Table 1. Additive null predictions for interactions between mutations.

Most interactions result in high expression phenotypes because the wildtype in the presence of CI has no expression, meaning that mutations are either neutral or increase wildtype expression. If an effect of a mutation is positive, the additive model states that the effect remains positive (and the same), independent of the genetic background. As such, these predictions are true only for a system that is tightly repressed, where the wildtype has no expression. ‘High +’ indicates predictions that result in expression levels above the biologically meaningful limit, which is defined by the unrepressed P_R promoter (shown in Figure 2A). We treat these predictions as high expression phenotypes. We consider three categorical single component effects (‘no expression’, ‘intermediate expression’, and ‘high expression’), and show the categorical effect predicted by the additive null model for the system. We use categorical effects only to provide an intuition for what the additive model predicts - to obtain actual predictions of system DMEs, we use convolution (as explained in detail in Materials and methods section Naïve convolution of component distributions as the null model for additivity between mutations).

		Effects of mutations in trans
		No expression	Intermediate expression	High expression
Effects of mutations in cis	No expression	No	Intermediate	High
	Intermediate expression	Intermediate	Intermediate +high	High +
	High expression	High	High +	High +