holding 5 c.c. and was driven at a constant rate by break induction appreciably in strength.

Transcription

1 THE REACTION BETWEEN ACETYL CHOLINE AND MUSCLE CELLS. BY A. J. CLARK. (Pharmacological Department, University College, London.) ACETYL CHOLINE is exceptionally well adapted for the study of the laws governing the reactions between drugs and cells, for the following reasons: (1) It produces graded reactions over a remarkably wide range of concentrations. (2) It affects a variety of tissues and produces different types of actions in different tissues. (3) It acts rapidly and its action is quickly and completely reversible, hence a large number of experiments can be performed on a single preparation. The action of acetyl choline hydrochloride was studied on both the isolated ventricle and rectus abdominis of Rana temporaria. The drug used came from three sources, namely, a sample kindly given me by Dr H. H. Dale, a preparation of Messrs British Drug Houses and a preparation of Messrs Kahlbaum. The three samples did not differ appreciably in strength. Experiments on the heart. Acetyl choline when it acts on the intact isolated frog's heart produces several actions. It diminishes the frequency of the sinus rhythm, diminishes the rate of conduction between the auricle and ventricle and decreases the force of contraction of the auricle and ventricle. In order to obtain a quantitative measure of the action of the drug it was obviously desirable to study one effect alone, and the effect chosen was the depression of the force of contraction of the ventricle. A longitudinal strip of ventricle was cut off, consisting of about one-third of the ventricle. It was suspended in a container holding 5 c.c. and was driven at a constant rate by break induction shocks. The usual frequency was 20 per minute. The stimulus was passed through the length of the strip to eliminate any effects due to alterations produced by the drug in conduction. In most cases the responses were recorded isometrically by a light lever attached to a strip of steel. The lever gave a deflection of 1 cm. when 2 grm. tension was applied, and the relation between excursion and tension was linear up

2 ACETYL CHOLINE. to 5 grm. tension. The tensions recorded usually were less than this. In some cases an isotonic lever was used. This provided a more sensitive measure of very slight effects but did not give as accurate a measure of actions approaching maximal, that is, complete arrest. The Ringer's fluid had the following percentage composition: Air NaCl 0*65; KCl 0*014; CaCl2 anhyd..0024; NaHCO3 0 05; ph 8*0. was bubbled through the container. I found that acetyl choline decomposed fairly rapidly in dilute solution, and particularly rapidly in the alkaline oxygenated Ringer's fluid; care therefore was taken to use freshly diluted drug. The drug was sometimes added to the fluid in the container and sometimes the final dilution was made outside and the fluid in the container changed. Hearts showed great individual variation in their sensitivity to the drug, but the response of a single strip was fairly uniform. In particular the strips did not show any well-marked increase or decrease in sensitivity after prolonged isolation. The responses given during the first hour often were irregular but a heart after 24 hours' isolation showed the same,sensitivity as a heart after 1 hour's isolation. I found that changes in ph from 8-0 to 7 0 produced no demonstrable variation in the response of the heart to acetyl choline. Andrus and Carter(l) found that the drug acted on the heart more powerfully at ph 7 0 than at ph 8&0, but it seems possible that their results may have been due to the drug being destroyed more rapidly in alkaline than in neutral solution. Since slight changes in reaction did not appear to produce a measurable effect bicarbonate Ringer's fluid was used in preference to fluid buffered with borates because the preparation contracted more vigorously with the former fluid. Acetyl choline produces its maximal action on the heart sometimes in a fewl seconds and always within a minute. After this the heart partially recovers, Fig. 1. Partial recovery of heart during' but the degree of recovery is very ~exosure to acetyl choline. The lower upper curves are from experivariable, as is shown in Fig. 1. A similar ments on different hearts. In both et v.as noted bystraucases l 531 acetyl choline 10' molar was effect wvas noted by istraub2} when introduced at the arrow, and the muscarine acted on the heart. The second portions of the curves show the significance of this effect wfll be dis- for 30 actions minutes. after exposure to the drug cussed later. This recovery effect is a source of error in quantitative experiments. 35-2

3 532 A. J. CLARK. I took the greatest effect produced by the drug as the measure of its action and in cases where the immediate effect was followed by a sharp rise, as sometimes happened, the results were discarded. The isometric measurements obtained in the manner described do not provide a true, measure of the isometric response of the heart but they were found to be a more satisfactory quantitative measure than records of isotonic contractions. Fig. 2 shows a series of measurements obtained with the -_ -U -I - f -5-4 Log molar cona. Fig. 2. Relation between conoentration and action of acetyl choline on the frog's heart Ordinate: percentage of maximal possible action. Abscissa: logarithm of molecular conoentration. Curve I, isotonic (Straub's cannula); Curve II, isometric (ventricular strip). whole heart perfused with a Straub's cannula holding 0 5 c.c. of fluid. This preparation was about ten times as sensitive as the isometric strip; but when the concentration of the drug was increased the heart. soon reached a condition in which it was unable to lift the apex of the ventricle against the weight of the water, and after this point visible movements continued but no accurate measurement could be obtained. Heart strips prepared in the manner described and suspended in air will contract regularly and without diminution in force, for at least 30 minutes, and therefore this preparation could be used to measure the absolute quantity of drug needed to produce a particular action, as opposed to the concentration of drug which produced the same actioa

4 ACETYL CHOLINE _- - PER CENT ACTIoA / I x Ii: Log molar conc. Fig. 3. Action of acetyl choline on Rectus abdominis as a function of concentration. I, isotonic; II, isometric. Abscissa and ordinate as in Fig. 2. Fig. 4. Action of aoetyl choline on Rectus abdominis. Specimen curves of isotonic contractions and relaxations Ordinate-movements of lever point. W =wash-out.

5 534 A. J. CLARK. when the drug was present in excess. For this purpose a quantity of solution from 05 to 2*5 mg. was added to the moist strip. Quantities above 1 mg. were added by means of a capillary pipette while smaller quantities were added by dipping a weighed thread in the solution, weighing the thread again, and then cutting off a length which would contain the correct amount of solution. Experiments on Rectus abdominis. Acetyl choline produces a contraction of the Rectus abdominis of R. temporaria, and acts in concentrations comparable to those which produce depression in the heart. The isolated Rectus abdominis was suspended in Ringer's fluid and its movements were recorded by an isotonic lever producing a tension on the muscle of about 2 grm. Acetyl choline was found to produce a much more extensive isotonic than isometric response, as is shown in Fig. 3. Tracings of typical contractions produced by acetyl choline are shown in Fig. 4. The relation between concentration and action. The relation between the concentration of acetyl choline hydrochloride and the isometric response of the frog's ventricle is shown in Fig. 5, and the same relation P7'R CENT1 ACTION 1TT 60 I C M Fig. 5. Action of acetyl choline on heart (isometric) as a function (i) of concentration, and (ii) of absolute amount of drug added. Ordinate: action expressed as percentage of maximal possible action. Abscissa: along top (and curve I). Log. of molar concentration of drug added in excess in dilute solutions. Along bottom (and curve II). Log of gram molecules of drug added in concentrated solution to moist heart.

6 ACETYL CHOLINE. 535 for the isotonic response of the Rqctus abdominis is shown in Fig. 6. In both cases the action produced by the drug is expressed as the percentage of the maximal possible action which it can produce. The drug ACPTI~ Fig Log molar conc. Action of acetyl choline in producing isotonic contraction of the Rectus abdominis as a function of concentration. Ordinate and abscissa as in Fig. 2. produces depression of the heart and the maximal action is total arrest of the heart. By the aid of a reading microscope it is possible to measure contractions which are less than 1 p.c. of the original amplitude; it is possible, therefore, to measure actions between 90 p.c. inhibition and complete arrest with considerable accuracy. On the other hand, it is not possible to measure reductions of less than about 5 p.c. of the normal response. In the case of the Rectus abdominis a contraction of less than 1 mm. on the record could be detected, and this was less than 1 p.c. of a maximal contraction. On the other hand, there is no sure measure of the maximal contraction that the muscle can produce, and therefore the figures for contractions above 90 p.c. of maximal are somewhat uncertain. In both cases the figures observed lie along a curve which can be fitted closely by the equation K. x = 0 y, where x = molecular concentration of the drug; y= action produced expressed as percentage of maximal action; K = constant. Curves drawn according to this formula are shown in Fig. 2, curve II, Fig. 3, curve I, Fig. 5, curve I,

7 536 A. J. CLARK. and Fig. 6. Inspection of these curves shows that the responses observed follow the theoretical curve fairly closely. If K.$= loo y, x must be a linear function of -y. The wide range of concentrations used necessitates the plotting of x on a logarithmic scale and Fig. 7 shows Log x plotted against log,_y, and loo-y I ~~~~~~100-y x E 1-5 ~v- 10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-0 x x 0-5 0~~~~~~~~~~~~~~~~01 / EBw -/*U -b-, -ff-o Log x Fig. 7. The relation between the concentration of acetyl choline and the response produced. Ordinate: Log Y" Abscissa: Log. of molar conc. of acetyl choline. Curve I. Action on isometric response of frog's ventricle (calculated from exp. in Fig. 2, curve II). Curve II. Action on isotonic contraction of frog's Rectus abdominis (calculated from exp. in Fig. 6). inspection shows that the relation is linear. formula Log K + Log x =Log YOO-y Curve I in Fig. 7 follows the within the limits of error; Log K being Curve II in Fig. 7 follows, however, the formula LQg K+ 0-8 Log x - Log Y or K. x058= V

8 ACETYL CHOLINE. 537 I made a number of experiments to try and determine the value of n in the formula K. xn. Unfortunately it is impossible to get very exact quantitative measurements of the responses of either the frog's ventricle or Rectus abdominis. The variations in repeated responses of the tissue to the same concentrations are shown in the figures, and indicate the limits of accuracy of these experiments. I obtained values for n varying from 0-8 to 1.1, and the average value of n was very close to unity. Values for n below one were somewhat more frequent than values above one. I concluded that the probable value of n was one. The following values were found for K. In 15 experiments upon heart strips contracting isotonically K varied from 33,000,000 to 1,600,000, and the average value was 10,000,000. In 19 experiments upon heart strips, where the response was measured isometrically, K varied from 20,000,000 to 100,000 with an average value of about 1,000,000. In six experiments upon the Rectus abdominis the value of K varied from 400,000 to 10,000 with an average of 40,000. These figures show that one heart may be 200 times more sensitive to acetyl choline than another heart. This is not a seasonal variation, for such differences were observed on successive days. Graded actions in a single series of experiments could be measured over a 10,000-fold range of concentrations. There was, moreover, a 3000-fold difference between the sensitivity of the most sensitive ventricle and the least sensitive Rectus abdominis. In the case of the ventricle the inhibition of an isometric response was measured and in the case of the Rectus abdominis the production of an isotonic contraction. In all cases the results obtained could be fitted, within the limits of experimental error, by the formula given above. It appears improbable, therefore, that the agreement between the measurements obtained and the formula is a chance one. The rate of action of acetyl choline. Acetyl choline can act extremely rapidly on the ventricle. Measurements on a rapidly moving drum in one case showed that when the drug was poured directly on to the ventricle a solution of 5 x 10- molar acetyl choline produced half its final action in less than a second. The rate of action varied greatly in different preparations, as is shown in Fig. 1. The action with more dilute solutions was less rapid but in all cases the drug produced half its final action in less than 30 seconds. The rate of removal of the drug on washing out was equally rapid. In this latter case the recovery of the heart was slower after high than after low concentrations of the drug had been applied. In the case of the ventricle

9 538 A. J. CLARK. both the rate of action and the rate of removal of acetyl choline appear to be determined chiefly by the rate of diffusion of the drug through the sponge-like tissue of the heart, and hence no satisfactory analysis of these rates can be made. The Rectus abdominis reacts more slowly than the ventricle to acetyl choline, and the rates of reaction and of wash-out are shown in Table I. TABLE I. Rate of action of acetyl choline on Rectus abdominis. Molecular concentration 5 x x x 10-f 1.5 x 1O- 5 x 1O- 5 x 1O-4 25 x x 1O Time in seconds till half final contraction Time in seconds after washing out till half relaxation Unfortunately, the significance of these latter figures is somewhat doubtful, because even to certain types of instantaneous stimulus the Rectus abdominis gives a sluggish response. For example, if the muscle was extended with a weight of 5 grm. I found that when the weight was removed the muscle contracted slowly and took nearly three minutes to produce half of the resultant change in length. The rate of change in length, therefore, does not give a measure of the rate of union between the drug and the muscle. Table I shows, however, that in the case of the Rectus abdominis the higher the concentration of the drug the more rapid is its action, and that the time needed for removal of the drug is greater after high than after low concentrations. The influence of temperature on the action of acetyl choline. Alterations in temperature produce no certain effect upon the amount of action produced by acetyl choline upon either the heart or the Rectus abdominis. This is shown in Tables II and III. Increase of temperature, however, increases both the rate of action of the drug and also the rate at which it is washed out, as is shown in Table IV. This table also shows that the rate of contraction, and the rate of relaxation on washing out, TABLE II. Influence of temperature on the action of acetyl choline on the heart. (The figures show the percentage reduction of the response of the heart.) Mol. concentration of acetyl choline hydrochloride 5 x x O0 Temperature 110C C C C

10 ACETYL CHOLINE. 539 TABLE III. Influence of temperature on the action of acetyl choline in causing contraction of Rectus abdominis. (The figures show the contraction expressed as a percentage of maximal contraction.) Mol. concentration of acetyl choline hydrochloride 5 x 10H 5 x 1O5 Temperature 5 C. 41* C C TABLE IV. Influence of temperature on the rate of action of acetyl choline on Rectus abdominim. (The figures show the time in seconds until half the action is produced.) Contraction on introduction Relaxation on washing out of drug of Mol. concentration drug of acetyl A, _ choline hydrochloride 5 x 10^ 5 x 10-5 x 10^ 5 x 10- Temperature 70 C C C are affected equally by a rise of temperature. This is in accordance with the observation that changes in temperature do not alter the final equilibrium between the drug and the muscle as indicated by the extent of action -produced. If we suppose the action of acetyl choline to be proportional to the degree of combination of the drug with some element of the muscle, then the absence of an action of temperature on the final equilibrium state shows that the heat of reaction of the drug with the tissue is comparatively small. The quantity of drug which reacts with the heart. The results obtained when small amounts of drug are added to the moist ventricular strip show at 'on'ce that the total quantity of drug necessary to produce an action on the heart is very small. For example, the total amount of drug added which was satfficient to produce a 50 p.c. reduction in the response of the heart strip in Fig. 5 was only grm. molecules. Figs. 8 and 9 are types of the records from which Fig. 5 was compiled, and they show that the action of acetyl choline on the moist ventricular strip is exactly similar to its action on the strip immersed in solution, and therefore the two sets of actions can be compared quantitatively. Fig. 5 shows, however, that the relation between the quantity of drug added in concentrated solution and the amount of action produced is not the same as that already shown to exist between the concentration of the drug (when present in excess) and its action. For example, the concentration of drug needed to produce 90 p.c. of full inhibition is

11 540 A. J. CLARK. 100 times that needed to produce 10 p.c., but when small quantities of drug are added then the quantity required to produce 90 p.c. of full inhibition is 1000 times that needed to produce 10 p.c. Fig. 8. Action of acetyl choline on the isotonic contraction of ventricular strip (weight 30 mg.). The curves show either (i) effect of immersion in 5 c.c. solution, or (ii) effect of adding a small quantity of concentrated solution. (i) Molar concentrations of solutions x 168: B, 2-5; C, 0-9; F, 5*0 and G, 2-5. (ii) Gram molecules of drug added x 1(P2: A, 0-6; D, 0 3 and E, 1-5. Fig. 9. Action of acetyl choline on isometric response of ventricular strip (weight 25 mg.; frequency 20 per min.). Upper curves. Effect of immersion in solution. Molecular concentration x 108: 5, 25, 50, 250, 500, Lower curves. Effect of adding small quantities of drug to moist strip. Gram molecules added x li"s: 1-25, 12-5, 125, 1250, 12,500 and 62,500.

12 ACETYL CHOLINE. The quantity of drug entering the muscle cells. The figures obtained permit an approximate calculation of the amount of drug actually entering the muscle cells and thus the determination of the relation between this factor and the amount of action produced. In the records shown in Fig. 5 the addition of 5 c.c. of solution at a concentration of 4 x 10- molar produced a 50 p.c. inhibition of the heart. The 5 c.c. of fluid contained 2 x 10-8 grm. mol. of drug, and the action observed could be produced by the addition to the moist strip of grm. mol. Therefore the amount of drug taken up by the heart must have been too small to aflect appreciably its concentration in the 5 c.c. of fluid. A 50 p.c. reduction in the response must therefore have been associated with a concentration of 4 x 10-6 molar around the heart cells. When, therefore, grm. mol. added in concentrated solution produce a 50 p.c. reduction in force, sufficient of this quantity must remain in the intercellular fluids of the heart to maintain a concentration of 4 x 106 molar and the remainder is presumably absorbed by the heart cells. I found that moderate pressure between filter paper caused a moist heart strip to lose about 30 p.c. of its weight. A study of sections of the frog's ventricle showed that about 50 p.c. of the area of the section was occupied by intertrabecular spaces. The heart strip may therefore be assumed to consist of about 50 p.c. of muscle cells, and 50 p.c. of intercellular and intertrabecular fluid. With these assumptions the amount of drug that enters the heart cells can be calculated. TABLE V. The quantity 'of acetyl choline hydrochloride absorbed by the heart cells , 4 5 Quantity of Quantity of drug drug which which produces must remain Concentration of reduction when outside cells to dilute solution added in produce the Reduction of needed to produce concentrated concentration contraction reduction solution shown in col. 2 p.c. (Mol. conc. x 107) (G. mols. x 1012) (G. mols. x 1012) Exp. 31. Ventricular strip 25 mg. Isometric contraction Exp. 6. Ventricular strip 30 mg. Isotonic contraction * Quantity of drug that can *enter cells (G. mols. per mg. of cells x 1012)

13 542 A. J. CLARK. Table V and Fig. 10 give the results of a series of calculations made on these assumptions and they show that the amount of drug taken up by the cells varies approximately as (concentration)2. The relation between the amount of action produced (y) and -9 the concentration (x) is however expressed by the formula K.x= y a loo-y' -10 There is, therefore, no direct relation between the amount of action produced and the amount of drug entering the -11 cells İn the first experiment in Table V a 10 p.c. reduction was produced in a _12 strip weighing 25 mg. by a 2 x 10-7 mol. solution and in the moist strip by a 0 quantity of 3.3 x grm. mol.; this _13 latter quantity would, however, only produce a concentration of 1-3 x 10-7 mol if distributed equally throughout the Fig. 10. Relation between the con- 25 mg. of fluid and tissue. In this case, centration of acetyl choline and the therefore, the concentration of drug amount of drug taken up by the thad- heart cells (two experiments). Orside the cells must actually have been dinate: Log of gram molecules of drug taken up by 1 mg. of tissue. less than the concentration of drug Abscissa: Log of molar concentraaround the cells. On the other hand, tion of drug. when larger quantities of drug are added its concentration must be considerably greater within than around the cells. These experiments suggest, therefore, that t,he action of acetyl choline in producing inhibition of the heart cells, and the entrance of the drug into the cells are two independent processes, which have no certain relation to each other. The amount of drug reaction with a single cell. The experiments with small quantities of drug permit the calculation of the amounts of drug that unite with a single cell. Table V shows that a 50 p.c. reduction in the isometric response of the heart is produced by 6.2 x grm. mol. per milligram of heart cells, and that a demonstrable action occurs when about one-hundredth of this amount enters the heart cells. The isotonic records shown in Fig. 8 and Table V show that a demonstrable action is produced when about grm. mol. per milligram of heart cells is taken up by the tissue. The average measurements of the spindleshaped heart cells of the frog are 130,u x 10,u (Skramlik(3)). Each

14 ACETYL CHOLINE. 543 cell, therefore, has approximately a cubic content of 3400Au3, and a surface area of 2000 u2. One mg. of heart tissue will contain, therefore, approximately 300,000 cells, and this will have a total surface of 6 sq. cm. One molecule of a fatty acid in a condensed film on the surface of water covers a surface of about 20 x sq. cm. (Langmuir, Adam), a molecule of cholesterol about 40 x sq. cm., and each fatty acid chain of lecithin about 50 x sq. cm. (Leathes(4)). It appears probable, therefore, that a molecule of acetyl choline will cover between 20 and 100 x sq. cm. One grm. mol. may be taken as containing 7 x 1023 mol. and therefore if 1 mg. of heart cells takes up 6.2 x grm. mol., each heart cell will take up 7 x 102x 6.2 X x lo 2 = 14,000,000 mol. and this number will cover an area of the order of 10-7 sq. cm. whereas the cell has an area of 2 x 10-5 sq. cm. The smallest quantity of acetyl choline observed to produce an action, namely, grm. mol. per milligram of heart, would provide about 20,000 molecules per cell and these would cover an area of the order of sq. cm. These figures show that it is impossible that acetyl choline should act by forming a continuous layer over the surface of the heart cells, or by covering any larger area inside the cells. The amount of drug reacting with the Rectus abdominis. A few experiments with small quantities of fluid were performed on the Rectus abdominis. In one case the muscle weighed 0.1 grm. and a contraction 50 p.c. of the maximal was produced by immersion in 20 c.c. of 104mol. solution, or by adding to the moist muscle 2 x 10-9 grm. mol. of acetyl choline. This latter quantity would, however, produce a concentration of 10- mol. in only 0-02 c.c. This experiment suggests that the concentrated solution diffuses only into about one-fifth of the muscle. The result would be accounted for if the drug diffused into the tissue fluids of the muscle and the amount taken up by the muscle cells was negligible. This accords very well with the results obtained upon the heart, but I am not satisfied that the concentrated solutions diffused evenly throughout the muscle and therefore the experiments cannot be regarded as conclusive. Discussion. These experiments throw some light on the mode of action of acetyl choline on muscle cells. Straub(2) concluded that alkaloids act on heart muscle in two ways, for he showed that some alkaloids such as strychnine and morphine were concentrated in the heart cells whereas other drugs such as muscarine, pilocarpine and adrenaline

15 544 A. J. ClARK. were not so concentrated. He concluded that the action of these latter drugs was dependent on the potential difference between their concentrations within and without the cells. This conclusion was based on the fact that muscarine gradually entered the cells and as the drug accumulated in the cells its action on the heart diminished. This passing off of the action of a drug after prolonged exposure of a tissue to it has also been shown to occur when pilocarpine acts on the rabbit's isolated intestine (Neukirch(5)), and when adrenaline acts on the same tissfie (Jendrassik(6)). Wertheimer and Paffrath(7) investigated a series of choline compounds and found that the intensity of their action was inversely proportional to the rate at which they diffused into living tissues. For example, they found that acetyl choline had 1000 times as intense an action as choline upon the isolated gut of the guinea-pig but that choline diffused through frog's skin 1000 times as rapidly as acetyl choline. My results agree with the above observations in that they show that there is no direct relation between the amount of acetyl choline which enters the heart cells and the action of the drug on the cells. The results described can be explained most readily on the assumption that two processes are occurring, namely, an action of the drug on the cell surface which proceeis very rapidly and which commences at very high dilutions, and secondly, an entry of the drug into the cells which proceeds more slowly and commences at higher concentrations. I consider it is doubtful whether the partial recovery of the heart on prolonged exposure, as shown in Fig. 1, is due to the entry of the drug into the cells, because in the first place this recovery effect is remarkably variable as is shown by the two curves in Fig. 1, and secondly, because no similar recovery effect was observed when acetyl choline was allowed to act for periods as long as 2 hours upon the Rectus abdominis. This recovery effect on prolonged exposure of tissues to drugs with reversible actions, although it can be demonstrated with many drugs and various tissues, is certainly not a universal rule. No such recovery is observed when atropine is allowed to act upon the heart, nor when nicotine in low concentrations produces a contraction of the Rectus abdominis. Hill(s) observed that low concentrations of nicotine would maintain a contraction of the Rectus abdominis for an indefinite period, and I found that this was the case for the longest period measured, namely, about 2 hours. In view of the very great individual variations observed in the sensitivity of hearts to acetyl choline it appears possible that a heart

16 ACETYL CHOLINE. on prolonged exposure to the drug may acquire some form of tolerance to the drug quite independently of the entry of the drug into the cell. The relation between the concentration and action of acetyl choline in most cases follows the formula K. x Y and the simplest explanation of this fact is to suppose that a reversible monomolecular reaction occurs between the drug and some receptor in the cells. A similar type of curve is observed in the dissociation of dilute solutions of oxyhaemoglobin (Hartridge and Roughton(9)). My experiments do not exclude the possibility of the formula being K.Xn = y where n is a figure between 0*8 and 1F1. If n is a figure less than 1 the explanation of the relation between concentration and action would be much more difficult. Various writers have explained the relations observed between the concentration and degree of action of drugs on living tissues on the supposition that the curves are frequency curves due to variations in the susceptibility of the cells on which they act. This type of curve may be anticipated when a drug produces an irreversible action, and Peters(lo) showed that the rate of action of mercuric chloride on Paramwecia could thus be explained. Shackell(u) has applied this theory to the freely reversible action of adrenaline on arterial rings, and Gad dum(12) has adopted the same explanation for the relation between the concentration of adrenaline and its action on the isolated rabbit's uterus. The figures which he gives can, however, be fitted fairly closely by the formula given above for the action of acetyl choline on the heart. The great range of concentration over which acetyl choline produces a graded response necessitated the plotting of the concentration, in the figures of this paper, on a logarithmic scale, and this renders the relation between concentration and action somewhat less obvious. These curves, as shown in Figs. 5 and 6, are rectangular hyperbole, and cannot be interpreted as frequency curves. Between the limits of 15 and 85 p.c. of maximal action, however, the relafion between log concentration and action is almost linear, and Peters (lo) has pointed out that a simple exponential relation of this kind differs very little from the middle portion of a frequency curve. The true relation between concentration and action is therefore only to be established by the observations on the nearly minimal and nearly maximal actions. This fact shows the importance of studying the actions of drugs on tissues under conditions which permit the taking of measurements over the full range of actions of the drug. rh. LXI

17 546 A. J. CLARK. CONCLUSIONS. (1) Acetyl choline produces a graded action upon the isolated ventricle and Rectus abdominis of the frog over a 100,000-fold range of concentrations. (2) The relation between the concentration of the drug and the action produced can be expressed by the formula K.x= y where x = concentration Qf drug, y= action produced, expressed as maximal possible action, and K = constant. (3) This relation suggests that a reversible monomolecular reaction occurs between the drug and some substance either in the cell or on its surface. (4) The quantity of drug that is fixed by the cells is very small. It is calculated that a demonstrable action may be produced on the heart when only 20,000 molecules per cell are fixed: these could occupy only a very small fraction of its surface. (5) There does not appear to be any direct relation between the amount of drug entering the cells and the amount of action produced by it. These two processes seem therefore to be independent. REFERENCES. 1. Andrus and Carter. This Journ. 59. p Straub. Pfluiger's Arch p Skramlik. Zeit. f. d. ges. exp. Med. 14. p Leathes. Lancet, i. p Neukirch. Pfluiger's Arch p Jendrassik. Biochem. Zeitschr p Wertheimer and Paffrath. Pfluiger's Arch p Hill. This Journ. 39. p Hartridge and Roughton. Proc. Roy. Soc. A, 107. p Peters. This Journ. 54. p Shackell. Journ. Pharm. and Exp. Ther. 24. p Gaddum. This Journ. 61. p