This was one thing that worried me when we started with Holacracy. Interaction between the circles and how people work together across circle-boundaries - since I think Holacracy behaves "hostile" for matrix-organizations. What we observed:
1) we had lots of cross-link-roles. After short times, those roles died quickly wherever the collaborating was not regular and intense.
2) people started to act outside of circles and meetings and just work together in the background - which worked well. Collaboration is strong in our companies DNA, organization model doesn't affect that this much
Cross-link-roles don't work well for us. People tend to create new roles inside the circle or they form new circles. And most of between-circle-interaction happens in the background.