Sphere particle relationship

So I'm trying to come up with a system where interaction between a range of spheres can allow me to quantify it's interactive intensity in order to determine a set of rules.

I started out with a point and a sphere cloud. I added a sphere from pointcloud to visualize the overall sphere.

Then I turned all those points into other sphere clouds, and added spheres within points for those too in order to visualize them.

Because I'm trying to find system where I can determine how these smaller (set 2) spheres touch and interact, I need to know a way (or an equation) to figure out when they do touch and how the radius of the overall sphere (set 1) + number of particles (also in set 1) affect how the spheres in set 2 touch and interact. Also I know the number of particles in set 2 don't matter, but their radius does.

And after I figure this smaller problem out, I'll be trying to figure out a way multiple sets of overall spheres can interact based on their quantified intensities that are based on the their individual particle spheres. But before I get to that, does anyone know a way to figure out the problem I have at hand?