Injury, Recovery and Death in Relation to Conductivity and Permeability

In this case the addi- tive effect is represented by a plane surface parallel to the plane which forms the base of the model. The height of this plane is indicated by the shading in the figure. Other methods (as mixing unequally toxic solutions or keeping the concentration of one salt Ca constant while varying effect a curved surface very difficult to determine and not easily represented or measured on the model. With solutions of more than three components the results cannot be expressed in a solid model; but a graphical expression may easily be obtained in the follow- ing way. Let us suppose that equally toxic solutions of A, B, C and D are to be mixed. A mixture of the first

three may be made and called solution 1 (different mix- tures may be called solution 2, etc. ) . To solution 1 various amounts of D may be added and the results plotted as shown in Fig. 55, in which the additive effect is expressed by the dotted line and the growth in the mixtures by the unbroken line. Antagonism at any point may be easily expressed. For example, the antagonism at the point FIG. 55. — Method of expressing antagonism in mixtures containing more than three com- ponents: three of the components (A, B and C) are combined into solution I and varioue amounts of the fourth component (D) are added; the ordinates represent growth; the abscis- sae represent the composition of the mixtures; thus at the point M the mixture contains 62.5 o.o. of solution 1 to each 37.5 c.c. of solution Z); the antagonism at M is ON -r MN.

tions or by the method of keeping the concentration of one salt constant while varying that of the others, the dotted line would become a curved one. If we mix such solutions as NaCl 0.12 M and CaCl2 0.164 M the antagonism curve resembles the one in Fig. 49. If, however, we reduce the concentration by one-half there will be less toxicity and in consequence the antag- onism will appear less pronounced. In order to illus- trate this, curves have been prepared which are diagram- matic composites of the curves obtained by the use of several pairs of salts ; these composite curves are shown

in Fig. 56. For the sake of simplicity they are represented as having been obtained by the use of one pair of salts, which are designated as A and B. The curve CDE, there- fore, represents diagrammatically the growth of roots Fia. 56. — Effect of dilution on the forms of antagonism curves: the ordinates represent the growth of roots in solutions, the composition of which is represented by the abscissae; for example, on the curve CDE the ordinate at G represents growth in a mixture of A 0.1 M and B 0.12 M in such proportions that 75% of the dissolved molecules are A and 25% are B; on the curve which lies immediately above CDE the ordinate at G represents growth in a mixture of A 0.05 M and B 0.06 M in such proportions that 75% of the dissolved molecules

in mixtures of equally toxic solutions of two salts, A and B. The abscissas represent molecular proportions ; thus the point G represents a mixture in which the dissolved molecules are 75% A and 25% B ; the point H a mixture in which the dissolved molecules are 50% A and 50% B. The ordinates represent the growth of roots in the various mixtures. The antagonism at any point is the total growth minus the growth which would have taken place if no antagonism existed. This antagonism is best expressed as percentage of the growth which would have taken place in the absence of antagonism. Hence the antagonism at the point G is expressed as 100 (GD — FG)-±-FG.

The figure shows in a diagrammatic way the effect of dilution on the form of an antagonism curve. The lowest curve CDE shows the effect on growth of various mix- tures of two equally toxic solutions A 0.1 M + B 0.12 M. The next curve shows the form of the antagonism curve when all of these mixtures were diluted by the addition of an equal volume of water (A 0.05 M + B 0.06 M). The next curve was produced by growing plants in mixtures of A 0.0025 M + B 0.03 M. The topmost curve was obtained with mixtures of A 0.001 M + B 0.0012 M.

The pairs of pure solutions were in each case equally toxic, as is shown by the fact that the two ordinates at the ends of each curve are equal in height. It will be observed that as the solutions become more dilute, the antagonism curve becomes flatter, and it is evident that at still greater dilutions it must tend to become a horizontal straight line. In order to give a complete description of the changes in the antagonism curve as dilution increases, it is neces- sary to construct a solid model. This might have as its base a triangular diagram as previously described. The apices of the triangle would in that case represent, A, B, and H20.

It is more suitable for our present purpose to employ a square as the base and to represent the composition of the solutions according to the scheme shown in Fig. 57. In this figure the abscissae have the same significance as in Fig. 56, while the ordinates represent various dilutions of the mixtures. Thus all points on the line CD represent distilled water, while a point such as E, halfway between A and C, represents a mixture containing equal quantities of distilled water and of A 0.1 M. The points on the line EF, therefore, represent the same mixtures as the corresponding points on the lowest line, ex- cept that the concentrations are in all cases just one-half as great as those represented on the base line. It is evident that the growth in any concen- tration may be expressed by erecting at the proper point a line perpendicular to the plane of the paper. In this way, we

gives a complete description of the changes in growth produced by diluting the various mixtures. Such a model is shown in Fig. 58. In all of these cases the measurements are made after growth has ceased and in consequence they represent a final condition of development. If, however, we use electrical conductivity as a criterion of antagonism, we obtain curves which change constantly. (See Fig. 78). In this case the best method of procedure is to construct the time curves of the death process and to compare the

FIG. 57. — Diagram representing the composition of solutions (this serves as the base of the solid model shown in Fig. 58): the lowest line represents various mixtures of solutions of two salts, A and B; the line EF represents the same mixtures diluted with equal volume of water; any line drawn parallel to EF will express the same mixtures diluted to a degree corres- ponding to the position of the line, the FIQ. 58. — A solid model which gives a complete description of the changes produced in th e form of the antagonism curve by altering the concentrations of the solutions.

velocity of the process in various mixtures. A series of such time curves is shown in Fig. 59. In the preceding pages a theory is developed which enables us to predict the behavior of Laminaria when transferred from sea water to certain solutions, e.g., NaCl Fio. 59. — Curves showing the net electrical resistance of Laminaria agardhii in 0.52 M NaCl, in 0.278 M CaCl:, and in mixtures of these (the figures attached to the curves show the molecular per cent, of CaCls in the solution). The curves show the calculated values (from constants obtained by trial) which are given in Table X, the points show the observed values (some are omitted in order to avoid undue crowding) ; each represents the average of eii or more experiments. Probable error of the mean less than 10% of the mean.

0.52 M and CaCl2 0.278 M. If the theory is sound it should also enable us to predict the behavior of the tissue in mixtures of these solutions. In order to test this theory experiments were made with a variety of mixtures. The solutions employed are given in Table IX. The electrical resistance of the tissue in these solutions, is shown in Fig. 59. The curves are in good agreement with the formula This is evident from Figs. 59 to 63, which show the curves calculated by means of this formula and also the observed values.

As previously explained, this formula is based upon the assumption that the electrical resistance is propor- tional to a substance, M, which is formed and decomposed by the reactions We assume that when the tissue is transferred from sea water to NaCl, or to CaCl2, or to a mixture of these two solutions, the reactions 0 — >S — >A cease, while the reactions A — >M — >B continue. By assuming various values of K A (the velocity constant of the reaction A — > M) and of KM (the velocity constant of the reaction M — > B), and employing these in the formula, we obtain curves which closely approximate those which we find by experi-

ment. The values of the velocity constants which are thus obtained, are given in Table X. It is evident from Table X, that as the per cent, of CaCl2 in the mixtures increases (beginning at 1.41% CaCl2) the value of KM first falls and then rises, its FIG. 60. — Curve of net electrical resistance of Laminaria agardhii in 95.24 NaCl + 4. 76 CaClj (unbroken line) the trial curve (broken line) calculated from the velocity constants KA experiments: probable error of the mean less than 10% of the mean. All readings were

minimum value occurring in 97.56 NaCl + 2.44 CaCl2 (which is the mixture in which the tissue lives the long- est.). It seems reasonable to assume that in each mixture a substance is formed which reduces the value proportional to the amount of this substance, which may be assumed to occur in maximum amount in 97.56 NaCl + 2.44 CaCl2. The simplest assumption which we can make is that NaCl and CaCl2 combine with some constituent of the protoplasm, as X2, to form a compound.8 If we suppose that the compound is Na4XCa, formed by the revers- ible reaction

we can calculate the amount of Na4XCa which is formed in each mixture of NaCl and CaCl2. If antagonism really depends on the production of a salt compound, it is evident that some mechanism must exist which insures that an increase in the total concen- Fio. 61. — Curve of net electrical resistance of Laminaria agardhii in 85 NaCl + 15 CaCil (unbroken line) ; the trial curve (broken line) calculated from the velocity constants KA = .000364 and KM =.0073. Each observed point represents the average of six or more experi- ments: probable error of the mean less than 10% of the mean. All readings were made at

tration of salts can have but little effect as compared with that produced by a change in their relative proportions. * It is assumed that XZa, Na4XCa, and ZC18 are in solution. Since the per cent, of XZa which is transformed to Na4XCa is negligible, the con- centration of XZ2 may be regarded as constant. It is easy to see how such a mechanism must exist if the formation of the salt compound takes place at a surface (at the external surface of the cell or at internal surfaces). In a surface, substances usually exist in a dif- ferent concentration from that which they have elsewhere

Fia. 62. — Curve of net electrical resistance of Laminaria agardhii in 65 NaCl + 35 CaCh (unbroken line), the trial curve (broken line) calculated from the velocity constants KA= .000481 and KM=. 00859. Each observed point represents the average of six or more experi- ments: probable error of the mean less than 10% of the mean. All readings were made at in the solution. If NaCl and CaCl2 migrate into the sur- face, so as to become more concentrated there than in the rest of the solution, their concentration in the surface must increase as their concentration in the solution increases until a certain point (called the saturation point) is reached. Beyond this point an increase in their concen- tration in the solution produces no effect on their concentration in the surface.

the salt compound, if it takes place in the surface, will not be affected by an increase in the concentration of the salts in the solution. It will, however, be affected by changes in the relative proportions of the salts. The Fia. 63. — Curve of net electrical resistance of Laminaria agardhii in 38 NaCl + 62 CaCl* (unbroken line) and the trial curve (broken line) calculated from the velocity constants KA = .000530 and KM = .0090. Each observed point represents the average of six or more experiments: probable error of the mean less than 10% of the mean. All readings were

number of molecules of salt in a unit of surface will remain nearly constant, but if the proportion of NaCl in the solution be increased some of the CaCL in the surface will be displaced by NaCl. Below the saturation point the relative proportions of the salts will be of less importance than their total concentration: this is the case at low concentrations in the region of the so-called "nutritive effects. " It has been pointed out by the writer9 that while va- riations in concentration affect the form of the antagonism curve, they do not in general affect the proportions which are most favorable for life processes.

It is therefore evident that if we wish to preserve the favorable character of a mixture when the concentration of any antagonistic substance is increased we must at the same time increase the concentration of the others in the same proportion. In discussing the results of his experiments on ani- mals, Loeb10 states that the law of direct proportionality, found in such cases is in reality Weber's law.11 In regard to the significance of this, Loeb says :

1 1 Since this law underlies many phenomena of stimu- lation, if appears possible that changes in the concentra- tion of antagonistic ions or salts are the means by which these stimulations are brought about, as suggested by my ion-protein theory and by the investigations of Lasareff." In view of the importance of these relations it seems desirable to point out that the hypothesis of the writer explains the mechanism which makes one proportion better than others and preserves this preeminence in spite of variations in concentration.

We assume that CaCl2 accumulates in the surface to a greater degree than NaCl. The increase in concentra- tion of CaCl2 in the surface is supposed to be ten times as great as the corresponding increase of NaCl, so that the proportions in the surface are those given in Table XI. For example, when the proportions in the solution are 97.56 NaCl + 2.44 CaCl2, the proportion of NaCl to CaCl2 in the surface is as 97.56 to 24.40, which is equivalent12 to 80 NaCl + 20 CaCl2.

As previously explained it is assumed that the reaction takes place in a surface which is saturated with respect to NaCl and CaCla BO that while one of these may be displaced by the other (in case their relative proportions in the solution are altered) the total concentration does not change; for convenience this concentration is taken as 100 and the sum of NaCl + CaCl2 is therefore always equal to 100. Proceeding in the same manner with the other mix- tures, we get the values given in Table XI. Starting with

FIG. 64. — Shows the increase of a hypothetical salt compound Na4XCa (see Table XI) and the corresponding decrease of the velocity constants KN, K o, Ks and KM (these constants are given in Table X). The figures on the abscissae give the molecular per cent, of CaCla in the mixture. The mixture containing 62.0% CaCh is taken as the standard of comparison: proceeding from this to the mixtures containing less CaCh we find that Na4XCa increases and the velocity constants decrease as shown by the ordinates. In order to facilitate com- parison the values of KN have been multiplied by 0.989; of Ko by 0.991; of Ksby 0.383; and

the lowest value (that in 62.0% CaCl2) we observe that there is an increase as the per cent, of CaCl2 decreases until 2.44% is reached (the amount of this increase is shown in Column 6 of the table). Conversely we find (Table X) that the velocity constants are higher in 62.0% CaCl2 than in any other mixture and that they decrease as the per cent, of CaCl2 decreases to 2.44%. Thus in the case of KM the value in 62.0% CaCL is 0.009, in 2.44% CaCl2 it is less by 0.00354, while in 15.0% it is less by 0.0017, and in 35.0% by 0.00041 ; if we multiply these num- bers by the constant factor 0.251 they agree very closely with the figures for the increase in Na4XCa. These values are plotted in Fig. 64, which shows that the decrease in KM is directly proportional to the increase in the amount of Na4XCa. Hence we assume that Na4XCa acts as a negative catalyzer or inhibitor of the reaction M — >B. An inspection of Table X shows that the value of KA fluctuates with that of KM, except that as CaCl2 increases the value of KA rises more rapidly than that of KM. This is also obvious from Fig. 59, which shows that the greater the per cent, of CaCl2 in the mixture, the greater the maximum attained. Since this maximum increases as the value of KA -r- KM increases, it is evident that the value of KA -T- KM must rise as the per cent, of CaCl2 becomes greater. The value of KA-^ Kuin the solution containing 1.41% of CaCl2 is 0.03333 while in the solution containing 62.0% CaCl2 it is 0.05889, an increase of 0.02556. If we calculate this increase for the other mixtures and plot the values so obtained against the per cent, of CaCL in the sur- face, we obtain a straight line as shown in Fig. 65. This indicates that CaCl2 catalyzes13 the reaction A —> M • for if this were not the case the value of KA and J^^-would rise

In the absence of Na4XCa it would appear that NaCl catalyzes the death process, since death is more rapid in NaCl 0.52 M than in 0.26 M. and fall in such a way that the value of KA -v- KM would remain constant. It is evident from Figs. 64 and 65 that the values of KA and KM are determined by the amount of Na4XCa and by the per cent, of CaCl2 in the mixture, and that when these values are experimentally determined for any two FIG. 65. — Graph showing the increase of KA -i-KAfand the value of K R +Ksas the molecular

per cent, of CaCb increases. The figure shows that CaCh acts as a catalyzer of the reaction A — >• M (which has the velocity constant K^) and also of the reaction R — >~ S (which has the velocity constant K^)- The figures on the ordinate at the right show the values of K K -f- Ks; those on the ordinate at the left show the increase in the value of K A •— K M over the value found in the mixture containing 1.41 % CaCh. The abscissae denote molecular per cent, of CaCh in the surface (not in the solution).

mixtures they can be calculated for any other mixture. When this is done we can calculate the course of the death curve in that mixture. Having thus accounted for the death curves, we may turn our attention to the process of recovery. We find that, when tissue is removed from a mixture of NaCl and CaClo, and replaced in sea water, the resistance at once rises or falls and after a time becomes stationary. This rise or fall of resistance may be called recovery.

we replace the tissue in sea water the reactions 0 — >• 8 — >A — >M — >B proceed at the rates which are nor- mal for sea water. The manner in which the rate of recovery is calculated has already been explained in detail. It is assumed that during the exposure to any of the mixtures the following reactions occur: (1) N— >0— ^P;(2)# — >S— >T ; (3)A—+M-+B. By assuming values of the velocity constants of these reactions we can approximate the observed results. The velocity constants thus found are given in Table X. An inspection of the table shows that all these velocity constants behave like KA #nd KM in that as the per cent, of CaCl2 in the mixture increases (beginning with 1.41% CaCl2) the value of the velocity constant first falls and then rises, and that this value in every case reaches its minumum in the mixture containing 97.56 NaCl + 2.44 CaClo. It would therefore appear that the reactions N — *• 0 — •*• P and R — *> 8 — •*- T are inhibited by Na4XCa in the same manner as the reactions A — >• M — >• B. This is borne out by an inspection of Fig. 64, in which the decrease14 of the velocity constants is plotted, together with the increase of Na4XCa.