Fisher suggested advantageous genes would spread through populations as a wave so we sought genetic waves in evolving populations, as follows. By fusing a fluorescent marker to a drug efflux protein (AcrB) whose expression provides Escherichia coli with resistance to some antibiotics, we quantified the evolution and spread of drug-resistant E. coli through spacetime using image analysis and quantitative PCR. As is done in hospitals routinely, we exposed the bacterium to a gradient of antibiotic in a 'disk diffusion' drug susceptibility test that we videoed. The videos show complex spatio-genomic patterns redolent of, yet more complex than, Fisher's predictions whereby a decelerating wave front of advantageous genes colonises towards the antibiotic source, forming bullseye patterns en route and leaving a wave back of bacterial sub-populations expressing AcrB at decreasing levels away from the drug source. qPCR data show that E. coli sited at rapidly-adapting spatial hotspots gain additional copies of acr, the operon that encodes AcrB, within h and imaging data show resistant sub-populations thrive most near the antibiotic source due to non-monotone relationships between inhibition due to antibiotic and distance from the source. In the spirit of Fisher, we provide an explicitly spatial nonlinear diffusion equation that exhibits these properties too. Finally, linear diffusion theory quantifies how the spatial extent of bacterial killing scales with increases in antibiotic dosage, predicting that microbes can survive chemotherapies that have been escalated to × the clinical dosage if the antibiotic is diffusion-limited.
boy turning the wheel which ran loose on the screw outdide the thread, fitting the key-way running along the screw. As the screw advanced, the boss of the wheel pressed against the nut through which the screw moved, and thus it was kept back and did not advance with the screw. To drill a hole along the rib of the stall, or in a corner, a ratchet was provided, so that it could be turned without the necessity of a support on the wall side of the apparatus. This upright was so made that it could be fitted to any seam from X feet 9 inches to 8 feet thick, by placing various distance pieces either at the top or the bottom. One of these measured 3 feet 6 inches long, another 2 feet 4 inches, and a third 1 foot 6 inches, and these three could be combined. The drill was keyed to the screw, so that the screw pushed forward the drill, and turned it at the same time. He had also arranged the screw so that it would work out of the centre of a hollow drill. The end of the screw was fixed in the upright, instead of working through it, which lessened the distance between the working face and the upright, and this in pits with little room in front of the face was of great importance. Mr. CRAIG, Manager of the Harecastle Colliery, said, that when the Moss pits at Harecastle were opened about five years ago, and the levels commenced from the bottom of the shaft, great difficulty was experienced from the explosive gas, preventing generally the use of powder, and it was frequently necessary to stop up the places for days on opening out seams which generated large volumes of gas.
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