Heterogeneity coordinates bacterial multi-gene expression in single cells

For a genetically identical microbial population, multi-gene expression in various environments requires effective allocation of limited resources and precise control of heterogeneity among individual cells. However, it is unclear how resource allocation and cell-to-cell variation jointly shape the overall performance. Here we demonstrate a Simpson's paradox during overexpression of multiple genes: two competing proteins in single cells correlated positively for every induction condition, but the overall correlation was negative. Yet this phenomenon was not observed between two competing mRNAs in single cells. Our analytical framework shows that the phenomenon arises from competition for translational resource, with the correlation modulated by both mRNA and ribosome variability. Thus, heterogeneity plays a key role in single-cell multi-gene expression and provides the population with an evolutionary advantage, as demonstrated in this study. Author summary Microbes perform multitasking for a wide range of purposes, including survival, adaptation, colonization, and evolution. Both modelling and experimental results at the ensemble level reveal trade-offs between different tasks due to resource competition, but it is unclear how single cells allocate limited intracellular resources to perform multitasking, and how does a population coordinate single cell performances during multitasking to maximize population efficiencies. In this study, we address this question by using bacterial multi-gene overexpression as the basic form of multitasking. We discovered and analyzed a statistical phenomenon called Simpson's paradox, where competing proteins in single cells correlate positively at each constant condition, although the proteins correlate negatively when all conditions are combined. We demonstrate that the phenomenon arises from competition for translational resources, with the correlation modulated by heterogeneity of both mRNA and ribosomes. We further show that heterogeneity coordinates multiple functional modules, conferring an evolutionary advantage on the population. Our work discloses that heterogeneity in the form of Simpson's paradox is an important phenomenon in coordinating multi-gene expression.