The public and private benefit of an impure public good determines the sensitivity of bacteria to population collapse in a snowdrift game.

When cooperation is critical for survival, cheating can lead to population collapse. One mechanism of cooperation that permits the coexistence of cooperators and cheaters is an impure public good, whose public benefits are shared, but with a private benefit retained by the cooperator. It has yet to be determined how the contributions of the public and private benefit affect population survival. Using simulations and experiments with ß-lactamase-expressing bacteria, we found that for a given amount of public and private benefit, the population was most sensitive to collapse when initiated from an intermediate fraction of cooperators due to the near-concurrent collapse of the cooperator and cheater populations. We found that increasing the ratio of public to private benefit increased sensitivity to collapse. A low ratio allowed cooperators to survive on their private benefit after the public benefit could not rescue the cheaters. A high ratio allowed the cheaters to survive to high concentrations of ampicillin due to the high public benefit. However, small increases in ampicillin caused a rapid decline in the entire population as the private benefit was insufficient to allow self-rescue of the cooperators. Our findings have implications in the persistence of populations that rely on cooperation for survival.

Insights into Ligand-Mediated Activation of an Oligomeric Ring-Shaped Gene-Regulatory Protein from Solution- and Solid-State NMR.

The 91 kDa oligomeric ring-shaped ligand binding protein TRAP (trp RNA binding attenuation protein) regulates the expression of a series of genes involved in tryptophan (Trp) biosynthesis in bacilli. When cellular Trp levels rise, the free amino acid binds to sites buried in the interfaces between each of the 11 (or 12, depending on the species) protomers in the ring. Crystal structures of Trp-bound TRAP show the Trp ligands are sequestered from solvent by a pair of loops from adjacent protomers that bury the bound ligand via polar contacts to several threonine residues. Binding of the Trp ligands occurs cooperatively, such that successive binding events occur with higher apparent affinity but the structural basis for this cooperativity is poorly understood. We used solution methyl-TROSY NMR relaxation experiments focused on threonine and isoleucine sidechains, as well as magic angle spinning solid-state NMR 13C-13C and 15N-13C chemical shift correlation spectra on uniformly labeled samples recorded at 800 and 1200 MHz, to characterize the structure and dynamics of the protein. Methyl 13C relaxation dispersion experiments on ligand-free apo TRAP revealed concerted exchange dynamics on the µs-ms time scale, consistent with transient sampling of conformations that could allow ligand binding. Cross-correlated relaxation experiments revealed widespread disorder on fast timescales. Chemical shifts for methyl-bearing side chains in apo- and Trp-bound TRAP revealed subtle changes in the distribution of sampled sidechain rotameric states. These observations reveal a pathway and mechanism for induced conformational changes to generate homotropic Trp-Trp binding cooperativity.