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Regeneration, or growth and repair.
ОглавлениеThe phenomenon of regeneration, or the restoration of lost or amputated parts, is a particular case of growth which deserves separate consideration. As we are all aware, this property is manifested in a high degree among invertebrates and many cold-blooded vertebrates, diminishing as we ascend the scale, until at length, in the warm-blooded animals, it lessens down to no more than that vis medicatrix which heals a wound. Ever since the days of Aristotle, and especially since the experiments of Trembley, Réaumur and Spallanzani in the middle of the eighteenth century, the physiologist and the psychologist have alike recognised that the phenomenon is both perplexing and important. The general phenomenon is amply discussed elsewhere, and we need only deal with it in its immediate relation to growth186.
Regeneration, like growth in other cases, proceeds with a velocity which varies according to a definite law; the rate varies with the time, and we may study it as velocity and as acceleration.
Let us take, as an instance, Miss M. L. Durbin’s measurements of the rate of regeneration of tadpoles’ tails: the rate being here measured in terms, not of mass, but of length, or longitudinal increment187.
From a number of tadpoles, whose average length was 34·2 mm., their tails being on an average 21·2 mm. long, about half the tail {139} (11·5 mm.) was cut off, and the amounts regenerated in successive periods are shewn as follows:
| Days after operation | 3 | 7 | 10 | 14 | 18 | 24 | 30 |
| (1) Amount regenerated in mm. | 1·4 | 3·4 | 4·3 | 5·2 | 5·5 | 6·2 | 6·5 |
| (2) Increment during each period | 1·4 | 2·0 | 0·9 | 0·9 | 0·3 | 0·7 | 0·3 |
| (3)(?) Rate per day during each period | 0·46 | 0·50 | 0·30 | 0·25 | 0·07 | 0·12 | 0·05 |
The first line of numbers in this table, if plotted as a curve against the number of days, will give us a very satisfactory view of the “curve of growth” within the period of the observations: that is to say, of the successive relations of length to time, or the velocity of the process. But the third line is not so satisfactory, and must not be plotted directly as an acceleration curve. For it is evident that the “rates” here determined do not correspond to velocities at the dates to which they are referred, but are the mean velocities over a preceding period; and moreover the periods over which these means are taken are here of very unequal length. But we may draw a good deal more information from this experiment, if we begin by drawing a smooth curve, as nearly as possible through the points corresponding to the amounts regenerated (according to the first line of the table); and if we then interpolate from this smooth curve the actual lengths attained, day by day, and derive from these, by subtraction, the successive daily increments, which are the measure of the daily mean velocities (Table, p. 141). (The more accurate and strictly correct method would be to draw successive tangents to the curve.)
In our curve of growth (Fig. 35) we cannot safely interpolate values for the first three days, that is to say for the dates between amputation and the first actual measurement of the regenerated part. What goes on in these three days is very important; but we know nothing about it, save that our curve descended to zero somewhere or other within that period. As we have already learned, we can more or less safely interpolate between known points, or actual observations; but here we have no known starting-point. In short, for all that the observations tell us, and for all that the appearance of the curve can suggest, the curve of growth may have descended evenly to the base-line, which it would then have reached about the end of the second {140} day; or it may have had within the first three days a change of direction, or “point of inflection,” and may then have sprung at once from the base-line at zero. That is to say, there may
Fig. 35. Curve of regenerative growth in tadpoles’ tails. (From M. L. Durbin’s data.)
have been an intervening “latent period,” during which no growth occurred, between the time of injury and the first measurement of regenerative growth;
Fig. 36. Mean daily increments, corresponding to Fig. 35.
{141}
or, for all we yet know, regeneration may have begun at once, but with a velocity much less than that which it afterwards attained. This apparently trifling difference would correspond to a very great difference in the nature of the phenomenon, and would lead to a very striking difference in the curve which we have next to draw.
The curve already drawn (Fig. 35) illustrates, as we have seen, the relation of length to time, i.e. L ⁄ T = V. The second (Fig. 36) represents the rate of change of velocity; it sets V against T;
| The foregoing table, extended by graphic interpolation. | |||
| Days | Total increment | Daily increment | Logs of do. |
|---|---|---|---|
| 1 | — | ||
| — | — | ||
| 2 | — | ||
| — | — | ||
| 3 | 1·40 | ||
| ·60 | 1·78 | ||
| 4 | 2·00 | ||
| ·52 | 1·72 | ||
| 5 | 2·52 | ||
| ·45 | 1·65 | ||
| 6 | 2·97 | ||
| ·43 | 1·63 | ||
| 7 | 3·40 | ||
| ·32 | 1·51 | ||
| 8 | 3·72 | ||
| ·30 | 1·48 | ||
| 9 | 4·02 | ||
| ·28 | 1·45 | ||
| 10 | 4·30 | ||
| ·22 | 1·34 | ||
| 11 | 4·52 | ||
| ·21 | 1·32 | ||
| 12 | 4·73 | ||
| ·19 | 1·28 | ||
| 13 | 4·92 | ||
| ·18 | 1·26 | ||
| 14 | 5·10 | ||
| ·17 | 1·23 | ||
| 15 | 5·27 | ||
| ·13 | 1·11 | ||
| 16 | 5·40 | ||
| ·14 | 1·15 | ||
| 17 | 5·54 | ||
| ·13 | 1·11 | ||
| 18 | 5·67 | ||
| ·11 | 1·04 | ||
| 19 | 5·78 | ||
| ·10 | 1·00 | ||
| 20 | 5·88 | ||
| ·10 | 1·00 | ||
| 21 | 5·98 | ||
| ·09 | ·95 | ||
| 22 | 6·07 | ||
| ·07 | ·85 | ||
| 23 | 6·14 | ||
| ·07 | ·84 | ||
| 24 | 6·21 | ||
| ·08 | ·90 | ||
| 25 | 6·29 | ||
| ·06 | ·78 | ||
| 26 | 6·35 | ||
| ·06 | ·78 | ||
| 27 | 6·41 | ||
| ·05 | ·70 | ||
| 28 | 6·46 | ||
| ·04 | ·60 | ||
| 29 | 6·50 | ||
| ·03 | ·48 | ||
| 30 | 6·53 |
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and V ⁄ T or L ⁄ T2 , represents (as we have learned) the acceleration of growth, this being simply the “differential coefficient,” the first derivative of the former curve.
Fig. 37. Logarithms of values shewn in Fig. 36.
Now, plotting this acceleration curve from the date of the first measurement made three days after the amputation of the tail (Fig. 36), we see that it has no point of inflection, but falls steadily, only more and more slowly, till at last it comes down nearly to the base-line. The velocities of growth are continually diminishing. As regards the missing portion at the beginning of the curve, we cannot be sure whether it bent round and came down to zero, or whether, as in our ordinary acceleration curves of growth from birth onwards, it started from a maximum. The former is, in this case, obviously the more probable, but we cannot be sure.
As regards that large portion of the curve which we are acquainted with, we see that it resembles the curve known as a rectangular hyperbola, which is the form assumed when two variables (in this case V and T) vary inversely as one another. If we take the logarithms of the velocities (as given in the table) and plot them against time (Fig. 37), we see that they fall, approximately, into a straight line; and if this curve be plotted on the {143} proper scale we shall find that the angle which it makes with the base is about 25°, of which the tangent is ·46, or in round numbers ½.
Had the angle been 45° (tan 45° = 1), the curve would have been actually a rectangular hyperbola, with V T = constant. As it is, we may assume, provisionally, that it belongs to the same family of curves, so that Vm Tn , or Vm ⁄ n T, or V Tn ⁄ m , are all severally constant. In other words, the velocity varies inversely as some power of the time, or vice versa. And in this particular case, the equation V T2 = constant, holds very nearly true; that is to say the velocity varies, or tends to vary, inversely as the square of the time. If some general law akin to this could be established as a general law, or even as a common rule, it would be of great importance.
Fig. 38. Rate of regenerative growth in larger tadpoles.
But though neither in this case nor in any other can the minute increments of growth during the first few hours, or the first couple of days, after injury, be directly measured, yet the most important point is quite capable of solution. What the foregoing curve leaves us in ignorance of, is simply whether growth starts at zero, with zero velocity, and works up quickly to a maximum velocity from which it afterwards gradually falls away; or whether after a latent period, it begins, so to speak, in full force. The answer {144} to this question-depends on whether, in the days following the first actual measurement, we can or cannot detect a daily increment in velocity, before that velocity begins its normal course of diminution. Now this preliminary ascent to a maximum, or point of inflection of the curve, though not shewn in the above-quoted experiment, has been often observed: as for instance, in another similar experiment by the author of the former, the tadpoles being in this case of larger size (average 49·1 mm.)188.
| Days | 3 | 5 | 7 | 10 | 12 | 14 | 17 | 24 | 28 | 31 |
| Increment | 0·86 | 2·15 | 3·66 | 5·20 | 5·95 | 6·38 | 7·10 | 7·60 | 8·20 | 8·40 |
Or, by graphic interpolation,
| Days | Total increment | Daily do. |
|---|---|---|
| 1 | ·23 | ·23 |
| 2 | ·53 | ·30 |
| 3 | ·86 | ·33 |
| 4 | 1·30 | ·44 |
| 5 | 2·00 | ·70 |
| 6 | 2·78 | ·78 |
| 7 | 3·58 | ·80 |
| 8 | 4·30 | ·72 |
| 9 | 4·90 | ·60 |
| 10 | 5·29 | ·39 |
| 11 | 5·62 | ·33 |
| 12 | 5·90 | ·28 |
| 13 | 6·13 | ·23 |
| 14 | 6·38 | ·25 |
| 15 | 6·61 | ·23 |
| 16 | 6·81 | ·20 |
| 17 | 7·00 | ·19 etc. |
The acceleration curve is drawn in Fig. 39.
Here we have just what we lacked in the former case, namely a visible point of inflection in the curve about the seventh day (Figs. 38, 39), whose existence is confirmed by successive observations on the 3rd, 5th, 7th and 10th days, and which justifies to some extent our extrapolation for the otherwise unknown period up to and ending with the third day; but even here there is a short space near the very beginning during which we are not quite sure of the precise slope of the curve.
We have now learned that, according to these experiments, with which many others are in substantial agreement, the rate of growth in the regenerative process is as follows. After a very short latent period, not yet actually proved but whose existence is highly probable, growth commences with a velocity which very {145} rapidly increases to a maximum. The curve quickly—almost suddenly—changes its direction, as the velocity begins to fall; and the rate of fall, that is, the negative acceleration, proceeds at a slower and slower rate, which rate varies inversely as some power of the time, and is found in both of the above-quoted experiments to be very approximately as 1 ⁄ T2 . But it is obvious that the value which we have found for the latter portion of the curve (however closely it be conformed to) is only an empirical value; it has only a temporary usefulness, and must in time give place to a formula which shall represent the entire phenomenon, from start to finish.
Fig. 39. Daily increment, or amount regenerated, corresponding to Fig. 38.
While the curve of regenerative growth is apparently different from the curve of ordinary growth as usually drawn (and while this apparent difference has been commented on and treated as valid by certain writers) we are now in a position to see that it only looks different because we are able to study it, if not from the beginning, at least very nearly so: while an ordinary curve of growth, as it is usually presented to us, is one which dates, not {146} from the beginning of growth, but from the comparatively late, and unimportant, and even fallacious epoch of birth. A complete curve of growth, starting from zero, has the same essential characteristics as the regeneration curve.
Indeed the more we consider the phenomenon of regeneration, the more plainly does it shew itself to us as but a particular case of the general phenomenon of growth189, following the same lines, obeying the same laws, and merely started into activity by the special stimulus, direct or indirect, caused by the infliction of a wound. Neither more nor less than in other problems of physiology are we called upon, in the case of regeneration, to indulge in metaphysical speculation, or to dwell upon the beneficent purpose which seemingly underlies this process of healing and restoration.
It is a very general rule, though apparently not a universal one, that regeneration tends to fall somewhat short of a complete restoration of the lost part; a certain percentage only of the lost tissues is restored. This fact was well known to some of those old investigators, who, like the Abbé Trembley and like Voltaire, found a fascination in the study of artificial injury and the regeneration which followed it. Sir John Graham Dalyell, for instance, says, in the course of an admirable paragraph on regeneration190: “The reproductive faculty … is not confined to one portion, but may extend over many; and it may ensue even in relation to the regenerated portion more than once. Nevertheless, the faculty gradually weakens, so that in general every successive regeneration is smaller and more imperfect than the organisation preceding it; and at length it is exhausted.”
In certain minute animals, such as the Infusoria, in which the capacity for “regeneration” is so great that the entire animal may be restored from the merest fragment, it becomes of great interest to discover whether there be some definite size at which the fragment ceases to display this power. This question has {147} been studied by Lillie191, who found that in Stentor, while still smaller fragments were capable of surviving for days, the smallest portions capable of regeneration were of a size equal to a sphere of about 80 µ in diameter, that is to say of a volume equal to about one twenty-seventh of the average entire animal. He arrives at the remarkable conclusion that for this, and for all other species of animals, there is a “minimal organisation mass,” that is to say a “minimal mass of definite size consisting of nucleus and cytoplasm within which the organisation of the species can just find its latent expression.” And in like manner, Boveri192 has shewn that the fragment of a sea-urchin’s egg capable of growing up into a new embryo, and so discharging the complete functions of an entire and uninjured ovum, reaches its limit at about one-twentieth of the original egg—other writers having found a limit at about one-fourth. These magnitudes, small as they are, represent objects easily visible under a low power of the microscope, and so stand in a very different category to the minimal magnitudes in which life itself can be manifested, and which we have discussed in chapter II.
A number of phenomena connected with the linear rate of regeneration are illustrated and epitomised in the accompanying diagram (Fig. 40), which I have constructed from certain data given by Ellis in a paper on the relation of the amount of tail regenerated to the amount removed, in Tadpoles. These data are summarised in the next Table. The tadpoles were all very much of a size, about 40 mm.; the average length of tail was very near to 26 mm., or 65 per cent. of the whole body-length; and in four series of experiments about 10, 20, 40 and 60 per cent. of the tail were severally removed. The amount regenerated in successive intervals of three days is shewn in our table. By plotting the actual amounts regenerated against these three-day intervals of time, we may interpolate values for the time taken to regenerate definite percentage amounts, 5 per cent., 10 per cent., etc. of the {148}
| The Rate of Regenerative Growth in Tadpoles’ Tails. (After M. M. Ellis, J. Exp. Zool. VII, p. 421, 1909.) | |||||||||||
| Series† | Body length mm. | Tail length mm. | Amount removed mm. | Per cent. of tail removed | % amount regenerated in days | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 6 | 9 | 12 | 15 | 18 | 32 | |||||
| O | 39·575 | 25·895 | 3·2 | 12·36 | 13 | 31 | 44 | 44 | 44 | 44 | 44 |
| P | 40·21 | 26·13 | 5·28 | 20·20 | 10 | 29 | 40 | 44 | 44 | 44 | 44 |
| R | 39·86 | 25·70 | 10·4 | 40·50 | 6 | 20 | 31 | 40 | 48 | 48 | 48 |
| S | 40·34 | 26·11 | 14·8 | 56·7 | 0 | 16 | 33 | 39 | 45 | 48 | 48 |
† Each series gives the mean of 20 experiments.
Fig. 40. Relation between the percentage amount of tail removed, the percentage restored, and the time required for its restoration. (From M. M. Ellis’s data.)
amount removed; and my diagram is constructed from the four sets of values thus obtained, that is to say from the four sets of experiments which differed from one another in the amount of tail amputated. To these we have to add the general result of a fifth series of experiments, which shewed that when as much as 75 per cent. of the tail was cut off, no regeneration took place at all, but the animal presently died. In our diagram, then, each {149} curve indicates the time taken to regenerate n per cent. of the amount removed. All the curves converge towards infinity, when the amount removed (as shewn by the ordinate) approaches 75 per cent.; and all of the curves start from zero, for nothing is regenerated where nothing had been removed. Each curve approximates in form to a cubic parabola.
The amount regenerated varies also with the age of the tadpole and with other factors, such as temperature; in other words, for any given age, or size, of tadpole and also for various specific temperatures, a similar diagram might be constructed.
The power of reproducing, or regenerating, a lost limb is particularly well developed in arthropod animals, and is sometimes accompanied by remarkable modification of the form of the regenerated limb. A case in point, which has attracted much attention, occurs in connection with the claws of certain Crustacea193.
In many Crustacea we have an asymmetry of the great claws, one being larger than the other and also more or less different in form. For instance, in the common lobster, one claw, the larger of the two, is provided with a few great “crushing” teeth, while the smaller claw has more numerous teeth, small and serrated. Though Aristotle thought otherwise, it appears that the crushing-claw may be on the right or left side, indifferently; whether it be on one or the other is a problem of “chance.” It is otherwise in many other Crustacea, where the larger and more powerful claw is always left or right, as the case may be, according to the species: where, in other words, the “probability” of the large or the small claw being left or being right is tantamount to certainty194.
The one claw is the larger because it has grown the faster; {150} it has a higher “coefficient of growth,” and accordingly, as age advances, the disproportion between the two claws becomes more and more evident. Moreover, we must assume that the characteristic form of the claw is a “function” of its magnitude; the knobbiness is a phenomenon coincident with growth, and we never, under any circumstances, find the smaller claw with big crushing teeth and the big claw with little serrated ones. There are many other somewhat similar cases where size and form are manifestly correlated, and we have already seen, to some extent, that the phenomenon of growth is accompanied by certain ratios of velocity that lead inevitably to changes of form. Meanwhile, then, we must simply assume that the essential difference between the two claws is one of magnitude, with which a certain differentiation of form is inseparably associated.
If we amputate a claw, or if, as often happens, the crab “casts it off,” it undergoes a process of regeneration—it grows anew, and evidently does so with an accelerated velocity, which acceleration will cease when equilibrium of the parts is once more attained: the accelerated velocity being a case in point to illustrate that vis revulsionis of Haller, to which we have already referred.
With the help of this principle, Przibram accounts for certain curious phenomena which accompany the process of regeneration. As his experiments and those of Morgan shew, if the large or knobby claw (A) be removed, there are certain cases, e.g. the common lobster, where it is directly regenerated. In other cases, e.g. Alpheus195, the other claw (B) assumes the size and form of that which was amputated, while the latter regenerates itself in the form of the other and weaker one; A and B have apparently changed places. In a third case, as in the crabs, the A-claw regenerates itself as a small or B-claw, but the B-claw remains for a time unaltered, though slowly and in the course of repeated moults it later on assumes the large and heavily toothed A-form.
Much has been written on this phenomenon, but in essence it is very simple. It depends upon the respective rates of growth, upon a ratio between the rate of regeneration and the rate of growth of the uninjured limb: complicated a little, however, by {151} the possibility of the uninjured limb growing all the faster for a time after the animal has been relieved of the other. From the time of amputation, say of A, A begins to grow from zero, with a high “regenerative” velocity; while B, starting from a definite magnitude, continues to increase, with its normal or perhaps somewhat accelerated velocity. The ratio between the two velocities of growth will determine whether, by a given time, A has equalled, outstripped, or still fallen short of the magnitude of B.
That this is the gist of the whole problem is confirmed (if confirmation be necessary) by certain experiments of Wilson’s. It is known that by section of the nerve to a crab’s claw, its growth is retarded, and as the general growth of the animal proceeds the claw comes to appear stunted or dwarfed. Now in such a case as that of Alpheus, we have seen that the rate of regenerative growth in an amputated large claw fails to let it reach or overtake the magnitude of the growing little claw: which latter, in short, now appears as the big one. But if at the same time as we amputate the big claw we also sever the nerve to the lesser one, we so far slow down the latter’s growth that the other is able to make up to it, and in this case the two claws continue to grow at approximately equal rates, or in other words continue of coequal size.
The phenomenon of regeneration goes some way towards helping us to comprehend the phenomenon of “multiplication by fission,” as it is exemplified at least in its simpler cases in many worms and worm-like animals. For physical reasons which we shall have to study in another chapter, there is a natural tendency for any tube, if it have the properties of a fluid or semi-fluid substance, to break up into segments after it comes to a certain length; and nothing can prevent its doing so, except the presence of some controlling force, such for instance as may be due to the pressure of some external support, or some superficial thickening or other intrinsic rigidity of its own substance. If we add to this natural tendency towards fission of a cylindrical or tubular worm, the ordinary phenomenon of regeneration, we have all that is essentially implied in “reproduction by fission.” And in so far {152} as the process rests upon a physical principle, or natural tendency, we may account for its occurrence in a great variety of animals, zoologically dissimilar; and also for its presence here and absence there, in forms which, though materially different in a physical sense, are zoologically speaking very closely allied.
