# nmr (c41b1)

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 uppon 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.

Everthing 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 | Syntax of the NMR commands

* Function | Purpose of each of the commands

* Examples | Usage examples of the NMR analysis commands

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 uppon 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.

Everthing 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 | Syntax of the NMR commands

* Function | Purpose of each of the commands

* Examples | Usage examples of the NMR analysis commands

Top

Syntax

[SYNTAX NMR functions]

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

NB! STOP has to be specified so that enough memory may be allocated.

It is a good idea to specify the other parametters as well (they default to 1).

The command TRAJ QUERY UNIT int (

to obtain necessary data from the trajectory files.

Syntax

[SYNTAX NMR functions]

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

NB! STOP has to be specified so that enough memory may be allocated.

It is a good idea to specify the other parametters as well (they default to 1).

The command TRAJ QUERY UNIT int (

**»**dynamc ) may be usedto obtain necessary data from the trajectory files.

Top

General discussion regarding the NMR analysis module

1. 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 *NB the sign is important for the spectral densities

P 10.83D07

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

+inf

/

J(W) = \ COS(W*t) C(t) Dt = J(|W|)

/

0

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.

+TMAX

/

J_{fast}(W) = \ COS(W*t) [C(t)-C_{plateau}] Exp[-t/RTUMBL] Dt

/

0

+inf

/

J_{slow}(W) = \ COS(W*t) C_{plateau} Exp[-t/RTUMBL] Dt

/

0

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 interia 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).

2. DYNA option

---------------

The DYNAmics command reads in the trajectory from fortran units

opened with sequential numbers.

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 (

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.

3. other NMR properties supported

---------------------------------

3.1 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

3.2 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,

4. 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.

5. 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 (» (chmdoc/misc )).

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

6. 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.

7. RESET

--------

Resets all assignements of the NMR module. Destroys all lists and

is equivalent to exiting and re-entering the module.

8. Miscellaneous command manipulations

--------------------------------------

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).

General discussion regarding the NMR analysis module

1. 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 *NB the sign is important for the spectral densities

P 10.83D07

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

+inf

/

J(W) = \ COS(W*t) C(t) Dt = J(|W|)

/

0

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.

+TMAX

/

J_{fast}(W) = \ COS(W*t) [C(t)-C_{plateau}] Exp[-t/RTUMBL] Dt

/

0

+inf

/

J_{slow}(W) = \ COS(W*t) C_{plateau} Exp[-t/RTUMBL] Dt

/

0

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 interia 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).

2. DYNA option

---------------

The DYNAmics command reads in the trajectory from fortran units

opened with sequential numbers.

**»**dynamcFIRSTU 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 (

**»**correl ).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.

3. other NMR properties supported

---------------------------------

3.1 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

3.2 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,

**»**correl .4. 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.

5. 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 (» (chmdoc/misc )).

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

6. 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.

7. RESET

--------

Resets all assignements of the NMR module. Destroys all lists and

is equivalent to exiting and re-entering the module.

8. Miscellaneous command manipulations

--------------------------------------

**»**miscom 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).

Top

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.

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.