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NMR Analysis Module

The NMR commands may be used to obtain a set of time series for a number of NMR properties from a trajectory. Among the possible properties are relaxation rates due to dipole-dipole fluctuations (T1, T2, NOE, ROE), chemical shift anisotropy and Deuterium order parameters for oriented samples. The documentation assumes that users are already familiar with NMR. Several textbooks are available for users interested in more information. The NMR command invokes the NMR subcommand parser.

Because several properties are based upon the position of nuclei that may not have been included in the PSF (and the trajectory) the module has its own building submodule (see BUILD) to construct atoms. For example, the H_alpha on the C_alpha can be constructed without invoking HBUILD for T1 and T2 calculations.

Everything is stored on the HEAP and no variables are kept when the module is left (there is no nmr.fcm common block). Everything is re-initialized when the module is exited with the END command.

Warning

The module has not been used in numerous situations and caution should be the rule. In case of doubt it is best to study the source code.

Syntax

NMR   enter the NMR module
END   exit the NMR module

Subcommands:

BUIL name  4 x single-atom-selection [DIST  real] [THETA  real] [DIHE  real]

CSA        4 x single-atom-selection  -
           [THE1  real] [PHI1  real] [THE2  real] [PHI2  real] -
           [S11  real]  [S22  real] [S33  real]

DQS        2 x atoms-selection   [CTDI real]

SET        [HFIELD  real]  [RTUMBL  real]  [CUT real]
           [GAMMA real [atoms-selection]]

RTIM       2 x atoms-selection [RTUMBL real]  [HFIELD real]
           [CSAR DSIGMA real] [CUT real] [STAT]
           {ANIS} [DRAT real] [DTSX real DTSY real DTSZ real]


DYNA       traj-specification -
           [CUT real] [RTUMBL real] [HFIELD real] [TMAX real] -
           [ORIENT { MASS }   atom-selection [NOCOMP] ]
                   { WEIGH }
           [UNIT INTEGER] {quantity}
           [DSIGma real] [ILISt integer] [MODFree integer] [MFDAta integer]
           [SAVE ]

DYNA        WRSTAT [ILISt integer] [ISDLIST integer]

WRIT       { LIST }   [UNIT  INTEGER]
           { COOR }
           { CSA  }
           { DQS  }
           { RTIM }

RESE       [KEEP]

name::= an arbitrary name chosen by the user (four characters)
atom-selection::= a selection of a group of atoms
single-atom-selection::= a selection of a single atom
quantity::= none or any combination of C(t), R(t), PROP, UVEC, VERBOSE

traj-specification::= FIRStu int [ NUNIt int ]
                      [ BEGIn int ]   [ SKIP int ]  STOP int

Note

STOP has to be specified so that enough memory may be allocated. It is a good idea to specify the other parameters as well (they default to 1). The command TRAJ QUERY UNIT int (Dynamics) may be used to obtain necessary data from the trajectory files.

General discussion regarding the NMR analysis module

RTIM (Relaxation TIMes)

This serves as a set-up for the DYNA command but can also be used to calculate the relaxation parameters for a rigid body if keyword STAT is specified.

For the dipole-dipole relaxation rate properties the rotational tumbling time are taken in PS, the magnetic field in TESLA (note that 11.74 T yields 500 MHz for a proton H). The Relaxation Times are in 1/SEC. The gyromagnetic ratio of a nucleus are obtained from the first letter in the TYPE() TYPE array and can be modified using the SET commands. The default GAMMA constants are taken from table 2.1 in “NMR of Proteins and Nucleic Acid” by K. Wuthrich.

Nucleus Gamma [RADIAN/(TESLA*SEC)]:
H 26.75D07
C 6.73D07
N -2.71D07
P 10.83D07

Note

the sign is important for the spectral densities

All the time series of all particles involved in a RTIM selection are kept on the HEAP. The total number of time series is indicated in the output, so is the HEAP required storage. Very large sets of long trajectory can be broken down (one can use the repeated loops of the MISC command to do this).

In the NMR analysis module, the spectral densities are defined as

J(W) = \int_0^\infty cos(Wt) C(t) \mathrm{d}t = J(|W|)

following the convention of R.M. Levy et al., JACS 103, 5998 (1981), or E.T. Olejniczak et al., JACS 106, 1923 (1983). Notice that this convention differs from other notations such as in “Principles of Nuclear Magnetic Resonance in One and Two Dimensions” by R.R. Ernst, G. Bodenhausen and A. Wokaun, Oxford 1987, where there is a factor of 2 to account for an integral from -inf to +inf (see section 2.3 of that reference).

The fast part (decays on time scale of ps) and the slow part (decays from the rotational diffusion with RTUMB) are integrated separatly.

J_\mathrm{fast}(W) & = \int_0^\mathrm{[TMAX]} cos(Wt) [C(t) - C_\mathrm{plateau}] e^{-t/\mathrm{[RTUMBL]}} \mathrm{d}t \\
J_\mathrm{slow}(W) & = \int_0^\infty cos(Wt) [C(t) - C_\mathrm{plateau}] e^{-t/\mathrm{[RTUMBL]}} \mathrm{d}t

Many papers report different formulas for T1, T2, T1R, NOE and ROE. See for instance Levy and M. Karplus p. 445 “Trajectory studies of NMR relaxation in flexible molecules”, Chap 18, p. 445, American Chemical Society 1983. See also, I. Solomon, Phys. Rev. 99, 599 (1955). In the NMR module, the expressions used are:

Spectral densities: J(0) J(W1) J(W2) J(W1-W2) J(W1+W2)

1/T1  = FACT*(3*J(W1)+J(W1-W2)+6*J(W1+W2))
1/T2  = FACT*(4*J(0)+3*J(W1)+6*J(W2)+J(W1-W2)+6*J(W1+W2))/2
1/T1R = FACT*(3*J(0)+5*J(W1)+2*J(W1+W2))  (T1 in rotating frame, to be checked)
NOE   = 1+(GAMMA2/GAMMA1)*(-J(W1-W2)+6*J(W1+W2))/(3*J(W1)+J(W1-W2)+6*J(W1+W2))
ROE   = FACT*(3*J(W1)+2*J(W1-W2))

with the prefactor given by:

FACT  = 1/10 * ((MU0/4*PI)*PLANCK/(TWO*PI)*GAMMA1*GAMMA2)**2 * (PSEC/ANGS**6)

where PLANCK = 6.62618D-34, ANGS=1.0D-10, PSEC = 1.0D-12, MU0 = 4*PI*1D-07 the permitivity of vacuum in SI units. The rates are converted to [1/SEC] by the factor FACT. Note that the spectral density contains the distance dependent part <r**-3>**2.

The order parameters are calculated from the average of plateau = 3/4 <Y2/R**3>**2 + 3 <Y1/R**3>**2 + 1/4 <Y0/R*3>**2 using COMPLEX arithmetics.

If CSAR DSIG {real} is given the contribution of chemical shift anistropy to the relaxation will also be calculated for bonds less or equal to 1 Angstrom length using the value DSIG for the chem. shift anisotropy. For N15 nucleus a value of -160 ppm is recommended and the director is approximately directed along the N-H bond. A unit vector can be generated using the BUILD facility of the NMR module if other axis are desired. The expressions for the chemical shift anistropy relaxation were taken from Goldman’s book on NMR:

1/T1 =  (2/15)*(1.0E-06*DSIGMA*W1)**2*J(W1)/<1/R**6>
1/T2 =  (2/15)*(1.0E-06*DSIGMA*W1)**2*((2/3)*J(0)+(1/2)*J(W1))/<1/R**6>

where DSIGMA is in ppm and W1 is GAMMA1*HFIELD. The distance dependence in J(W) is also removed here.

The relaxation contribution due to CSA is added to give the total relaxation value for the spin pair in the output to ILIST file command when DSIG keyword is present in DYNA command.

Keyword ANIS: Anisotropy is now implemented for an axially symmetric molecule, i.e. Dy ~ Dz of the principle axes of inertia or diffusion tensor, so that Dparallel and Dperpendicular to a long axis can be used. Obtain these values from the relaxation data via a program such as ROTDIF (Walker O, Varadan R, Fushman D. 2004. J. Magn. Reson. 168:336-345), or via hydrodynamics calculations. DRAT {real} is the ratio Dparalell/Dperp. of the diffusion tensor DTSX, DTSY, DTSZ {real} is the diffusion tensor axes, typically using orient will align the coordinate set with the longest axes of inertia along x (so it would be 1.0 0.0 0.0 but any alignment could be chosen). For alignment the coordinates of the comparison set are used.

Note

Tau1,2,3 are calculated from value of DRAT and RTUMBL With keyword STATic {logical} the relaxation parameters will be calculated for global tumbling with a correlation time RTUMBL or in case of anisotropy with Tau1,2,3 and the structure in the comparison set.

It should be noted that since global and internal motions are modeled separately, that anisotropy has no effect on the correlation functions, i.e. S2, but mixes into the calculation of relaxation parameters. Equations used follow those in Barbato et al., Biochem. 31, 5269-78 (1992) and further description is given in Buck et al., 2005 (submitted to JACS).

DYNA option

The DYNAmics command reads in the trajectory from fortran units opened with sequential numbers. see Dynamics.

FIRSTU is the unit assigned to the first file of the trajectory, and must be specified. NUNIT gives the number of units to be scanned, and defaults to 1. BEGIN, STOP, and SKIP are used to specify which steps in the trajectory are actually used. BEGIN specifies the first step number to be used. STOP specifies the last. SKIP is used to select steps periodically as follows: only those steps whose step number is evenly divisible by STEP are selected. The default value for BEGIN is the first step in the trajectory; for STOP, it is the last step in the trajectory; and for SKIP, the default is 1. A similar logic is used in the CORREL module (see Correlation Functions).

Keyword CUT can be used to specify a cutoff for the distance between nuclei to be included in the calculation.

ORIE is used to reorient all coordinate frames of a trajectory with respect to the comparison set; if NOCOMP keyword is present, orientation will be wrt the first frame of the trajectory piece to be analyzed. This is done to obtain the internal dipole-dipole correlation functions in the molecular frame assuming internal motions and overall rotation are independent. Overall rotation is assumed to be isotropic and to correspond to an exponential correlation function with a characteristic time equal to RTUMBL (ps).

HFIELD is the magnetic field strength in tesla. Default = 11.74 Tesla which yields a Larmor frequency of 500 MHz for protons. The value of TMAX is the maximum time used to numerically integrate the fast part of the internal correlation function. A simple trapezoidal rule is used. The default value of TMAX is 0.0, the correlation function should be examined to set a reasonable value for TMAX [for instance, see R. Bruschweiler, B. Roux, M. Blackledge, C. Griesinger, M. Karplus and R. Ernst. “Influence of Rapid Intramolecular Motions on NMR Cross-Relaxation Rates. A Molecular Dynamics Study of Antamanide in Solution”, J. am. Chem. Soc. 114, 2289 (1992)].

If RTUMB .le. 0.0 then no analytic overall rotation contribution is computed. This is to be used with trajectories that retain the overall diffusion.

Output includes a rough estimate of the effective correlation time for the analyzed (NH) motions, and an entropy estimate using the “diffusion in a cone” model (Yang&Kay,JMB263,p369 (1996) “model 3”)

  • DSIGma adds a CSA contribution to the relaxation rate (see also CSA below) The TOTAL rates (and the rates written to the ILISt file) contain this CSA contribution, whereas the rates printed immediately after each spin-system do not.
  • ILISt specifies a file for compact writing of relaxation parameters. The columns are relaxation rates as defined above (in 1/sec) R1, R2, NOE, ROE, R2/R1, <S2>, Sconf, Taue, TMXE, and atom identifiers. Here <S2> is the plateau value (generalized order parameter), Sconf is an entropy estimate using the diffusion-in-a-cone model (Yang&Kay,JMB263,p369 (1996) “model 3”) neglecting alternative Sconf values for S2 < 1/64, and using approximation A=-0.11 as suggested by Yang&Kay. Taue is the effective correlation time for this motion computed from the integral of the correlation function C(t) out to TMXE, the first time when C(t) is <= <S2>.
  • MODFree and MFDAta specify files that can be used as input to Art Palmer’s ModelFree NMR analysis program
  • The SAVE keyword adds relaxation parameters for subsequent statistical averaging (DYNA WRSTAT)

The output is written to UNIT. The output level is controlled by the keywords:

C(t) dipole-dipole relaxation correlation functions
R(t) dipole-dipole time series
PROP CSA and DQS for solid state NMR properties
UVEC unit vectors for CSA and DQS solid state NMR
VERBOSE all quantites will be written out (including all coordinate frames!)

DYNA WRSTAT is a special form of the command, which simply computes averages and standard-deviations of the relaxation parameters that were SAVEd in previous DYNA commands, and writes them out to ILIST and ISDLIST, respectively. Accumulators are zeroed in preparation for a new round of statistics collection.

In addition to the correlation functions, relaxation parameters are calculated (see above). It should be noted that spin-spin distances and anisotropy (specifically the angle of the vector with the long axis) are taken as the trajectory average. If a constant distance, e.g. 1.02A for N-H is desired you need to alter the source-code.

other NMR properties supported

CSA (Chemical Shift Anisotropy)

Construct the principal axis from a z-matrix

1          u
 \        /          theta 2-3-u   (theta=0 gives u along 2-3)
  2 --- 3*           phi   1-2-3-u (phi=0 gives a cis)

“u” is the end of the unit vector indicating a principal axis starting from atom 3

CSA = SUM_{axis_i}  S_ii (Z(i)**2 - 0.5 *(X(i)**2+Y(i)**2) )

where X(i), Y(i), and Z(i) are the components of the i-th unit vector of the chemical shift tensor elements and S_ii is the magnitude of the i-th tensor element. The chemical shift tensor is a symmetric second rank tensor and is determined by 3 chemical tensor elements and 3 unit vectors. The value of the chemical shift parallel, Z(i)**2, and perpendicular, 0.5*(X(i)**2+Y(i)**2, are also given independently.

For example, the N15- chemical shift anisotropy for the peptide backbone has been studie by Mai W., Hu W., Wang C., and Cross TA. “Orientational constraints as three-dimensional structural constraints from chemical shift anisotropy: the polypeptide backbone of gramicidin A in a lipid bilayer”. Protein Science (1993) Apr;2(4):532-42.

CSA  S11 37.0 S22  62.0  S33 202.0   -
     the1   71.0  phi1 180.0 the2  -90.0 phi2 90.0 -
     select resid 2 .and. type C   end  -
     select resid 3 .and. type H   end  -
     select resid 3 .and. type N   end

DQS (Deuterium Quadrupol Splitting)

Construct the unit vector between a pair of atoms and project it onto the reference Z-direction.

DQS = (3*Z**2-1)/2.0,

where Z is the projection along the Z axis of the unit vector of a carbon-deuterium bond. This particular property could also be easily computed from the options of the CORREL module, Correlation Functions.

BUILD

The build command is useful for constructing hydrogen atoms, or any other particle, that is involved in the calculation of an NMR propertiy but is not present explicitly in the trajectory file. An example would be the NMR relaxation times T1, T2 of the H_alpha, which is not included in the extended atom potential function (e.g., in toph19.inp). The syntax is simply a Z-MATRIX input line, where the first three atoms have well-defined coordinates. The name given to the new atom is arbitrary. By default the RESID and RESNAM are the same as that of the first atom-selection and the SEGID is called “BUIL”. The atom position is stored starting from NATOM+1, at the end of the coordinate list. The coordinates are re-built automatically before computing any NMR property.

WRITE

The WRITE command is used to write out most information. The default output is used unless a UNIT number is given (that unit is not closed by the NMR module). The keywords LIST (write out all the list of all properties, mostly used for debugging), COOR (mostly to have access to the coordinates constructed by the BUILD option), and the NMR properties (CSA, DQS and RTIM). The level of printout detail is controlled by PRNLEV (see (chmdoc/misc.doc)). This will change in future versions and the printout level will be controlled by direct keywords. The present levels of printout are:

PRNLEV OUTPUT
0 (default) normal output for all options and commands
1 value of DQS, CSA for individual structure
2 Value of the spectral densities J(W1)
3 Larmor Frequencies
4 Dynamics steps, time and NCOORD Fast and plateau part of the spectral densities
5 Associated unit-vectors for CSA and DQS COOR ORIENT normal output in DYNAM (angle and axis printed)
6 Correlation function for relaxation Integrand in calculations of spectral densities
7 Spin-spin time series used to compute the correlation function
8 Full spin trajectory

SET

The SET command is useful to enter a the value of the gyromagnetic ratio GAMMA for a new type of nucleus (with the atom selection) and add it to the default list of nuclei (the gyromagnetic ratio GAMMA is involved in the relation OMEGA=GAMMA*HFIELD, where OMEGA is the Larmor frequency). The nuclei now supported by the NMR module are: H, C, N, and P. It is also possible to use the SET command to give values for RTUMBL and HFIELD which are kept for the relation calculations.

RESET

Resets all assignements of the NMR module. Destroys all lists and is equivalent to exiting and re-entering the module.

Miscellaneous command manipulations

Miscellaneous Commands are supported within the NMR module, allowing opening and closing of files, label assignments (e.g., LABEL), and repeated loops (e.g., GOTO), parameter substitutions (e.g., @1, @2, etc...) and control (e.g., IF 1 eq 10.0 GOTO LOOP).

Examples

These examples are meant to be a partial guide in setting up input files for NMR. The test cases may be examined for a wider set of applications. There is 1 file: nmrtest1.inp which can be submitted through nmrtest.com.

Example (1)

NMR
reset

! Relaxation times
! H - N pair
RTIMES  select type N end    select type H end
WRITE RTIMS rtumbl 500.0 hfield 11.74 cut 3.5 iwrite 6

END

Produces a verbose output of all the N-H dipole-dipole relaxation rates within a distance of 3.5 angstroms in the presence of a magnetic field of 11.74 Tesla and assuming a isotropic tumbling of 500 picoseconds. Print out to unit 6.

Example (2)

NMR
reset
BUILD HA1 select type CA  .and. resid 2 end  dist     1.08 -
          select type C   .and. resid 2 end  theta  109.28 -
          select type N   .and. resid 2 end  dihe  -120.00

WRITE COOR select segid BUIL .or. resid 2 end

END

Build the position of hydrogen bonded to CA #1 with ZMATRIX syntax and print out the coordinates to verify the structure (verification should always be done). The NAME of the atom built is HA1, the RESNAM and the RESID are the same as those of the first selected atom, the SEGID is called BUIL by default. The coordinates are added at the end of the structure (after NATOM). The command ZMAT can be called from outside the NMR module and supplements the IC table with a “gaussian-like” zmatrix.

Example (3)

NMR
reset
! Phosphate group chemical shift anisotropy for lipids
! from J. Herzfeld et al., Biochem. 17, 2711 (1978).
CSA  S11 -76.0   S22 -17.0  S33 110.0 -
     the1   180.00  phi1  0.0 the2  90.00  phi2 0.0 -
     select resid 1 .and. type P end -
     select resid 1 .and. type O11 end  -
     select resid 1 .and. type O12 end

write CSA

build HA select type C11 .and. resid 1 end  dist     1.08 -
         select type C12 .and. resid 1 end  theta  109.28 -
         select type O12 .and. resid 1 end  dihe   120.00

build HB select type C11 .and. resid 1 end  dist     1.08 -
         select type C12 .and. resid 1 end  theta  109.28 -
         select type O12 .and. resid 1 end  dihe  -120.00

DQS select type C* end select type H* end
write DQS

END

Defines the Chemical Shift Anisotropy of a phosphate group in the phospholipids DPPC with the experimental principal axis values and print it. Construct the coordinates of two hydrogen (deuterium) and calculate the order parameters of the static structure.

Example (4)

open read unformatted unit 50 name nmrtest1.trj
DYNA nunit      1   firstu    50   begin   100   stop  10000   skip 100 -
     rtumbl 500.0   hfield 11.74   cut     3.5   tmax    3.0   -
     iwrite     6   C(t)           R(t)           -
     orient         select type CA end

Calculate the NMR properties from trajectory nmrtest1.trj re-orienting all the frames with respect to the carbon CA of the COMP cordinate set. For the relaxation correlation function integrals are cut at a TMAX of 3.0 psec. Write out the time series and the correlation function.

Example (5)

! build the position of chemical shift director with ZMATRIX syntax
build X  select type N   .and. resid 2 end  dist     1.00 -
         select type H   .and. resid 2 end  theta    0.00 -
         select type C   .and. resid 2 end  dihe     0.00

! build the position of chemical shift director with ZMATRIX syntax
build X  select type N   .and. resid 3 end  dist     1.00 -
         select type H   .and. resid 3 end  theta    0.00 -
         select type C   .and. resid 3 end  dihe     0.00


RTIMES CSAR dsigma 160.0 rtumbl  500.0 hfield 11.74  -
            select type N end  select type X end

open read unformatted unit 50 name nmrtest1.trj
DYNA nunit      1   firstu    50   begin   100   stop  10000   skip 100 -
     rtumbl 500.0   hfield 11.74   cut     3.5   tmax    3.0   -
     iwrite     6   -
     orient         select type CA end

Defines fictitious unit vectors with the build facility and calculate the chemical shift anisotropy relaxation for N15. The anisotropy is about 160 ppm between the principal axis if a near cylindrical symmetry is assumed.

Example (6)

(see also test/c33test/nmrtest2.inp)

RTIMES STAT CSAR DSIG 170.0 rtumbl  500.0 hfield 11.74  -
      ANIS DTSX 1.0 DTSY 0.0 DTSZ 0.0 DRAT 1.2 CUT 2.3 -
            select type N end  select type X end

Calculates the relaxation parameters for mainchain N-H spin pairs assuming a rigid molecule (coordinates in the comparison set) tumbling as a symmetric top with the long axis aligned along x (thus DTSX,y,z are 1,0,0) and a Dparallel/Deper ratio of 1.2. Dipole-Dipole and CSA contributions are calculated

Example (7)

RTIMES rtumbl  500.0 hfield 11.74  -
      ANIS DTSX 1.0 DTSY 0.0 DTSZ 0.0 DRAT 1.2 CUT 2.3 -
            select type N end  select type X end

open read unformatted unit 50 name nmrtest1.trj
DYNA nunit      1   firstu    50   begin   100   stop  10000   skip 100 -
     rtumbl 500.0   hfield 11.74   cut     2.3   tmax    3.0   -
     iwrite     6  C(t) modf 6 mfda 6 dsig 170.0 -
     orient         select type CA end

Calculates the relaxation parameters for mainchain N-H spin pairs from the trajectory after alignment with the maincain CA in the comparison set. Anisotropic tumbling as a symmetric top is modeled with the long axis aligned along x (thus DTSX,y,z are 1,0,0) and a Dparallel/Deper ratio of 1.2. However, N-H vector angles to the long axis are trajectory averaged. Both correlation functions for the internal motions as well as relaxation parameters are calculated.