Consistent theoretical description of nuclear spin long-lived states decay under conditions of reversible ligand-protein binding.

Determining the stability constant of the complex formed by an organic ligand with a protein is the first stage in the screening of new drugs. Nuclear spin long-lived states, in particular the singlet state, can be used to study the reversible binding of ligands to proteins. In a complex with a protein, the spins of the ligand interact with the spins of the protein, the system of protein and ligand nuclei can relax by a dipole-dipole mechanism, and the lifetime of the singlet state is strongly reduced. In this theoretical study, a system of encounter theory equations with the condition of fast relaxation in free protein was solved to determine the lifetime of the LLS in the presence of protein. It was shown that in the limit of fast chemical exchange, the relaxation of the LLS of the ligand nuclei due to dipole interaction with the protein nuclei is reduced to relaxation by the mechanism of dipole interaction with one proton of the protein, which is located at some effective distance from the ligand nuclei. Numerical calculations were made to test the applicability of the approximations used to process the experimental lifetime dependencies on the ligand concentration and external field, and it was shown that these approximations coincide with the limit of fast exchange in strong and weak magnetic fields, but not in the medium field. An analytical expression for the lifetime of the singlet state of ligand nuclei in an arbitrary magnetic field in the absence of protein was obtained.