Divergence Involving Global Regulatory Gene Mutations in an Escherichia coli Population Evolving under Phosphate Limitation

Many of the important changes in evolution are regulatory in nature. Sequenced bacterial genomes point to flexibility in regulatory circuits but we do not know how regulation is remodeled in evolving bacteria. Here, we study the regulatory changes that emerge in populations evolving under controlled conditions during experimental evolution of Escherichia coli in a phosphate-limited chemostat culture. Genomes were sequenced from five clones with different combinations of phenotypic properties that coexisted in a population after 37 days. Each of the distinct isolates contained a different mutation in 1 of 3 highly pleiotropic regulatory genes (hfq, spoT, or rpoS). The mutations resulted in dissimilar proteomic changes, consistent with the documented effects of hfq, spoT, and rpoS mutations. The different mutations do share a common benefit, however, in that the mutations each redirect cellular resources away from stress responses that are redundant in a constant selection environment. The hfq mutation lowers several individual stress responses as well the small RNA-dependent activation of rpoS translation and hence general stress resistance. The spoT mutation reduces ppGpp levels, decreasing the stringent response as well as rpoS expression. The mutations in and upstream of rpoS resulted in partial or complete loss of general stress resistance. Our observations suggest that the degeneracy at the core of bacterial stress regulation provides alternative solutions to a common evolutionary challenge. These results can explain phenotypic divergence in a constant environment and also how evolutionary jumps and adaptive radiations involve altered gene regulation.

QUASISTATIONARY DISTRIBUTIONS AND FLEMING-VIOT PROCESSES IN FINITE SPACES

Consider a continuous-time Markov process with transition rates matrix Q in the state space Lambda boolean OR {0}. In In the associated Fleming-Viot process N particles evolve independently in A with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Lambda is finite, we show that the empirical distribution of the particles at a fixed time converges as N -> infinity to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N -> infinity to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1/N.