The "coarse-grained" bead modeling methodology, BMM, is generalized to treat electrostatics at the level of the nonlinear Poisson-Boltzmann equation. This improvement makes it more applicable to the important class of highly charged macroions and highly charged peptides in particular. In the present study, the new nonlinear Poisson-Boltzmann, NLPB-BMM procedure is applied to the free solution electrophoretic mobility of low molecular mass oligolysines (degree of polymerization 1-8) in lithium phosphate buffer at pH 2.5. The ionic strength is varied from 0.01 to 0.10 M) and the temperature is varied from 25 to 50°C. In order to obtain quantitative agreement between modeling and experiment, a small amount of specific phosphate binding must be included in modeling. This binding is predicted to increase with increasing temperature and ionic strength.