The program quadric_diffusion uses the quadratic representation approach of Brüschweiler, et al. [Science 268:886-889, (1995)] to determine the diffusion tensors for spherical, axially-symmetric and fully anisotropic motional models from experimental nitrogen-15 or carbon-13 spin relaxation data.

Current version is 1.14

© Copyright 1998, Arthur G. Palmer, III

L. K. Lee, M. Rance, W. J. Chazin and A. G. Palmer, Rotational diffusion anisotropy of proteins from simultaneous analysis of 15N and 13Cα nuclear spin relaxation, J. Biomol. NMR 9, 287-298 (1997).

Quadric_diffusion is now available as compiled executables for Linux and Macintosh OSX operating systems.

If you download quadric_diffusion and decide to use it, then please email agp6@columbia.edu, so that we can add you to our users list. This way we can reach you with bug reports and updates. If you download the program, please check this site frequently for updates in case of bug fixes (and please send email regarding any bugs you think you find).

If you need access to source code or executables for other computer architectures, please contact Arthur G. Palmer (agp6@columbia.edu).

Version History

• Version 1.0 – Initial release
• Version 1.1 – Error in calculation of ψ fixed. Rotations for axial case fixed to conform to z-y-z convention
• Version 1.11 – Fixed error in calculation of F-statistic comparing axial and anisotropic models
• Version 1.12 – Earlier versions reported Dxx/Dyy incorrectly (reported value actually was Dyy/Dxx)
• Version 1.13 Added override to default bond lengths and CSA values
• Version 1.14 – Fixed root bracketing error in r2r1_tm

Usage: quadric_diffusion control_file

The control_file contains the following information:

    axial_ratio_low axial_ratio_high #steps
    number_of_atom_types 'atom_1' ... 'atom_n'
    atom_1_tm_file_name
    ...
    atom_n_tm_file_name
    input_pdb_file_name
    output_pdb_file_name (for axially symmetric model)
    output_pdb_file_name (for anisotropic model) 

The first line constains estimates of the minimum and maximum axial ratio (Dpar/Dper) for grid searching, and the number of steps to use for the grid search. Each atom name must be enclosed in single quotations, e.g. ‘N’ or ‘CA’ for amide nitrogen or alpha carbon spins. For example, to analyze nitrogen-15 data, the second entry would be:

    1 'N' 

To analyze nitrogen-15 and carbon-13 data simultaneously, the second entry would be:

    2 'N' 'CA'

The atom_n_tm_file contains the local correlation time of atom_n for each residue determined either from a model-free analysis of nitrogen-15 or carbon-13 spin relaxation data using the modelfree program or determined from the nitrogen-15 or carbon-13 R₂/R₁ ratio using the r2r1_tm program. One file must exist for each atom type. The atom_n_tm_file contains one line for each residue to be analyzed. Each line contains the following fields:

    residue_number tm tm_uncertainty

For both the control_file and tm_file, lines starting with “#” are ignored. The residue number in the tm_file must match the residue number in the input_pdb_file.

For each model (spherical, axially-symmetric, and anisotropic diffusion), the diffusion tensor and Euler angles are output. The chi-square and F statistics are calculated for comparing models. The program also returns the predicted effective diffusion constant for each residue and the squared residual from the fitting process. For diagnostic purposes, spherical harmonic functions of the NH or CH bond vectors (in the diffusion reference frame) are also output. For the anisotropic model, uncertainties are obtained by Monte Carlo simulationsand the results for uncertainties for the φ and ψ angles can be inaccurate if the values of the angles are near 0, π or -π. The program contains a crude fix, but if your values of φ or ψ are near these values you might want to print the actual Monte Carlo results and inspect them. See the program listing for more information.

For axially symmetric and anisotropic diffusion models, the structure in the input_pdb_file is rotated to the diffusion frame. To be meaningful, prior to analysis, the center of mass of the molecular structure should be translated to coordinate origin by using the program pdbinertia. The angles φ, θ, and ψ represent the Euler angles in the z-y-z convention with the rotations being applied to the original molecule to generate the rotated molecule. In the z-y-z convention, the first rotation is about z, the second rotation is about the intermediate y axis and the third rotation is about the final z-axis. Output structures from the two analyses may differ by 90° rotations.

R2R1_TM

The program r2r1_tm calculates a local effective correlation time from the R2/R1 ratio, in which R2 and R1 are the spin-spin and spin-lattice relaxation rate constants for nitrogen-15 or carbon-13 spins. The local correlation times are used as input for the quadric_diffusion program.

Usage:   r2r1_tm [-1] > tm_file

The program prompts for the following information:

     nucleus_type (15N or 13C)
     XH_bond_length (Ang.) X_CSA (ppm) [enter a blank line to accept defaults]
     proton_spectrometer_field for R1 (MHz)
     proton_spectrometer_field for R2 (MHz)
     initial_tm_estimate (ns)
     r2r1_file_name

The input r2r1_file contains one line for each residue to be analyzed. Each line contains the following fields:

     residue_number      R2/R1_ratio     r2/r1_uncertainty

The input residue numbers should correspond to residue numbers in a pdb file for the molecule. Lines beginning with ‘#’ are ignored in the r2r1_file. If the -1 flag is included on the command line, then the input r2r1_file is not read and the user is prompted to enter a single R2/R1_ratio and uncertainty. The functionality with the -1 flag is essentially the same as using the tmest program of earlier releases.

The output tm_file contains one line for each residue analyzed. Each line contains the following fields:

residue_number      tm      tm_uncertainty