Dynamical transition in proteins and non-Gaussian behavior of low-frequency modes in self-consistent normal mode analysis.

Self-consistent normal mode analysis (SCNMA) is applied to heme c type cytochrome f to study temperature-dependent protein motion. Classical normal mode analysis assumes harmonic behavior and the protein mean-square displacement has a linear dependence on temperature. This is only consistent with low-temperature experimental results. To connect the protein vibrational motions between low and physiological temperatures, we have incorporated a fitted set of anharmonic potentials into SCNMA. In addition, quantum harmonic-oscillator theory has been used to calculate the displacement distribution for individual vibrational modes. We find that the modes involving soft bonds exhibit significant non-Gaussian dynamics at physiological temperature, which suggests that it may be the cause of the non-Gaussian behavior of the protein motions probed by elastic incoherent neutron scattering. The combined theory displays a dynamical transition caused by the softening of few "torsional" modes in the low-frequency regime ( <50 cm(-1) or <6 meV or >0.6 ps). These modes change from Gaussian to a classical distribution upon heating. Our theory provides an alternative way to understand the microscopic origin of the protein dynamical transition.

Single-atom test of all-atom empirical potentials: Fe in myoglobin.

The measured Fe vibrational density of states in deoxy-myoglobin, obtained from nuclear resonance vibrational spectroscopy, is compared to results from a normal-mode analysis using an all-atom empirical potential. Substantial disagreement reveals that for this one atom, the empirical potential does not accurately describe the actual forces. A Green function technique is developed to calculate the iron vibrational spectrum of deoxy-myoglobin by coupling the independently calculated heme and globin normal modes; nonbonded interactions between the heme molecule and the protein are essential for a good fit to the measurements. A projection of the eigenvectors from this potential onto the displacements induced by binding of CO demonstrates that normal modes over a broad range centered around 50-150 cm(-1) may drive the ligand-induced structural changes.

Direct determination of the complete set of iron normal modes in a porphyrin-imidazole model for carbonmonoxy-heme proteins: [Fe(TPP)(CO)(1-MeIm)].

Detailed Fe vibrational spectra have been obtained for the heme model complex [Fe(TPP)(CO)(1-MeIm)] using a new, highly selective and quantitative technique, Nuclear Resonance Vibrational Spectroscopy (NRVS). This spectroscopy measures the complete vibrational density of states for iron atoms, from which normal modes can be calculated via refinement of the force constants. These data and mode assignments can reveal previously undetected vibrations and are useful for validating predictions based on optical spectroscopies and density functional theory, for example. Vibrational modes of the iron porphyrin-imidazole compound [Fe(TPP)(CO)(1-MeIm)] have been determined by refining normal mode calculations to NRVS data obtained at an X-ray synchrotron source. Iron dynamics of this compound, which serves as a useful model for the active site in the six-coordinate heme protein, carbonmonoxy-myoglobin, are discussed in relation to recently determined dynamics of a five-coordinate deoxy-myoglobin model, [Fe(TPP)(2-MeHIm)]. For the first time in a six-coordinate heme system, the iron-imidazole stretch mode has been observed, at 226 cm(-)(1). The heme in-plane modes with large contributions from the nu(42), nu(49), nu(50), and nu(53) modes of the core porphyrin are identified. In general, the iron modes can be attributed to coupling with the porphyrin core, the CO ligand, the imidazole ring, and/or the phenyl rings. Other significant findings are the observation that the porphyrin ring peripheral substituents are strongly coupled to the iron doming mode and that the Fe-C-O tilting and bending modes are related by a negative interaction force constant.

Iron normal mode dynamics in (nitrosyl)iron(II)tetraphenylporphyrin from X-ray nuclear resonance data.

The complete iron atom vibrational spectrum has been obtained by refinement of normal mode calculations to nuclear inelastic x-ray absorption data from (nitrosyl)iron(II)tetraphenylporphyrin, FeTPP(NO), a useful model for heme dynamics in myoglobin and other heme proteins. Nuclear resonance vibrational spectroscopy (NRVS) provides a direct measurement of the frequency and iron amplitude for all normal modes involving significant displacement of (57)Fe. The NRVS measurements on isotopically enriched single crystals permit determination of heme in-plane and out-of-plane modes. Excellent agreement between the calculated and experimental values of frequency and iron amplitude for each mode is achieved by a force-field refinement. Significantly, we find that the presence of the phenyl groups and the NO ligand leads to substantial mixing of the porphyrin core modes. This first picture of the entire iron vibrational density of states for a porphyrin compound provides an improved model for the role of iron atom dynamics in the biological functioning of heme proteins.

Iron normal mode dynamics in a porphyrin-imidazole model for deoxyheme proteins.

Iron vibrational modes of a deoxyheme protein model (2-methylimidazole)(tetraphenylporphinato)iron(II), [Fe(TPP)(2-MeImH)], have been studied by refining normal mode calculations to nuclear resonance vibrational spectroscopy (NRVS) data. The NRVS measurements give quantitative frequencies and iron amplitudes of all modes with significant Fe vibrational motion. Modes with in-plane displacement of iron are distinguished from those involving out-of-plane motion by measurements on oriented single-crystal samples. Normal modes having large overlaps with in-plane nu(42), nu(50), and nu(53) modes of the porphyrin core are identified, as well as several modes with large iron-imidazole stretch components. An out-of-plane mode at 78 cm(-1) shows significant doming of the porphyrin core, but the largest Fe doming motion arises from the coupling of phenyls and imidazole at 25 cm(-1).