Bivalent associations in Mus domesticus 2n = 40 spermatocytes. Are they random?

The establishment of associations between bivalents from Mus domesticus 2n = 40 spermatocytes is a common phenomenon that shows up during the first prophase of meiotic nuclei. In each nucleus, a seemingly random display of variable size clusters of bivalents in association is observed. These associations originate a particular nuclear architecture and determine the probability of encounters between chromosome domains. Hence, the type of randomness in associations between bivalents has nontrivial consequences. We explore different models for randomness and the associated bivalent probability distributions and find that a simple model based on randomly coloring a subset of vertices of a 6-regular graph provides best agreement with microspreads observations. The notion of randomness is thereby explained in conjunction with the underlying local geometry of the nuclear envelope.