ABSTRACT
A study has been made of acrasin, the agent inducing chemotaxis in the amoebae of cellular slime moulds.
A method has been developed for subjecting sensitive amoebae to a fluctuating gradient set up by an artificial source that can be renewed at intervals of as little as a few seconds with fresh test solution.
Amoebae orient to a gradient maintained with the cell-free liquid freshly obtained from the immediate surroundings of a natural source.
Acrasin solution as secreted loses its activity very rapidly at room temperature.
A highly active stable solid is obtained by drying methanolic culture extracts ; it resists boiling and exposure to acids and alkalis. Its solubility decreases rapidly in passing up the alcohol series.
The original instability has been shown to be due to the presence of another extracellular slime-mould product, possibly an enzyme; it, unlike acrasin, cannot pass rapidly across a dialysis membrane, is heat labile, and can be precipitated by ammonium sulphate.
The advantages of the organism’s itself inactivating acrasin are considered.
Some of the advantages of a source’s releasing acrasin in pulses are discussed ; but it is not essential for orientation for it to do so.
Sensitive amoebae not only are oriented by an acrasin solution but are caused to secrete acrasin: this is the basis of a chemotactic relay system.
In the life cycle of the cellular slime moulds Dictyostelium and Polysphondylium, the vegetative stage, in which separate amoebae feed on bacteria and multiply, is succeeded by a fruiting stage, in which the amoebae co-operate to produce a stalked spore mass ; this stage is initiated when they begin to converge on certain collecting centres (Olive, 1902; Raper, 1940a, b, 1941; Bonner, 1944). Both Olive and Potts (1902), without offering any evidence, thought it likely that chemotaxis was involved in this orientation ; and there the matter rested, except for a quite inadequate explanation involving negative hydrotaxis (von Schuckmann, 1925; Harper, 1926), till 1942, when Runyon showed that amoebae placed on one side of a cellophane dialysis membrane would duplicate the pattern of an aggregation that had formed on the other side; he concluded that a chemical agent was responsible. Bonner (1947), having pointed out that many types of agent would pass through cellophane, was in fact able by a great variety of experiments to exclude the influence of all other likely ones. More directly, he showed that when the amoebae were exposed to a slow current of water, they would approach a collecting point from downstream only while moving at random upstream of it. This made it probable that a chemical was indeed involved ; but it might have been that the amoebae were reacting to a current when the chemical was present—a type of response so common, for example, among insects (Dethier, 1947). However, as in other experiments of Bonner’s the amoebae were attracted in still water, it could be concluded that they were reacting to a chemical gradient. The evidence for the existence of the substance was sufficient to warrant Bonner’s naming it—acrasin—though he was not able to isolate it in vitro.
Olive, influenced by Pfeffer’s work (1884), tried to attract slime-mould amoebae with solutions of sugar and malic acid; fifty years later, Hirschberg & Rusch (1950) tried, with as little success, with echinochrome and dimethylcrocetin. Raper & Thom’s demonstration (1941) that Dictyostelium and Polysphondylium grown in mixed cultures aggregated separately showed that the stimulus was highly specific and made it unlikely that chemicals used (or supposedly used) by other organisms for a similar purpose would be effective.
Pfützner-Eckert (1950) claimed that sensitive amoebae of Dictyostelium mucoroides would move towards a cell-free block of agar on which an aggregation centre had rested; but I have not been able to repeat this experiment. However, it has proved possible to isolate acrasin in vitro, as has been briefly reported (Shaffer, 1953).
CULTURE METHODS
Dense cultures were obtained by inoculating slime-mould spores and Aerobacter aerogenes or Escherichia coli on agar plates rich in nutrient, prepared according to Bonner’s (1947) recipe: after about 2 days at room temperature these furnished the acrasin sources used. The reactions of individual amoebae could only be studied in very much less populous cultures, which could be most easily produced by Singh’s method (1946). The bacteria were grown separately on nutrient agar and then spread thinly on plates of 1% agar containing 0·5% sodium chloride adjusted to pH 6·5—6·8 ; these plates were inoculated with mould spores, and when all the food had been consumed there were sufficiently few amoebae present for agar to be visible between them. Sometimes the sodium chloride was omitted or replaced by a buffer.
EARLY EXPERIMENTS WITH NEGATIVE RESULTS
Pfeffer (1884) observed the orientation of plant sperm to the tip of a glass capillary tube containing a test solution; Went (1926) found that the amputated tip of an oat coleoptile could be functionally replaced in some respects by a piece of agar on which it had rested. These two methods are now classical, and many variations of them have been used in the present study in attempts to set up artificial gradients to which amoebae would react. The question of which amoebae are sensitive to acrasin is discussed in another paper (Shaffer, 1956a) ; here it may be said that they become sensitive at varying times before aggregation begins, so that sensitive ones can most regularly be obtained by thoroughly stirring up, with a glass rod, one of the streams into which the amoebae condense as they converge on a centre. The stream chosen should have been recently formed and still be flat, finely branched, and without any signs of developing swellings, which are liable to develop into secondary centres. The stirred cells may be rapidly carried on the end of the rod to any convenient site or swept there over the agar surface; they may be spread thinly or left in a streak or small heaps. Desiccation must be kept to a minimum. Raper & Thom (1941) found that Dictyostelium discoideum and D. mucoroides grown together would enter communal aggregations ; and it has been shown that both these species and D. purpureum use the same acrasin for chemotaxis (Shaffer, 1953), so that test cells from these species may be used indifferently.
As for the acrasin sources, in experiments in which they have to be picked up with a glass needle, transplanted and sometimes bathed, it is easiest to use large, old centres, in which the cells are firmly packed. In D. discoideum, the aggregate migrates as an elongated slug before it begins to construct a fruiting body (Raper, 1935); this stage is the most convenient of all sources, because it secretes acrasin (Bonner, 1949) and is surrounded by a slime sheath, which protects it from damage when it is handled. Moreover, it tends to stay in contact with the water drop or agar on which it is placed : true, if conditions are too dry, it turns up its tip—which is most active in acrasin production (Bonner, 1949)—into the air (Raper, 19406), but this can be gently pushed down again. In other species, which lack the migratory stage, young fruiting bodies may be used as sources : they too are protected by a sheath ; but they tend to leave the substratum immediately, and they are continuously being converted into non-secreting differentiated cells.
In the following tests the agar blocks were cut out with mounted rectangular fragments of razor-blades and placed on a culture plate 100-300 μ away from sensitive amoebae, variously grouped : the tips of capillary tubes were arranged so as to lie near amoebae in the film of liquid on an agar surface or to touch the bottom of a dish containing sensitive amoebae under water, prepared by Bonner’s method (1947). The test blocks and solutions were obtained as follows: sometimes, they were variously buffered from pH 4 to 8 (the limits for aggregation determined by Hirschberg & Rusch, 1950) with Mcllvaine’s at one-tenth of the standard concentration.
A centre or migrant slug was removed, and the agar under it swept clear of cells and cut out.
Small blocks of agar from 100 μ to several millimetres thick and of area just greater than that of the slugs to be placed on them were loaded in a saturated atmosphere with from 1 to 50 slugs (groups 105—106 times smaller constitute an effective natural source). The slugs were left there for 1 min. to 1 hr. and then the blocks were carefully cleaned of cells.
From 1 to 50 slugs were bathed for 30 sec. to 30 min., in a saturated atmosphere, with a drop of water that formed a barely visible layer or extended up to 500µ from their edges. The slugs were not more than half immersed, for if they were completely covered they rounded up and degeneration began; this was in line with the findings of Potts (1902) and Bonner (1947) that aggregation but neither migration nor fruiting would occur under water. The continued healthiness of a slug was recognized by its remaining elongate with a sharply defined tip. The water was collected in capillary tubes or absorbed on dry agar blocks or fragments of washed filter-paper.
Slugs were sucked up a capillary pipette, with the minimum of water, and heated to 50° C. for a few minutes. The contents were tested as before, or the dead slugs were expelled on to agar near sensitive cells. Other slugs were picked up with a needle, brought up to a block of solid carbon dioxide and replaced, dead, on the agar.
In no case were amoebae found to collect at the artificial sources or to orient preferentially to them.*
Two possible explanations were available to account for these negative results. First, the living sources might have imposed additional characteristics on the chemical signal. Arndt’s time-lapse film (1929, 1937) showed that aggregation was rhythmic in D. mucoroides; and it might have been that acrasin had to be delivered in pulses. However, though Bonner’s film (1944) of D. discoideum showed that waves of rapid inward movement did pass over some aggregations, they did not do so in every case. Moreover, the pulses were produced at intervals of about 5 min. and appreciable movement occurred between them; so one might have expected an artificial source, providing a single pulse, to have stimulated readily detectable orientation, even if only temporarily. The other possible explanation was that the secreted chemical rapidly disappeared because of inherent instability or active destruction or volatility, though the last was improbable as it would not have explained the results obtained with capillary tubes.
THE THEORY OF CHEMOTAXIS
A single molecule, continually buffeted by those of the medium, pursues an irregular and random course; so that from its direction at any moment, it is not possible to learn whence it has come whatever receptor organs are available. When a directional element is not provided by a current or the movement of the source itself, this can only be located by sensing the distribution of the chemical ; and since the position of each molecule is determined by chance, the judgement must be based on sufficient numbers to make it probable that the direction in which the concentration increases most steeply is one that leads towards the source. This limits the possible sensitivity. As each of them functions as one of a crowd, the molecules used should, on grounds of economy, be as small as is consistent with specificity.
It might be expected that the least difference of concentration, Δc, detectable by either simultaneous or successive comparison, would not be constant but would be related to the average concentration, c, at the points of comparison. If Δc/c were constant, that is if the Weber-Fechner Law were obeyed—as Bonner and Savage (Bonner, 1947) assumed that it was—the maximum distance from which an amoebae could be attracted to a point source would be independent of the absolute amount of any stable chemical that was secreted, for this does not effect its distribution. Even if Δc/c were large when c was small and tended to fall to a minimum value as c increased, the range at which the source could be detected would tend to reach a maximum as more chemical was produced.
This limiting range could be extended if the chemical were removed some time after its emission. This may become clearer if the outputs by a source during successive minutes are considered separately—legitimate if the chance of a molecule’s inactivation is unrelated to the concentration. The molecules secreted during a given minute would at first be crowded together near the source ; then they would move outwards, tending to an equal distribution (zero concentration) everywhere. The concentration pattern the cells would experience would be the summation of the outputs of all the minutes. It is clear that if the chemical were removed in a first-order reaction, the fraction of molecules left from earlier outputs, which would have a flatter distribution, would be less than from the later ones. As a result, the summated relative concentration gradient would become greater, though the concentration would be reduced. Provided, then, that the source could increase its output sufficiently, cells of a given sensitivity would be attracted from a greater distance, even in an infinitely extensive medium, if the active chemical disappeared. If the limits of diffusion—whether set by the boundaries of the medium or the presence of other sources—were near to the source, the removal of the chemical would become not merely a means of extending the range but a necessity in order to maintain, for long periods of time, any effective range at all. If it were not removed, the gradient produced by the secretions of later minutes would have to be detected against an obscuring background of ever-growing strength. The signal could indeed be strengthened by greater secretion, but as this would be converted into ‘noise’, the benefit would be short-lived; and the final situation would be worse than before, because the accumulation of the chemical in the medium would depress its secretion by the source.
However, it would be possible to extend the period during which a source could guide cells in a limited environment using a stable chemical if this were released in short pulses, the intervals between them during which the gradient would be undetectable being of such a length that the cells would still be moving predominantly in the direction in which they had been oriented by the last pulse when they again received direct guidance from the next one. Such an arrangement would also make the most efficient use of the chemical produced, whether it were stable or not.
These considerations pointed to one or both of the same conclusions as did the last section, namely, that acrasin rapidly disappeared from the external medium and that it was released in pulses.
THE ISOLATION OF ACRASIN
If either conclusion was correct, sensitive cells might only react to an experimental source if it could be renewed at frequent intervals. It was clear that such a source would have to be a liquid rather than an impregnated agar block ; the difficulty was that if the sensitive cells were under water, each addition of liquid would upset any diffusion gradient, and if the cells were on agar, the added liquid would not remain localized and reinforce the gradient but would simply spread over the surface. This was overcome by sandwiching the sensitive cells between an agar block and a glass slide; liquid could then be added repeatedly to the meniscus round the outside of the block without its mechanically disturbing any diffusion gradients inside. With this method it was possible to renew the artificial source as often as every 5 sec. with material taken from the vicinity of the natural source only 2 sec. earlier.
The moist chamber used had glass slides for top and bottom and an opening at one side through which glass instruments could be introduced. With a micropipette, a number of water drops, some of about 10−2 ml. and others of 10−3 ml. or smaller, were deposited on the lower slide, leaving a central area clear of all but two small drops, 5-10 mm. apart. With a glass rod, the drops could be moved about on the slide, if this was not too clean, and smaller droplets detached from them as needed. Migrant slugs of D. discoideutn were transferred, individually with a needle, to one of the central drops; they were placed parallel to each other but separated. The test cells had been grown on saline agar 0η5-1 mm. thick. A small block of it, about 2-3 mm. square, carrying at least part of a flat stream or of an early finely branched aggregation from which the centre had been removed, was cut out. The block was picked up on the razor blade, turned upside-down, and gently eased off with a glass rod into the second central droplet of water. With care, at least part of the stream was trapped between block and slide and could be brought into any desired relationship with the edge of the block: having regard to Bonner’s (1947) figures for the greatest distance from which cells could be attracted to a natural source, the preferred position of the stream was parallel to and about 150-200 μ from the edge. The block was cut with slightly sloping sides, the surface above after inversion being rather larger than the lower one : this made it possible to observe cells on both sides of the edge, when there was a little liquid round the block.
The water bathing the slugs was changed till it contained no more loose cells, and only enough of it was left to extend halfway up each slug and 50-100 μ away from its side. Then the block was gently pushed to and fro, after first removing almost all the water around it: this completely disrupted the stream and ensured that the amoebae were unoriented but free to respond. After a delay of 2 to 3 min., which allowed time for the return of motility but not of intercellular organization, the transfer of liquid from the slugs to the edge of the block was begun (Fig. 1). About 10−5 ml. from round the nearest slug was carried over in a pipette, or dragged across with the bent tip of a glass rod, and then replaced with water from one of the drops on the floor of the chamber; at 10 sec. intervals, further transfers were made from successive slugs. Thus, with a row of thirty slugs, each was allowed to secrete acrasin into the surrounding water for at least 5 min. before this was collected. If the experiment was lengthy, it was necessary to remove some of the liquid accumulated round the agar block to prevent excessive dilution of the later transfers.
Usually, the amoebae could be seen, within 5-10 min., to be oriented perpendicularly to the edge ; they first began to reach it after 20-30 min. or more, depending on the distance they had to travel. If they were not started too far away, they were still more or less parallel to each other on their arrival there. The orientation of the amoebae agreed with expectation, since, if acrasin were present in the liquid at the edge of the block, it would be rather evenly distributed through it, and the internal gradient would be normal to the surface.
It was known (Shaffer, 1956 a, b) that the leading end of an undisturbed stream fragment, or of a reorganized group of amoebae from a stirred-up stream, might not advance at all even in the presence of an acrasin gradient, or that it might do so even in its absence. Moreover, a small proportion of the amoebae from disintegrated streams might move at random in such a gradient. So, for example, in a test, a stream fragment might reach the edge of the agar block by chance and yet simulate one that had been attracted there ; its front end, once escaped from under the block, would almost never find its way back, and the rest of it would continue to grow by collecting sensitive amoebae. Because of these possibilities, the criterion that an acrasin gradient was present if and only if amoebae crawled towards the edge was too simple : attraction to the edge was considered positive only if a large number of moving amoebae able to make independent judgements of the gradient agreed in their orientation. If most of the amoebae did not move, the experiment had to be abandoned.
Positive results could still be obtained even if the length of time the water bathed the slugs and the frequency at which the drops were transferred were both much reduced. It was found convenient to use two, or only one, small groups of slugs for supplying acrasin solution and to transfer rather larger drops of it to the block once a minute. No positive results were obtained if no liquid was added to the edge or if untreated water only was added whatever the frequency.
However carefully the slugs were handled, it was difficult to ensure that not a single loose cell was present in the washings; though it was unlikely that the very few that were transferred to the block were responsible for the attraction, because the test amoebae moved parallel to one another, whereas when a natural source was placed against the edge, they converged on it.
To eliminate all loose cells, the washings had to be filtered: each drop was deposited on the upper surface of a small piece of Millipore membrane, about 5 mm. square, to which a wax border had been applied ; with another pipette, it was collected from underneath it a few seconds later and transferred to the agar block. The amoebae oriented to the cell-free source.
It was possible that asymmetrical addition of washings to the block produced underneath it a slight slow water current and that it was this, when it carried acrasin, that stimulated orientation. To investigate this, a block was selected that had under it at least some sensitive amoebae near each of its sides. To minimize any currents set up as a result of its absorption of water during the subsequent test, it was first soaked in water. After the excess had been removed, the upper surface was covered with a fragment of cover-slip to prevent evaporation from it. When acrasin solution was added, repeatedly, as evenly as possible all the way round, each group of amoebae crawled outwards perpendicularly to the side closest to it, except for those near the corners, which adopted an intermediate position.
The possibility that the amoebae were led to the edge by reacting to a gradient of some sort produced by their own metabolism, which they did only when activated by acrasin, could be ruled out by working with a long and very narrow block under which the amoebae were positioned to one side of the mid-line : if plain water was added to the edge nearer to them and acrasin solution to that further away, the amoebae crawled towards the latter.
It was concluded that the amoebae were guided by a gradient of acrasin.
THE REACTIONS TO AN ARTIFICIAL GRADIENT
Amoebae confined under a slab of agar showed a variety of behaviour patterns ; but as these were much the same as those occurring in other environments (Shaffer, 1956 b), they will not all be detailed here. Separate sensitive amoebae were guided by the artificial source as already described ; and, if started near enough to the edge, they were still in parallel formation as they crawled out from under the block. Usually this pattern was distorted, because the oriented amoebae soon began to attract their neighbours. If there were rather few amoebae present, they lined up, mainly end to end in single file, to form parallel threads, which entered minute but growing clumps at the edge of the block. As more amoebae joined in, each thread became a delicately branched aggregation. Groups of amoebae were drawn out into arrowheads aimed at the source. The closer the amoebae were to each other and the further they started from the edge, the greater the opportunity they had to interact, producing numbers of variously branched streams. The front end of each of these was guided by the resultant acrasin gradient, whether this led it to the edge of the block, to the neighbouring streams on its flanks, or even back to the cells following it, in which case a ring was produced; alternatively, it simply stopped moving and formed an independent and perforce very flat centre. At times, some or all of a stream disintegrated : its constituent amoebae separated from each other and then reoriented independently to the gradient. Though streams that did reach the edge of the block had no gradient to guide them further, they crawled on for varying distances, because of their inherent motility, and then began to pile up in stationary heaps. As a result of the continual disturbance of the water, these usually became detached from the glass.
Sensitive amoebae, that might or might not have previously been in an aggregation but had not aggregated after more than an hour under an agar block, would almost at once begin to form branching and mutually attractive streams when exposed to acrasin solution : this showed that acrasin stimulated them to secrete acrasin.
THE INSTABILITY AND STORAGE OF ACRASIN
It was now necessary to consider why the earlier tests with artificial sources had failed. An explanation exclusively in terms of the need for releasing acrasin in pulses became unlikely : positive results had been obtained with transfer frequencies varying from 10 sec. to 2 min.; moreover, films of the agar-block test showed cells moving smoothly towards the edge without waves or pulsation.
The alternative explanation in terms of instability was investigated by detaining the acrasin solution during transfer: it was collected every minute with one of a number of micropipettes used in rotation ; it was delivered to the edge of the block after a delay of as many minutes as there were pipettes. The very large number of variables involved in collecting and testing made quantitative assay extremely difficult; nevertheless, it was established that, in general, solution stored 5 min. was weaker than that stored but 1 min. or not at all, that stored 20 min. only rarely had any detectable effect, and that held longer had none.
Whereas the single application of fresh solution, which set up a gradient continuously declining in strength, did not excite perceptible orientation, the repeated addition of solution 10 min. old might do so after about 10 min. Despite this finding and the advantages of releasing acrasin in pulses discussed above, to which must be added that of enabling a chemotactic relay system to function in an orderly way (Shaffer, 1956c), there was still nothing to suggest that the single pulse produced by an unrenewed artificial source, provided that it was strong enough for long enough, could not cause easily detectable even if temporary orientation.
It seemed likely that acrasin would be considerably more stable at a lower temperature. In order to test this, each drop of solution, after filtering through Millipore, was collected with a separate micropipette, which was then immediately dropped into one of a series of holes in a brass block cooled by solid carbon dioxide. To examine the potency of the solution, a pipette was withdrawn each minute, and its contents, after thawing, added to the edge of an agar block, as in the regular test. The operations on the acrasin solution—collection and filtering, transfer to the brass block, freezing, thawing, and transfer to the agar—together took less than a minute. A solution thawed after several days in the cold was still very active in causing the orientation of sensitive amoebae, though it rapidly lost its activity at room temperature. That temperature gradients were not responsible was shown by freezing the solution after it had been kept at room temperature for an hour and then testing it, as before, after thawing : no orientation was induced.
In an experiment to confirm Runyon’s finding (1942) that the stimulus to aggregation would pass through cellophane dialysis membrane, slugs were grouped in a drop of water on a small raft of this material. Every few minutes, water was added underneath the cellophane and then collected again: it oriented amoebae in an agar-block test. It was found to differ from the cell-free acrasin solution obtained by filtration through Millipore in being stable at room temperature. It was concluded that acrasin activity was associated with molecules small enough to pass rapidly through cellophane and that loss of activity was due to reaction with much larger molecules, possibly of an enzyme, also present extracellularly.
CHEMICAL EXTRACTION
An attempt was then made to extract acrasin chemically. The method adopted was to pour absolute methyl alcohol, cooled on solid carbon dioxide, on to a phosphate-buffered culture plate in which aggregation was general. After 4 min. in a cold-room, the liquid was poured off and dried in vacuo below-10° C. The residue was extracted with a small volume of methyl alcohol, which was then filtered and again dried. An aqueous solution of the product, which had a pH of about 5 and was strongly buffered, had a very high acrasin activity. Activity was retained after boiling for more than an hour and after exposure to excess N/10 hydrochloric acid or N/100 sodium hydroxide. Dry acrasin was considerably less soluble in absolute ethyl alcohol than in methyl.
A cell-free aqueous extract of an aggregating culture had the power to inactivate acrasin but lost it after it had been boiled : the fraction that could be precipitated with half-saturated ammonium sulphate was shown to be responsible. This knowledge suggested a more convenient procedure for obtaining acrasin. Agar bearing aggregations was simply dropped into boiling water, the solution evaporated, and the residue extracted. Acrasin was collected in a rather purer form by continuously dialysing it away from its attacker during aggregation.
A single addition of a concentrated acrasin solution to the edge of a test agar block produced dramatic orientation of the amoebae within 2-3 min. : they could have been exposed to only a single pulse from the added acrasin.
DISCUSSION
Acrasin (named or unnamed) has been sought, on and off, for more than half a century. Its elusiveness may have frustrated the research worker; but the instability that has been found to lie behind it is most probably of value to the slime mould in enabling it to maintain effective guidance for its amoebae. The discovery that the amoebae produce a protein—probably an enzyme—that inactivates acrasin extracellularly tends to support the view that this action is of use. Separated from its attacker, acrasin is a remarkably stable molecule; but apart from this, there is still little known of its nature, other than its being soluble only in water and solvents very much like it.
When and where the inactivator is produced has not yet been investigated; but however its secretion is related to that of acrasin’s, it would be extremely costly in time and material for a source to set up a detectable relative concentration gradient of acrasin at a considerable distance from itself. In fact, the maximum range from which amoebae can be directly attracted is about 350μ (Bonner, 1947)—the sort of distance one might have expected for a process based on diflfusion. With a series of relays each covering this distance, it would be possible to increase the total range more or less indefinitely, both cheaply and quickly. Such a system does indeed exist, based on the action of acrasin in stimulating amoebae to secrete acrasin, and it permits an aggregation to extend for several centimetres.
When thousands and even hundreds of thousands of separate acrasin sources are present in a single aggregation, the problem of maintaining detectable gradients is vastly aggravated. To see what effect the inactivation might have, we must make a number of assumptions; and as these have not yet been tested, an exact treatment is scarcely called for. If the inactivator is secreted by all the amoebae and is comparatively stable, we may expect it to be more evenly distributed than the acrasin. If, as a first approximation, we assume that it is present in the medium at the same concentration throughout the aggregation area, that it is an enzyme, and that Michaelis kinetics are obeyed, the reaction velocity of inactivation will be roughly proportional to the local acrasin concentration when this is well below that corresponding to the Michaelis contant and will tend to a limiting value when it is much higher. Thus, inactivation of acrasin by an enzyme will be at least as efficient as that by a first-order reaction, which was discussed above: at low concentrations of acrasin it will approximate to the latter, and at high ones it will be better, in that, in effect, it will tend simply to reduce the background against which the gradient has to be detected.
Though the release of acrasin in pulses has been shown not to be an essential of the orientation mechanism, it may none the less be of value, partly in facilitating the maintenance of a gradient, partly in economizing the chemical (if this is of importance to the organism), and it is quite probably involved in the rhythmic movements during aggregation photographed by Arndt (1929) and Bonner (1944).
The problems that slime moulds have faced in using chemotaxis in morphogenesis are further considered in another paper (Shaffer, 1956d).
ACKNOWLEDGEMENT
I should like to thank the members of the Department of Biology, Princeton University, for their hospitality during my tenure of a Dill Fellowship, especially Dr J. T. Bonner for his, and for his interest in this work, and Dr F. I. Tsuji for his help. To Dr B. N. Singh I am grateful for sending me cultures, and to Dr M. G. M. Pryor I am deeply indebted for his continuing encouragement.
REFERENCES
Dr J. T. Bonner has since told me that he too had no success with similar sources.