Location of EPR-Active Spins Buried in Proteins from the Simulation of the Spin−Lattice Relaxation Enhancement Caused by Dy(III) Complexes

A computational method is described that simulates the EPR microwave power saturation characteristics of a protein sample containing an EPR signal from a buried free radical in a frozen solution containing paramagnetic spin−lattice relaxation-enhancement agents such as [Dy(III)HEDTA], where HEDTA is N-hydroxyethylenediaminetriacetate. The specific experiment modeled in this work is the EPR progressive power saturation experiment, where a series of spectra are recorded with increasing microwave power incident on the sample. A fit of the data series yields a characteristic power at half saturation, or P 1/2, that is proportional to the spin−lattice relaxation rate of the signal observed in the sample. The addition of DyHEDTA to the protein solution increases P 1/2 through dipole−dipole coupling to the buried free radical by an amount strongly dependent on the distance r from the fast-relaxing DyHEDTA to the slow-relaxing radical. The measured value of P 1/2 reflects an ensemble of protein molecules in which each buried spin interacts with a specific distribution of DyHEDTA molecules. To simulate the effect of DyHEDTA on the P 1/2 of the buried radical spin, we have created a Monte Carlo-type method that models the power-saturation characteristics of the bulk sample by creating saturation profiles of individual, randomly oriented spin ensembles. These individual spin ensembles incorporate arbitrary structural data for the protein as a region where the individual molecules of DyHEDTA are spatially excluded from the calculation, as opposed to previous methods where simple geometric models were employed. The calculation method is validated mathematically and is used to simulate experimental data from the heme−nitric oxide-containing protein systems myoglobin and horseradish peroxidase to demonstrate the effectiveness of the new simulation method.