A "toy model" of molecular evolution of sequences in copolymers is proposed and implemented using a molecular-dynamics-based algorithm. The model involves coupling of conformation-dependent and sequence-dependent properties. It is shown that this model allows the realization of two main possibilities: ascending and descending branches of evolution (in terms of information content of a sequence), depending on the interaction parameters shaping the conformation of a polymer globule. The problem of adequate description of information complexity of copolymer sequences is studied. It is shown that Shannon's entropy or compressibility of a sequence gives preference to random sequences and therefore cannot be applied for this purpose. On the other hand, the Jensen-Shannon divergence measure turns out to give the description of information complexity which corresponds to our intuitive expectations. In particular, this characteristic can adequately describe two branches of evolution mentioned above, exhibiting a singularity on the boundary of these regimes.