CHAPTER XIIThe Wavy Path of the Ameba

In the preceding chapters we discussed the various factors which characterize ameboid movement: the streaming of the endoplasm, the formation of ectoplasm, and the behavior of the surface film. The discussion has involved only momentary cross-sections of the life of an ameba, following the method of investigation in general use for the solving of problems connected with ameboid movement. It has been tacitly assumed that if one could explain ameboid movement at any particular cross-section in time, one understood the whole process of ameboid movement no matter how long it continued, excepting, of course, the action of various kinds of stimuli that produced changes in direction, speed, etc., of streaming. It was not assumed that time was an element in the practical sense in the explanation of locomotion. A few seconds’ or a few minutes’ comprehensive observation was supposed to furnish sufficient basis for an explanation.

Sometime ago I discovered however that the path of an ameba as it moves over a flat surface free from particles possesses character; it is not an aimless irregular zigzagging here and there, such as has been generally supposed, and in occasional instances asserted, to be the case. On the contrary, the path of an ameba during the course of an hour or two consists of a succession of gentle right and left-hand curves alternating with each other. The general appearance of the path is that of a flattened spiral. Having observed a part of an ameba’s path, therefore, one can predict with considerable accuracy in what direction the ameba will continue to move. Thus that scientific bugaboo “Random Movement” is evicted from that strongest of his strongholds, the aimless wanderings of the ameba.

The mechanism producing the sinuosities in the path of the amebas is easily disturbed by external or internal stimulation of various sorts, resembling in this respect the spiral path of a paramecium, which is also easily changed by the presence of varioussolid and dissolved substances in the culture medium. But the mechanism controlling the direction of the path of an ameba is apparently much more delicate than that in paramecium, for it is only occasionally that a considerable succession of regular sinuosities are described by an ameba in moving over a flat surface. On the other hand, a few fair curves are found in the path of practically every ameba if carefully observed for an hour or more under favorable conditions.

To observe the path an ameba describes in moving over a flat surface, the following conditions must be fulfilled. One must have a small glass dish with a flat bottom, polished preferably, but not necessarily, of the size of a small petri dish, but square so as to fit into a mechanical stage. The dish should be filled with culture fluid free from solid particles. Centrifuging the culture medium, or dialyzing distilled water in the culture medium, will yield a satisfactory medium. It is only by experience that one can pick out an ameba that seems to be in an optimum condition for this purpose, that is, free from strong internal stimuli, such as those from a large mass of food, etc. Just as we speak of “clean-limbed” athletes, meaning thereby a high degree of muscular coördination, so one who has worked with these animals for some time acquires the capacity to pick out “clean-limbed” amebas; though how these differ from others is just as impossible to describe adequately as to tell what a clean-limbed athlete is. But having selected two or three amebas that move in a well coördinated manner and passed them through two or three changes of water free from particles, they are placed in the middle of a dish and allowed to remain for ten or fifteen minutes before observations are begun. A small shade should be placed in front of the dish if very strong light can reach it. It does not matter if diffuse light reaches the dish. A camera lucida with its appurtenances is absolutely essential. In addition to the ordinary precautions the edge of the paper must be laid parallel with the side of the mechanical stage, for a number of sheets of paper will have to be used up in the course of an hour or two and these must be pasted together properly to reconstruct the path. The best magnification shows the ameba two to five cm. long on the paper. Drawings should bemade quickly but carefully, beginning and ending with the posterior end of the ameba.

One of the best examples of the sinuous path of an ameba is shown inFigure 33.It is the path of anAmoeba bigemmafrom a natural out-door culture. The observations were made under the conditions outlined above. The temperature, which is an important factor, was unfortunately not recorded, but it was about 28° C.

Practically the whole of the path of this ameba consists of right and left-hand curves which are nearly uniform in length, each wave being about eight to ten times the length of the ameba. Since the drawings were made at intervals of a minute, the waves are therefore from eight to ten minutes long in time, measuring from crest to crest. Some of the waves are flatter than others, for example wave No. 4, but otherwise it is like the others. Wave 7 is a double wave due to a change of direction. Instead of turning to the right at 9:23 the ameba changed its direction and turned to the left. The smoothness with which this turn was made indicates that it originated in the mechanism producing the sinuous course itself, or that it proceeded from a very slight stimulus external to it. At 9:49 the direction of movement was changed again, but just enough to disturb the formation of a smooth wave. The general direction of locomotion was not changed. It may be assumed that this change was produced by a stimulus external to the wave-producing mechanism. The irregularity and shortness of wave 13 was probably due to the same stimulus that disturbed wave 11. Shortly after 9:58 the ameba came within sensing range of a mass of debris which it pushed away and followed, thus causing a change in the direction of movement. Although waves begin to appear again after this, some of them very smooth, they are not typical for they are too short, ranging from a little over three lengths (wave 16) to a little over six lengths (wave 23). It is likely that the disturbance caused by the mass of debris at 9:58 together with the onset of the division crisis produced the succession of atypical waves. An external disturbance that is sufficiently strong to change the direction of locomotion usually persists for the duration of at least one wave length thereafter. It will be noted that

Figure 33. Illustrating the path of anAmoeba bigemmaunder controlled conditions, in ordinary diffuse light from a north window. For convenience of reference the waves in the path are numbered from 1 to 23. The figures were drawn with the aid of a camera lucida at intervals of one minute. The path was recorded from 8:58 to 10:26, when fission occurred. After fission, the path of one of the daughter cells was followed for a short time, but the ingestion of a mass of debris destroyed the regularity of the path. The vertical lines at the point where fission occurred indicate that the figuresabovethe lines were moved up the length of the lines. The first figure beyond wave 13 was influenced in its movements by a mass of debris lying to its left. Average length of the ameba, 150 microns.

the approach of the division crisis did not tend to destroy the action of the wave mechanism, but only slowed down movement and shortened the waves. The path of one of the daughter amebas was followed for a short time, in which there is evidence of a wavy path, but it soon came upon a small mass of debris which it ingested and soon thereafter reversed its direction of movement. This behavior made it unprofitable to continue further observation of this ameba. For the gradual change in direction to the left from wave 1 to 6 in the path of the parent ameba, no adequate explanation has suggested itself.

That amebas react to light has been shown by Verworn (’89), Davenport (’97), Harrington and Leaming (’00), Mast (’10) and especially Schaeffer (’17). It appeared desirable therefore to control the rays of light, for it was thought possible that light might be a factor in the formation of the wavy path. Since no method has yet been devised that permits of the observation of the path of the ameba other than a succession of camera lucida outlines, it is impossible to omit light altogether in the experiments. The next best procedure was therefore followed, viz., the alternation of periods of darkness of a few minutes’ duration with brief—ten-second—periods of light, to permit the drawing of camera lucida outlines. The dish in which the amebas were observed was placed in a light-tight box and all light excluded except that which passed through “Daylite” glass with an opal surface on both sides between the condenser and the light source. None but parallel beams, passed through a condenser, reached the ameba. The metal parts of the objective were also blackened. The work was done in a dark room.

Figures 34 and 35 show sections of the path of twoAmoeba discoidesunder these experimental conditions. The amebas were for the most part in clavate shape, which is the most favorable shape for the formation of smooth waves. In figure 34, from 2:29¼ to 2:42¼ the ameba was in continuous light. A section of a little more than one wave is shown. Although pseudopods were thrown out at considerable distances to the right and left of the path, a smooth, wavy path was nevertheless maintained. At 2:42½ the light was turned off until 2:58½ except for two ten-second flashes at 2:47 and 2:52. During the first period of

Figure 34. The path of anAmoeba discoidesunder light controlled conditions. At 2:42¼ the light was turned off until 2:52, except for a ten-second flash at 2:47. The smoothness of the wavy path was thus maintained in complete darkness. Length of the ameba, about 400 microns.

Figure 35. Path of anAmoeba discoidesshowing that continuous light is unnecessary for the maintenance of a wavy path. The ameba moved under light controlled conditions from 3:02¼ to 3:13¼. From then until 3:43 the light was turned off except for 10-second flashes at 3:18, 3:22½, 3:24, and so on. The ameba had probably come to rest for some reason between 3:24 and 3:30½, for an unexpectedly small amount of space was covered in that time. In spite of this disturbance, however, the evidence indicates that light is without causal effect in the wavy path of the ameba. Length of the ameba, 450 microns.

darkness the ameba merely kept on in the direction it was going when the light was turned off. But during the second period of darkness the ameba changed its course in such a way as to make a smooth curve. In the third period of darkness the ameba continued on its course completing the wave. It is thus apparent that continuous light is not necessary to the formation of waves nor is it detrimental to their formation.Figure 35shows essentially the same thing asFigure 34.The light was turned on from 3:30½ to 3:32. During this time the behavior of the ameba was irregular, but whether this was caused by the light or not, cannot be stated. At 3:43 the ameba came into contact with a small particle which changed its course. The slow speed of movement of these two amebas was due to the low temperature (20° C.), the experiments being performed in January. Theapparent connection between longer waves and darkness has not yet been investigated.

Figure 36shows the path of anAmoeba proteusunder controlled light conditions as above described, but instead of moving over a polished plate glass surface as in the previous experiments, the ameba in this experiment moved over a fine ground-glass surface. It will be observed that for the first twenty minutes the path shows smooth waves, although at 11:53 and 11:55 there was a slight disturbance which was associated with the formation of numerous pseudopods. From 12:07 on, however, the path becomes irregular, the wave-like character being almost obliterated. Associated with this irregularity is the presence of numerous pseudopods. This is a sample of a number of records which indicates that inproteusanddiscoidesthe presence of numerous pseudopods in some way prevents the ameba from moving in a path marked by smooth and conspicuous waves.

Figure 36. Showing how smooth waves in the path of anAmoeba proteusin clavate shape become disturbed by the projection of prominent pseudopods. Although there was considerable disturbance due to the formation of pseudopods at 11:53 the conformation of the wave was not changed until the stage preceding the one at 12:07, when the formation of numerous pseudopods resulted in an irregular path. Length of the ameba, about 600 microns.

When a wave in the path for some reason becomes unusually long, there is likely to be a very abrupt and decided change in the direction of movement, which is away from theconvexside of the wave.Figure 37is inserted here to illustrate this point. The ameba should have turned to the left at 3:43 to keep the waves of typical size, and at 3:45 a pseudopod was extended in this direction a short distance, but again the curve toward the right persisted. But at 3:48½ the ameba broke up into several pseudopods at right angles with the main axis, and through one

Figure 37. An illustration showing that sudden changes from the expected direction of the wavy path are centrifugal, not centripetal; that is, away from the focus of the wave, not toward it. The tendency to break away from the first smooth wave became apparent at 3:45, as indicated by the extension of pseudopods near the anterior end. In the stage about two minutes later, a number of small pseudopods were thrown out in various directions. At 3:48½ several large pseudopods were thrown out near the anterior end almost at right angles to the main axis, instead of at an angle of about sixty degrees or less, as is the usual case. The same thing occurred at 3:57, except that the angle of the pseudopod was not so large.

of these the ameba moved on with the reestablishment of the wavy path. The tendency to wave formation evidently has to overcome resistance of some sort.

Figure 38.Amoeba dubiausually moves with numerous large pseudopods, but this illustration shows that there is very good reason for concluding that there is a tendency in this ameba to move in wavy paths. Length of the ameba, 400 microns.

Although amebas in clavate shapes describe the smoothest waves in their paths, waves may also be detected in the paths of amebas that habitually form many pseudopods. The path of anAmoeba dubiais shown in Figure 38. The ameba moved on an opal surface under light-controlled conditions. If we had not already seen howproteus,discoides, and especiallybigemmaformed smooth waves in their paths, we should hardly be able to understand the apparently aimless path ofdubia. But having seen how a regular succession of smooth waves appears under favorable conditions in the paths of these amebas, there can be little question but that the staggering path of adubiaalso is to be interpreted as a succession of waves, although they are somewhat irregular.

These four species of amebas,proteus,dubia,discoidesandbigemmaare the only species that have been specially investigated as to their paths, and they all show such paths, as we have seen. The presumption is strong therefore that it is a common characteristic of amebas.

To learn something of the nature of the wave-forming mechanism in the ameba, it is necessary to find some agencies that modify the activity of this mechanism. That there are such factors is of course evident enough from what has been said already about wavy paths, and from the appearance of the paths themselves. But the factors which influence the formation of waves in so far as they may be known or reasonably suspected, are internal and therefore difficult to make use of experimentally.

One of the most readily applied stimuli that is known to affect the character of ameboid movement is temperature. In general, the lower the temperature, the slower the movement. This has frequently been observed and recorded. Such behavior is to be expected from a viscous fluid like protoplasm. This may therefore be a purely physical phenomenon. But the lowering of the temperature has also another effect on the movement of amebas: it creates in them a tendency to cross their paths more frequently.Figure 33is a typical example of the path of an ameba in a high temperature (28° C.). It did not cross its path at all during the hour and a half it was under observation. When the temperature is low (20° C.) the path becomes contracted and the ameba seems unable to get away from the place it happens to be in. Movement of course continues but it is slower, and a large number of loops occur in the path. Figure 39 indicates the general path of an ameba under controlled conditions in a temperature a little lower than room temperature, that is, about 20° C. During the four hours that it was under observation the ameba crossed its path eight times and made a number of very short turns besides. Leaving out of account the loops in the path there are a number of sections which may be interpreted as waves, such as for example the pronounced waves a short distance from the end of the path. All these waves are shorter but much deeper than the waves made in a higher temperature. The loops in the path (all excepting the first, which is a compound loop) represent each a single wave which have become so deep and contracted that they havebecome transformed into circles. As the temperature decreases, the crests of the waves rise higher and higher, and the bases contract more and more, until the two sides of the waves come together, resulting in the formation of circles (Figure 40). The actual size of the wave also decreases at the same time from about eight times the length until it is only two or three times the length of the ameba. Temperature affects therefore the wave mechanism independently of the mere viscosity of the endoplasm. The speed of movement is not merely slowed down, but the character of the waves themselves is changed.

Figure 39. The path of anAmoeba dubiain comparatively low temperature (18° C.). The large number of loops and deep waves in the path are due to the low temperature. The experiment was performed under light controlled conditions. Length of the ameba, 350 microns.

Amebas sometimes react to stimuli by moving around the source of the stimulus at a more or less uniform distance through one or more quadrants of a circle, instead of reacting positively, negatively, or indifferently, in a definite manner, to the source of the stimulus (Schaeffer ’16, ’17). SeeFigure 41.The explanation that has been given by this investigator is that the encircling is due to a balance between the tendency to move ahead in the original direction (“Functional inertia”) and a tendency to react positively. But now that we know that amebas tend to formwaves in their paths, the explanation of encircling becomes simpler and perhaps also more convincing.

Figure 40. Diagram illustrating how the deepening of the waves in the path of an ameba due to decreased temperature may lead to loops in the path. The heavy line represents the wavy path, and the light lines with the arrows indicate the direction taken when loops are formed. The point in the path where the direction is most easily changed is where one wave grades off into the next, as indicated by the lettera.

In the first place, instances of encircling are relatively rare in the reaction of amebas, much rarer than one would expect if it depended merely upon a balance between two tendencies, one to move ahead and the other to move toward the source of the stimulus. Any explanation of this phenomenon has therefore to account for the rarity with which it occurs as well as the operation of the phenomenon itself. This the explanation based upon the position of the source of the stimulus with reference to the configuration of the wavy path can do satisfactorily.

In the experiments with temperature it was found that when the temperature is 20° C. or lower, the waves tend to curl up, to become transformed into circles. That is, the base of one

Figure 41. Showing the phenomenon of encircling, after Schaeffer. The ameba moved around a perpendicular beam of red light. The reaction was neither distinctly positive nor negative.

wave, instead of running into the base of the next wave is reflected backwards to form a circular curve. All the evidence thus indicates that the weakest point is at the base of the wave. A constantly acting stimulus may therefore break the wave here if it cannot break into it elsewhere, and so change the direction of the path. InFigure 42are shown a few diagramatic waves in the path of an ameba together with several reflected curves at 1, 2 and 3 indicating the points at which the direction is most easily changed as evidenced by the temperature experiments. If a particle within sensing range of the ameba lie ata,b, orc, and stimulate the ameba only slightly but still enough to break up the wave formation, the ameba will take a curved path around the particle as indicated by the dotted lines. But if the same particle lay at any other point with reference to the position of the wave, as ate,f, org, the ameba would not have changed its course. Briefly, the following conditions must be satisfied to enable the phenomenon of encircling to appear: (1) The particle must lie a little to the side of the ameba’s path. (2) It must lie abreast of the point at which the ameba begins to change its direction of movement (i. e., at the base of the wave) when describing

Figure 42. Diagram illustrating the relation of the phenomenon of encircling to the wavy path of the ameba. The weakest point in the path, i. e., where the wave may be broken most easily, is where one wave merges into another, as indicated by the experiments with low temperature,a,b,c. The direction of movement of the ameba is the reverse of what it would have been had there been no stimulus producing encircling. The same stimulus ate,f, orgwould not produce encircling because it is more difficult for the ameba to move away from the concave side of the wave.

waves. (3) It must stimulate the ameba just strong enough positively to break into the wave-forming process. Encircling then is due to a “balance” between a positive stimulus and a tendency to move in a curve. This explanation conforms with all the data at hand and explains also the rarity of the phenomenon, for the chances of encircling occurring on this view are rather less than one-fifth as frequent as if encircling took place whenever a balance between a tendency to react positively and to move straight ahead occurred.

That the wavy path is broken up by the receipt of a stimulus, that is, by a true sensation, rather than by direct effect of some agency radiating from the particle, is indicated by the fact that stimuli proceeding from various substances, such as keratin, glass, carbon, light beams, etc., have all the same effect.

In attempting to explain the characteristic nature of the path of the ameba, one’s attention centers first, perhaps, upon its orderliness; a result undoubtedly of the general impression propagated through hastily written textbooks and general papers, that an ameba’s whole life is a direct response to its environment. As the recorded facts of the life of this organism are accumulating, it is coming to be seen that the ameba possesses all the fundamental attributes of animals generally, in addition to many special ones. So that as a matter of fact, if the ameba did not showsome character and orderliness in its locomotion, then for the first time should we be especially interested in what would have to be regarded as a very striking and exceptional characteristic.

For it is very well known, and it is generally recognized by everybody, that moving organisms usually move in an orderly manner; it is recognized that organisms tend to move in straight paths excepting where interrupted by the action of some special stimulus. When an organism changes its direction of motion frequently and abruptly, we call it erratic. The mad dashings-about of the hunter-cilitaeDidiniumand the unceasing gyrations of the whirligig beetle excite one’s curiosity because these organisms do not move as other organisms do; they contradict our expectation of movement in a straight line.

But why should organisms generally tend to move in straight paths? This fundamentally important question has received almost no attention, excepting that rapidly moving animals like birds, flying insects, fishes and other rapidly swimming animals of various kinds and rapidly running animals tend to move in straight paths because of the physical inertia of the mass of the organism. It is easier for a rapidly moving organism to move in a straight line than to change its direction of movement frequently and abruptly.

The ameba however is a very slow moving animal, as animals go, for it (proteus) moves only about 600 microns per minute. Under the microscope, however, which magnifies speed as well as size, the endoplasmic particles rush along rapidly enough to suggest that even here mere physical inertia might be a determining factor in the path of the ameba, which for considerable segments is often very nearly straight. Such suspicion is not justified, however, for the viscosity of the endoplasm taken in connection with the heterogeneous composition of the ameba, makes it improbable that mere physical inertia can affect the path of the ameba.[5]

It is not even necessary that movement of the endoplasmicstream be interrupted in order that a straight path may be maintained. An ameba may stop movement for a minute or more and then be much more apt to resume movement in the originaldirection than in any other. This is brought out by the following series of experiments.

Of sixty cases of feeding on various kinds of particles, by as many different amebas, in which the direction of movement before and after a particle was eaten was recorded, thirty-nine moved off in the same direction after eating as before eating. By moving off in the same direction is meant that the ameba did not move more than 22½° to the right or to the left of the direction of movement before feeding. The circle was thus divided into octants, and the expectation of movement in the same direction after eating a particle, if it were a matter of chance, would have been seven and one-half cases instead of thirty-nine.

But it is not only the process of feeding that has to be considered in this connection, for feeding occasionally is affected by a side pseudopod while the main body of the ameba moves on without being visibly affected as to its direction of movement. No such case is included in the figures just given. In each of these sixty cases the endoplasmic streams of locomotion were completely stopped, from about twenty seconds to seventeen minutes. In most cases the endoplasmic stream was also completely disorganized, the ameba assuming a nearly spherical form in which more or less well marked though small cross currents of endoplasm could be detected. The direction of the light was without effect, for the paths extended in every direction with respect to the light both before and after feeding. Further, it has been shown that ordinary diffuse light is without effect on the movements of the ameba (Schaeffer, ’17). It may be concluded therefore that the ameba tends to keep on moving in straight paths even if the highly disorganizing act of feeding and the consequent resting period of a few seconds to many minutes supervenes at some point in its path. To what this induction of the original path is due is not clear, thought it is possible that the physical condition of the ectoplasm at the anterior end is different from that elsewhere and that it requires less energy in consequence, or for some other reason, to flow in the original direction. This explanation is based on the observation that it is easier for the ameba to activate the remnants of old pseudopods than to form new ones (Schaeffer, ’17).

The most interesting feature of the path of the ameba is of course the waves. The path of an ameba closely resembles the projection of a helical spiral on a plane surface, and this at once calls to mind the spiral swimming of flagellates, ciliates, rotifers, larvae or various groups of animals, swarm spores and zoöspores of various algae and fungi. But before we take up the general subject of spiral movement, it will be worth while to see what other evidence there is beside the wavy path, that indicates that the “spiral urge” is present in the ameba.

It is well known that in a number of the small amebas, especially the soil amebas, there are two trophic stages, an ameboid stage and a free swimming flagellate stage. The change from one stage to the other is a matter of a few minutes only. In the flagellate stage (Figure 43) the amebas resemble a small flagellate like chilomonas, very closely. Their manner of swimming is very similar. And it is especially noteworthy in this respect that they revolve on their long axis and describe a well marked, regular spiral path, just as do the flagellates and ciliates. Unfortunately no records have yet been made of the paths these amebas describe when in the true ameboid stage. Since, therefore, as we shall see later, the slightly unsymmetrical shape of the flagellate stage is not the cause of the spiral path, it is probable that the mechanism controlling the activity of the flagellum can produce orderly locomotion only when the organism follows a spiral path.

Much has been written about the fundamental similarity or identity between flagella and pseudopods. All writers who have expressed themselves on this point incline to think that there is such similarity, that flagella are really very slender and very agile pseudopods. I am not going to record here the evidence for this conclusion, for I have recently had the good fortune to make some very convincing observations on a hitherto undescribed ameba

Figure 43. The flagellate stage of a soil ameba, after Wilson.a, stained preparation showing the two flagella arising from the blepharoplast,d, which is connected with the caryosome,c, the central chromatin mass. Much of the chromatin is deposited on the nuclear membrane.b, a drawing from a live flagellate showing flagella, nucleus,c, and a vacuole.

(which for the sake of reference will here be calledflagellipodia,Figure 44) whose pseudopodia stand about midway between typical flagella and typical pseudopods in their activity. In its general characteristics it stands nearA. radiosa, but quite unlike the stiff, static pseudopods whichradiosavery frequently forms, this ameba has usually five or more slender pseudopods of which one or two or more are in slow flagellate motion. The distal third or half of the pseudopod is in the shape of a corkscrew. The free end of the pseudopod travels around in a circle (anti-clockwise in all instances observed), making one revolution in about three seconds. If this motion were very rapid it would act like a propeller and the ameba would swim through the water. The part of the pseudopod back of the mobile portion is usually also thrown into a spiral of gradually decreasing diameter until the spirality disappears. This portion of the pseudopod is not mobile in the same way that the distal portion is. Sometimes the whole of a pseudopod is thrown into a spiral, all of the turns being of equal size and only slightly motile. More than half of all thepseudopods formed become spiralized at one time or another of their existence, the greater number of these being however relatively immotile. Pseudopods frequently fall into spirals while they are being extended.

Figure 44.Amoeba flagellipodia.a, showing nucleus, 4 microns in diameter, and four vacuoles.b, a pseudopod of three spiral turns which in a few seconds grew into one of six spiral turns,c.d, a pseudopod of a number of spiral turns, which a few seconds later took on a shape shown ate. The tip of the pseudopod atfturned screw-like anti-clockwise, when looking at the tip and at the main body of the ameba. The tip made one complete revolution in about three seconds.

A better transition form between pseudopods and such flagella as are found, for example, in the peranemas, could hardly be imagined. The difference between crawling and swimming would seem to be merely a matter of speed of movement of the pseudopod.[6]But important as such a transition form is for theoreticalpurposes in understanding the nature of both flagella and pseudopods, it is of special importance for our present purpose because it shows a strong tendency for pseudopods to fall into spirals and to move in spirals. This tendency is found not only in this species of ameba but is observed also occasionally inradiosa(Figure 7, p. 30) and in several other species. In these latter species the pseudopods are stiff and not capable of waving about in the water, as are those offlagellipodia, whether in the spiral shape or not. Inradiosathe pseudopods may become spiralized only as a preliminary to withdrawal. It is evident therefore that the spiral urge can express itself best in a plastic pseudopod.

Taking all these observations together, the tendency of pseudopods to move in a spiral manner, the tendency of the ameba as a whole to move in a spiral path when in the flagellate stage, and the wavy path of amebas which is smoothest when in the clavate stage, all these observations seem to confirm the supposition that the wavy path is in reality a flattened spiral, and that the spiral urge in ameba is a very fundamental factor in the process of locomotion. In other words, there is present in ameba an automatic regulating mechanism controlling the direction of movement so that when free from stimulation a spiral path is followed.

Where can such a mechanism be located? In organisms of fixed form, such as vertebrates, the mechanism controlling and coördinating locomotion is in the central nervous system. Even in some protozoa (Euplotes) a motorium has been found whose function apparently is that of coördinating the action of at least some of the motile organs (Sharp, ’13, Yocom, ’18). But in ameba there is no fixed form. The ameba is continually mixing itself up. No two masses of protoplasm ever occupy the same space relations to each other for more than a moment, excepting perhaps within the nucleus. But the nucleus as a whole is continually changing its position with regard to the rest of the ameba, and almost certainly its position at any given moment in the ameba is the result, not of its own activity, but of the endoplasm and the ectoplasm. A formed nucleus, moreover, is not necessary to concerted movement, forProtamoeba, in which no granules of chromatin have been found, and there certainly is no formed nucleus present, moves in a concerted manner, though I am unableto state definitely whether it moves in a wavy path. (I have seen this organism only a few times, and on none of these occasions was I able to make the test). It seems therefore possible that the agency responsible for the movement of amebas in flattened spiral paths can be located at any particular point within the ameba. It seems more likely that this mechanism is a spatial aspect of the intimate colloidal activity occurring in such changes of phase as are associated with the phenomenon of contractility and streaming.

Seeing then that movement in spiral paths is possible in animals not possessed of fixed morphology, it becomes of great interest to see whether the spiral paths of free swimming ciliates, flagellates, etc., are similar to those observed in amebas.

Although the spiral paths of flagellates and swarm spores were first studied by Naegli in 1860, and subsequently discussed by numerous botanists and zoölogists, it was not until Jennings in a number of papers (’98-’04) on the spiral paths of numerous species of one-celled organisms and rotifers, described the essential facts underlying spiral movement, that the significance of this method of locomotion began to be realized. His work marked the beginning of a healthy reaction against the conception of ridiculous simplicity of structure and function which had for several decades been settling upon these organisms. He showed that the spiral path is not a purposeless, senseless reaction on the part of these small organisms, but that it is fraught with meaning, and that it may be regarded as one of the most important of their many activities.

In a paper “On the significance of the spiral swimming of organisms” Jennings (’01) develops the thesis that spiral swimming is an acquired habit, an adaptation which has become fixed in these organisms so that they would not be condemned to swim in circles, which would necessarily follow from their asymmetrical form. The organism, in other words, swims in a spiral in order to be able to swim in a generally straight course. This explanation involves of course the supposition that the unsymmetrical shape of the body was developed first, and then, since this led to circular paths, revolution on the long axis became necessary in order that a straight course might be maintained.

But in the explanation of body form in one of the rotifers he (l. c., p. 376) says: “In some of these primitively bilateral animals this spiral method of swimming has resulted in the production of an unsymmetrical form analogous to that of the infusoria.”

It is of course quite possible theoretically, that some of the unsymmetrical structures on an organism that habitually swims in spirals, are theresultof its spiral swimming, and that other structures which go to make the organism unsymmetrical, are the cause of the spiral swimming. This hypothesis is not an attractive one, however, for, because of the endless variety of asymmetrical differentiation in spiral swimming organisms, it would be impossible to tell for the large majority of organs or organelles whether they were the cause or the effect of spiral swimming.

Before taking up the hypothesis thatall moving organisms are subject to the tendency to move in spiral paths, a hypothesis which accords with all the known pertinent facts, it may be well to examine the thesis that rotation on the long axis is an adaptation which has been developed to compensate for the effect of an unsymmetrical shape of the body.

It will be noted first that this question cannot be decided by direct observation or experiment. The entire body of real evidence is written in phylogeny, and that is for this purpose a closed book. It is only the interpretations of observations that bear on this problem, and it is these interpretations that it is of interest to examine.

Referring now only to the ciliates, all of which have numerous motile organs, it has been observed by numerous writers that cilia are not confined to one or two methods of contraction, but that there is great latitude in the extent and direction of their activity. This is very well illustrated by a paramecium or a stentor whose ciliary systems enable these animals to execute a great variety of maneuvers depending upon the character of stimulation, the amount of food in the body, etc. (Jennings, ’06, Schaeffer, ’10). The cilia are under the control of the animal in the same way as the legs and arms of a man are under his control. Now supposing that the bodies of these organisms became unsymmetricalduring the phylogenetic history and as a result became unable to continue to swim in a straight path, the pertinent question to ask is: Was it easier for these organisms to learn to revolve on their long axis than to learn to beat their cilia a little harder on the side toward which they swerved? Observation of the forms before us does not afford any evidence that rotation was the easiest solution. Moreover, if it was an acquired habit, is it not strange that it should have been easier to acquire the rotating habit for every single species of the six or seven thousand unicellulars which now obey the spiral urge, as well as the swarm spores and zoöspores, than to change the beat of the cilia in some other way, in at least a few species? This explanation also makes inevitable the assumption that the ancestors of our present unsymmetrical protozoans were symmetrical and swam in straight courses without revolving, a condition of affairs which contrasts strongly with present conditions, for none of the most nearly symmetrical unicellulars and swarm spores now swims without revolving on the long axis. It is therefore exceedingly improbable that spiral swimming is the result of an acquired habit.

Now what evidence is there in support of the hypothesis that the spiral path is a necessary accompaniment of locomotion, except as it may be broken by the effect of stimulation?

As a problem in engineering, it is clear that the shape of the body is not responsible for the spiral course, for almost every conceivable shape is met with in organisms swimming in spiral paths. The frequent spiral turns in the path of stylonychia cannot be the result of the shape of the body, which is almost, if not quite, as well adapted for swimming through the water as is that of a euglena or a fish, but for revolution on its long axis it is not nearly so well adapted. Moreover, some of the euglenas turn the ventral or smaller lip out in the spiral turns, while others turn the dorsal or larger lip out (Mast, ’10). Since there is no other asymmetry of shape in these euglenas, it is clear that the shape of the body has nothing to do with causing the spiral path. The immediate cause of spirality must therefore be the work of the motile organ, and not the shape of the body.

Similar observations on paramecium have shown that it isthe special action of the cilia of a paramecium that causes it to rotate and not the shape of the body. Again the shape of aStentor caeruleusis subject to very great variation due to varying amounts of food eaten, and to surgical operation, but a spiral path is nevertheless maintained while the body shape undergoes marked changes.

Although all free-swimming unicellular organisms revolve on their long (antero-posterior) axis, an occasional one does not move in spirals. This is observed in the large colonial flagellateVolvoxoccasionally, but not always (Mast, ’10). Since it is more frequently seen in the larger individuals, it is probable that the formation of spirals is prevented because of the increased physical inertia of the colony; for the older and larger colonies are much more unsymmetrical than the younger and smaller, owing to the unequal distribution of the reproductive elements.Spondylomorumand several other colonial forms describe smaller spirals than smaller solitary organisms. These colonial organisms consisting of from four to twenty thousand cells, each of which may be possessed of cilia, are marvels of locomotory coördination, but it is not at all clear how this coördination is brought about. Since the colonies are symmetrical however, the spirality of the path is clearly due to the special action of the cilia.

Some organisms possess body shapes that seem to be due to the habit of spiral swimming. Jennings (’01) describes a species of rotifer whose body forms a segment of a spiral. When swimming a spiral path is described, “of which its own twisted body forms a part” (p. 376). Elsewhere he has pointed out that the oral groove of a paramecium likewise coincides with its own spiral path. Indications of such correspondence between the axis of a structure and the spiral path the organism possessing it, describes, are numerous among free swimming animals. But such correspondence (with an imaginary spiral path) is also found in organisms that do not swim freely. One of the most interesting of such cases is found in theOscillatoriaceae. In a previous chapter it was seen that many of these organisms are capable of moving about by means of a film of what is probably protoplasm, which moves spirally around the filament. A particle attached to this film describes a spiral path like that of a flagellateor a ciliate. Most of theOscillatoriaceaethat are capable of movement, consist of straight filaments; but two of the genera,ArthrospiraandSpirulina, are spirally twisted in such a way that the spiral axis of the filament corresponds approximately to the spiral path of a particle attached to the surface film of anOscillatoriafilament, except, of course, in size. (The movement of the surface film of neitherArthrospiranorSpirulinahas been studied).

That the spiral shape of a rotifer, for example, may be caused by swimming in a spiral path might perhaps be regarded as a plausible explanation, but it seems to me that it would be more satisfactory to explain the spiral shape of rotifers andArthrospira, the direction of the oral groove of paramecium and similar structures in other organisms, as due to the same fundamental process that causes the spiral path in locomotion. This explanation is purely mechanistic and avoids the teleological element on which the other explanation ultimately depends.

Most of the asymmetrical shapes of the flagellates, ciliates, rotifers, etc., have originated in phylogeny without regard to swimming in spiral paths, and indeed in spite of it. In spindle-shaped organisms like euglena or paramecium the amount of energy required to revolve on the long axis, as compared with that required for forward movement, is small. But in stylonychia, a dorso-ventrally flattened ciliate, much more energy is required to revolve the animal, proportionally, than is needed for forward movement. It is of course perfectly evident that as a problem in engineering it requires much more energy to revolve a flat plate on its long axis than a spindle-shaped solid, in a dense medium like water. But in spite of all the obstacles to revolution which asymmetry of body form presents, none of them are serious enough to prevent revolution from occurring, unless the keeled rotiferEuchlanis(Jennings, ’01) presents such a case. Observation would lead one to believe, however, that the compressed body forms of some of the hypotrichans and some of the flagellates such as phacus, have made revolution on the long axis very difficult; but not difficult enough to destroy the tendency to revolve and describe spirals. In short, these organisms spiralize in spite of asymmetry, not because of it.

A simple but decisive experiment by Jennings (’06) showed that the revolution and the forward movement of a paramecium is due to the oblique stroke of the cilia, for the severed posterior portion of a paramecium, which is symmetrical, nevertheless still revolves during progression. The question now arises whether this oblique stroke is analyzable into components in another way than by local stimulation; for example, can one increase or decrease the amount of revolution faster than the amount of progression? Observation of paramecium and euglena in different temperatures answers this question affirmatively. Organisms from the same culture were subjected to two temperatures, the culture temperature of 21° C. and 8° C. At temperatures lower than 8° C. the paramecia quickly precipitated to the bottom of the dish.

In 21° C. paramecia revolve once while swimming 5.5 body lengths.

In 21° C. euglenas revolve once while swimming 4.2 body lengths.

In 8° C. paramecia revolve once while swimming 3.6 body lengths.

In 8° C. euglenas revolve once while swimming ¼ to 2 body lengths.

The effect of decreased temperature is therefore to retard forward movement and to increase proportionally the number of spiral turns, for a revolution of the body on the long axis is the equivalent of one turn in the spiral path. It will be recalled that a similar result was obtained with amebas; in the lower temperature the rate of forward movement was reduced and the tendency to deepen the waves increased. In both these classes of organisms, differences in temperature enable one to separate the forward movement component from the spiral component, in the same way and in general to the same extent.

In clear water of optimum temperature or somewhere near it, paramecia and euglena (Euglena gracilis, which does not readily react to light) often swim for long stretches without change of direction. When the temperature is lowered, however, the stretches of straight paths become much shorter. In a temperature of 8° C. changes of direction become very frequent. Inparamecium some of these changes are probably due to shock of some sort, judging from mere appearance; but in many cases the change of direction is preceded by a slowing up of forward movement and the swinging of the anterior end in a wide circle one or more times around. Occasionally one observes slow forward movement with wide swinging of the anterior end, for considerable distances. In euglena this condition is more marked than in paramecium; frequently the anterior end spins around with the posterior end as a pivot for several minutes at a time, in low temperatures.

These observations are strikingly analogous to the circles formed in the paths of amebas in low temperatures, and geometrically they bear the same relation to the spiral paths of ciliates and flagellates as the circles do to the wavy path of the ameba.

Besides the effect of temperature on paramecium and euglena, effects which are continuous and automatic, it is of course well known that the spiral path may be readily broken into by appropriate stimulation of the sense organs. The automatic locomotory mechanism is then for the time being controlled with reference to the character of the stimulus and the experience of the organism. But as soon as the effect of the stimulus has disappeared, the automatic mechanism again controls locomotion.

Sense organs of orientation, including organs of equilibration, break in upon the spiral mechanism controlling direction of movement, and eliminate its effect. It thus happens that no animals with image-forming eyes or equilibrating organs move in spirals in three-dimensional space when these organs are functional. Conversely, animals without image-forming eyes or equilibrating organs move in spiral paths. In addition to the ciliates, flagellates, protophyta, swarm spores and zoöspores of algae and fungi, Oscillatoriaceae and rotifers, may also be mentioned the larvae of many worms, echinoderms and molluscs. All these are within the grip of the spiral urge. The grip is indeed slight, as we have seen, but in the absence of stimulation it is none the less absolute.

The movements of none of the animals in the higher groups have been studied in any detail. Excepting the movements of some of the ciliates, flagellates, amebas, rotifers, a few scattered protophyta and swarm spores our knowledge of the movementsof spiral swimming organisms is of the most casual and fragmentary sort. Nothing beyond the mere fact that these organisms describe some kind of a spiral swimming, is known.

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