In this paper we consider one of the ways to obtain HP-copolymers with specially designed "proteinlike" sequences such that in the dense globular conformation all the hydrophobic H-units form the core of this globule, while polar P-units constitute the envelope of this core. Namely, we assume that some low molecular reagent Z is added to the dilute solution of homopolymer H-globules and that it induces a polymeranalogous reaction H+Z-->P. We present the full theoretical analysis of the macrokinetics of the corresponding chemical reaction and show that at a certain interrelation between the diffusion coefficient of the reagent Z and the constant of the chemical reaction it is possible to end up with a copolymer chain with proteinlike statistics in the sense described above. We analyze the statistical properties of the sequences in resulting copolymer chains for the general case. Also we consider the scattering properties and spinodal of the melts of these chains. (C) 2003 American Institute of Physics.