Injury, Recovery and Death in Relation to Conductivity and Permeability

A series of experiments was performed in which tissue was placed in CaCl2 for 30 minutes, then in NaCl for 10 minutes, then in CaCL for 60 minutes. The tissue was allowed to recover in sea water, after which it was placed in CaCl2 for 360 minutes, and then in NaCl (Fig. 48). In this case the observed time was not corrected (i.e., was not multiplied by a factor) as in the previous calcu- lations. In consequence the calculated and observed values do not correspond at the beginning of each expos- ure, the only exception being after recovery in sea water, in which case it was assumed38 that equilibrium had been

" This involves the assumption that 0 is not restored to any extent dur- ing recovery in sea water. This assumption may not be correct, especially at the start, but even in that case the present calculation would not be appreciably altered. 88 In this case the tissue did not remain long enough in sea water to establish equilibrium, but it was so nearly established that only a very small error is involved in regarding it as complete. In cases where it is not completely established the final equilibrium may be approximated by extrapolation.

reached and that in consequence A0 = 30 M (the value of M being that of the observed resistance less 10). This value of A was taken for the subsequent calculations. Fio. 48. — Curves showing the net electrical resistance of Laminaria agardhii in NaCl 0.52 M, in CaCli 0.278 M and in sea water. Unbroken line, calculated values; broken line, observed values. Average of ten or more experiments; probable error of the mean less than 10% During the subsequent exposure to CaCl2 A0 diminished to Al according to the formula

and this value was used in calculating the fall of resist- ance during the final exposure to NaCl. Experiments similar to those shown in Figs. 44, 45, 46, 47, and 48 have been made, in which mixtures of NaCl plus CaCl2 have been used in a variety of ways. In this case we employ for the calculations the constants appro- priate for each mixture, as given on page 140. In general the agreement is satisfactory. With so large a number of constants it might seem possible to fit any sort of curve, and hence the significance of the actual accomplishment might be lessened. This, however, is by no means the case.

It should be noted that we do not employ new constants to fit these curves, but that in every case we use the con- stants already determined as the result of other and quite different experiments. In view of this the results have a special significance. If we accept the conclusions stated above we are obliged to look upon recovery in a somewhat different fashion from that which is customary. Recovery is usu- ally regarded as due to the reversal of the reaction which produces injury. The conception of the writer is funda- mentally different; it assumes that the reactions involved are irreversible (or practically so) and that injury and recovery differ only in the relative speed at which certain reactions take place.

It would seem that these experiments, and those pre- viously described, afford a sufficient test of the theory. It has been found that the agreement between the calcu- lated and observed values is satisfactory whenever a sufficiently large number of readings are averaged in arriving at the observed values. In the foregoing account many details are necessar- ily omitted, owing to lack of space. These, however, are not essential to the main purpose, which is to show how the process of injury and recovery may be analyzed and subjected to mathematical treatment. Starting with cer- tain assumptions we have formulated equations by means of which we can predict the behavior of the tissue. If the

predictions are fairly accurate it is natural to infer that the assumptions are in accordance with the facts. It is evident from an examination of the figures that the equa- tions enable us to predict with considerable accuracy the behavior of tissues in solutions of NaCl and CaCl2, as well as the recovery curves after any length of exposure to either of these solutions. But we must not lose sight of the fact that the predictive value of the equations does not depend on the validity of these assumptions and would in no way be impaired if they were to be given up. The equations have a permanent value which is quite inde- pendent of assumptions.

The mechanism which has been postulated in devel- oping these equations consists essentially of a series of catenary reactions. There can be no doubt that, as Loeb (1912, D) has emphasized, catenary reactions play a large part in life phenomena, and it would seem that the role assigned to them in the present discussion involves no unreasonable assumption. A substance which acts as a member of such a caten- ary system may, as Hopkins (1913) has remarked, be of great importance in the organism even if present in very small amount.

It may be desirable to call attention to certain features of this mechanism which are of general interest from a theoretical viewpoint. It is evident that by means of a simple catenary system we can account for practically all the processes which occur in the organism. If such a system is present in the egg we can easily picture all of the subsequent development as due to this system, without the introduction of any new reactions. All that we need to postulate is that during development the relative rates of the reactions change. The processes involved in irrita-

bility, as well as those concerned in injury and death, may be accounted for in this same way. We thus arrive at a very simple conception of the underlying mechanism of life processes, which may be useful in formulating a theory of living matter. If life is dependent upon a series of reactions which normally proceed at rates bearing a definite relation to each other, it is clear that a disturbance of these rate-rela- tions may have profound effects upon the organism. It is evident that such a disturbance might be produced by changes in temperature (in case the temperature coeffi- cients of the reactions differ) or by chemical agents. The same result might be brought about by physical means, especially where structural changes occur which alter the permeability of the plasma membrane or of internal structures (such as the nucleus and plastids) in such a way as to bring together substances which do not nor- mally interact.39

This investigation of fundamental life processes shows that they appear to obey the laws of chemical dynamics. It illustrates a method of attack which may throw some light upon the underlying mechanism of these processes and which may assist materially in the analysis and con- trol of life-phenomena. When one toxic substance acts as an antidote to another, we speak of this as antagonism. If the antagon- istic substances are mixed in such proportions that tox* icity disappears we have a physiologically balanced solution as defined by Loeb.1

In seeking an accurate measure of antagonism the writer made experiments on growth. It was found that both NaCl and CaCl2 are toxic to plants, as shown by the fact that in solutions of these substances there is less growth than in distilled water.2 In a series of experi- ments on wheat, it was found that the growth of roots in NaCl 0.12 M was practically the same as in CaCL 0.164 M. These solutions were therefore regarded as equally toxic. On mixing equally toxic salt solutions, we may encounter one of the following conditions :3

1. The toxicity is unaltered, that is, the toxic action of the two salts is additive. Each salt produces its own toxic effect precisely as though the other were not present. This is expressed by the horizontal dotted line LJM in Pig. 49. It is evident that we cannot get increased growth by mixing two such solutions unless the salts have an antag- onistic action. If we mix equal volumes of A 0.1 M and B 0.1 M the dilution of A from 0.1 M to 0.05 M is exactly compensated by the introduction of molecules of B. Or, to put it in another way, the toxic effect depends on the number of molecules present (if both kinds of mole- cules are equally toxic and there is no antagonism) and it makes no difference whether the solutions are pure or mixed.

If the toxic effect depends on ions, rather than on mole- cules, then, since the number of ions may be somewhat increased by mixing solu- tions, the toxicity may be correspondingly increased; but the amount of this increase would ordinarily be negligible. We then get a rising somewhere the dotted line, such the unbroken line LKM. We then get a c which somewhere falls below the dotted line, such as the line interrupted by cir- cles LHM* The considerations here set forth apply in all cases where two equally toxic solutions are mixed, whether their

FlG- 49.— Curves showing the growth of roots in mixtures of equally toxic solutions of two salts A and B: the ordinatee represent growth; the abscissae represent the composi- tion of the mixtures, thus A 50, B 50 means a mixture in which the dissolved molecules are 50% .4 and 50% B: the horizontal dotted iine (MM) represents the growth which would occur if there were no antagonism (additive effect); LKM is the antagonism curve; LIIM, curve expressing increased toxicity (opposite of antagonism); thequan- titative expression of antagonism at the

concentration is the same or not. Thus, if a solution of A 0.05 M is just as toxic as a solution of B 0.1 M, mixtures of the two will give a horizontal straight line (as in Fig. 49) provided their effects are additive. Emphasis should be laid upon the fact that the method of mixing two equally toxic solutions eliminates disturb- ances due to variations of osmotic pressure. If a mole- cule of A is twice as toxic as a molecule of B, a solution of A 0.05 M will be just as toxic as a solution of B 0.1 M, provided there are no other factors to be considered. But if the osmotic pressure of the 0.05 M solution of A is less than that of the 0.1 M solution of B, there will in many cases be better growth in the 0.05 M solution of A. In order to make the solution of A appear equally toxic with the solution of B, the concentration of A must be some- what increased, say to 0.055 M. We thus compensate for the variation in osmotic pressure, and this compensation is not destroyed when the 0.055 M solution of A is mixed with the 0.1 M solution of B. If the effects of the salts are additive, we must therefore get a horizontal straight line, as shown in Fig. 49.

It is evident that this straight line furnishes a quanti- tative criterion of antagonism. All that is necessary is to determine what concentrations of A and B are equally toxic, mix these solutions in various proportions, and determine the amount of growth. The antagonism in any mixture may then be expressed in a very simple manner. In the curve LKM (Fig. 49) the antagonism in a mixture in which the molecules are 50% A and 50% B may be expressed as KJ-^JE. JE is the growth which would have been obtained if the effect of the salts had been additive (that is, if there had been no antagonism, but each salt had produced its effect inde-

pendent of the other.) KJ is the increased growth due to antagonism ; it is best expressed as percentage of JE or as In the same way increased toxicity (when the mixture is more toxic than either of the pure solutions) may be expressed as JH -=- JE. This sometimes occurs, but it is much less common than antagonism.5 The percentages refer to molecular proportions; that is, 75 per cent. CaCla + 25 per cent. NaCl means a solution in which 75 per cent, of the dissolved molecules are CaCl2 and 25 per cent, are NaCl.

As an illustration of this method the results given in Table VII may be cited. In this case the growth in the various mixtures was in part determined directly and in part was calculated from results obtained by growing plants in mixtures having almost the same composition as the solutions given in the table. In another method6 of measuring antagonism we may look at the matter from the following standpoint. A cer- tain amount of growth occurs in distilled water as shown in Fig. 50; when salts are added to distilled water the

PIG. 50. — Curve showing antagonism between two salts, A and B. The additive effect is GH. Antagonism at the ordinate / may be expressed ae 100 X FH+GH; the opposite of antagonism ae 100 X EH +GH. The dotted line represents growth in distilled water. The abscissae represent the molecular concentrations of the salts. growth is lessened. The lessening of growth due to the action of the salts where no antagonism (or its opposite) occurs is regarded as the additive effect. When the salts are antagonistic growth is less hindered. The additive effect is then GH; the antagonism is FH and may be expressed as 100 X FH -~ GH. The opposite of antagon- ism is 100 X EH-+-GH.

We may now consider the effect of mixing two solu- tions which are not equally toxic. Suppose solution A 0.1 M to be twice as toxic as solution B 0.1 M. The effect of mixing these, if the effects were equally additive, would be the same as mixing a solu- tion of A 0.1 M with another solution A just half as toxic, or in other words, would be the same as decreasing the concentration of A. In this case the curve expressing purely additive effects would not be a straight line, but would assume the form of a curved line, convex to the horizontal axis, similar to VTW in Fig. 51. This is evi- dent7 from the curves given by Magowan, showing growth in toxic solutions of various A 100^ concentrations.

thlS additive CUrVe dmates express growth; the abscissae express experimentally, and then to th.e. dotted line VTW expresses the growth PYnrPQQ anf a D'nniQTn rmmrH- niem (additive effect); T't/TF, antagonism express diiidgo quaj curv^. VSWt curve expressirig increased tfltivplv for AVarrmlp at tVlP toxici1>v .(opposite of antagonism); the UtllVtJlj , 1U1 tJJLeHllpic, dl -ic quantitative expression of antagonism at the as UT -=- TP. But the labor would be much greater than by the method of mixing equally toxic solutions. The additive curve would be determined by growing plants, not in mixtures of A with B, but in mixtures of A with another solution of A having the same toxicity as B. Or

we might use mixtures of B with another solution of B having the same toxicity as A. The two methods might not give exactly the same result. This is an additional argument in favor of using equally toxic solutions. An illustration of this method is found in the results given in Table VIII. The growth in the various mixtures (additive and antagonistic) was in part determined directly and in part was calculated from results obtained by growing plants in mixtures having almost the

The percentages refer to molecular proportions; that is, 75 per cent. CaClz+25 per cent. NaCI means a solution in which 75 per cent, of the dissolved molecules are CaCh and 25 per cent, are NaCI. same composition as the solutions given in the table mentioned. For the sake of completeness it may be mentioned that other types of antagonism curves are found; for example, flat-topped curves and also curves with two maxima, as shown in Fig. 52. If instead of mixing two equally toxic solutions we keep the concentration of one salt constant while varying that of the other, it becomes very difficult to determine the additive curve, especially when variations in osmotic pressure influence the result. It is therefore difficult to obtain an accurate quantitative expression of antagonism by this method, and in critical cases it may be impossible to de- cide whether antagonism exists or not.

Emphasis should be laid on the fact that the growth of parts not in immediate contact with the solution does not furnish a trustworthy criterion of antagon- ism. Thus the leaves of wheat FIG. 52.— Types of antagoni8m (WniCn are nOt in COntact With the growth; the abscissa express the The method of mixing equally toxic solutions has also a great advantage when three solutions are employed. As an illustration of this we may take mixtures of NaCl + KC1 + CaCl2. In the case of wheat it was found that the roots grew equally well in solutions of NaC1.12 M, KC1.13 My and CaCl2 0.164 M. Mixtures of these solutions were prepared and the growth of the roots in these mixtures was measured after a period of 30 days. In order to show the results graphically, the composition of the solutions may be conveniently expressed by means of a triangular diagram as drawn in Fig. 53.

The diagram consists of an equilateral triangle, the apices of which represent equally toxic pure solutions. Thus the point A represents pure CaCL (0.164 M), B represents pure KC1 (0.13 M), and C represents pure NaCl (0.12 M). All points on the sides of the triangle represent mixtures of two solutions only, the composition depending on the position of the point. Thus the point Fia. 53. — Diagram representing the composition of various mixtures of KC1 -f- NaCl -|- Cadi: this serves as the base of the solid model shown in Fig. 54.

H represents a solution made by mixing the equally toxic solutions NaCl 0.12 M and KC1 0.13 M in such proportions that in the mixture 50% of the dissolved molecules are NaCl and 50% are KCL In the same way G represents a solution in which the molecular proportions are NaCl 25% + KC1 75% ; / represents NaCl 75% + KC1 25% ; E represents KC1 50% + CaCl2 50% ; K represents NaCl 50% + CaCl2 50%. All points in the interior of the triangle represent mix- tures of the three equally toxic solutions NaCl 0.12 M, KC1 0.13 M, and CaCl2 0.164 M. Along the line FJ are represented mixtures in which the dissolved molecules are

25% CaCl2; the line EK represents mixtures in which the dissolved molecules are 50% CaCL ; the line DL mix- tures in which the dissolved molecules are 75% CaCl2. In the same way FG means 75% KOI; EH, 50% KC1; DI, 25% KC1; GL, 25% NaCl; HK, 50% NaCl; and IJ, 75% NaCl. The point M is on the line FJ, meaning 25% CaCl2; it is also on the line EH, meaning 50% KC1 ; and likewise on the line GL, meaning 25% NaCl. It therefore repre- sents a mixture of the three equally toxic solutions, NaCl 0.12 M, KC1 0.13 M, and CaCl2 0.164 M, in which the dissolved molecules are 25% CaCL + 50% KC1 + 25% NaCl. In the same way the point 0 represents a mixture in which the dissolved molecules are 50% CaCl2 25% KC1 + 25% NaCl.

It is obvious that the composition of any solution can be represented by selecting a suitable point on the dia- gram. At any such point an ordinate may be erected ex- pressing the growth of the plant in that solution. When this has been done for a sufficient number of points, a solid model may be constructed which gives a complete description of the growth of the plant in all the solutions. Such a model is shown, in Fig. 54. The ordinates represent the aggregate length of roots per plant of wheat at the end of 30 days. The ordinates in the pure solutions are equal (55 mm.), showing that the solutions are equally toxic. The ordinates were in part determined directly by experiment and in part calculated from data obtained by growing plants in solutions of approximately the same composition as those represented.

From such a model the antagonism in any solution may be determined at once by measuring with calipers the height of the ordinate at the required point, subtract- ing 55, which is the amount of growth in the pure solutions, and in this case (since all the pure solutions are equally toxic) the amount of growth which would occur if the toxic actions of the salts were additive (that is, if each salt exerted its own toxic effect independently of the other salts) ; the result should then be divided by 55.