A three-factor model can explain symmetry breaking and the n-1 rule during X-chromosome inactivation

X-chromosome inactivation (XCI) is a mammalian gene regulatory process that via chromosome-scale transcriptional silencing, leaves active a single X chromosome per diploid genome complement. The mechanisms that enable cells to select the appropriate number of X chromosomes to inactivate while leaving others active remain unclear. We demonstrate that all known chromosomal counting scenarios during XCI can be accounted for by a three-factor mathematical model that includes (1) Xist, the long noncoding RNA (lncRNA) responsible for gene silencing during XCI in eutherians, (2) an X-linked transcriptional activator of Xist, and (3) the autosomally-encoded SPEN, an Xist RNA-binding protein that is essential for gene silencing during XCI. In our model, symmetry between active X chromosomes is broken by stochastic differences in the number of Xist molecules that associate with the X chromosomes at the onset of XCI. Subsequently, integrated positive and negative feedback loops amplify then propagate superstoichiometric assemblies of SPEN complexed with Xist on the inactive chromosome(s), and select for levels of X-linked activator that enable only one X chromosome per diploid genome complement to remain active. Thus, asymmetric propagation of the SPEN-Xist ribonucleoprotein complex may play an essential role in symmetry breaking and chromosomal counting during XCI, independently of or in concert with cis-acting networks of DNA regulatory elements. Our results also have conceptual implications for gene regulatory circuits on autosomes.