Time-resolved Stokes shift in proteins with continuum model: Slow dynamics in proteins

Reported time-resolved Stokes shifts (TRSS) of free tryptophan (Trp) and free p-coumaric acid (CA) in water, and Trp in monellin, apomyoglobin, and isoalloxazine (Iso) of flavin mononucleotide (FMN) in the reductase component (C1 protein) of p-hydroxyphenylacetate hydroxylase were analyzed with continuum model. All unknown parameters of these systems in the theoretical equations were determined to obtain the best fit between the observed and calculated TRSS, according to a non-linear least square method. TRSS of free Trp at 295 K was also analyzed with four sets of reported dielectric constants and solvent relaxation times of water. Agreement between the observed and calculated TRSS of the free Trp was excellent. In CA the calculated TRSS could satisfactorily reproduce the observed one. Frequency-dependent dielectric constants of Trp in the proteins and Iso in C1 protein were expressed with 2- and 3-relaxation times. Static dielectric constant, ɛ0, intermediate permittivity, ɛ1, dielectric constant of Iso, ɛc, 2-relaxation times, τ1 and τ2, μe and D0 in the 2-relaxation time analyses were determined by the best-fit procedures. Agreements between the observed and calculated TRSS of Trp in native, denatured monellins, apomyoglobin, and Iso in C1 protein were excellent. No further improvements were obtained with 3-relaxation time analyses. Origin of the slow decaying component of TRSS in apomyoglobin was interpreted with continuum model and compared with molecular dynamics (MD) simulation model and a continuum model by Halle and Nilsson [J. Phys. Chem. B 113 (2009) 8210]. Frozen states revealed with MD model were reproduced with the 3-relaxation time analysis.