained the mechanism of this uneven distribution. Comparable phenomena are known to physical chemistry. Of these, the simplest type of distribution is the partition between two immiscible solvents.

If a substance be soluble in two immiscible solvents in contact with one another it will be distributed in a certain ratio between the two, this ratio being known as the “partition coefficient” (Nernst 1923).

Partition phenomena may undoubtedly occur between adjacent cells. Accordingly there may be an inequality of distribution between the various tissues of the body. In such phenomena of partition lies the possibility of an efficient explanation for the observed differences of growth rate characteristic of different tissues.

The data obtained by Jellet (1875) (cited by Nernst, 1923) indicate the nature of the distribution of acid between two alkaloids in the event that the total acid present is not sufficient to saturate the total quantity of alkaloids. Jellet determined that hydrochloric acid will be distributed between certain alkaloids in the following ratios :

The analogy of partition coefficients is of value for it enables us to give a real value to the growth constant k, namely the relative concentration in each tissue of some essential growth controlling substance. If the mass attained by the whole organism at any given time be taken as a measure of the growth controlling substance thus far available, then those organs which increase more rapidly than the body as a whole may be considered as having a distribution coefficient greater than unity. Observations upon the rabbit (after birth) indicate that the adrenal is such an organ.

Throughout post-natal life in the male Flemish Giant the value of characteristic of the adrenal bodies, with reference to cleaned body weight, is 1·19 whereas in the Polish, k = 1·34. The cause of this difference is unknown but these constants are inherited characters. The size of the testis is related to that of the adrenal. Let us use the symbol kt to represent the coefficient of distribution between the adrenal and testes of some testis-growth controlling substance t. If this be done, although the testis is relatively much larger in Polish than in Flemish males the value kt is identical for both varieties. During the first forty days of post-natal life the value of kt = 0·74, thereafter a sudden break occurs and the value of kt becomes 2·30 for both Flemish and Polish rabbits.

Prior to the break in each animal the distribution coefficient kp between pituitary and testis has a value of 1·4. After the break at the fortieth day kp for the Giant = 5·1 and for the Polish = 5·8. But at the time of this break my data do not indicate any change in the value of k for the pituitary body on body weight—which throughout post-natal life in all male rabbits approximates 0·55. The significance of this coincidence of the onset of the juvenile depression with alteration of glandular interrelationships remains to be elucidated.

The distribution theory of the growth of parts which is here proposed is characterised by a practical utility as well as by a considerable theoretical significance. The use of the coefficient of distribution, k, has led to a simple generalisation by which the varied relationships of pituitary, thyroid, adrenal, testis, etc., in all their apparent diversity, may be accurately described. Changes in the value of k may be correlated with significant events, and may so facilitate the analysis of cause and consequence in the diversification of form and even of species.

The adherence of any series of observations to one simple quantitative expression gives interest to a hypothesis of the mechanism whereby such uniformity is brought about. If the equation itself can be regarded as having the physical significance proposed, two assumptions must be justified.

First and foremost, it has been supposed that the restriction of growth in any body tissue is due to some inadequacy of its immediate environment. Whatever the cause of this deficiency (the cause of growth limitation in the body as a whole), each individual tissue tends to be affected to a constant and specific degree. The uniformity of that relation has been described by the hypothesis that each tissue, by reason of its essential structure, tends to establish an individual equilibrium with its milieu. In the absence of a further alteration of its properties the equilibrium point would tend to remain constant. It seems reasonable to suppose that in each case the relation of this equilibrium point to its katabolic expenditure will determine the amount of subsequent growth. Hence, in the comparison of any two tissues, a difference of their specific “equilibrium values” would be reflected in their relative rates of growth.

Fig. 7.

Diagrammatic representation of eight varieties of possible growth relations, which are special forms of the general equation y = axk + c. The quantitative relation between any two growing parts x and y (above and below the base line respectively) depends upon the values of the three constants (1) their initial relative size (a), as shown to the left of each figure, (2) their relative growth rate (k), shown by change of absolute size during time (from left to right), and (3) the existence of some growth inactive component (c), which is shown in solid black. Data belonging to types A, B, C, or D would be rectilinear on plain graph paper ; types E and F would give a straight line when log x is plotted against log y ; types G and H will give a rectilinear plot only when the value of the constant (c) is eliminated before logarithms are used.

Fig. 7.

Diagrammatic representation of eight varieties of possible growth relations, which are special forms of the general equation y = axk + c. The quantitative relation between any two growing parts x and y (above and below the base line respectively) depends upon the values of the three constants (1) their initial relative size (a), as shown to the left of each figure, (2) their relative growth rate (k), shown by change of absolute size during time (from left to right), and (3) the existence of some growth inactive component (c), which is shown in solid black. Data belonging to types A, B, C, or D would be rectilinear on plain graph paper ; types E and F would give a straight line when log x is plotted against log y ; types G and H will give a rectilinear plot only when the value of the constant (c) is eliminated before logarithms are used.

Secondly, one must postulate that, in some cases, only a portion of any tissue, organ, or structure may be actually concerned in further growth. The theory must also take into account the possible presence of cells no longer capable of enlargement or for the presence of now living substances whose mass would in no way contribute to the amount of subsequent synthetic activity. If, on the occasion when a stable equilibrium is established, some inert component be present in one of the participating tissues or primordia, this circumstance will be indicated by the presence of a constant c in the equation :

formula

where y = the dependent variable, e.g. pituitary weight,

x = independent variable, e.g. body weight,

k = equilibrium constant, giving ratio of distribution of growth essentials as indicated by the relative growth rate,

a = constant of relative initial magnitudes of the growth active components of the primordia of x and y,

c—constant, a numerical correction for the amounts of inert substances present in either or both primordia. No direct physical significance can be given to the value of this constant because it represents the composite value of the inert components of the primordial x and y. If those components be represented by m and n respectively, in the above equation

formula

Since this expression contains two unknowns, without further information no solution is possible.

Fig. 8.

Thyroid weight in relation to cleaned body weight. The same data that show a “break” in Fig. 2 are shown to offer an alternate rectilinear interpretation when corrected by the removal of a constant, as in H of Fig. 7, suggesting that the “break “is due to the mode of plotting and is therefore of no functional significance.

Fig. 8.

Thyroid weight in relation to cleaned body weight. The same data that show a “break” in Fig. 2 are shown to offer an alternate rectilinear interpretation when corrected by the removal of a constant, as in H of Fig. 7, suggesting that the “break “is due to the mode of plotting and is therefore of no functional significance.

According to this scheme the progress of organogenesis has been necessarily divided into two phases: (1) the phase of active chemical differentiation, during which the equilibrium value for the tissue in question is undergoing change, i.e. the “formative period” of Roux; and (2) the later stage of a simple quantitative development of a pattern already laid down, and characterised by the relative stability of the tissue-milieu equilibrium. It is this latter stage that may exhibit a constant value for its relative growth rate (k). It is this phase of organogenesis that has contributed to our knowledge of heterogonic growth.

From the foregoing assumptions one may predict the occurrence of eight general types of developmental relationship according to the values of a, c and k. Most of the known examples of simple heterogony belong to two or three of these groups.

An experimental confirmation of the distribution hypothesis would require that in any given case there could be isolated some specific substance, of which the available quantity regulated the amount of possible growth in one or more tissues ; and that it be further shown that some sort of partition (whether equal or unequal) actually takes place among the tissues concerned with reference to that growth controlling substance.

Several fragmentary lines of evidence from animal and plant data indicate that such experimental confirmation may be available. Among the most complete of these are the observations of Turner (1922) and of Murneek (1926). The latter demonstrated that in the case of the tomato plant stem growth could be terminated either when one, two, or more fruits developed, the precise occasion being determined by the amount of available nitrogen present in the soil, whether scanty, moderate, or abundant. If the fruit be removed the period of stem growth is prolonged. It is apparent that in that instance the specific substance essential for growth and present in a limiting amount is fixed nitrogen. Murneek concludes that the nitrogen has been divided between the plant and the fruit, the latter manifesting the greater affinity for this growth essential. The observed cessation of shoot growth upon the occasion of fruit development suggests that the proportion of nitrogen then remaining for the plant tissues soon proves inadequate for their growth.

  1. Throughout post-natal life the relative weights of the pituitary body, thyroid, thymus and adrenals in the rabbit may be expressed by the equation y = axk + c.

  2. A similar association is indicated in the rat for the weights of eyeballs, liver, pancreas, hypophysis, thyroid, adrenals, submaxillary glands, kidney and fresh skeleton (data from Donaldson, 1924).

  3. In giant and pigmy rabbits, the ultimate proportions of body parts are not the same, but (for any given body weight) corresponding tissues in the two groups tend to exhibit an identical relation to total body mass.

  4. The adrenals and testes of the Polish rabbits are relatively much larger than those of the Flemish. But in each case the growth of the adrenal approximates to a constant power function of body weight. Moreover, in these two groups and in their hybrids, the growth of the testes adheres to a simple association with adrenal weight identical for each.

  5. These data suggest the generalisation that in a growing organism the magnitude of any part tends to be a specific function of the total body mass or of some portion so related to the whole.

  6. These associations may be explained by surmising that each tissue is in equilibrium with the internal milieu with regard to the distribution of nutrient growth essentials ; that in each case the equilibrium point would be determined by the nature of the cell and after differentiation would tend to remain constant ; and that the relative enlargement of each tissue is limited by the excess of the equilibrium value over the katabolic expenditure.

  7. According to the above hypothesis of organ growth, the equation y = axk + c may possess a physical significance. Eight types of growth relationships may thus exist, differing because of the apparent inactivity of one or more constants in this equation.

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