Recognition of complex patterned substrates by heteropolymer chains consisting of multiple monomer types.

We propose a statistical mechanical model of surface pattern recognition by heteropolymers with quenched monomer sequence distribution. The chemically heterogeneous pattern consists of different adsorption sites specifically distributed on a surface. The heteropolymer sequence is complementary with respect to the pattern. The concepts of recognition probability and recognition temperature are introduced. The algorithm for calculating the recognition probability is based on efficient recurrence procedures for evaluating the single-chain partition function of a chain macromolecule consisting of multiple monomer types, which interact with multiple types of adsorption sites. The temperature dependencies of the recognition probability are discussed. We address the critical role of the commensurability between the heteropolymer sequence and the distribution of the surface adsorbing sites on the polymer adsorption. Also, we address the question of how many types of monomer units in the heteropolymer are required for unambiguous recognition of compact target patterns. It is shown that perfect pattern recognition can be achieved for the strong-adsorption regime in the case of specifically structured compact patterns with multifunctional adsorption sites and heteropolymers with multiple monomer types when the degeneracy of the ground state is suppressed. The pattern recognition ability increases with the number of different types of monomer units and complementary adsorption sites. For random heteropolymers and patterns, the free energy change associated with the recognition process decreases linearly with increasing this number. Correlated random heteropolymers are capable of recognizing related patterns on a random background.