Electrophoretic mobility is proportional to charge. If members of a charge ladder (Figure 25-26) have the same friction coefficient (that is, the same size and shape), then the charge of the unmodified protein divided by its electrophoretic mobility, z0/μ0, is equal to the charge of the nth member divided by its electrophoretic mobility (z0 + ˆ†zn)/μn. Setting these two expressions equal to each other and rearranging gives

where z0 is the charge of the unmodified protein, ˆ†zn is the charge difference between the nth modified protein and the unmodified protein, μn is the electrophoretic mobility of the nth modified protein, and μ0 is the electrophoretic mobility of the unmodified protein. The migration time of the neutral marker molecule in Figure 25-26 is 308.5 s. The migration time of the unmodified protein is 343.0 s. Other members of the charge ladder have migration times of 355.4, 368.2, 382.2, 395.5, 409.1, 424.9, 438.5, 453.0, 467.0, 482.0, 496.4, 510.1, 524.1, 536.9, 551.4, 565.1, 577.4, and 588.5 s. Calculate the electrophoretic mobility of each protein and prepare a plot of ˆ†zn versus (μn/μ0) - 1. If the points lie on a straight line, the slope is the charge of the unmodified protein, z0. Prepare such a plot, suggest an explanation for its shape, and find z0.

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