Toward Quantitative Interpretation of Methyl Side-Chain Dynamics from NMR by Molecular Dynamics Simulations

Abstract

Advances in molecular dynamics (MD) force fields 1-3 have recently allowed the nearly quantitative interpretation of protein backbone dynamics as measured by NMR spin relaxation 4,5 and residual dipolar couplings. 6 These improvements were solely due to modification of the backbone ,ψ dihedral angle potential, as implemented in the AMBER99SB 2 and CHARMM22/CMAP 1 force fields. Amino acid side-chain motions, on the other hand, often play an important functional role, but their accurate simulation has been a considerable challenge in the past. [7][8][9] Because changes in side-chain motions are not necessarily correlated to changes in protein backbone mobility, 10 it is unclear how these force-field modifications affect side-chain dynamics. Here, we compare experimental and simulated side-chain NMR relaxation parameters of calbindin D 9k and ubiquitin and report significant improvements in the quantitative representation of sidechain motions by computation.Methyl groups are the dynamically best studied side-chain moieties of proteins. 9-15 Deuterium relaxation experiments of 13 CH 2 D methyl groups report on picosecond-nanosecond dynamics and measure up to five different relaxation rates for each methyl group at a given B 0 field. 14 They allow the unambiguous extraction of spectral densities J(0), J(ω D ), and J(2ω D ), where ω D is the Larmor frequency of deuterium. As shown here, these spectral densities lend themselves to direct comparison with computer simulations ( Figure 1). Alternatively, model-free dynamics parameters 14,16,17 can be determined from the experiment first and compared with the corresponding simulated parameters (Figure 2).Methyl side-chain dynamics of calbindin in its calcium-bound form have recently been reported. 18 Up to five spectral densities J(ω) have been determined for each of the 37 analyzable methyl groups and interpreted in terms of a model-free analysis.Here, a 50 ns MD simulation of Ca 2+ -bound calbindin (PDB entry 3ICB 19 with the mutation P34M) was performed using the AMBER 8 20 simulation program with the parameter set AMBER99SB following the protocol described previously. 4 The starting configuration was generated by immersing the calbindin structure in a cubic box with 5778 explicit SPC water molecules and neutralizing counterions. Production dynamics were run at 300 K and 1 atm pressure, with snapshots saved every 1 ps.The spectral densities J(ω) ) ∫ -∞ ∞ C(t)cos(ωt)dt are backcalculated from the trajectory by using the following parametrization of the reorientational time-correlation function C(t) of the methyl C-H bond vectors:where τ c is the experimentally determined overall tumbling correlation time, C CC (t) is the reorientational correlation function of the C-C bond that connects the methyl group with the rest of the protein, and C CH3 (t) is the correlation function describing the methyl group rotation itself. Equation 1, which is a modification of the extended model-free approach, 17,21 factors C(t) into three parts by assuming statistical independence between C-...

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Calculation of Proteins’ Total Side-Chain Torsional Entropy and Its Influence on Protein–Ligand Interactions

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