Computational spectroscopy of ubiquitin: Comparison between theory and experiments

Abstract

Using the constrained molecular dynamics simulation method in combination with quantum chemistry calculation, Hessian matrix reconstruction, and fragmentation approximation methods, the authors have established computational schemes for numerical simulations of amide I IR absorption, vibrational circular dichroism (VCD), and two-dimensional (2D) IR photon echo spectra of the protein ubiquitin in water. Vibrational characteristic features of these spectra in the amide I vibration region are discussed. From the semiempirical quantum chemistry calculation results on an isolated ubiquitin, amide I local mode frequencies and vibrational coupling constants were fully determined. It turns out that the amide I local mode frequencies of ubiquitin in both gas phase and aqueous solution are highly heterogeneous and site dependent. To directly test the quantitative validity of thus obtained spectroscopic properties, they compared the experimentally measured amide I IR, 2D IR, and electronic circular dichroism spectra with experiments, and found good agreements between theory and experiments. However, the simulated VCD spectrum is just qualitatively similar to the experimentally measured one. This indicates that, due to delicate cancellations between the positive and negative VCD contributions, the prediction of protein VCD spectrum is critically relied on quantitative accuracy of the theoretical model for predicting amide I local mode frequencies. On the basis of the present comparative investigations, they found that the site dependency of amide I local mode frequency, i.e., diagonal heterogeneity of the vibrational Hamiltonian matrix in the amide I local mode basis, is important. It is believed that the present computational methods for simulating various vibrational and electronic spectra of proteins will be of use in further refining classical force fields and in addressing the structure-spectra relationships of proteins in solution.

Optimization of Model Parameters for Describing the Amide I Spectrum of a Large Set of Proteins

“…These so called building block approaches have proven comparatively successful for simulation of polypeptides with regular secondary structures, 7 but have been found less successful for simulation of real proteins such as ubiquitin. 10 As a crucial element of these approaches, the concept of the "floating oscillator model" was established. 11 This refers to a simplified representation of the protein vibrations that only considers one vibrating amide I oscillator per peptide unit that interacts with other oscillators via transition dipole coupling (TDC).…”

“…[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] This method exploits the linear correlation found between the C=O bond length, stretching frequency and electrostatic potential at the atoms of NMA, 18,31,32 which provides a link between perturbation of molecular (and electronic) structure by the electric field of the solvent and the resulting shift of the vibrational frequency. Parametrized electrostatic calculations using the building block approach have been used in protein amide I sim-ulations of ubiquitin, 10,33 other proteins 34 as well as polypeptides in membrane environment. 29,35 These calculations are generally combined with MD simulations that provide coordinate trajectories, which are then utilized for calculating instantaneous normal modes and the resulting spectral line shapes.…”

“…36 It has been clearly demonstrated that heterogeneity in the site frequencies needs to be well reproduced in order to obtain agreement with spectra, as shown for ubiquitin by Cho and co-workers. 10 Solvent interactions were recently accounted for in a similar way in a calculation of the amide I absorption of a small helix-turn-helix protein 37 using otherwise a conceptually different building block approach -the Cartesian coordinate transfer method -developed by Keiderling, Bour and co-workers. 38,39 Here, the challenge of amide I simulations is addressed by attempting to find optimized parameters for the physical models used to describe the intrinsic frequencies and couplings between amide I oscillators.…”

Simulation of Vibrational Spectra of Large Molecules by Arbitrary Time Propagation

“…The Fourier procedures pursued in the presented work were also successfully used in the past, e.g. for generation of the infrared absorption (IR) and optical activity (vibrational circular dichroism, VCD) in connection with empirical 12 or ab initio 20 based force fields. In this work, we investigate a variant of these approaches which differs from the previous schemes in that the time propagation is based directly on the force field matrix instead of the harmonic Hamiltonian.…”

“…Although the molecular size remains the main limitation for quantum mechanical calculations, the exciting possibility of obtaining accurate vibrational force fields for the whole molecules appears realistic owing to the latest advances in quantum chemistry. [10][11][12] In the meantime, the Cartesian transfer tensor techniques 13 obtained spectroscopically accurate fields for large molecules from quantum-chemical computations on smaller fragments. 3,14 In principle, such fragmentation approaches would enable calculation of the vibrational spectra for arbitrarily large structures.…”