THE WAVY PATH OF THE AMEBA AND THE SPIRAL PATHS OF CILIATES AND OTHER
ORGANISMS
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
[Illustration: 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 called _flagellipodia_,
Figure 44) whose pseudopodia stand about midway between typical flagella
and typical pseudopods in their activity. In its general characteristics
it stands near _A. radiosa_, but quite unlike the stiff, static
pseudopods which _radiosa_ very 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 the pseudopods 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.
[Illustration: 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 at _e_. The tip of the pseudopod at _f_
turned 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 theoretical purposes 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 in
_radiosa_ (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 of _flagellipodia_, whether in the spiral
shape or not. In _radiosa_ the 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, for
_Protamoeba_, 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 unable to 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 the _result_ of 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 that _all 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
unsymmetrical during 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 is the special
action of the cilia of a paramecium that causes it to rotate and not the
shape of the body. Again the shape of a _Stentor caeruleus_ is 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 flagellate _Volvox_ occasionally,
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. _Spondylomorum_ and 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 the _Oscillatoriaceae_. 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 flagellate or a ciliate. Most of the
_Oscillatoriaceae_ that are capable of movement, consist of straight
filaments; but two of the genera, _Arthrospira_ and _Spirulina_, 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 an _Oscillatoria_ filament, except, of course, in
size. (The movement of the surface film of neither _Arthrospira_ nor
_Spirulina_ has 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 and _Arthrospira_, 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 rotifer _Euchlanis_
(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. In paramecium 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 movements of 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.
[Illustration: Figure 45. Showing the path walked by a normal
right-handed man (J. N.), blindfolded and counting his paces. The whole
path was 546 paces long. The command given was to walk in the direction
of the arrow until halted. The field was slightly rolling. The stump
made necessary a termination of the experiment.]
That a spiralizing mechanism is probably also present in organisms with
highly developed equilibrating and orienting senses would be the logical
expectation from what has been said regarding the presence of such a
mechanism in the lower forms of life; but the effect of such a mechanism
would naturally be suppressed when the orienting senses are functioning.
To test this point, man was selected for experiment. With eyes
blindfolded and ears plugged (this latter precaution was subsequently
found to be unnecessary) so as to render the orienting senses
ineffective, a normal man was directed to walk straight ahead over a
large field towards an object he had just looked at. Although a number
of experiments were made with several individuals, _none of them was
able to walk a straight path. All of them walked true spirals or series
of circles with remarkably smooth curves_ (Figures 45, 46). The spirals
were right and left handed in the same individual, and sometimes in the
same experiment. In these experiments the subject was totally
unconscious of the direction in which he was walking. No effort of
consciousness seemed capable of changing the _degree of curvature_ of
the spiral or circle and keep it smooth, though one could of course at
any time break into the spiral or circle and walk off in another
direction. (The writer himself walked in several experiments.) If one
has one’s mind _strongly_ on the direction of walking, thinking of each
step, the curve of the path shows small “wabbles”; but if one recites
something or counts his paces, the curves are quite smooth.
[Illustration: Figure 46. Illustrating a path walked by a normal
right-handed man (J. D.), blindfolded and counting his paces. The path
was 560 paces long and was walked over the same field as the path
illustrated in figure 45. The path had to be terminated because of a
clump of brush.]
Considerable unevenness of the ground has no effect on the curvature of
the spiral. Structural differences in the legs are also without effect,
for a person with one artificial leg walks quite as smooth a spiral as
one with two normal limbs.[7]
From these experiments on man, it follows that there is a “centre” in
the central nervous system which automatically coördinates and controls
movement during locomotion and, particularly from the point of view of
this discussion, the direction of locomotion when the orienting senses
are not functioning. This center must be very deep seated and automatic,
and in so far as its influencing the direction of locomotion is
concerned, it is of no discoverable use to man. It may be presumed to
have existed before the present orienting senses originated in man, for
there is very good evidence that horses and perhaps dogs, too, possess
this mechanism. For these animals, like man, tend to walk in circles
when lost, a peculiarity of behavior undoubtedly due to the activity of
this mechanism and not to stronger right or left legs, etc., as has
often been suggested (e. g., Thompson, ’17, p. 498). According to the
accounts of experienced hunters, rabbits also run in circles when hard
pressed by hounds, which may possibly be due to the suppression of the
functioning of the orienting senses by fear, thus allowing the automatic
directing mechanism to operate.
The facts are therefore that all organisms without orienting senses or
equilibrating organs, or animals possessing such organs which are
rendered ineffective by some means, will not move in straight paths nor
in any kind of irregular path, but _in orderly paths_, so that a given
segment of the path serves as a basis for predicting the further
direction of the path. And the degree of accuracy to which such
prediction may attain is proportional to the extent to which the
activity of the automatic regulating mechanism may be kept free from
outside interference. The organisms of which this holds true include,
as far as known, all the free-swimming unicellulars, swarm spores of
algae and fungi, uni-and multinucleate zoöspores, rotifers, a large
number of worms and worm larvae of all classes (excepting the nematodes)
and the larvae of many molluscs, echinoderms and copepods as well as
some adult copepods. Organisms restricted to two dimensions of space in
their movements, in which orderly paths have been recorded, are ameba
and man and perhaps we may include the horse and the dog. This is indeed
only a small number of organisms compared with all that can move; but
there are representatives in the list of all the large groups excepting
the higher plants, and without doubt observation will greatly extend the
list, for there are mentioned here only such organisms whose movements
have been definitely recorded or personally observed. As far as now
known, no organism lacking orienting organs moves in a straight line.
Many spermatozoa with flagellate tails seem, however, to do so, but no
careful studies of their paths have yet been made.[8]
The orderliness of the paths of these organisms when moving under such
conditions as described above, is itself orderly; that is, the path of
all these organisms is a spiral of one kind or another: (1) a helical
spiral, as in the free-swimming unicellulars; (2) a true spiral in one
plane, as in man; (3) a helical spiral projected on a plane surface, as
in ameba.
These facts point inevitably to the hypothesis that the movements of
these and all other moving organisms are controlled by an automatic
regulating mechanism, which is of essentially similar nature in all
organisms, as is indicated by the tendency to spiralize the path. This
mechanism, being automatic, absolutely controls the direction of the
path so long as outside interferences permit; but when sensory
stimulation occurs, or when changes in temperature, etc. occur, the
mechanism is no longer able to operate automatically or smoothly. The
direction of the path then depends upon the nature and direction from
which stimulation was received, and upon the degree and direction of
change of temperature, etc.
The importance of this conception of movement lies in the fact that it
enables us to look at a large mass of otherwise unrelated data from a
single point of view. Secondly, it permits of a mathematical treatment
of the whole subject of movement in organisms. And third, it replaces a
teleological explanation of spiral movement in unicellulars, swarm
spores, rotifers, etc., with a purely mechanistic explanation.