In many in vivo or in vitro situations, biofilaments manifest some annealed heterogeneity and should be considered as annealed random copolymers. The building blocks of the filaments differ from each other, for example, by the internal structure of the monomer, by the presence of some adsorbed species or by the curvature. Based on the copolymer concept, we embed the description of these systems in a common formalism. We demonstrate how the annealed heterogeneous nature of the filament is reflected by statistical correlations like the tangent-tangent correlation function or the cyclization probability. Our results show that annealed filaments adapt cooperatively to external constraints. This could contribute to explain anomalous elasticity manifested by biofilaments. Copyright (C) EPLA, 2014