Smoluchowski dynamics of the vnd/NK‐2 homeodomain from Drosophila melanogaster: First‐order mode‐coupling approximation

Abstract

This work is the first in a series devoted to applying mode coupling diffusion theory to the derivation of local dynamics properties of proteins in solution. The first-order mode-coupling approximation, or optimized Rouse-Zimm local dynamics (ORZLD), is applied here to derive the rotational dynamics of the bonds and compare the calculated with the experimental nmr 15N spin-lattice relaxation time behavior of the vnd/NK-2 homeodomain from Drosophila melanogaster. The starting point for the calculations is the experimental three-dimensional structure of the homeodomain determined by multidimensional nmr spectroscopy. The results of the computations are compared with experimentally measured 15N spin-lattice relaxation times T1, at 34.5 and 60.8 MHz, to check the first-order approximation. To estimate the relative importance of internal and overall rotation, both rigid and fluctuating dynamic models are examined, with fluctuations evaluated using molecular dynamics (MD) simulations. The correlation times for the fundamental bond vector time correlation function and for the second-order bond orientational TCF are obtained as a function of the residue number for vnd/NK-2. The stability of the corresponding local dynamics pattern for the fluctuating structure as a function of the length of the MD trajectory is presented. Diffusive dynamics, which is essentially free of model parameters even at first order in the mode-coupling diffusion approach, confirm that local dynamics of proteins can be described in terms of rotational diffusion of a fluctuating quasi-rigid structure. The comparison with the nmr data shows that the first-order mode coupling diffusion approximation accounts for the correct order of magnitude of the results and of important qualitative aspects of the data sensitive to conformational changes. Indications are obtained from this study to efficiently extend the theory to higher order in the mode-coupling expansion. These results demonstrate the promise of the mode-coupling approach, where the local dynamics of proteins is described in terms of rotational diffusion of a fluctuating quasi-rigid structure, to analyze nmr spin-lattice relaxation behavior.

General Framework for Studying the Dynamics of Folded and Nonfolded Proteins by NMR Relaxation Spectroscopy and MD Simulation

“…Because these eigenmodes do not necessarily coincide with the principal axes of the diffusion frame, the correlation times yield an estimate of the lower bound of the tumbling anisotropy. Isotropic RED fundamentally differs in objective and method from the mode-coupling Smoluchowski dynamics approach. − The latter aims at a prediction of overall tumbling behavior of a fluctuating protein system using a semiempirical Smoluchowski dynamics approach. , Isotropic RED, on the other hand, is based on a principal component analysis of irreducible lattice functions. The overall tumbling observed during a finite MD trajectory is extrapolated to an isotropic ensemble, and correlation times are empirically adjusted to optimally reproduce experimental NMR relaxation parameters.…”

“…Isotropic RED fundamentally differs in objective and method from the mode-coupling Smoluchowski dynamics approach. [26][27][28][29] The latter aims at a prediction of overall tumbling behavior of a fluctuating protein system using a semiempirical Smoluchowski dynamics approach. 26,29 Isotropic RED, on the other hand, is based on a principal component analysis of irreducible lattice functions.…”

“…[26][27][28][29] The latter aims at a prediction of overall tumbling behavior of a fluctuating protein system using a semiempirical Smoluchowski dynamics approach. 26,29 Isotropic RED, on the other hand, is based on a principal component analysis of irreducible lattice functions. The overall tumbling observed during a finite MD trajectory is extrapolated to an isotropic ensemble, and correlation times are empirically adjusted to optimally reproduce experimental NMR relaxation parameters.…”

“…The overall tumbling correlation times are determined from experimental data or estimated from hydrodynamic theory , or by combining MD simulations with a numerical solution of the overall tumbling diffusion equation. The latter method, termed mode-coupling Smoluchowski dynamics, has been applied to relaxation data of protein and DNA systems. − …”

“…The latter method, termed mode-coupling Smoluchowski dynamics, has been applied to relaxation data of protein and DNA systems. [26][27][28][29] NMR relaxation spectroscopy offers unique opportunities to study proteins that are partially folded or unfolded. [30][31][32][33][34][35][36] A detailed characterization of such states provides useful insights into the properties of protein folding intermediates and the protein folding process itself.…”