Linear Superposition and Prediction of Bacterial Promoter Activity Dynamics in Complex Conditions

Bacteria often face complex environments. We asked how gene expression in complex conditions relates to expression in simpler conditions. To address this, we obtained accurate promoter activity dynamical measurements on 94 genes in E. coli in environments made up of all possible combinations of four nutrients and stresses. We find that the dynamics across conditions is well described by two principal component curves specific to each promoter. As a result, the promoter activity dynamics in a combination of conditions is a weighted average of the dynamics in each condition alone. The weights tend to sum up to approximately one. This weighted-average property, called linear superposition, allows predicting the promoter activity dynamics in a combination of conditions based on measurements of pairs of conditions. If these findings apply more generally, they can vastly reduce the number of experiments needed to understand how E. coli responds to the combinatorially huge space of possible environments.Author Summary: Bacteria face complex conditions in important settings such as our body and in biotechnological applications such as biofuel production. Understanding how bacteria respond to complex conditions is a hard problem: the number of conditions that need to be tested grows exponentially with the number of nutrients, stresses and other factors that make up the environment. To overcome this exponential explosion, we present an approach that allows computing the dynamics of gene expression in a complex condition based on measurements in simple conditions. This is based on the main discovery in this paper: using accurate promoter activity measurements, we find that promoter activity dynamics in a cocktail of media is a weighted average of the dynamics in each medium alone. The weights in the average are constant across time, and can be used to predict the dynamics in arbitrary cocktails based only on measurements on pairs of conditions. Thus, dynamics in complex conditions is, for the vast majority of genes, much simpler than it might have been; this simplicity allows new mathematical formula for accurate prediction in new conditions.