model, it is proposed that an inhibitor produced 

 by a center inhibits the formation of other cen- 

 ters in the immediate area. In the other model, 

 no inhibitor is postulated and the distribution of 

 centers is accounted for by the removal of 

 cells, since without cells no centers can form. 

 In either model, the distribution and density 

 of centers depends upon the area that initially 

 formed centers control (either by withdrawing 

 cells from the surrounding substrate or through 

 the spread of inhibitor). Thus, if the time inter- 

 val between the appearance of centers is long 

 (a slow rate of center formation), a substantial 

 area would be occupied and later appearing 

 centers would be displaced at some distance 

 from those centers that form first. This situa- 

 tion would favor a spaced distribution of centers 

 and low center density (Fig. 7A). On the other 

 hand, if the time interval is short, initially 

 formed centers would have little opportunity to 

 establish territories before other centers would 

 appear. Since later appearing centers could 

 form at almost any distance from the first, this 

 situation would favor the establishment of ran- 

 dom, if not clustered, distributions (Fig. 7B). 

 While we cannot, with the data at hand, distinguish 

 between these models, the cell withdrawal hypo- 



A Slow rote of center formation- 



TERRITORY 



B. Fast rote of center formation- 



TERRITORY 



Fig. 7. 



The consequences of the rate of center formation on center 

 density and distribution. The faster the rate, the smaller 

 the area (territory) controlled by first formed centers. 



thesis is favored since it does not require the 

 postulation of an additional, unknown factor. 



We may conclude, then, that the non-random 

 distribution of centers (spaced or clustered) 

 occurs in Polysphondylium pallidum; that cen- 

 ter distribution is probably not the result of a 

 "spacing substance" present in the gaseous phase 

 of the environment; that what is involved in 

 establishing center density and distribution is the 

 rate of center formation and the number of cells 

 available for aggregation, i 



GRUN: It might be possible to find out 

 whether there is an inhibitory substance or sup- 

 pressor simply by taking strips of agar these are 

 growing in from between the centers and putting 

 them on a petridishbetween strips of agar which 

 have not had centers growing near them, "undif- 

 ferentiated" agar, and then see if amoebae placed 

 on this surface will stay off the experimental 

 strips. 



KAHN: Shaffer has done an experiment 

 similar to the one you suggest. Aggregates were 

 allowed to form on opposite sides of a thin agar 

 membrane. Under these conditions, it was pos- 

 sible to note that aggregates tend to organize 

 in the space between aggregates located on the 

 opposite side of the membrane. This suggests 

 that some sort of diffusable inhibitor (spacing 

 substance) may be produced that determines the 

 spatial distribution of aggregates. 



GRUN: It would be diffusing upward in this 

 case? 



KAHN: Yes. 



GREGG: Did you say that the centers form 

 in between the original centers? 



KAHN: Yes. 



GREGG: How does this correspond to Sus- 

 sman's thin membrane experiment? 



KAHN: I don't know. The observations are 

 certainly contradictory. 



EPEL: Do these centers all have varying 

 numbers of cells in them or does that vary 

 under these conditions, too? 



KAHN: In a rapidly aggregating population 

 of cells, one tends to get numerous aggregates 

 of "moderate" and approximately equal size. 

 In a slowly aggregating population, fewer, but 

 larger, aggregates are formed. 



GRUN: You didn't talk about the mineral oil. 



KAHN: No one really knows how mineral 

 oil influences aggregation. Perhaps it is behaving 

 as an absorbant (adsorbant?). Personally, I feel 



1 The data presented above will appear in full in Devel- 

 opmental Biology, 1966. 



128 



