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Optimisation of NMR dynamic models II. A new methodology for the dual optimisation of the model-free parameters and the Brownian rotational diffusion tensor.

ABSTRACT: Finding the dynamics of an entire macromolecule is a complex problem as the model-free parameter values are intricately linked to the Brownian rotational diffusion of the molecule, mathematically through the autocorrelation function of the motion and statistically through model selection. The solution to this problem was formulated using set theory as an element of the universal set [formula: see text]-the union of all model-free spaces (d'Auvergne EJ and Gooley PR (2007) Mol BioSyst 3(7), 483-494). The current procedure commonly used to find the universal solution is to initially estimate the diffusion tensor parameters, to optimise the model-free parameters of numerous models, and then to choose the best model via model selection. The global model is then optimised and the procedure repeated until convergence. In this paper a new methodology is presented which takes a different approach to this diffusion seeded model-free paradigm. Rather than starting with the diffusion tensor this iterative protocol begins by optimising the model-free parameters in the absence of any global model parameters, selecting between all the model-free models, and finally optimising the diffusion tensor. The new model-free optimisation protocol will be validated using synthetic data from Schurr JM et al. (1994) J Magn Reson B 105(3), 211-224 and the relaxation data of the bacteriorhodopsin (1-36)BR fragment from Orekhov VY (1999) J Biomol NMR 14(4), 345-356. To demonstrate the importance of this new procedure the NMR relaxation data of the Olfactory Marker Protein (OMP) of Gitti R et al. (2005) Biochem 44(28), 9673-9679 is reanalysed. The result is that the dynamics for certain secondary structural elements is very different from those originally reported.

SUBMITTER: d'Auvergne EJ

PROVIDER: S-EPMC2758375 | biostudies-literature | 2008 Feb

REPOSITORIES: biostudies-literature

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Optimisation of NMR dynamic models II. A new methodology for the dual optimisation of the model-free parameters and the Brownian rotational diffusion tensor.

d'Auvergne Edward J EJ Gooley Paul R PR

Journal of biomolecular NMR 20071218 2

Finding the dynamics of an entire macromolecule is a complex problem as the model-free parameter values are intricately linked to the Brownian rotational diffusion of the molecule, mathematically through the autocorrelation function of the motion and statistically through model selection. The solution to this problem was formulated using set theory as an element of the universal set [formula: see text]-the union of all model-free spaces (d'Auvergne EJ and Gooley PR (2007) Mol BioSyst 3(7), 483-4 ...[more]

PMID: 18085411

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Project description: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 R (1), R (2) 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.

Project description:BackgroundDynamic diffusion magnetic resonance imaging (ddMRI) metrics can assess transient microstructural alterations in tissue diffusivity but requires additional scan time hindering its clinical application.PurposeTo determine whether a diffusion gradient table can simultaneously acquire data to estimate dynamic and diffusion tensor imaging (DTI) metrics.Study typeProspective.SubjectsSeven healthy subjects, 39 epilepsy patients (15 female, 31 male, age ± 15).Field strength/sequenceTwo-dimensional diffusion MRI (b = 1000 s/mm2 ) at a field strength of 3 T. Sessions in healthy subjects-standard ddMRI (30 directions), standard DTI (15 and 30 directions), and nested cubes scans (15 and 30 directions). Sessions in epilepsy patients-two 30 direction (standard ddMRI, 10 nested cubes) or two 15 direction scans (standard DTI, 5 nested cubes).AssessmentFifteen direction DTI was repeated twice for within-session test-retest measurements in healthy subjects. Bland-Altman analysis computed bias and limits of agreement for DTI metrics using test-retest scans and standard 15 direction vs. 5 nested cubes scans. Intraclass correlation (ICC) analysis compared tensor metrics between 15 direction DTI scans (standard vs. 5 nested cubes) and the coefficients of variation (CoV) of trace and apparent diffusion coefficient (ADC) between 30 direction ddMRI scans (standard vs. 10 nested cubes).Statistical testsBland-Altman and ICC analysis using a P-value of 0.05 for statistical significance.ResultsCorrelations of mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) were strong and significant in gray (ICC > 0.95) and white matter (ICC > 0.95) between standard vs. nested cubes DTI acquisitions. Correlation of white matter fractional anisotropy was also strong (ICC > 0.95) and significant. ICCs of the CoV of dynamic ADC measured using repeated cubes and nested cubes acquisitions were modest (ICC >0.60), but significant in gray matter.ConclusionA nested cubes diffusion gradient table produces tensor-based and dynamic diffusion measurements in a single acquisition.Level of evidence2 TECHNICAL EFFICACY: Stage 1.

Project description:Introduction: Diffusion tensor imaging (DTI) is a magnetic resonance imaging (MRI) technique that measures the anisotropy of water diffusion. Clinical magnetic resonance imaging scanners enable visualization of the structural integrity of larger axonal bundles in the central nervous system and smaller structures like peripheral nerves; however, their resolution for the depiction of nerve fascicular morphology is limited. Accordingly, high-field strength MRI and strong magnetic field gradients are needed to depict the fascicular pattern. The study aimed to quantify diffusion tensor indices with high-field strength MRI within different anatomical compartments of the median nerve and determine if they correlate with nerve structure at the fascicular level. Methods: Three-dimensional pulsed gradient spin-echo (PGSE) imaging sequence in 19 different gradient directions and b value 1,150 s/mm2 was performed on a 9.4T wide-bore vertical superconducting magnet. Nine-millimeter-long segments of five median nerve samples were obtained from fresh cadavers and acquired in sixteen 0.625 mm thick slices. Each nerve sample had the fascicles, perineurium, and interfascicular epineurium segmented. The diffusion tensor was calculated from the region-average diffusion-weighted signals for all diffusion gradient directions. Subsequently, correlations between diffusion tensor indices of segmentations and nerve structure at the fascicular level (number of fascicles, fascicular ratio, and cross-sectional area of fascicles or nerve) were assessed. The acquired diffusion tensor imaging data was employed for display with trajectories and diffusion ellipsoids. Results: The nerve fascicles proved to be the most anisotropic nerve compartment with fractional anisotropy 0.44 ± 0.05. In the interfascicular epineurium, the diffusion was more prominent in orthogonal directions with fractional anisotropy 0.13 ± 0.02. Diffusion tensor indices within the fascicles and perineurium differed significantly between the subjects (p < 0.0001); however, there were no differences within the interfascicular epineurium (p ≥ 0.37). There were no correlations between diffusion tensor indices and nerve structure at the fascicular level (p ≥ 0.29). Conclusion: High-field strength MRI enabled the depiction of the anisotropic diffusion within the fascicles and perineurium. Diffusion tensor indices of the peripheral nerve did not correlate with nerve structure at the fascicular level. Future studies should investigate the relationship between diffusion tensor indices at the fascicular level and axon- and myelin-related parameters.

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Optimisation of NMR dynamic models II. A new methodology for the dual optimisation of the model-free parameters and the Brownian rotational diffusion tensor.

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Optimisation of NMR dynamic models II. A new methodology for the dual optimisation of the model-free parameters and the Brownian rotational diffusion tensor.

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