To consider three consecutive residues each with two states (helix and coil), the Lifson–Roig model uses a 4x4 transfer matrix instead of the 2x2 transfer matrix of the Zimm–Bragg model, which considers only two consecutive residues.
The transfer-matrix approach is especially elegant for homopolymers, since the statistical mechanics may be solved exactly using a simple eigenanalysis.
[3] The correlation matrix for this modification can be represented as a matrix M, reflecting the statistical weights of the helix state h and coil state c. The Lifson–Roig model may be solved by the transfer-matrix method using the transfer matrix M shown at the right, where w is the statistical weight for helix propagation, v for initiation, n for N-terminal capping, and c for C-terminal capping.
The partition function for the helix-coil transition equilibrium is where V is the end vector
[4] Analogous extensions of the Zimm–Bragg model have been put forth but have not accommodated mixed helical conformations.