Fermi resonance from a curvilinear perspective

Sibert, Edwin L.; Hynes, James T.; Reinhardt, William P.

doi:10.1021/j100235a004

Cited by 149 publications

(100 citation statements)

References 5 publications

(7 reference statements)

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“…6,[13][14][15][16][17][18] How protein dynamics might contribute to catalysis ranges from conformational gating, where conformational changes might even be rate limiting, 19,20 as is thought to be the case with DHFR, [21][22][23] to a much more speculative direct coupling of specific protein motions to the reaction coordinate, perhaps similar to the strong and selective Fermi resonance between the stretching and bending motions of C-H moieties. [24][25][26] Unfortunately, the study of protein electrostatics and dynamics has been limited by the challenges associated with the direct characterization of specific protein bonds, including their environment and motion.…”

Section: Introductionmentioning

confidence: 99%

Carbon−Deuterium Bonds as Probes of Dihydrofolate Reductase

2008

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Much effort has been directed towards understanding the contributions of electrostatics and dynamics to protein function and especially to enzyme catalysis. Unfortunately, these studies have been limited by the absence of direct experimental probes. We have been developing the use of carbon-deuterium bonds as probes of proteins and now report the application of the technique to the enzyme dihydrofolate reductase, which catalyzes a hydride transfer and has served as a paradigm for biological catalysis. We observe that the stretching absorption frequency of (methyl-d 3 ) methionine carbon-deuterium bonds show an approximately linear dependence on solvent dielectric. Solvent and computational studies support the empirical interpretation of the stretching frequency in terms of local polarity. To begin to explore the use of this technique to study enzyme function and mechanism, we report a preliminary analysis of (methyl-d 3 ) methionine residues within dihydrofolate reductase. Specifically, we characterize the IR absorptions at Met16 and Met20, within the catalytically important Met20 loop, and Met42, which is located within the hydrophobic core of the enzyme. The results confirm the sensitivity of the carbon-deuterium bonds to their local protein environment, demonstrate that dihydrofolate reductase is electrostatically and dynamically heterogeneous, and lay the foundation for the direct characterization protein electrostatics and dynamics, and potentially, their contribution to catalysis.

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Section: Introductionmentioning

confidence: 99%

Carbon−Deuterium Bonds as Probes of Dihydrofolate Reductase

2008

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“…Last, but not least, the internal coordinates offer a simple and physical picture of vibrational motions in question. [13][14][15][16] For example, in the curvilinear perspective, the dominant contributions to the nonlinear Fermi resonance arise from the anharmonic cubic kinetic energy and potential energy couplings. 8,13 This is expected, since the Fermi resonance couples the vibrational modes of the 2:1 frequency ratio.…”

Section: Introductionmentioning

confidence: 99%

“…[13][14][15][16] For example, in the curvilinear perspective, the dominant contributions to the nonlinear Fermi resonance arise from the anharmonic cubic kinetic energy and potential energy couplings. 8,13 This is expected, since the Fermi resonance couples the vibrational modes of the 2:1 frequency ratio. In the rectilinear perspective, however, a major component to the Fermi resonance is due to the harmonic force constants associated with the exact internal coordinates.…”

Section: Introductionmentioning

confidence: 99%

“…In the rectilinear perspective, however, a major component to the Fermi resonance is due to the harmonic force constants associated with the exact internal coordinates. 13 The kinetic energy operator is more complicated in curvilinear internal coordinates than in rectilinear coordinates. The purpose of this work is to present a simple algebraic way to obtain the gradients of the vibrational coordinates, whose inner products give the exact kinetic energy operator.…”

Section: Introductionmentioning

confidence: 99%

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Vibrational coordinates and their gradients: A geometric algebra approach

Pesonen

2000

The Journal of Chemical Physics

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The gradients of vibrational coordinates are needed in order to form the exact vibrational kinetic energy operator of a polyatomic molecule. The conventional methods used to obtain these gradients are often quite laborious. However, by the methods of geometric algebra, the gradients for any vibrational coordinate can be easily calculated. Examples are given, and special attention is directed to ring coordinates.

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“…[6][7][8][9] Third, local mode behavior can develop as a result of dynamical resonances embedded within generally nonseparable ͑or, mixed͒ eigenfunctions. 10 Fourth, as separability breaks down, eigenfunctions may lose essentially all resemblance to their zeroth order counterparts, such that spectral assignment based on a zeroth order Hamiltonian becomes impossible. 11 In addition to these features, lifetime broadening occurs for states above the dissociation threshold as they themselves become resonances embedded in a continuum of scattering waves ͑e.g., see Ref.…”

Section: Introductionmentioning

confidence: 99%

On the calculation of absolute spectral densities

Smith

Jeffrey

1996

The Journal of Chemical Physics

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On the relation of protein dynamics and exciton relaxation in pigment-protein complexes: An estimation of the spectral density and a theory for the calculation of optical spectra J. Chem. Phys. 116, 9997 (2002) A new method of calculating the absolute spectral density of a Hamiltonian operator is derived and discussed. The spectral density is expressed as the solution of an integral equation in which the kernel is a renormalized one-sided energy correlation function of the full microcanonical density operator and a microcanonical density operator for a reference Hamiltonian. The integral operator associated with this equation transforms a known spectral density function for the reference Hamiltonian into the spectral density of the full Hamiltonian. The integral equation, by virtue of its formulation in energy space, is inherently one-dimensional and offers no storage difficulties, and the elements of its kernel may be computed by applying the Lanczos algorithm to randomly selected eigenfunctions of the reference Hamiltonian. This spectral density correlation method offers a number of advantages over variational methods. In particular, it has the potential for overcoming the hitherto largely insurmountable problem of tracing over a multidimensional Hilbert space in order to compute the spectral density of a nonseparable molecular Hamiltonian.

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Fermi resonance from a curvilinear perspective

Cited by 149 publications

References 5 publications

Carbon−Deuterium Bonds as Probes of Dihydrofolate Reductase

Carbon−Deuterium Bonds as Probes of Dihydrofolate Reductase

Vibrational coordinates and their gradients: A geometric algebra approach

On the calculation of absolute spectral densities

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