Optimisation of NMR dynamic models I. Minimisation algorithms and their performance within the model-free and Brownian rotational diffusion spaces

The key to obtaining the model-free description of the dynamics of a macromolecule is the optimisation of the model-free and Brownian rotational diffusion parameters using the collected R1, R2 and steady-state NOE relaxation data. The problem of optimising the chi-squared value is often assumed to be trivial, however, the long chain of dependencies required for its calculation complicates the model-free chi-squared space. Convolutions are induced by the Lorentzian form of the spectral density functions, the linear recombinations of certain spectral density values to obtain the relaxation rates, the calculation of the NOE using the ratio of two of these rates, and finally the quadratic form of the chi-squared equation itself. Two major topological features of the model-free space complicate optimisation. The first is a long, shallow valley which commences at infinite correlation times and gradually approaches the minimum. The most severe convolution occurs for motions on two timescales in which the minimum is often located at the end of a long, deep, curved tunnel or multidimensional valley through the space. A large number of optimisation algorithms will be investigated and their performance compared to determine which techniques are suitable for use in model-free analysis. Local optimisation algorithms will be shown to be sufficient for minimisation not only within the model-free space but also for the minimisation of the Brownian rotational diffusion tensor. In addition the performance of the programs Modelfree and Dasha are investigated. A number of model-free optimisation failures were identified: the inability to slide along the limits, the singular matrix failure of the Levenberg–Marquardt minimisation algorithm, the low precision of both programs, and a bug in Modelfree. Significantly, the singular matrix failure of the Levenberg–Marquardt algorithm occurs when internal correlation times are undefined and is greatly amplified in model-free analysis by both the grid search and constraint algorithms. The program relax (http://www.nmr-relax.com) is also presented as a new software package designed for the analysis of macromolecular dynamics through the use of NMR relaxation data and which alleviates all of the problems inherent within model-free analysis

Mesodynamics in the SARS nucleocapsid measured by NMR field cycling

Protein motions on all timescales faster than molecular tumbling are encoded in the spectral density. The dissection of complex protein dynamics is typically performed using relaxation rates determined at high and ultra-high field. Here we expand this range of the spectral density to low fields through field cycling using the nucleocapsid protein of the SARS coronavirus as a model system. The field-cycling approach enables site-specific measurements of R1 at low fields with the sensitivity and resolution of a high-field magnet. These data, together with high-field relaxation and heteronuclear NOE, provide evidence for correlated rigid-body motions of the entire β-hairpin, and corresponding motions of adjacent loops with a time constant of 0.8 ns (mesodynamics). MD simulations substantiate these findings and provide direct verification of the time scale and collective nature of these motions

Farseer-NMR: automatic treatment, analysis and plotting of large, multi-variable NMR data

We present Farseer-NMR (https://git.io/vAueU), a software package to treat, evaluate and combine NMR spectroscopic data from sets of protein-derived peaklists covering a range of experimental conditions. The combined advances in NMR and molecular biology enable the study of complex biomolecular systems such as flexible proteins or large multibody complexes, which display a strong and functionally relevant response to their environmental conditions, e.g. the presence of ligands, site-directed mutations, post translational modifications, molecular crowders or the chemical composition of the solution. These advances have created a growing need to analyse those systems’ responses to multiple variables. The combined analysis of NMR peaklists from large and multivariable datasets has become a new bottleneck in the NMR analysis pipeline, whereby information-rich NMR-derived parameters have to be manually generated, which can be tedious, repetitive and prone to human error, or even unfeasible for very large datasets. There is a persistent gap in the development and distribution of software focused on peaklist treatment, analysis and representation, and specifically able to handle large multivariable datasets, which are becoming more commonplace. In this regard, Farseer-NMR aims to close this longstanding gap in the automated NMR user pipeline and, altogether, reduce the time burden of analysis of large sets of peaklists from days/weeks to seconds/minutes. We have implemented some of the most common, as well as new, routines for calculation of NMR parameters and several publication-quality plotting templates to improve NMR data representation. Farseer-NMR has been written entirely in Python and its modular code base enables facile extension

Time-averaged order parameter restraints in molecular dynamics simulations

ISSN:0925-2738ISSN:1573-500