/ . Embryol. exp. Morph. Vol. 68, pp. 23-35,1982
Printed in Great Britain © Company of Biologists Limited 1982
Size regulation in Dictyostelium
By WILL KOPACHIK1
Department of Biology, Princeton University,
New Jersey, U.S.A.
SUMMARY
The division of large aggregate centres into separate slugs was examined in two strains
of Dictyostelium discoideum which differ in size. The evidence is consistent with the hypothesis that the size of the slugs is determined by two factors; one is the ability of a tip to
inhibit surrounding cells from forming an independent, rival tip; the other is the ability of
the surrounding cells to resist being subjected to the inhibition of the newly arisen tip. If the
surrounding cells are easily inhibited, then the slugs produced will be large; if they are
resistant to inhibition the resulting slugs will be correspondingly small. An assay for tJp
inhibition was developed which was used to estimate the volume and distance over which
inhibition occurs, the time over which it acts and the effect of tip size and cell mass shape
on size regulation. The measurements and the results of experiments which showed inhibition
across a thin agar layer are consistent with the hypothesis that an inhibitor spreads out
from the tip by simple diffusion. In further studies it was found that although inhibition
strength varies with the size of the tip, the ability to inhibit was the same in both strains
whereas the resistance to inhibition was greater in the smaller strain.
INTRODUCTION
In Dictyostelium discoideum the size of the slug is regulated at two points
in the life cycle, one of which occurs at aggregation and the other at the time
of slug formation. Aggregation is the period when the cell mass initially forms
by the collection of cells to the centre of the aggregation territory. When there
is a sparse population of cells the size is determined solely by the territory
(Bonner & Dodd, 1962). In contrast, crowded populations do not show a
one to one correspondence between aggregate number and the number of
fruiting bodies because large aggregate cell masses divide to form separate
slugs. In studying the control of size in large aggregates Hohl & Raper (1964)
found there was a 'critical mass' or volume of cells above which complete
intercellular integration could not be maintained.
In this report we are concerned with mechanisms of size control of large
aggregates. Ultimately we would like to have a molecular understanding of
the control process, and as a first step toward this goal the experiments to
be described elucidate some of the properties of the process. A quantitative
method for studying this kind of size control is described in this paper.
1
Author's present address: Imperial Cancer Research Fund, Mill Hill Laboratories,
Burtonhole Lane, London NW7 IAD, U.K.
24
W. KOPACHIK
What is novel in the studies presented here is evidence that this size control
is achieved by two interlocking factors; the tip, which is the presumptive
stalk region of the fruiting body, suppresses the formation of secondary tips
in the surrounding cell mass, and the surrounding cells can differ in their
ability to be affected by the dominance of the tip. There is an upper limit to
the volume of the cell mass that can be inhibited; aggregates smaller than this
volume will generally maintain integrity whereas aggregates larger than this
volume will divide. An assay using a microchamber with precisely known
dimensions was developed to estimate the volume and distance over which
inhibition occurs, the time over which it acts and the effect of the tip size
and cell mass shape on size regulation. Theoretical calculations using these
results were found to support the hypothesis that an inhibitor spreads out
from the tip by simple diffusion and are consistent with the finding that the
inhibition can act across a thin agar membrane. In addition, the tip inhibition
mechanism will be compared to the aggregation process.
MATERIALS AND METHODS
Growth and harvesting of cells
The wild-type strain of D. discoideum, DdH and a mutant strain, P-4,
(Chia, 1975) were used. Although P-4 has normal growth and aggregation,
each aggregate forms a number of small slugs. Amoebae were grown and
harvested on agar plates as described using Escherichia coli as the bacterial
associate (Bonner, 1947). In some experiments cells were stained with vital
dyes in order to distinguish the darkly staining prestalk region of the slug;
neutral red or nile blue sulphate stock solutions contained 7-5 mg/100 ml water
(Allied Chemical and Dye, Corp.). To stain cells, vegetative amoebae were
washed off the plates in cold distilled water and spun down at 150 g for 2 min.
The cell pellet was resuspended in 15 ml of water containing 1 ml of the stock
solution for each 0-1 ml of packed cells in the pellet and spun down again.
After harvesting, the cells were used immediately, or they were resuspended
in 100% Bonner's saline solution (Bonner, 1947), dispensed on 1% nonnutrient water agar (Bacto-agar) and allowed to develop in the dark at 22 °C.
When slugs had formed prestalk and prespore cell masses were obtained by
transecting the slugs with a microknife as described by Gregg (1967).
Assessment of the slug volume
In order to determine precisely the sizes of slugs small wells were made
by embedding wire of appropriate diameter in electron microscopy plastic
(Spurr embedding kit, Polysciences, Inc.). The plastic was polymerized in
gelatin capsules at 60 °C for two days and the wires removed after softening
the plastic for 10 min in boiling water. The plastic blocks were sectioned on
an AO 820 microtome to the appropriate thickness for the volume required
Size regulation in Dictyostelium
25
and the sections placed over Millipore filters (HABP 04700). Slit wells were
made in a similar manner by embedding shim stock (3-45 mm x 125 jam). Cells
were transferred to the wells using a hair loop and the wells were placed in
Petri dishes over Millipore prefilters (AP10 04700) saturated with 2 ml of
17 mM-Sorensen phosphate buffer, pH 6-0. The cell masses were then incubated
in the light at 22 °C. The transformation of a cell mass to a slug is directed
by a single tip and therefore a measurement of the numbers of tips formed
in each well provides a means to determine the average slug volumes by dividing
the well volume by the number of tips per well.
Tip inhibition - distance and volume
To determine quantitative aspects of tip inhibition, such as the cell mass
volume and the distance over which inhibition is effective, tips taken from
average-sized slugs were grafted to prespore cell masses in standardized sizes
and shapes (20 x lOVm 3 disc wells and 21-5 x 106/tm3 slit wells). The number
of tips forming in wells with and without tip grafts were compared and, if the
intact grafted tip inhibits secondary tips from forming in prespore cell masses,
the average slug volume will be large. The distance over which inhibition acts
can most easily be determined using slit wells.
Effect of tip size on inhibition
To test for an effect of tip size the tips to be grafted were of a large size
range and the recipient prespore cell mass volume was 30 x 106 /mi3. The
volumes of the tips to be grafted were estimated by measurements of the tip
base and height, assuming that the tip is a cylinder.
Mode of transmission of the inhibitor
In order to test whether or not the inhibitor can diffuse across an extracellular space tip cells and prespore cells were separated by a thin agar
membrane (ca. 100-125/tm) made of 3 % Bacto-agar in 17 mM-Sorensen
phosphate buffer. Dialysis membranes (65/*m with MW cutoffs of 6-8000
and 12000 No. 3787-D20 from A. H. Thomas Co.), Millipore filters (0-45 jitn)
and Nucleopore membranes (0-6, 0-8 and 1-0 /*m) were also used in some
experiments in place of the agar membrane.
RESULTS
Determination of the average slug volume
The volumes of the wells used in these experiments ranged from 2-5 to
50 x 106 /*m3, each with nearly equal surface to volume ratios with the exception
of the smallest wells. The disc-shaped cell masses obtained by artificially
clumping the cells mimic the size and shape of the cell masses obtained normally
26
W. KOPACHIK
10
20
30
40
50
Volume of well (106/um3)
Fig. 1. The number of slugs vs. the volume of cell mass in disc wells. Mean values
for at least 10 wells at each volume are plotted for P-4 (A) and DdH (#). The
lines drawn were determined by linear regression analysis of the data: P-4 r = 0-99
and P < 0001; DdH r = 0-28 for the 20-50x 106/«n3 wells and P < 002 that
the r value is significantly different from 0. Bars represent one standard deviation
of the mean.
during aggregation, and provide a convenient way to obtain cell masses of
any volume desired.
The average number of slugs formed 11 h after placing the freshly harvested
cells in the wells is plotted for each volume in Fig. 1. The results with P-4
show clearly that the number of slugs/well increases with cell volume and that
P-4 cell masses form approximately three times as many slugs than the wildtype DdH strain. The increase in number of slugs with increased cell mass is
taken to mean that there is an upper limit to the size of the cell mass.
Both the P-4 and DdH lines were determined by linear regression analysis
of the data: for P-4 N = 93 wells, r = 0-99 and the mean ± S.D. is 3-7 ± 1-1 x 106
/*m3; for DdH only the N = 73 wells above 20 x 106 ^m 3 were used in the
analysis since as can be seen DdH cell masses less than 20 x 106/*m3 almost
always form only one slug, r = 0-28 and the mean + S.D. is 15-3 ± 3-0 x 106 /*m3.
The correlation coefficients for the P-4 and DdH data are significantly different
from 0 at P < 0-001 and 0-02 respectively.
The DdH slug volume determined here is almost identical to the value of
15xlO 6 /* m 3 reported by Hohl & Raper (1964) using their totally different
method.
Tip grafting experiments
The following experiments examine whether or not the anterior tip of the
slug inhibits the formation of independent rival tips. The tip inhibition assay
Size regulation in Dictyostelium
27
Fig. 2. Tip grafting procedure. Slugs were transected with a microknife and
prestalk and prespore regions (stippled) identified by vital-dye staining intensities.
Sagittal view of a plastic disc well is shown; a = 63 /tin, b = 640 /im volume =
20xl06/wm3. In other experiments slit wells were used in which a = 50 fim,
b = 3-45 mm and the width = 120/on volume = 21-5 x 106 mm3.
Table 1. Tip grafts to disc wells
Slug volumes of the prespore
celh masses
Tip donor
Prespore
recipient
With tip Jc±s.D.
Without tip JC±S.D.
(0 DdH
DdH
17-3 + 51 43*
7-2±3-6 39
DdH
91 + 5-1 34
16-5±5-5 33*
(2) P-4
7-0 + 3-4 30
P-4
9-9 ±5-8 32
(3) P-4
5-2 ±2-4 30
P-4
6-4±3-3 29
(4) DdH
The tip-grafting procedure is diagrammed in Fig. 2 and the_slug volumes (in 106/4m3)
were determined by measuring the number of slugs/well. X = mean; S.D. = standard
deviation; N = number of wells. * ' / ' tests for significance between wells with tip grafts
and wells without tip grafts P < 005.
is shown approximately to scale in Fig. 2. The results allow us to determine
whether the reduced size in P-4 slugs is a result of the P-4 tip producing a less
effective inhibitor or the prespore cells being more resistant to the inhibition
or both.
(i) Tip grafts to cell masses in disc wells
The first experiment was a homotypic graft (one strain was used for both
the tip graft and the prespore recipient). With DdH it can be seen that when
a tip is placed on the prespore cell mass as compared to a cell mass without a
tip the average slug volume significantly increases (Table 1 expt 1). Since the
well volumes were 20 x 106/*m3, it is obvious from the average slug volumes
in the inhibited wells (17-3 x 106/*m3) that the grafted tip almost completely
inhibited new tips from arising among the prespore cells. In addition, it should
28
W. KOPACHIK
be noted that the volume of cell mass dominated by the transplanted tip is
nearly the same as the volume of an average slug formed from cells placed
directly into the wells. This implies that tip grafts are as effective in inhibition
as tips which arise autonomously from cell masses.
Furthermore, in a heterotypic graft (a different strain was used for the tip
and the prespore cells) in which P-4 tips are used (expt. 2) it was found that
P-4 tips are nearly as effective as DdH tips in inhibition strength. However,
when P-4 prespore cell masses are used (expts 3 and 4) the prespore cells are
not significantly inhibited, regardless of whether a DdH or P-4 tip is grafted.
This evidence suggests that P-4 slugs are small as a result of some altered
prespore function which makes these cells much less sensitive to the normal
inhibitor levels.
(ii) Tip grafts to cell masses in slit wells
The distance over which inhibition can extend is also an important parameter
to consider because pre-tip aggregates are irregular in shape and the long and
narrow aggregates can be mimicked by prespore cell masses in slit wells. The
inhibition range in such cell masses can easily bs measured by tip grafts to
the approximate middle of the slit wells. Figure 3 shows the distribution of the
inhibition distances for the four graft types.
The mean distance between the fruiting bodies formed under the grafted tip
and the nearest neighbouring secondary tips was determined to be 852 ± 332 /*m
(mean ± S.D.) for DdH. The distribution of the distances (Fig. 3 a) is significantly
greater than the distribution of distances found between the tips arising from
the prespore cell masses (Fig. 3e) without the tip grafts {P < 0 005; one sided
Smirnov test). Each tip forming in the regulating prespore cell mass inhibits
approximately half of the distance separating it from its neighbours, that is
282 fim. The average DdH tip graft distance of inhibition was estimated by
assuming that the secondary tips adjacent to the tip graft inhibit over a distance
of 282 /tm so that the difference of 570 /*m is the tip graft distance of inhibition
in slit wells. Clearly then the tip graft prevents newly arising tips from forming
in an adjacent region.
The histograms show that there is total inhibition at distances less than
200 /tm and almost 95 % inhibition up to 400 /*m (Fig. 3 c). At greater distances
inhibition is drastically reduced and quite variable.
The results also support the conclusions reached regarding the cell type
responsible for the small P-4 phenotype. The P 4 tip inhibition distance
(Fig. 3 c) is not significantly different from the DdH distance (Fig. 3 a) in a
two-sided Smirnov test, P > 95 %, whereas the comparison tip grafts to DdH
and P-4 prespore cell masses (Figs. 3 a v. d and c v. b) shows that the inhibition
distance is significantly shorter when P-4 prespore cell masses are used (onesided Smirnov test, P < 0-005).
29
Size regulation in Dictyostelium
30
(b)
(a)
20
•
/
10
0
30
(c)
id)
- nJ"
20
10
_r
r
0
30
-n. . , .
(e)
20
r-
10
0
2
4
6
8
~n
i—i
10 12 14 16
0
2
4
6
8 10 12 14 16
Distance (Aim X 100)
Fig. 3. Distribution of tip graft to neighbouring tips (a, b, c, d) and tip-to-tip
distances in DdH(e) and P-4(/) prespore slit well cell masses. Graft type; mean
distance±S.D.; (N number of wells), {a) DdH tip with DdH prespore cells;
852±332/tm; (59). (b) P-4 tip with P-4 prespore cells; 450± 159/*m; (66). (c) P-4
tip with DdH prespore cells; 800 ±290/an; (56). id) DdH tip with P-4 prespore
cells; 422 ±168/on; (60). (e) DdH prespore cells without tip grafts; 564± 309/an;
(99). if) P-4 prespore cells without tip grafts; 33O± 134/on; (123).
(iii) The effect of cell mass shape on inhibition
The results just mentioned allow us to examine in more detail the interesting
possibility that the geometry of the cell mass surrounding a tip is an important
factor affecting inhibition and the size of the cell mass. In Table 2 the slug
volumes resulting from tip grafts onto prespore cells in disc wells or slit wells
are listed. Here it can be easily seen that tips grafted onto disc cell ma$ses
inhibit more cell volume than do tips grafted onto slit cell masses. The difference
in the number of slugs/well in disc and slit wells serves to emphasize this
effect of the cell mass shape on tip inhibition; this evidence suggests that
inhibition is more effective in circular cell masses than in long and narrow
cell masses.
2
EMB 68
30
W. KOPACHIK
Table 2. Effect of cell mass shape on inhibition
Slugs/well
->
Tip grafts
X+S.D. N
Volume inhibited
(106/tm3)
(A) Disc wells
1-4 ±0-8 43
17-3
4-9 ±1-9 58
6-8
(B) Slit wells
The tip-grafting procedure is shown in Fig. 2. The wells were filled with DdH cells and
the dimensions of the disc wells (20 x 106/mi3) and sHt wells can be found in the legend of
Fig. 2. X = mean; S.D. = standard deviation; TV = number of wells.
Fig. 4. Procedure to determine the effect of tip size on tip strength. The stippled
region of the slugs is the prespore region which was put into a 30 x 106/*m3 disc
well (a). One tip of various volume was grafted as shown to each prespore cell
mass, (b) = Millipore filter, (c) = Millipore prefilter.
(iv) The effect of tip size on inhibition
The important question to consider now is whether any of the size variation
is determined by the tip. It is possible that all tips regardless of the slug size
have equal inhibition strength and that only differences in the cell's response
to inhibition determine the slug size. An alternative hypothesis to consider
is that tip strength varies with tip size. A test was made to determine whether
or not tip strength varies with tip size, and if it does, whether large tips can
inhibit larger cell masses (Fig. 4).
There is a definite effect of tip size on the ability to inhibit secondary tip
formation; the larger the tip the greater its inhibition (Table 3). This result
will be discussed later because the evidence suggests that the attraction power
of aggregate centres is not affected by size.
(v) Experiments to determine the mode of transmission of inhibition
The following experiment involves separation of tip cells and prespore cells
to examine whether or not the tip inhibitor requires cell contact for transmission of the inhibition. Dissociated prestalk cells in a 50 ± 106 /*m3 disc well
were placed under a layer of agar, dialysis membrane, Millipore or Nucleopore
filters (Fig. 5). It is essential to put the prestalk cells under the barrier in order
to prevent the prestalk cells from rapidly reforming slugs and breaking contact
with the agar, dialysis membrane or filters.
Size regulation in Dictyostelium
31
Table 3. Effect of tip size on inhibition in DdH
Wells with
> one tip
(%)
Number of slugs/well
Tip volume
(lOVm3)
1
2
3
4
:
5
6
(1) Range 1 x 10 to
lxlO 7 /tm 3
Mean: 31xlO 6 /mi 3
(2) Range 1 x 105 to
8
15
20 "
Mean: 3-5xlO /«n
(3) Range 6 xlO 3 to
lxlO 6 /an 3
Mean: 34x 10*/mi3
^ = 58%
1
3
4
*
4
3
.
25%
' .
.
.
15
19 = 79%
Determination of the effect of the tip size results were obtained'by the procedure diagrammed in Fig. 4; the well dimensions for the 30 x 106/*m3 disc wells are 760/*m diafneter
:
and 65 /im depth.
Fig. 5. The experimental conditions to test whether cell contact is involved io
inhibition, (a) DdH prespore cell mass, (b) Agar membrane, dialysis membrane,
Millipore or Nucleopore filter, (c) 50 x 106/mi3 disc well, id) 3% Bacto-agar in
17mM-Sorensen phosphate buffer, pH60. (e) coverslip. (/) DdH prestalk cell
mass underneath the separation layer (b).
In five out of six trials with agar between the prestalk and prespore cells, tip
formation occurred at an average of 4-8 h after plating; control cell masses
formed tips in ca. 2 h, therefore the mean delay in tip formation was 2-8 h.
A view of one such experimental cell mass and its respective control is srjown
in Fig. 6. The photographs were taken 3 h after plating and it can be seen' that
a well-formed tip is present on the control prespore cell mass but not on the
cell mass over the prestalk cells. Generally the prestalk cells under the agar
migrate out of the well along the underside of the agar and the prespore cells
above spread out on the upper surface following the wave of the prestalk
cells. It is at this time some of the prespore cells form a tip. In addition, prespore cells were placed above and below the agar; no inhibition or detyy of
tip formation was observed.
Further experiments with dialysis membranes, Millipore and Nucleopore
filters showed no delay even when, to give more time for diffusion, the prestalk
32
W. KOPACHIK
Fig. 6. Delay of tip formation in prespore cell mass over prestalk cells, (o) Prespore
cell mass over prestalk cells. (6) Prespore cell mass control. The prespore cells
were taken from the same slug and the photograph was taken after 3 h of isolation,
bar = 0-25 mm.
cells were put into the wells 7 h before the prespore cells were placed on top
of the barrier. It appears then that the inhibitor can act without direct cell
contact.
DISCUSSION
The objective of this study was to uncover general rules governing size
regulation and the control of prestalk cell differentiation in the cellular slime
mould, D. discoideum. The tip was first shown to be the dominant organizer
region in slime moulds by Raper (1940). By grafting tips onto the sides of
migrating slugs he found that the slug divided approximately equally between
the tips. In extending these experiments, the experiments reported here, and
those of Hohl & Raper (1964), have shown that the average size of the cell
mass dominated by a single tip of strain DdH is around 15 x 10V m 3 - Thus,
there is an upper limit to the volume of cell mass that can be inhibited; aggregates
smaller than this volume will generally maintain integrity whereas aggregates
larger than this volume will subdivide. Therefore the size of the slugs and
fruiting bodies formed, even in large aggregates from crowded populations,
are kept under a certain size.
It is interesting to contrast what is now known about the regulatory mechanism
of tip inhibition with the well-studied aggregation process. First the average
distance over which inhibition acts (570 /tm) is somewhat less than the average
attraction distance of centres (1270/tm) reported by Bonner & Dodd (1962).
Nevertheless both processes involve distances which could be traversed by a
diffusing small molecule within roughly several hours (Crick, 1970).
A second observation is that tips form centrally in the cell mass, but this is
in contrast to the placement of centres during their initiation in small drops
of aggregating cells (Konijn, 1961). In drops at low density, Konijn found
that initiation of centres was random. The reasons why tip formation is
invariably position dependent are obscure, but one possibility is that some
diffusible activator builds up in the region with the highest cell density.
Size regulation in Dictyostelium
33
Consequently, it will be especially interesting to see if the recently discovered
stalk-cell-inducing factor (DIF) might play such a role in pretip cell masses
(Kay, Town & Gross, 1979).
Lastly, although tip inhibition varies with the size of the tip, there i$ no
effect of size on center attraction power. Konijn (1968) clearly showed that
in D. discoideum the chemotactic response of responding population$ of
amoebae is independent of the size of the attracting cell mass over the range
of 400-5000 cells. The important consequence is that the aggregate territory
dominated becomes independent of the cell density. He later speculated that
cyclic AMP release by each cell was reduced at high cell density and therefore
there is an upper limit to the centre attraction power. In contrast, the tip graft
experiments reported here show that inhibition strength steadily increases with
tip size. This would suggest that each cell in a tip gives off a constant amount
of the postulated inhibitor regardless of the density. It is possible that the
apparent proportional increase in inhibition of tips, which are the presumptive
stalk cell zones of the fruiting body, may be related to the intriguing problem
of size-regulated stalk to spore ratios (Bonner & Slifkin, 1949; MacWilliams
& Bonner, 1979).
In summary then, although both centre dominance over an aggregation
territory and tip inhibition over the surrounding cell mass seem to involve
diffusible factors, their regulatory mechanisms differ in at least two fundamental
ways.
Another factor which I have found to affect the outcome of tip inhibition
is the geometry of the distribution of the cells surrounding the tip. The main
finding in this regard was that long, thin cell masses in the slit wells formed
slugs which were 2-5-3 times smaller than the slugs resulting from disc-sh£ped
cell masses. It is possible that the cell mass shape affects size in this way
because tip dominance is limited by the inhibitor's range of diffusion. In these
same experiments I found that inhibition is very strong close to the tip and
that it weakens drastically at distances greater than 400 /im. Using an entirely
different grafting method Durston (1976) and Durston & Vork (1977) rnade
a significant observation which supports and complements the tip inhibition
experiments reported here. In their experiments segments of slugs were grafted
end to end and by this they showed that tip inhibition was strongest near the
tip and progressively weaker in segments farther from it.
It is possible with the available information to examine whether or not
simple diffusion is a mechanism by which inhibition is transmitted from the
tip. By simple diffusion I mean that the paths of the inhibitor molecules are
random walks from the tip and the motion of the individual molecules i$ not
facilitated by active transport or relay on the part of the surrounding cells.
It should be noted that pulsatile release and relay of the cAMP signal is a well
established part of the aggregation process and it is important to see if what
is now known about tip inhibition is also consistent with such a mechanism.
34
W. KOPACHIK
First of all, the gradient of inhibition in the slug, as pointed out by Durston
(1976), and the distance dependence of inhibition seen in slit wells is consistent
with the simple diffusion model. A relay mechanism however should not show
such a pattern of decreasing intensity with distance. Then there is the tip
grafting result which does not fit well with inhibition mediated by a pacemaker
signal. In a pacemaker model inhibition strength should either not be affected
by the size of the tip, or perhaps increase with decreasing size of the tip (Clark
& Steck, 1979). Either pacemaker model is difficult to reconcile with the fact
that large tips have greater inhibition power.
It has already been mentioned that the distance of inhibition is consistent
with a simple diffusion mechanism. The time for setting up a tip inhibition
gradient also supports this hypothesis. I found that a papilla of cells appeared
on the prespore cell mass in about an hour from the time of isolation of the
cells. Farnsworth (1973), however, made a more precise estimate of the time
needed for a cell mass to become completely resistant to inhibition. In his
experiments tips were removed from cell masses and the remaining cell mass
bisected for various periods of time by insertion of an impermeable plastic
barrier. He found that a barrier left in place for 34 min resulted in 50 % of
the cell masses forming two tips and thus, on the average, it takes 34 min for
a group of cells to become resistant to inhibition by a nearby rival tip. It
might be argued that this is too short for diffusion mechanisms to be operating.
However, according to calculations by Crick (1970) a diffusion gradient of
a small molecule could be set up over a distance of about 0-1 cm in several
hours assuming a reasonable diffusion coefficient. But the average distance of
inhibition in slit wells is about half of that distance and since the time required
varies with the length squared, the time necessary should be roughly one
quarter, or less than one hour. On this basis, and on the results of the experiment
which showed that the tip inhibition can act across an agar barrier, simple
diffusion is supported as a mechanism by which the tip dominates surrounding
cells.
Let me reiterate that the size of a slug is also significantly affected by the
cell strain and the position of the cells in the cell mass. There are two points
to be made. First of all, although tip strength in DdH varies with tip size, no
differences were found in tip strength between strain DdH and the smaller
strain P-4. This evidence is consistent with the hypothesis that the size of the
slug cell mass is determined by two factors; one is the ability of a tip to dominate
or inhibit cells from forming an independent, rival tip and the other is the
ability of the surrounding cells to resist being subjected to the inhibition of the
newly arisen tip. If the surrounding cells are easily inhibited, then the slugs
produced will be large; if they are resistant to inhibition the slugs resulting
will be correspondingly small.
At the present time the nature of the changes in prestalk and prespore cells
and in the mutant strain causing these differences in resistance to inhibition
Size regulation in Dictyostelium
35
are unclear. It is hoped that the experiments here will open the way to a genetic
approach to the problem of inhibition and resistance to inhibition.
This investigation was supported by National Institutes of Health Research Service
Award T32GM07312, a Sigma Xi Grant-in-Aid of Research, the Whitehall Foundation
and grants from the National Science Foundation and National Institutes of Health, to
Dr J. T. Bonner.
I would like to thank John T. Bonner and Edward C. Cox for comments which improved
the manuscript and David Trevan for his help with the figures.
REFERENCES
J. T. (1947). Evidence for the formation of cell aggregates by chemotaxis in the
development of the slime mold Dictyostelium discoideum. J. exp. Zool. 106, 1-26.
BONNER, J. T. & M. K. SLIFKIN (1949). A study of the control of differentiation: the proportions of stalk and spore cells in the slime mold Dictyostelium discoideum. Am. J. Botany
36, 727-734.
BONNER, J. T. & M. R. DODD (1962). Aggregation territories in the cellular slime molds.
Biol. Bull. mar. biol. Lab. Woods Hole 122, 13-24.
CHIA, W. K. (1975). Induction of stalk cell differentiation by cyclic-AMP in susceptible
variant of Dictyostelium discoideum. Devi Biol. 44, 239-252.
CLARK, R. L. & T. L. STECK (1979). Morphogenesis in Dictyostelium: An Orbital Hypothesis.
Science 204, 1163-1168.
CRICK, F. H. C. (1970). Diffusion in embryogenesis. Nature, Lond. 225, 420-422.
DURSTON, A. J. (1976). Tip formation is regulated by an inhibitory gradient in the Dictyostelium discoideum slug. Nature, Lond. 263, 126-129.
DURSTON, A. J. & F. VORK (1977). The control of morphogenesis and pattern in the
Dictyostelium discoideum slug. In Development and Differentiation in the Cellular Slime
Moulds (ed. P. Cappuccinelli & J. M. Ashworth), pp. 17-26. New York: North Holland,
Elsevier.
FARNSWORTH, P. (1973). Morphogenesis in the cellular slime mold Dictyostelium discoideum',
the formation and regulation of aggregate tips and the specification of developmental
axes. J. Embryol. exp. Morph. 29, 253-266.
GREGG, J. H. (1967). Cellular slime molds. In Methods in Developmental Biology (ed.
F. Wilt & N. Wessells), pp. 359-376. New York: Crowell-Collier.
HOHL, H. & K. B. RAPER (1964). Control of sorocarp size in the cellular slime molds.
Devi Biol. 9, 137-153.
KAY, R. R., TOWN, C. D. & J. GROSS (1979). Cell differentiation in Dictyostelium discoideum.
Differentiation 13, 7-14.
KONIJN, T. (1961). Cell aggregation in Dictyostelium discoideum. Ph.D. Thesis. University
of Wisconsin, Madison.
KONIJN, T. (1968). Chemotaxis in the cellular slime molds. II. The effect of cell derjsity.
Biol. Bull. mar. biol. Lab. Woods Hole 134, 298-304.
MACWILLIAMS, H. K. & J. T. BONNER (1979). The prestalk-prespore pattern in cellular
slime molds. Differentiation 14, 1-22.
RAPER, K. B. (1940). Pseudoplasmodium formation and organization in Dictyostelium
discoideum. J. Elisha Mitchell Sci. Soc. 56, 241-282.
BONNER,
{Received 11 August 1981, revised 9 November 1981)