Injury, Recovery and Death in Relation to Conductivity and Permeability

14 By the decrease in the velocity constant is meant the decrease which we observe as we pass from the solution containing the highest per cent, of calcium (38.0% NaCl + 62.0% CaCl2) to mixtures containing smaller The decrease of the amount of K A and KR is not shown in the figure because it depends not only on Na^XCa, but also on the per cent, of CaCl2. The fact that even in the presence of the maximum amount of Na4XCa these velocity constants are greater than in sea water is of course to be attributed to the other substances present in sea water.

We have seen that the value of KA -4- KM increases as the per cent, of CaCl2 increases and we interpreted this to mean that the reaction A — > M is catalyzed by CaCl2. In the same manner we infer that the reaction R — > 8 is catalyzed by CaCL, since we find that the value of KR •— Ks increases with increasing percentage of CaCl2, as shown in Fig. 65. It is not certain that the curve does not reach a minimum in the mixture of 97.56 NaCl + 2.44 CaCL, but for practical purposes we may, for the present, regard it as a straight line.15

The relation between KN and Ko is taken as constant in the proportion of 100 to 99. It is evident that when the constants have been empir- ically determined for two mixtures the constants for any other mixture can be calculated at once, since all of them depend in a definite manner on Na4XCa (KA and KR also depend on the per cent.of CaCl2). The agreement between the constants thus obtained by calculation and those found by trial is fairly close, as is evident from Figs. 64 and 65.16

Since in pure NaCl or CaCl2 the salt compound Na4XCa is not formed, we should expect that in these solutions all the reactions would be more rapid than in the mixtures. That this expectation is fully realized is evident from Table X. The velocity constants are somewhat higher in NaCl than in GaCL,; this is not explained by the assumptions already made, but it does not seem desirable at present to make additional assumptions for this purpose. We might expect the values of KA -4- KM and RR+- J£s to reach a maximum in CaClj. This is actually the case. It might perhaps be expected that these values would fall to a minimum in NaCl. This is the case with -BTA-f- &M, but not for KR -f- Ks

16 The constants obtained by calculation would fall exactly on the graphs in these figures while those found by trial are indicated by the points given. which the recovery curve rises depends on the value of 0 : the value of 0 -f 10 is shown for all the solutions17 in Fig. 66, which shows the agreement between observation and calculation in respect to the final level reached by the recovery curve, but not in respect to speed of recovery, which depends more on the value of S than on that of 0. The rate of recovery seems to be about the same in the mixtures as in the pure salts. In general it is found that

Fio. 66. — Curves showing the value of O + 10 in 0.52 M NaCl, in 0.278 M CaCh, and in mixtures of these (the figures attached to the curves show the molecular per cent, of CaCh in the solution). The ordinates give the relative values of O +|10, the value in sea water being arbitrarily taken as 100%. These values are obtained by exposing tissue to toxic solutions and then finding the level to which the resistance rises or falls after the tissue is replaced in sea water: they are therefore a measure of permanent injury. The abscissae give the length of exposure to the toxic solution. The curves show the calculated values (using the velocity constants given in Table X). The points show the observed values; each repre- sents the average of six or more experiments. Probable error of the mean less than 10% of

"The values of O + 10 for solutions containing 2.44 and 15.0% CaClj differ slightly from those given earlier for the reason that the curves here presented include a larger series of experiments. 10 is added to the value of 0 because the base line is taken as 10, just as in the case of M. cisely determined. This is owing to the fact that S affects only the speed of recovery (not the final level attained) FIG. 67.— Curves showing the (calculated) values of S in 0.52 M NaCl, 0.278 M CaClz, and in mixtures of these (the figures attached to the curves show the molecular per cent, of CaCl, Jn the solution). The curves show the values calculated from constants obtained by trial which are given in Table X. The abscissa; represent the time of exposure to the toxic solu- tion. The value of S at the start is in all cases 2.7.

and, as the speed is variable, the most satisfactory pro- cedure is to assume such values of KR and Ks in the equation18 as cause the closest approximation to the observed speed of recovery. The values of S thus obtained for each solution are shown in the figure. In general, the speed of recovery, as calculated from these values of S, is in satisfactory agreement with the observations. velocity constants in Table X, we are able to calculate the recovery curves for any solution after any length of exposure.

Fio. 68. — Curves showing the net electrical resistance (descending curve) of Laminaria agardhii in a mixture containing 97.56 mols of NaCl to 2.44 mols of CaCh and recovery in sea water (ascending curves). The figure attached to each recovery curve denotes the time of exposure to the toxic solution. In the recovery curves the experimental results are shown by the broken lines, the calculated results by the unbroken lines. The observed points represent the average of six or more experiments. Probable error of the mean less than 10% of

and calculated values, but it is possible to exhibit graphi- cally the data for three mixtures and for this purpose one in which recovery consists in a rise of resistance (Fig. 68), one in which it shows a moderate fall (Fig. 69), and FIQ. 69. — Curves showing the net electrical resistance (curve which ascends and descends) of Laminaria agardhii in a mixture containing 95.24 mols of NaCl to 4.76 mols of CaCh and recovery in sea water (descending curves). The figure attached to each recovery curve denotes the time of exposure to the toxic solution. In the recovery curves the experimental results are shown by broken lines, the calculated results by unbroken lines. The observed points represent the average of six or more experiments. Probable error of the mean less

one showing a very decided fall (Fig. 70) are presented. In general the agreement between observation and calcu- lation is satisfactory for all the solutions employed in the investigation. It might be thought that the number of constants is sufficient to make it possible to fit any sort of experimen- tal curve and that the consequent agreement between observed and calculated results is less significant than would otherwise be the case. But, as a matter of fact,

FIG. 70. — Curves showing the net electrical resistance (curve which ascends and descends) of Laminaria agardhii in a mixture containing 38 mols of NaCl to 62 mols of CaCl?, and re- covery in sea water (descending curves). The figure attached to each recovery curve denotes the time of exposure to the toxic solution. In the recovery curves, the experimental results are shown by the broken lines, the calculated results by the unbroken lines. The observed points represent the average of six or more experiments. Probable error of the mean less

the constants are so related to each other and to the salt compound, Na4XCa that the whole set of curves fits into a consistent scheme,^ so that when the constants are determined for any two mixtures the theoretical curves f gr all the other mixtures are thereby fixed. Under these circumstances the close agreement in the six different mixtures (ranging from 1.41 to 62.0% CaCl2) seems to be significant. There seems to be no doubt that the behavior of the tissue is such as to indicate an underlying mechanism which is the same in all cases.19 We have assumed that this mechanism consists in the production and decompo- sition of a substance, M, the amount of which, in the mix- tures, depends largely on a compound Na4XCa formed by the combination of Na and Ca with a constituent X of the protoplasm. It is not necessary to discuss these assumptions more fully at present. But it may be pointed out that two things seem to be fairly well estab- lished; (1) a consistent mechanism underlies the entire behavior of the tissue, and (2) its operation can be pre- dicted with a fair degree of accuracy by means of the equations which have been developed. The predictive value of these equations may be regarded as permanently established, since it does not depend on our views regard- ing the underlying assumptions.

The results of these experiments may be summarized as follows: 1. The equations which serve to predict the injury of tissue in 0.52 M NaCl and in 0.278 M CaCl2 and its sub- sequent recovery (when it is replaced in sea water) also enable us to predict the behavior of tissue in mixtures of these solutions, as well as its recovery in sea water after exposure to mixtures. 2. The reactions which are assumed in order to account for the behavior of the tissue proceed as if they

19 This is shown, for example, by the fact that the rapidity of permanent injury (as observed after replacement in sea water) corresponds through- out with the rate of death, and that the rate of change of M corresponds throughout with the rate of change of 0, 8 and A. In other words if ^e change the solution in such a way as to increase (or decrease) one of the reactions on which the resistance depends we simultaneously increase (or decrease) all the others in a definite and predictable manner.

were inhibited by a salt compound, formed by the union of NaCl and CaCl2 with some constituent of the proto- plasm (certain of these reactions are accelerated by CaCl2). 3. A quantitative theory is developed in order to explain: (a) the toxicity of NaCl and CaCl2; (b) the antagonism between these two substances; (c) the fact that the optimum proportions do not change with altera- tions of concentration, and (d) the fact that recovery (in sea water) may be partial or complete, depending on the length of exposure to the toxic solution.

It may be appropriate to call attention to some appli- cations of this theory. Antagonism has been explained by Loeb, and by the writer on the ground that antagon- istic substances prevent each other from entering the cell. As the writer has repeatedly pointed out20, this explanation encounters a difficulty in the fact that antagonistic substances penetrate the cell in a balanced solution (although the penetration is much slower than in unbalanced solutions). The proof of this has been obtained by the writer by means of the method of plas- molysis21 as well as that of electrical resistance22 ; it has recently been confirmed by Brooks23 by means of the method of tissue tension as well as of diffusion through a disk of living tissue and by direct determinations of the penetrating substances made by the writer (see page 216).

It is obvious that antagonistic substances must penetrate from a balanced solution since otherwise the cell could not obtain the salts necessary to its existence. As a way out of this difficulty, the writer has sug- gested24 that the slow penetration of salts may produce effects quite different from those produced by rapid penetration. This difficulty completely disappears if we adopt the standpoint outlined above in developing a dynamical theory of antagonism. From this point of view, we regard the slowness of the penetration of salts in balanced solutions, not as the cause of the antagonistic action but rather the result of it; or we may regard both the slow penetration and the increased length of life (or growth, etc.) by which we measure antagonism, as the results of certain life processes which are directly acted on by the antagonistic substances.

The essential feature of the explanation lies in the behavior of these life processes rather than in the manner or rate of penetration. We assume, as explained above, that certain life pro- cesses may consist of consecutive reactions of the type in which If is a substance which determines the rate of penetration of salts and the electrical resistance of the protoplasm. If the antagonistic substances are NaCl and CaCL, it appears that CaCl accelerates the reaction A — > M, while both A — >M and M — >B are inhibited by a salt compound formed by the union of NaCl and CaCl2 with a constituent of the protoplasm.

From this standpoint the slow penetration of antag- onistic substances should not have unfavorable results provided these substances are properly balanced at the start and remain so (i. e., if their relative proportions are not too much changed by unequal speed of diffusion, precipitation, chemical union, etc.) after they enter the cell. For they must affect the life processes mentioned above in quite the same way in the interior of the cell as at the surface, and these life processes will go on in the normal way so long as the antagonistic substances within the cell remain properly balanced.

The result will be the preservation of normal per- meability as well as of all other properties essential to life. It has been shown25 that the normal permeability may be regarded as a sensitive and accurate indicator of health and vitality. All factors which disturb it bring about temporary or permanent injury and eventually produce death if the action be sufficiently prolonged. It is therefore evident that the life processes which pre- serve normal permeability are of peculiar importance and that the manner in which they are influenced by antagonistic substances is of especial interest.

We may now turn our attention to another aspect of the subject. Explanations have been suggested by Loeb and others to account for the antagonistic action of various substances on living protoplasm, but none of them have thus far developed to the point where they enable us to predict what substances (including both elec- trolytes and non-electrolytes) will antagonize each other and what degree of antagonism may be expected. This kind of prediction is apparently made possible by a hypothesis formulated by the writer, as the result

28 Whatever effects are found at the outer surface of the cell may doubt- less be found also at many of the internal surfaces, such as the surfaces of vacuoles, plastids, microsomes, etc. See Chapter VII. Substances which alter the conductivity of protoplasm may be divided into (1) those which cause an increase, but not a decrease, of conductivity and (2) those which can produce a decrease of conductivity (followed by an increase).26 The hypothesis states that substances belonging to the first class will antagonize those belonging to the second, and vice versa. In order to predict which sub- stances will antagonize each other it is only necessary to determine to which of these classes the substances belong. The amount of antagonism may also be pre- dicted ; at least to a considerable extent, since the greater effect of the substances on permeability, the greater will be their antagonistic action. This relation may be obscured by secondary causes, so that the predictions which it allows will not be of equal value in all cases.27

As we have seen above, NaCl belongs to the first class, being able to increase conductivity but not to decrease it, while CaCl2 belongs to the second class, as it is able to decrease conductivity. 28 It was found that the antagon- ism between NaCl and CaCl2 in the case of Laminaria is well marked. These facts led the writer to formulate the hypothesis as stated above. The next step was to test the hypothesis by the investigation of other salts. Magnes- ium seemed of especial interest for this purpose, as in most of the writer's previous experiments (on other plants) it had shown no antagonism to sodium, though it might be expected on chemical grounds that magnesium and calcium would behave alike. To the surprise of the

The decrease is followed by an increase if the exposure is suffi- ciently prolonged. writer, it turned out that magnesium was able to decrease conductivity, though its effect was much inferior to that of calcium. The antagonistic relations for Laminaria were then investigated, and it was found that MgCl2 was able to antagonize NaCl, though its antagonistic action was much less than that of CaCl2. This unexpected and striking result strengthened the writer's confidence in the hypothesis and led to further investigations. One of these which was of special interest related to acids. For a number of reasons it was sup- posed that acid would not cause a decrease in permeabil- ity. But investigation showed that such a decrease actu- ally occurred in the presence of HC1 and it was then a simple matter to predict that antagonism would be found between NaCl and HC1. This turned out to be the case, the amount of antagonism corresponding to the amount of decrease of conductivity.

These results are also of interest in view of the fact that Loeb29 has shown that salts are antagonized by acids and has pointed out that this has a special significance for the theory of permeability, since it indicates that the permeability of the plasma membrane (for water and substances soluble in water) depends on the presence of protein rather than of lipoid substances. The investi- gations of the writer show that similar (though less striking) antagonism occurs in plants. This affords evidence of the protein character of the plasma mem- brane in plants and is in harmony with the fact that (as the writer has shown) various ions pass through the plasma membrane of plants,30 which would not be expected if it were composed of lipoid.

In carrying out these investigations a solution of HC1 having the same conductivity as sea water (about 0.119 M HC1) was prepared. Various amounts of this were added to a solution of NaCl 0.52 M (which had the same conductivity as sea water). Several lots of tissue were prepared with a view of making them as much alike as possible. One lot of tissue was placed in each of the mix- tures of NaCl + HC1 ; other lots were also placed in pure NaCl and in pure HC1.

The results are shown in Fig. 71. It will be seen that in pure NaCl and in pure HC1 the resistance fell rapidly, indicating injury; while in a mixture in which the dis- solved molecules are 99.09% NaCl and 0.91% HC1, the resistance fell less rapidly, indicating that this mixture was less injurious than either of the pure solutions. In other words, the salt and the acid have an antagonistic action. This antagonism may be expressed quantita- tively (as previously explained31) in the following man- ner : The ends of the antagonism curve are connected by a straight line32 and an ordinate is erected at the point on the curve which is to be measured. For example, the ends of the 30 minute curve in Fig. 71 are connected by the dotted line. The antagonism at the point A (repre- senting a mixture in which the dissolved molecules are 99.09% NaCl and 0.91% HC1) is expressed as AB-+-BC.

The rise in resistance at the end of 1 minute in pure HC1 agrees with the results previously described.33 32 This should in many cases be a curved line, provided the pure solu- tions are not equally toxic. But in the present case the curvature would be small, and at the maximum point of the curve very small indeed. This line expresses the additive effect; i.e., the effect which would be produced if there were no antagonism, and each component of the solution acted independently. (See page 72).

FIG. 71. — Antagonism curve of Laminaria agardhii in NaCl 0.52 M, in HCI 0.119 M, and in mixtures of these. The ordinates represent net electrical resistance (expressed as per cent, of the normal net resistance) ; the abscissae represent the molecular proportions in the mix- tures. Thus NaCl 50, HCI 50 means a mixture of NaCl 0.52 M and HCI 0.119 M in such proportions that 50% of the dissolved molecules is NaCl and 50% is HCI. Each curve repre- sents a single experiment. All readings were taken at 18° C. or corrected to this temperature.