Extending recent work on a generic bipolar model proposed to study the nanochain formation of amelogenin molecules, we conduct a systematic investigation in this paper on the self-assembly of such a model via sweeping the relative parameter space. The bipolar model consists of a short-range attraction and an off-center Coulomb repulsion for the supermolecule. Through the Brownian dynamics simulation of both translational and rotational motions, we study the kinetics of the self-assembly and the structure of clusters formed within the system for various interaction settings. From the results of structure factor and cluster analysis, we find that the range of the repulsive interaction has a sensitive impact in controlling the duster size, while the strength of the attractive interaction dominates the cluster morphology such that the greater the attraction among particles, the more elongated the cluster formed.