@nbro - to directly address your question on what is the biological basis for a potential pool:
In the mini-column, the cells compete with the local mini-column mates. The share close proximity and have intermingled dendritic arbors and receptive fields. According to the literature, the spacing of this local mini-columns group is about 30 um apart with a total dendritic arbor reach of about 0.5 mm diameter. The working value of 16 cells in the HTM model is somewhat less than the usual biological figure of about 100 cells in a mini-column; I don’t think it actually makes a lot of difference in function. There are local inhibitory interneurons that mediate the voting between the cells in a mini-column. The winning predictive cell (if there is one) fires this local inhibitory interneuron and silences its partners.
There are also other, longer spatial range, inhibitory cells between the mini-columns that mediate the voting and sparsity between these mini-columns. Depending on what you chose as the input fields and output fields of these inhibitory interneurons you form the larger column structures. These interneurons determine the size of the spatial pool. As you have noted - this is a tunable parameter.
This post gives references and nails down some of the key parameters of column spacing:
Recapping:
Short range inhibitory interneurons control the predictive voting in a mini-column.
Longer range inhibitory interneurons control the density/sparsity/spacing (pick your choice of wording) between the mini-columns. (the spatial pooling function)
I hope this helps.