The transfer matrix method for lattice proteins—an application with cooperative interactions

The transfer matrix method for generating lattice conformations of proteins is explained and applied to lattice proteins having high-level cooperativity to represent hydrophobic interactions. The main advantage of the method is the extremely efficient attrition-free generation and enumeration of compact conformations. We review the application of the method for the generation and complete, exact enumeration of all conformation for linear and cyclic chains in 2D on the square lattice and in 3D on the cubic lattice. We show for compact conformations that the growth of the chain in a piecewise way, cross-section by cross-section, is much more efficient than the traditional linear chain growth. We discuss an extension of the method by including information about the amino acid sequence. We develop a Zimm–Bragg [J Chem Phys 31 (1959) 476–85]-like theory of hydrophobic cluster formation by using the transfer matrix method. We show that the transfer matrix approach to the generation and averaging over chain conformations can be formulated as an algebraic problem. We show also how the transfer matrix method can be extended to off-lattice proteins.