Distribution of bacteria in the velocity gradient centrifuge

Cells in different parts of the cell cycle can be separated by brief centrifugation in a density stabilized gradient: the Mitchison-Vincent technique. The position of a cell in the tube depends upon its size, shape, and density, upon the gradients of density, viscosity, and centrifugal force through which it sediments, and upon time. A program to compute the velocities and integrate the velocity profile for particles of a particular size class is presented. Because enteric bacteria are a form intermediate between right cylinders and prolate ellipsoids of revolution, the program uses values for the frictional coefficient intermediate between those calculated for ellipsoids and for cylinders. The formula f=6pietab(a/b)1/2 possesses this property and because of its simplicity greatly speeds the calculations. A second program computes the distribution of masses and then of sedimentation constants for a bacterial population, expressed either as a frequency distribution or as total mass per s-class. The effect of the known variation in cell size at division is included in these calculations, which apply to organisms undergoing balanced, asynchronous growth in which mass increase is proportional to cell size. The two programs in conjunction compute the mass or cell-number profile in an arbitrary gradient. The programs have been used to design gradients to maximize the resolution of the technique.