Diffusion through agar blocks of finite dimensions: a theoretical analysis of three systems of practical significance in microbiology

A number of experimental methods in biology depend on the kinetics of diffusion of a substance through a gel. This paper reviews the diffusion equations, gives the experimental limitations for some useful cases, and presents computer simulations for cases that cannot be treated analytically. While double diffusion is not considered, three single-diffusion situations are treated. (1) Systems for the study of chemotaxis in the gliding bacterium Myxococcus xanthus. Experimental designs used for this in many cases in the literature were inappropriate and mathematical analysis of these is presented. (2) The development of gradient plates. The time necessary for vertical diffusion to become substantially complete and before diffusion in the direction of the original slant has proceeded significantly is calculated. (3) The application to antimicrobial disk susceptibility tests. The basis of the measurement of antibiotic sensitivities with disks containing antimicrobial agents, as routinely used in clinical microbiological and testing laboratories, is analysed and the limitations are assessed and improvements suggested.