A general secular equation for cooperative binding of n-mer ligands to a one-dimensional lattice

The binding of n-mer ligands to a one-dimensional lattice involving many ligand species and complex multiple-binding mechanisms is studied. We show that, when derived using the sequence-generating function method of Lifson, the secular equation of any binding system with a finite number of "elementary units" can be expressed in a matrix determinant form that is very symmetric and easy to construct. In other words, for any binding system whose elementary units are known, the secular equation of the system can be obtained readily without going through the formal derivation of the equation. We also show that the "determinant" secular equation obtained using the present procedure can be employed directly to the calculation of binding isotherms.