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# CONSTRAINTS¶

The following forms of constraints are available in CHARMM:

## Holding atoms in place¶

CONS HARMonic {[ABSOlute] absolute-specs force-const-spec   coordinate-spec }
{ BESTfit   bestfit-specs  force-const-spec   coordinate-spec }
{ RELAtive  bestfit-specs  force-const-spec 2nd-atom-selection}
{ CLEAr                                                       }

force-const-spec ::=  { FORCE real } atom-selection [MASS]
{ WEIGhting  }

absolute-specs ::=  [EXPOnent int] [XSCAle real] [YSCAle real] [ZSCAle real]

bestfit-specs  ::=  [ NOROtation ] [ NOTRanslation ]

coordinate-spec::= { [MAIN] }
{  COMP  }
{  KEEP  }

The potential energy has a harmonic restraint term which allows one to prevent large motions of individual atoms. There are three forms for this restraint, ABSOLUTE, BESTFIT, and RELATIVE. It is possible to combine multiple restraints in one energy calculation, but no atom may participate in more than one harmonic restraint set.

### ABSOLUTE positional restraints¶

Absolute positional restraints specify a location a cartesian space where an atom must remain proximal. This is the original positional restraint in CHARMM. The form for this potential is as follows for coordinates:

where is a reference set of coordinates. If MASS is specified in the command line, then k is multiplied by the mass of the atom resulting in a natural frequency of oscillation for the restraint of sqrt(k) in AKMA units. An atom restrained with MASS FORCE 1.0 will oscillate at 8 cycles/picosecond if free of other interactions. For most operations involving harmonic restraints, mass weighting is recommended. There are three reasons for this. First, the results obtained will be similar regardless of what atom representation is used (extended vs. explicit) for hydrogen atoms. Second, Hydrogen atoms are allowed greater relative freedom if present. And third, the character of the normal modes of a molecule are unperturbed with mass weighting (essential if normal modes or low frequency motions are of interest).

Note, there is no longer a prefactor of 0.5 on the force constant specification. This is appropriate in that exponent values other than “2” are allowed. This differs from the earlier versions of CHARMM (up to version 16).

The restraint force constant can be set to any positive value (specified by the FORCE keyword followed by the desired value). The force constants may also be obtained from the weight array, in which case the FORCe keyword is not read. When using this option, a negative values may be used for some atoms, however, the total weight must be positive.

The reference coordinates can be the current set at the point when restraints are specified (the default) or a set can be the comparison set (COMP keyword). When multiple CONS HARM commands are used, the KEEP option preserves the reference coordinates from the previous restraints. This is useful in cases where the force constant is to be modified, but no other changes are desired.

The variables XSCAle, YSCAle, and ZSCAle are global scale factors for ABSOLUTE harmonic restraint terms. The default scale factor is 1.0 for all terms. If multiple harmonic restraint sets are used, they may have different scale factors. The RELATIVE and BESTFIT types do not allow a scale factor at present.

CONS HARM FORCE 1.0 MASS SELE atom * * CA  END  COMP

This command harmonically restrains all alpha-carbons to the current positions in the comparison coordinates with a force constant of 24 (assuming a mass of 12).

### BESTFIT positional restraints¶

This restraint is similar to the absolute restraints except that the reference coordinates are (implicitly) rotated and translated so as to bestfit the selected atoms. This best fit is done in a manner that minimizes the restraint energy. Due to the nature of the best fit, this restraint term does not add any net force or torque to the system.

Note

1. An exponent may not be specified (it is set to 2)
2. Global scale factors do not apply
3. At present, there is no Hessian code for this restrain
4. There is no energy partition (ANAL command) for this restraint
CONS HARM BESTFIT  MASS FORCE 1.0 COMP SELE SEGID A END
CONS HARM BESTFIT  MASS FORCE 1.0 COMP SELE SEGID B END

These commands will restrain segments A and B to the geometries they have in the current comparison coordinates. This restraint will not add a net force or torque to the system (unlike the ABSOLUTE restraint type). Segments A and B can move (rotate/translate) independently with no change in the restraint energy. See also CONS RMSD below.

### RELATIVE positional restraints¶

The relative positional restraints are similar to the bestfit restraint except there is no reference coordinates. In this case, one part of the system is restrained to have the same shape as another part of the system. The two restraint sets are implicitly bestfit by an optimal rotation/translation (minimizing the restraint energy).

Note

1. An exponent may not be specified (it is set to 2)
2. Global scale factors do not apply
3. At present, there is no Hessian code for this restrain
4. There is no energy partition (ANAL command) for this restraint
5. The atoms of the two sets are matched on-to-one in sequential order.
6. If the two sets do not have the same number of atoms, an error will be issued and the set lists will be truncated.
7. Both sets must be specified and must not use set number 1.
CONS HARM RELATIVE WEIGHT SELE segid a1 END SELE segid a2 END NOROT NOTRAN

This command will force two replicas (A1 and A2) to have the same coordinates based on the values in the weighting array (as best fit weights).

CONS HARM RELATIVE MASS FORCE 10.0 SELE SEGID A END SELE SEGID B END

This command will force two segments (A and B) to have the same shape, but they may have very different locations and orientations. Atoms are matched one-to-one by selected atom number.

### GENERAL INFORMATION¶

It is important to understand some aspects of how the restraints are set in order to get the most flexibility out of this command. When CHARMM is loaded, each atom has associated with it a harmonic force constant initially set to zero. Each call to the CONS HARM command changes the value of this constant for only those atoms specified. When this command is invoked with an atom selection (and KEPP is not specified), only the reference coordinates (XREF,YREF,ZREF) for selected atoms are modified.

Warning

Each atom may participate in AT MOST one harmonic restraint term. This is a coding limitation designed to maximize compatibility with older CHARMM scripts (i.e. doing a series of minimizations with a decreasing series of force constants). This could be easily modified with a bit of work to increase the capability (at the expense of script compatibility).

When multiple restraint sets are used, it is important to note that all selections should be exclusive. When they are not exclusive, then atoms will be assigned to the restraint of the most recent CONS HARM command which selected that atom. In other words, the restraint set number is an atomic property. If restraint sets are broken up, then an error message will be issued. If an entire set is replaced, then the new restraint replaces the old one (without a warning message).

### OTHER COMMANDS¶

The harmonic restraints may no longer be read and written to files. The PRINT command still functions for harmonic restraints for information. To examine or modify the internal harmonic restrain data, the SCALar command (arrays: CONStraints,XREF,YREF, and ZREF) may be used (see SCALar : commands to manipulate scalar atom properties). In addition, one may look at the contributions to the energy in detail using the ANALysis command, see Analysis Commands.

## Holding dihedrals near selected values¶

Using this form of the CONS command, one may put restraints on the dihedral angles formed by sets of any four atoms. The improper torsion potential is used to maintain said angles.

The command for setting the dihedral restraints is as follows:

CONS DIHEdral [BYNUM int int int int] [FORCe real] [MIN real] [PERIod int]
[   atom-selection    ]              [ COMP   ]   [WIDTh real]
[     4X(atom-spec)   ]              [ MAIN   ]

CONS CLDH

Syntactic ordering:  DIHE or CLDH must follow CONS, and FORCE, MIN and

where:      atom-spec ::= { segid resid iupac }
{ resnumber iupac   }

DIHEdral adds a torsion angle to the list of restrained angles using the specified atoms, force constant, minimum and periodicity. If an atom selection is used, then the first 4 selected atoms (in order) will define the dihedral angle. If either MAIN or COMP is specified and [MIN real] is not, then the minimum angle value will be determined by the current dihedral angle value in the corresponding coordinate set.

WIDTh is specified in degrees.

If the PERIodicity is zero (improper type), then the force constant has units of kcal/mol/radian/radian, else it has units of kcal/mol.

CLDH clears the list of restrained dihedrals so that different angles or new restraint parameters can be specified.

### Other commands¶

The PRINT CONS command, see Print, will work for restraints.

## Holding puckering coordinates near selected values¶

Using this form of the CONS command, one may put restraints on the puckering coordinates formed by sets of any six atoms. Harmonic potential is used to for the restraint.

The command for setting the puckering restraints is as follows:

• Syntax:

CONS PUCKering [ BYNUM 6x(int) ] [ KCONst 3x(real) ] [ VALUe 3x(real) ] [ EXPOnent 3x(real) ]
[ atom-selection ]
[ 6X(atom-spec) ]

CONS CLPC

Syntactic ordering: PUCK or CLPC must follow CONS, and KCONst, VALUe and EXPOnent must follow PUCK.

PUCKering adds harmonic restraint to the puckering coordinates of the selected six atoms. The puckering coordinates are given by Q, theta, and phi as defined by Cremer & Pople, see: D. Cremer and J. A. Pople, JACS 97:6, page 1354, 1975. NCSU variable is set that is equal to the total number of puckering restraints.

The restraining potential energy is given by

Epuck = EQ + Etheta + Ephi


where EQ, Etheta, and Ephi are potentials given by

EQ     = KCON(1)*(Q -     VALU(1))**EXPO(1)
Etheta = KCON(2)*(theta - VALU(2))**EXPO(2)
Ephi   = KCON(3)*(phi -   VALU(3))**EXPO(3)


CLPC clears the list of restrained puckering coordinates.

• Other commands:

The PRINT CONS command, see print, will work for restraints.

QUICK command can be used to calculate the puckering coordinates, see print

## Holding Internal Coordinates near selected values¶

CONStraint IC  [BOND real [EXPOnent integer] [UPPEr]]
[ANGLe real] [DIHEdral real] [IMPRoper real]

Using this form of the CONS command, one may put restraints on any internal coordinate. For this energy term, the IC table is used. At each energy call, the reference (zero-force) value of each IC is set to the value currently in the IC table. All nonzero bond entries are restrained with the bond constant, using the optional EXPOnent (default 2) in the potential K*(S-S0)**EXPOnent. Second derivatives are currently supported only with EXPOnent=2. The angle, dihedral, and improper terms are only harmonic. The DIHEdral term only applies to IC’s of normal type, and the IMPRoper term only applies to the improper IC type (those with a “*”)

If UPPEr is specified the reference bond length is taken as an upper limit and the restraint potential is applied only if S>S0; this is intended for use with distance restraints from NMR NOE data. All nonzero angle entries are restrained with the angle constant. All dihedrals are restrained with the dihedral constant using the improper dihedral energy potential. If any IC entry contains an undefined atom (zeroes), then the associated bonds,angles, and dihedral will not be restrained.

The force constant has units of for both angle and dihedral restraints. The bond force constant has units of .

This restraint term is very flexible in that the user may chose which bonds... to restrain by editing an IC table. The major drawback is that all bonds must have the same force constant. The same is true for angles and dihedrals. By listing some IC’s several times, the effective force constant is increased. Also, if only angle restraints are desired, then the bond and dihedral constants can be set to zero eliminating their contribution.

## The Quartic Droplet Potential¶

CONStraint DROPlet [FORCe real] [EXPOnent integer] [NOMAss]

This restraint term is designed to put the entire molecule in a cage. Is is based on the center of mass (or center of geometry if NOMAss is specified) so that no net force or torque is introduced by this restraint term. The potential function is;

## How to fix atoms rigidly in place¶

CONS FIX atom-selection-spec { [PURG]                     }
{ [BOND] [THET] [PHI] [IMPH] }

This command will fix all selected atoms and unfix all non-selected atoms. For example, the command; CONS FIX SELE NONE END will remove all fixing of atoms (except for lonepairs).

This command fixes atoms in place by setting flags in an array (IMOVE) which tells the minimization and dynamics alogrithms which atoms are free to move. If atoms are fixed, it is possible to save computer time by not calculating energy terms which involve only fixed atoms. The nonbond and hydrogen bond algorithms in CHARMM check IMOVE and delete pairs of atoms that are fixed in place from the nbond and hbond lists respectively. In addition the PURG or individual energy term options specified with the CONS FIX command allow all or some of the internal coordinate energies associated with fixed atoms to be deleted. Interactions between fixed and moving atoms are maintained.

Note

Because some energy terms are deleted from fixed systems, the total energy calculated with fixed atoms will be different from the total energy of the same system with all atoms free. The forces on the moveable atoms will however be identical. The purpose of this feature is to remove the computational cost of energy terms that do not change for simulations where a large fraction of the atoms are fixed. It is not recommended for any other purpose.

The way CHARMM keeps track of fixed atoms is by the IMOVE array in the PSF. The IMOVE array is 0 if the atom is free to move, and has the value 1 if it is fixed. A value of -1 indicates that this atom is a lonepair.

Warning

The purge options modify the PSF. The effects of this command cannot be undone by the subsequent releasing of atoms.

Warning

The fixing of atoms does not work for constant pressure simulations.

## Constrain centers of mass for selected atoms¶

CONS HMCM FORCe real RDISt real [WEIGhting or MASS] -
reference-spec atom-selection

where:
reference-spec ::= [REFX real] [REFY real] [REFZ real]
at least one must be specified.

This command will harmonically restrain centers of mass from the selected atoms to the absolute reference point specified with REFX, REFY and REFZ, or to a line specifying REFX, REFY or REFZ, or to a plane specifying any two of REFX, REFY, and REFZ. The force constant of the harmonic potential is set with the FORCe keyword. A reference distance can be given with RDISt (default: ZERO). Mass weighting is switched off by default but can be selected by using the WEIG key.

The primary use of this command is during the reconstruction of all-atom representations from low resolution models with virtual particles at side chain centers.

Example 1:

CONS HMCM FORCE 50.0 WEIG REFX 10.4 REFY 12.1 REFZ 1.3 -
SELECT RESID 21 .AND. .NOT. -
( TYPE H* .OR. TYPE N .OR. TYPE C .OR. TYPE O ) -
END

This will create a harmonic restraint with a force constant of 50 kcal/mol that holds the side chain center of mass at residue 21 of a protein near (10.4, 12.1, 1.3).

Example 2:

cons hmcm force 100.0 mass refx 10.0 -
select segid ligand end

This will create a harmonic restraint with a force constant of 100 kcal/mol that keeps the center of mass of segment “ligand” on a line with x value 10.0 but no restraints on the y or z values.

## Fixing bond lengths or angles during dynamics¶

SHAKE is a method of fixing bond lengths and, optionally, bond angles during dynamics, minimization (not ABNR and Newton-Raphson methods), coordinate modification (COOR SHAKe command), and vibrational analysis (explore command). The method was brought to CHARMM by Wilfred Van Gunsteren (WFVG), and is referenced in J. Comp. Phys. 23:327 (1977). When hydrogens are present in a structure, it will allow a two-fold increase in the dynamics step size if SHAKE is used on the bonds.

To use SHAKE, one specifies the SHAKE command before any SHAKE constraints usage. The SHAKE command has the following syntax:

SHAKE { OFF                                               }
{ shake-opt  fast-opt  2x(atom-selection) [NOREset] }

shake-opt:== [BONH]  { [MAIN]     } [TOL real] [MXITer integer]
[BOND]  { COMP       }
[ANGH]  { PARAmeters }        [SHKScale real]
[ANGL]

fast-opt:== { [ FAST  [ WATEr water-resn ] ] }
{   NOFAst                       }

BONH specifies that all bonds involving hydrogens are to be fixed. BOND specifies all bonds. ANGH specifies that all angles involving hydrogen must be fixed. ANGL specifies that all angles must be shaken. BOND is implied if any angles are fixed, otherwise, only the 1-3 distances would be fixed. Coordinates must be read in before the SHAKE command is issued, unless the PARAmeter option is specified.

SHAKE constraints are applied only for atom pairs where one atom is in the first atom selection and one atom in the second atom selection. The default atom selection is ALL for both sets.

TOL specifies the allowed relative deviations from the reference values (default: ). MXITer is the maximum number of iterations SHAKE tries before giving up (default: 500).

When the SHAKE command is used, it will check that there are degrees of freedom available for all atoms to satisfy all their constraints. Angles cannot be fixed with SHAKE if one has explicit hydrogen arginines in the structure as the CZ carbon has too many constraints. This is a general problem for any structure which has too many branches close together.

SHAKE is not recommended for fixing angles. The algorithm converges very slowly in the case where one has three angles centered on a tetravalent atom and the constraints are satisfiable only using out of plane motions.

The use of SHAKE modifies the output of the dynamics command. The number appearing to the right of the step number is the number of iterations SHAKE required to satisfy all the constraints. This number should generally be small.

When ST2’s are present, SHAKE constraints are automatically applied for the O-H bonds and H-O-H angles.

There is a PARAmeter option for the SHAKe command. This option causes the shake bond distances to be found from the parameter table rather than from the current set of coordinates. This option is NOT compatible with the use on angle SHAKE constraints, and it will give an error if this is tried.

With these commands, the bond energy may be zeroed without any minimization with the command sequence;

SHAKE BOND PARA
COOR SHAKE [MASS]
SHAKe FAST [WATEr water-resn] [OLDWatershake]
[ MXITer <iterations> TOL <tolerance> ] [PARAmeter] [COMP]

This command specifies the use of the new vector/parallel and analagous scalar fast SHAKE constraint routines (implemented Aug 2000).

Certain assumptions are made when this command is issued: The only bonds involved are between heavy atoms and hydrogens, except for water molecules specified by the

WATEr water-resn sub-command.

This selection is used to indicate the water molecules that have an H-H bond. It is assumed that the selection will include all atoms in the water molecule and that said molecule contains exactly two X-H bonds and one H-H bond where X is any heavy atom. Testing for “hydrogen-ness” is done via the CHARMM hydrog() function which makes it’s choice based on atomic mass.

By default, water molecules selected with the WATEr sub-command will be constrained via the use of a special water-SHAKE routine which uses the direct inversion method. This algorithm is from 25 to 30 % faster than the normal iterative, scalar SHAKE routine. For the rest of the heavy atom -hydrogen bonds, a vector/parallel version of the original SHAKE routine is used. This is about 5X the scalar SHAKE. If the optional keyword OLDWatershake is used, the vector/parallel (not the watershake) routines are used.

The rest of the keywords are the same as in the original SHAKE command.

Note

FAST has to be the second word in command line.

## NOE¶

NOE
Invoke the module

RESEt
Reset all NOE restraint lists. This command clears all
existing NOE restraints. Resets scale factor to 1.0

PNOE
Turn on the restraint between a given atom specified
by ASSIgn and a point specified by CNOX, CNOY and CNOZ
intead of a restraint between two atoms.
The use of this restraint is desirable for docking,
and loop refinements. CAVE: PNOE itself is NOT a
command -- the PNOE feature is invoked implicitely by
the presence of the CNOX, CNOY, CNOZ point specification.

ASSIgn [KMIN real] [RMIN real] [KMAX real] [RMAX real] [FMAX real]
{MINDIST} {RSWI real [SEXP real]} {SUMR}
[TCON real] [REXP real] {2X(atom_selection)}
{[CNOX real] [CNOY real] [CNOZ real] 1X(atom selection) }

Assign a restraining potential between the atoms of the
first selection and the atoms of the second selection.

Where multiple atoms are selected,
R = [ average( Rij**(1/REXP) ) ]**REXP
where (i) runs over the first atom selection and (j)
runs over the second atom selection.
The default REXP value is 1.0 (a simple average).
An REXP value of 3.0 may be optimal for NOE averaging.

If SUMR keyword is present, R is computed as following,
R = [ Sum_ij ( Rij**(1/REXP) ) ]**REXP
In this case, REXP=-1/6 might be typically used.

If the key work MINDIST is specified, then the NOE constraint
will be active only between the pair of atoms from the two selected
set of atoms that happend to be  the nearest at all time during
the dynamics (useful to resolve ambiguous distance restraints).

/  0.5*KMIN*(RAVE-RMIN)**2    R<RMIN
/
/    0.0                        RMIN<R<RMAX
E(R)=
\    0.5*KMAX*(RAVE-RMAX)**2    RMAX<RAVE<RLIM
\
\  FMAX*(RAVE-(RLIM+RMAX)/2)  RAVE>RLIM

If RSWItch is specified, a soft-square NOE potential will be used,
where the square-well function is used for distances within a
specified "switching" region (specified by the RSWItch keyword),
whereas outside this region a "soft" asymptote is used:

/ 0.5*KMIN*(RAVE-RMIN)**2                    R<=RMIN
E(NOE)=  0.0                                   RMIN<R< RMAX
\ 0.5*KMAX*(RAVE-RMAX)**2               RMAX<R<=RMAX+RSWITCH
\ A+B/(RAVE-RMAX)**SEXP+FMAX*(RAVE-RMAX)     R> RMAX+RSWITCH

where,

A,B  are determined such that both E and force are continuous.
FMAX defines the final asymptote slope (default 1.0)
RSWI defines the switching start point (default 1.0)
SEXP exponent of the soft asymptote    (default 1.0)

and
RAVE=R                     TCON=0

RAVE=RRAVE**(-1/3)         TCON>0

RRAVE=RRAVE*(1-DELTA/TCON)+R**(-3)*DELTA/TCON

for initial conditions, RRAVE=RMAX**(-3)
DELTA is the integration time step.  For minimization,
the value is either 0.001ps or the previous simulation value.

Where: RLIM = RMAX+FMAX/KMAX (the value of RAVE where the
force equals FMAX)

Defaults for each entry: KMIN=0.0, RMIN=0.0,
KMAX=0.0, RMAX=9999.0, FMAX=9999.0
TCON=0.0, REXP=1.0

MPNOe INOE <integer> {[TNOX real] [TNOY real] [TNOZ real]}
Define INOE as a moving point-NOE with target position
TNOX, TNOY, TNOZ -- the initial position is that given
in the previous assign statement of the NOE (CNOX...).

NMPNoe <integer>
No of steps over which the point-NOE's are moved from
their initial points (CNOX...) to the target points (TNOX...).

Reads restraint data structure from card
file previously written.
WRITe UNIT <integer> [ANAL]
Writes out the restraint data in card format to a file on the
specified unit. A CHARMM title should follow the command.
SCALE are saved together with the lists in the NOE common block.
The ANAL option will print out the distances and energy data
computed with the current main coordinates.
PRINT [ANAL [CUT real]]
Same as the WRITe command except to the output file and slightly
more user friendly form. A positive CUT value will list only
those that have a distance that exceeds RMAX by more than DCUT.
SCALe [real]
Set the scale factor for the NOE energy and forces.
Default value: 1.0
TEMPerature real
Specify the temperature for the old format.
END
Return to main command parser.

Also, the old syntax is supported:

ASSIgn rminvalue  minvariance  maxvariance  2X(atom_selection)

For this format,

KMAX=0.5*Kb*TEMP/(maxvariance**2)
KMIN=0.5*Kb*TEMP/(minvariance**2)
RMIN=rminvalue
RMAX=rminvalue

No other commands (I/O or loops) are supported inside the NOE module. Looping can be performed outside if necessary. The units are Kcal/mol/A/A for force constants and Angstroms for all distances.

EXAMPLE. Set up some NOE restraints for one strand of a DNA-hexamer in a file to be streamed to from CHARMM.

*  SOME NOE RESTRAINTS FOR DNA. ASSUME PSF, COORD ETC ARE ALREADY PRESENT
*
! First clear the lists
NOE
RESET
END
! Since there are many identical atom pairs we use a loop
set 1 1
label loop
NOE
!   Sugar protons, same in all six sugars (don't pay any attention to
!     the numeric values)
ASSIgn  SELE ATOM A @1 H1' END SELE ATOM A @1 H2'' END -
KMIN 1.0 RMIN 2.7 KMAX 1.0 RMAX 3.0 FMAX 2.0
ASSIgn  SELE ATOM A @1 H3' END SELE ATOM A @1 H2'' END -
KMIN 1.0 RMIN 2.7 KMAX 1.0 RMAX 3.0 FMAX 2.0
END
incr 1 by 1
if 1 le 6 goto loop
! Now do some more specific things

OPEN WRITE UNIT 10 CARD NAME NOE.DAT
NOE
SCALE 3.0  ! Multiply all energies and forces by 3
WRITE UNIT 10
* NOE RESTRAINT DATA FROM DOCUMENTATION EXAMPLE
*
PRINT ANAL  ! See what we have so far
PRINT ANAL CUT 2.0 ! list
END
RETURN

EXAMPLE2. Set up some NOE restraints with soft asymptote (protein G)

...

if @?rexp eq 0   set rexp = -0.166666666666667
if @?kmin eq 0   set kmin = 1
if @?kmax eq 0   set kmax = 1
if @?fmax eq 0   set fmax = 1
if @?rswi eq 0   set rswi = 3
if @?sexp eq 0   set sexp = 1
NOE
RESET
ASSI rmin 1.8 rmax 5.5 -
SELE resid 39 .AND. type HG1# end SELE resid 34 .AND. type HB# end -
rexp @rexp fmax @fmax rswi @rswi sexp @sexp kmin @kmin kmax @kmax SUMR
ASSI rmin 1.8 rmax 6.5 -
SELE resid 39 .AND. type HG2# end SELE resid 34 .AND. type HB# end -
rexp @rexp fmax @fmax rswi @rswi sexp @sexp kmin @kmin kmax @kmax SUMR
ASSI rmin 1.8 rmax 5 -
SELE resid 34 .AND. type HA end SELE resid 39 .AND. type HN end -
rexp @rexp fmax @fmax rswi @rswi sexp @sexp kmin @kmin kmax @kmax SUMR

PRINT ANAL
END

EXAMPLE3. Set up moving point-NOE restraints for docking of a ligand

...

NOE
RESET
assign kmax 10.0 rmax 2.0 fmax     10.0 -
CNOX   -7.899 CNOY   40.864 CNOZ   50.967 -
sele atom LGND     1 H27  end
assign kmax 10.0 rmax 2.0 fmax     10.0 -
CNOX  -10.033 CNOY   38.295 CNOZ   50.258 -
sele atom LGND     1 N16  end
assign kmax 10.0 rmax 2.0 fmax     10.0 -
CNOX  -11.621 CNOY   36.654 CNOZ   48.924 -
sele atom LGND     1 H28  end
assign kmax 10.0 rmax 2.0 fmax     10.0 -
CNOX  -17.948 CNOY   39.618 CNOZ   60.275 -
sele atom LGND     1 H42  end
print anal
NMPNoe      40000
MPNOe INOE      1 -
TNOX   13.177 TNOY   45.357 TNOZ   49.337
MPNOe INOE      2 -
TNOX   11.043 TNOY   42.788 TNOZ   48.628
MPNOe INOE      3 -
TNOX    9.455 TNOY   41.146 TNOZ   47.294
MPNOe INOE      4 -
TNOX    3.128 TNOY   44.111 TNOZ   58.645
END

...

## Restrained Distances¶

Apply general restrained distances allowing multiple distances to be specified. This restraint term has been added to allow for facile searching of a reaction coordinate, where the reaction coordinate is estimated to be a linear combination of several distances.

(By Bernard R. Brooks - NIH - March, 1995)

RESDistance [ RESEt ] [ SCALE real ] [ KVAL real  RVAL real [EVAL integer] -
[ POSItive ] [ IVAL integer ]  repeat( real first-atom second-atom ) ]
[ NEGAtive ]

E = 1/EVAL *  Kval * Dref**EVAL

Where:

Dref =  K1*R1**Ival + K2*R2**Ival + ... + Kn*Rn**Ival - Rval

Where K1,K2,...Kn are the real values in the repeat section and
R1,R2,...Rn are the distances between specified pair of atoms.

RESEt       Reset the restraint lists. This command clears the
existing restraints. Resets the scale factor to 1.0

SCALe real  Set the scale factor for the energy and forces.
Default value: 1.0

POSITIVE    Include this restraint only when Dref is positive.
NEGATIVE    Include this restraint only when Dref is negative.

If anything else is on the command line then a new restraint is added to the list of distance restraints.

KVAL real     The force harmonic constant
RVAL real     The target distance
IVAL integer  The exponent for individual distances.
EVAL integer  The exponent (default 2). EVAL must be positive.
repeat( real first-atom second-atom )
The real value is a scale factor for the distance between
the first and second specified atoms in the pair.

EXAMPLES: 1. Create a reaction coordinate for QM/MM 2. Set up some restraints to force three atoms to make an equilateral triangle.

!!! 1 !!!  Create a reaction coordinate for QM/MM

OPEN WRITE CARD UNIT 21 name reaction.energy
OPEN WRITE FILE UNIT 22 name reaction.path
TRAJECTORY IWRITE 22 NWRITE 1 NFILE 40 SKIP 1
* trajectory of a minimized reaction path
*

SET ATOM1  MAIN 11 OG
SET ATOM2  MAIN 11 HG
SET ATOM3  MAIN 23 OD1

SET 1 1
SET V -5.0
LABEL LOOP

SKIP NONE             ! make sure all energy terms are enabled
RESDistance  RESET KVAL 2000.0  RVAL @v -
1.0   @atom1  @atom2    -1.0   @atom2  @atom3

MINI ABNR NSTEP 200 NPRINT 10
PRINT RESDistances    ! print a check of distances
TRAJ WRITE            ! write out the new minimized frame

SKIP RESD             ! turn off the restraint energy term
ENERGY                ! recompute the energy without restraints
WRITE TITLE UNIT 21   ! write out the current restraint distance and energy
* @V ?ENER
*

INCR 1 BY 1           ! increment the step counter
INCR V BY 0.25        ! increment the restraint value
IF 1 LT 40.5 GOTO LOOP

RETURN

!!! 2 !!! Make a water nearly an equilateral triangle

set atom1  WAT 1 O
set atom2  WAT 1 H1
set atom3  WAT 1 H2

RESDistance  RESEt

RESDistance  KVAL 1000.0  RVAL 0.0 -
1.0   @atom1  @atom2  -
1.0   @atom1  @atom3  -
-2.0   @atom2  @atom3
RESDistance  KVAL 1000.0  RVAL 0.0 -
1.0   @atom1  @atom2  -
-2.0   @atom1  @atom3  -
1.0   @atom2  @atom3
RESDistance  KVAL 1000.0  RVAL 0.0 -
-2.0   @atom1  @atom2  -
1.0   @atom1  @atom3  -
1.0   @atom2  @atom3

print resdistances
mini abnr nstep 200 nprint 10
print resdistances
stop

!!! 3 !!! Prevent an atom from moving more than 20A from the others,
! but have no restraint energy when no distance is large.

set atom1 SOLV 1 OH2
set atom2 SOLV 2 OH2
set atom3 SOLV 3 OH2
set atom4 SOLV 4 OH2
set atom5 SOLV 5 OH2

RESDistance  RESEt

RESDistance  KVAL 1.5E-12  RVAL 6.4E7 IVAL 6 POSITIVE -
1.0   @atom1  @atom2  -
1.0   @atom1  @atom3  -
1.0   @atom1  @atom4  -
1.0   @atom1  @atom5  -
1.0   @atom2  @atom3  -
1.0   @atom2  @atom4  -
1.0   @atom2  @atom5  -
1.0   @atom3  @atom4  -
1.0   @atom3  @atom5  -
1.0   @atom4  @atom5

print resdistances
mini abnr nstep 200 nprint 10
print resdistances
stop

## External Forces¶

PULL { FORCe  <real> } XDIR <real> YDIR <real> ZDIR <real> [PERIod <real>]
{ EFIEld <real> }
[SWITch <int>] [SFORce <real>]
[WEIGht] [atom-selection]
{ TORQue <real> } [PERIod <real>]
[AXIS | XDIR <real> YDIR <real> ZDIR <real> -
XORI <real> YORI <real> ZORI <real>]
{ OFF       }
{ LIST      }

A force will be applied in the specified direction on the selected atoms either as a constant:

FORCe <value> specified in picoNewtons (pN)


or oscillating in time:

FORCe*COS(TWOPI*TIME/PERIod), FORCe <pN> PERIod <ps>

time is counted from the start of the dynamcis run. or forces due to an electrical EFIEld (V/m) (possibly also oscillating).

Partial charges are then taken from the PSF and used to calculate the force. If WEIGht is specified the forces are multiplied by the wmain array.

The invocation of a non-zero SWITch value will result in a linearly time-varying force. This command must be used in conjunction with a dynamics routine (using leap-frog integrator). The force is switched linearly between SFORce <pN> (starting force) and FORCe <pN> (end force) over the course of the simulation.

TORQue <pN/A> either uses the axis defined by a prior COOR AXIS command (or any COOR command which sets the corman axis) or an axis has to be specified with the *DIR and *ORI keywords. Torque code fromi J Wereszczynski & I Andricioae: PNAS (2006)103:16200

Each invocation of this command adds a set of forces to the previously defined set.

PULL OFF  ! turns off all these forces.
PULL LIST ! produces a listing.

## RMSD Restraints¶

The RMSD restraint is useful to manipulate and control macromolecular conformations. The restraint is related to the CONS HARM BestFit, which sets up harmonic restraints with respect of a reference structure. However, because all the reference data structure is stored in XREF, YREF, ZREF, this command allows only a single bestfit restraint. In addition, it allows only a restraint to zero value of RMSD. It is useful to allow multiple such bestfit RMSD restraint to progress from one conformation to a second conformation of a molecular system. The new command CONS RMSD allows such multiple bestfit restraint. In fact, that is principally the advantage over the BESTfit method (only the data structure is changed, the energy subroutines themselves are the same). The method can also be used to performed targetted trajectories.

The form of the new restraint energy is:

Where RMSD is the (possibly mass-weighted) root-mean-square-deviation (RMSD) of the current coordinates with respect to a reference structure, is a force constant, and is a constant value setting a relative distance with respect to the RMSD of the structure. The restraint energy is equivalent the normal BestFit energy. The forces have been checked with the TEST FIRST command.

All the data structure is stored dynamically on the HEAP and thus, no extra permanent (static) storage is introduced. The size of initial HEAP storage is set by the MAXRmsd integer the first time that the command is issued (by default this is set to the number of atoms if nothing is specified).

By specifying the RELATIVE keyword, it is possible to impose a 1-D constraint to simultaneously constrain a given structure with respect to two end-point structures. This is achieved by constraining the difference (RMSD2 - RMSD1) instead of just the RMSD1 or RMSD2 values individually, where RMSD1 and RMSD2 are the RMSD values of given structure from endpoint structure 1 and 2 respectively. This allow full freedom of movements orthogonal to the relative axis. For the relative RMSD constraint, the form of the new restraint energy is:

The syntax is very similar to all current restraints in CHARMM:

CONS RMSD { RELAtive } {MAXN integer} {NPRT} orient-specs  force-const-spec -
coordinate-spec atom-selection
CONS RMSD  SHOW
CONS RMSD  CLEAR

orient-specs     ::=  [ NOROtation ] [ NOTRanslation ]

force-const-spec ::=  { FORCE real } [MASS]  {OFFSet real} { BOFFset real}

coordinate-spec::= { [MAIN] }
{  COMP  }

CONS CLEAR      ! removes all multiple RMSD restraints

CONS RMSD SHOW  ! prints all current RMSD restraints with all parameters.

The specific terms are:

 RELAtive Employ relative RMSD restraint using two reference structures as defined above NPRT This suppresses the printout of the RMSD to URMSD unit in a dynamics simulation. The default is to print all RMSD. MAXN Maximum number of RMSD restraints (replaces MAXRMSD used in previous versions) default setting = 10 COMP Use comparison cordinate set as reference (default uses main). FORCE Force constant for RMSD term in kcal/mol/A^2 OFFSet RMSD value in A^ at which the structure is restrained BOFFset offset at which to begin applying the harmonic RMSD restraint, useful in specifying a flat-bottom RMSD potential around the reference structure

IMPORTANT NOTES:

1. The MAXRMSD variable specifying total number of restrained atoms used before has been replaced by the variable MAXN specifying the number of RMSD restraints. This allows dynamic allocation of memory for storing reference structures during atom selection for the RMSD restraint, which reduces memory usage significantly

2. The c32 release contained additions including the ZETA potential and the ability to fit one set of atoms using RMSD and apply the forces to another set of atoms. These are not included in the present version due to their inability to pass TEST FIRST

3. RMSD restraints can be used with DYNAmics command.

DYNAmics ... [ RMSD URMSD integer ]  This will cause the RMSD values

for each of the RMSD restraints to be written to the unit specified by URMSD, unless the NPRT option is specified when the RMSD restraint is defined.

## Rg/RMSD Restraint¶

RGYRation { FORCe <real> } REFErence <real> [RMSD] [COMParison] [ORIEnt]
OUTPut_unit <integer> NSAVe_output <integer>
SELEction <atom selection> END
{ RESEt      }

This restraint force restraints the central moment of the selected atoms about 1) the center of geometry of the selected atoms (Rg restraint) or 2) a specified reference structure structure (RMSD). The form of the restraint term is:

where

and

or

The specific terms are:

 RGYR Invoke the Rg/RMSD restraint term parser in CHARMM FORCe Use a restraint force constant (CONST above) of kcal/mol/A^2 REFErence Use a target Rg/RMSD value of , in A. RMSD Employ RMSD based restraint instead of Rg restraint. COMP Use comparison cordinate set as reference (default uses main). ORIEnt Do a coor orie on coordinates before computing RMSD. OUTPut During dynamics write Rg/RMSD history to unit . NSAVe Save Rg/RMSD history every steps. RESEt CLear Rg/RMSD restraint flags, release memory.

Usage:

The following examples illustrate the use of this restraint term.

1. Add an Rg restraint potential to dynamics run, save trajectory information to unit. Base Rg calculation on Ca positions only.

open unit 12 write form name traj.rgd

RGYRestraint Force 50 Reference 12.9 -
output 12 nsave 50 select type ca end
2. Add an RMSD based restraint to target a conformational change in a loop.

open unit 1 read form name open.crd
close unit 1

open unit 1 read form name closed.crd
read coor card compare unit 1
close unit 1

coor orie rms select type ca end
coor rms select ( ires 12:24 .and. .not. hydrogen ) end

Calc drms = ?rms / 6
Calc rmsd = ?rms - @drms
set count 1
label domini

rgyr force 50 reference @rmsd rmsd comp -
select ( ires 12:24 .and. .not. hydrogen ) end

mini conj nstep 400 tolenr 0.00001 cutnb 12 ctofnb 10 ctonnb 8 -
inbfrq -1 atom cdie vatom vswitch fshift bycb

rgyr reset

coor rms select ( ires 12:24 .and. .not. hydrogen ) end

open unit 1 write form name o2c_@count.pdb
write coor pdb unit 1
*  Coordinates from frame @count of open to closed path.
*  Current loop rmsd (residues 12-24 ca only) is ?rms A.
*

incr count by 1
Calc rmsd = @rmsd - @drms

if rmsd gt 0.1  goto domini
3. Use RMSD restraint to unfold a helical peptide with RMSD computed based minimum RMSD at each step (Oriented).

set rmsd 2
label unfold

rgyr force 100 reference @rmsd rmsd comp orient select type ca end

mini conj nstep 400 tolenr 0.00001

rgyr reset

coor orie rms select type ca end

open unit 1 write form name frame@rmsd.pdb
write coor pdb unit 1
*  Coordiantes from frame with reference rmsd = @rmsd, current rmsd= ?rms
*

incr rmsd by 2
if rmsd le 10 goto unfold

## Distance Matrix Restraint¶

DMCOnstrain FORCe real REFErence real OUTPut_unit integer
NSAVe_output integer CUTOff real NCONtact integer
{SELE {atom selection} WEIGt real}(ncontact times)

THIS COMMAND ADDS A Quadratic POTENTIAL to restrain the reaction coordinate. The reaction coordinate is defined as a weighted sum of contacts.

where

Usage:

The following examples illustrate the use of this restraint term.

1. Add an distance matrix restraint potential to dynamics run, save trajectory information to unit. This example applies a distance restraint of the form given above between pairs of side chain centers-of-mass for a set of 54 contacts and restrains the system to a fractional value of the overall reaction coordinate of 0.625. Each restraint term is given a weight based on the amount of time the given contact was formed in the native state simulation. For details of the method used here, the reader is referred to: [Sheinerman and Brooks, JMB, 278, 439 (1998).]

 open unit 25 write form name "dmc/GB1H.rho"

define bb -
sele segid agb1 .and. -
(type ca .or. type c .or. type n .or. type o ) end
define sd -
sele segid agb1 .and. .not. (bb .or. hydrogen) end

set dmforce 2000.
set dmref  0.625
set dmsave 100
DMCO FORCe @dmforce     REFE @dmref OUTPut 25 NSAVe @dmsave -
CUTOff 6.5 NCONtact  54
sele sd .and. (resi   2  .or. resi   4 ) end WEIGht  0.8158139980007818
sele sd .and. (resi   4  .or. resi  21 ) end WEIGht  0.9665094391591674
sele sd .and. (resi   4  .or. resi  24 ) end WEIGht  0.9879192119842544
sele sd .and. (resi   4  .or. resi  27 ) end WEIGht  0.9895819946415852
sele sd .and. (resi   4  .or. resi  51 ) end WEIGht  0.9408263780596178
sele sd .and. (resi   5  .or. resi  18 ) end WEIGht  0.9415959785662404
sele sd .and. (resi   6  .or. resi   8 ) end WEIGht  0.9999909781703169
sele sd .and. (resi   6  .or. resi  17 ) end WEIGht  0.9995401666453647
sele sd .and. (resi   6  .or. resi  31 ) end WEIGht  0.9999999999999796
sele sd .and. (resi   7  .or. resi  16 ) end WEIGht  0.9796513289404690
sele sd .and. (resi   7  .or. resi  52 ) end WEIGht  0.7780795300785477
sele sd .and. (resi   7  .or. resi  54 ) end WEIGht  0.6905994027412474
sele sd .and. (resi   8  .or. resi  17 ) end WEIGht  0.8323463051907218
sele sd .and. (resi   8  .or. resi  35 ) end WEIGht  0.9731361885884368
sele sd .and. (resi   8  .or. resi  38 ) end WEIGht  0.9174238684004473
sele sd .and. (resi   8  .or. resi  40 ) end WEIGht  0.9754236727233426
sele sd .and. (resi   8  .or. resi  55 ) end WEIGht  0.9151151195555089
sele sd .and. (resi   9  .or. resi  14 ) end WEIGht  0.6645390074837504
sele sd .and. (resi   9  .or. resi  56 ) end WEIGht  0.7285333256999120
sele sd .and. (resi  17  .or. resi  19 ) end WEIGht  0.8912444191627017
sele sd .and. (resi  17  .or. resi  34 ) end WEIGht  0.8920438869599703
sele sd .and. (resi  19  .or. resi  21 ) end WEIGht  0.7259406753340431
sele sd .and. (resi  19  .or. resi  30 ) end WEIGht  0.6711322572172727
sele sd .and. (resi  19  .or. resi  34 ) end WEIGht  0.7844587325555364
sele sd .and. (resi  21  .or. resi  27 ) end WEIGht  0.9999999531742481
sele sd .and. (resi  23  .or. resi  25 ) end WEIGht  0.9999999994693732
sele sd .and. (resi  23  .or. resi  26 ) end WEIGht  0.9999999999991671
sele sd .and. (resi  24  .or. resi  27 ) end WEIGht  0.9979691873576392
sele sd .and. (resi  24  .or. resi  51 ) end WEIGht  0.6964187937040895
sele sd .and. (resi  25  .or. resi  28 ) end WEIGht  0.8927269972864454
sele sd .and. (resi  25  .or. resi  29 ) end WEIGht  0.8210307146883757
sele sd .and. (resi  26  .or. resi  29 ) end WEIGht  0.8905543107011445
sele sd .and. (resi  27  .or. resi  30 ) end WEIGht  0.9612292542758489
sele sd .and. (resi  27  .or. resi  31 ) end WEIGht  0.9999999983165117
sele sd .and. (resi  28  .or. resi  53 ) end WEIGht  0.9290808245024628
sele sd .and. (resi  30  .or. resi  33 ) end WEIGht  0.9273633852785603
sele sd .and. (resi  30  .or. resi  34 ) end WEIGht  0.9852961901326586
sele sd .and. (resi  31  .or. resi  53 ) end WEIGht  0.9960510555412353
sele sd .and. (resi  32  .or. resi  44 ) end WEIGht  0.9811553525890055
sele sd .and. (resi  35  .or. resi  40 ) end WEIGht  0.9996382371796980
sele sd .and. (resi  35  .or. resi  44 ) end WEIGht  0.9529057898756480
sele sd .and. (resi  35  .or. resi  55 ) end WEIGht  0.9921250365257495
sele sd .and. (resi  38  .or. resi  40 ) end WEIGht  0.9469272633832431
sele sd .and. (resi  40  .or. resi  55 ) end WEIGht  0.9855702226874301
sele sd .and. (resi  40  .or. resi  57 ) end WEIGht  0.7830957174831968
sele sd .and. (resi  44  .or. resi  55 ) end WEIGht  0.9999950887381377
sele sd .and. (resi  45  .or. resi  54 ) end WEIGht  0.9994979068986675
sele sd .and. (resi  47  .or. resi  49 ) end WEIGht  0.9878049213251836
sele sd .and. (resi  47  .or. resi  50 ) end WEIGht  0.9999916748639699
sele sd .and. (resi  47  .or. resi  52 ) end WEIGht  0.9881469299868514
sele sd .and. (resi  50  .or. resi  52 ) end WEIGht  0.9973918765679025
sele sd .and. (resi  51  .or. resi  53 ) end WEIGht  0.8168211946297691
sele sd .and. (resi  52  .or. resi  54 ) end WEIGht  0.8871232193909784
sele sd .and. (resi  54  .or. resi  56 ) end WEIGht  0.8700639041799975

## PATH¶

Syntax: CONS PATH spline-pts [COMP] [TEST unit]
FORCe real TZERo real atom-selection
:
:
:
FORCe real TZERo real atom-selection

CONS PATH CLEAR

CONS PATH POST

where:
spline-pts ::= { SPLUnit unit           }
{ SPLIne  atom-selection }

This command will harmonically restrain the projections of centers of mass onto an arbitrary three-dimensional path. The path is specified with cubic splines. Essentially, this is achieved by first projecting each center of mass (COM) onto a cubic spline interpolated path to establish an initial projection position (TINI). Then a restraint is applied to the COM with respect to its TINI. For N spline points,

1.0 <= TINI <= N


where, for example, if TINI = 3.48 then the COM is projected onto the spline piece between spline point 3 and spline point 4 while the digits to the right of the decimal place corresponds to the cubic spline parameter that gives the X, Y, Z coordinates that lie on spline piece 3.

The initial reference coordinates (used for determining TINI) can be the current set (default) or a comparison set (COMP keyword).

The spline-pts are selected either from an atom selection if SPLIne is given or read from a previously opened unit given with the SPLUnit keyword. By default, the spline-pts are taken from the main set. If the COMP key is specified in the absence of the SPLUnit keyword then the spline-pts are taken from the COMP set. However, if both the COMP and SPLUnit keys are used then the spline-pts are taken from the coordinates that are read from the external file. Thus, it is possible to define the initial coordinates separately from the spline points by using the COMP key along with SPLUnit.

The reference point (relative to TINI) is specified by TZERo and is recommended to have a value that is near TINI (usually, within 1.0 of TINI). A negative TZERo value specifies a reference point to the “left” of TINI while a positive TZERo value speficies a reference point to the “right” of TINI.

The restraint force constant can be set to any positive value (specified by the FORCE keyword followed by the desired value). Multiple centers of mass can be defined for a given path by repeating the FORCe, TZERo, and atom-selection.

The functional form of the restraint potential is:

                                     2
U(T) = FORCE * [ (T - TINI) - TZERO ]

where T is the instantaneous projection onto the spline of a given center of mass.

The spline interpolation (derived from user defined spline points) and COM projections can be visualized by specifying the TEST key followed immediately by a user defined output unit. The output data structure is shown in Example 4 below.

Using CONS PATH POST will output infornation to OUTU. This is convenient when used in conjunction with analyzeCHARMM.pl (MMTSB Toolset). The output takes on the form:

PATH =  1 COM =   1 TINIT =   1.36523799 TZERO =   -0.10000000 ABSTZERO =   1.26523799 TPRIME =   1.26773721

Each COM is written while specifying which path the COM corresponds with, the COM number, the initial T-value from the first simulation window, the relative TZERO (relative to the initial T-value), the absolute TZERO, and TPRIME (the COM projection onto the path).

The primary use of this command is to restrain the movement of a specific center of mass parallel to a user defined path. For instance, DNA can be restrained to translocate along its phosphate backbone while resembling a screwing motion.

Example 1:

CONS PATH SPLINE SELECT TYPE P .AND. SEGID N01F END -
FORCE 5 TZERO 0.35 SELECT SEGID N01F .AND. RESID 18 END -
FORCE 5 TZERO 0.35 SELECT SEGID N01F .AND. RESID 19 END -
FORCE 5 TZERO 0.35 SELECT SEGID N01F .AND. RESID 20 END

This will use the phosphorous atoms to generate a cubic spline. Then it will create a harmonic restraint with a force constant of 5 kcal/mol that holds the centers of mass at residues 18, 19, and 20 to its corresponding TINI+0.35 position.

Example 2:

CONS PATH COMP SPLINE SELECT TYPE P .AND. SEGID N01F END -
FORCE 2 TZERO 0.27 SELECT SEGID N01E .AND. RESID 5 END -
FORCE 2 TZERO 0.27 SELECT SEGID N01E .AND. RESID 6 END -
FORCE 2 TZERO 0.27 SELECT SEGID N01E .AND. RESID 7 END

This will use the phosphorous atoms to generate a cubic spline. Then it will create a harmonic restraint with a force constant of 2 kcal/mol that holds the centers of mass at residues 5, 6, and 7 to its corresponding TINI+0.27 position. However, TINI is determined from the comparison set and not the default main set. Note that COM at residues 5-7 from segid N01E are restrained with respect to the phosphorus atoms of segid N01F (and not segid N01E).

Example 3:

OPEN UNIT 77 READ FORM NAME "SPLINE.PTS"

CONS PATH COMP SPLUNIT 77 -
FORCE 10 TZERO -0.5 SELECT SEGID N01E .AND. RESID 8 END -
FORCE 10 TZERO -0.5 SELECT SEGID N01E .AND. RESID 9 END -
FORCE 10 TZERO -0.5 SELECT SEGID N01E .AND. RESID 10 END

This will use the coordinates contained in the file “SPLINE.PTS” (and not from the comparison set) to generate a cubic spline. The name of the file containing the spline points is irrelevant but the format must be arranged as follows:

-48.847 75.201 8.114
-68.551 73.231 9.000
-55.690 77.369 8.591
48.049 74.225 10.388

Then it will create a harmonic restraint with a force constant of 10 kcal/mol that holds the centers of mass at residues 8, 9, and 10 to its corresponding TINI+(-0.5) position. However, TINI is determined from the comparison set and not the default main set.

Example 4:

OPEN UNIT 88 WRITE FORM NAME "VISUALIZE.PDB"

CONS PATH TEST 88 SPLINE SELECT TYPE P .AND. SEGID N01F END -
FORCE 1 TZERO -0.19 SELECT SEGID N01F .AND. RESID 14 END -
FORCE 1 TZERO -0.19 SELECT SEGID N01F .AND. RESID 12 END -
FORCE 1 TZERO -0.19 SELECT SEGID N01F .AND. RESID 13 END

This will use the phosphorous atoms to generate a cubic spline. Then it will create a harmonic restraint with a force constant of 1.0 kcal/mol that holds the centers of mass at residues 14, 12, and 13 to its corresponding TINI+(-0.19) position. Furthermore, the spline interpolation and COM projections can be visualized from the file “VISUALIZE.PDB” where the contents of the file are arranged as follows:

ATOM      1  P     1 S   1      20.356  13.969  16.245     1 0.000
ATOM      2  O1P   1 S   1      18.599  13.199  16.040     1 0.271
ATOM      3  O2P   1 S   1      17.720  12.850  15.920     1 0.407
ATOM      4  O5*   1 S   1      16.840  12.543  15.780     1 0.543
ATOM      5  C5*   1 S   1      15.959  12.292  15.612     1 0.679
ATOM      6  C4*   1 S   1      15.076  12.112  15.409     1 0.814
ATOM      7  C3*   1 S   1      14.192  12.017  15.165     1 0.950
ATOM      8  P     2 S   2      13.866  12.006  15.063     2 0.000
ATOM      9  O1P   2 S   2      12.107  12.179  14.397     2 0.271
ATOM     10  O2P   2 S   2      11.254  12.395  14.000     2 0.407
ATOM     11  O5*   2 S   2      10.435  12.684  13.567     2 0.543
ATOM     12  C5*   2 S   2       9.661  13.034  13.104     2 0.679
ATOM     13  C4*   2 S   2       8.946  13.436  12.615     2 0.814
ATOM     14  C3*   2 S   2       8.299  13.879  12.107     2 0.950
ATOM     15  P     3 S   3       8.081  14.050  11.915     3 0.000
ATOM     16  O1P   3 S   3       7.084  15.038  10.846     3 0.271
ATOM     17  O2P   3 S   3       6.684  15.562  10.296     3 0.407
ATOM     18  O5*   3 S   3       6.336  16.103   9.738     3 0.543
ATOM     19  C5*   3 S   3       6.027  16.655   9.174     3 0.679
ATOM     20  C4*   3 S   3       5.746  17.216   8.605     3 0.814
ATOM     21  C3*   3 S   3       5.480  17.781   8.035     3 0.950
ATOM     22  P     4 S   4       5.384  17.990   7.824     3 0.000
ATOM     23  COM   1 C   1       6.747  15.474  10.388     3 0.385
ATOM     24  COM   2 C   2      18.152  13.017  15.981     1 0.340
ATOM     25  COM   3 C   3      11.047  12.460  13.896     2 0.441

Similar to the PDB Format:

Column 1 = RECORD NAME
Column 2 = ATOM NUMBER
Column 3 = ATOM TYPE (Points along a spline path have spline points
represented as a DNA backbone while COM points are
represented as type "COM").
Column 4 = RESIDUE NAME (Numbered according to either spline piece
number for splines or COM numbers for COM).
Column 5 = CHAINID (S = Spline and C = COM)
Column 6 = RESIDUE NUMBER (Same as Column 4)
Column 7 = X-COOR   |  These X, Y, Z-COOR are interpolated points
Column 8 = Y-COOR   |  for splines and projection points for COM
Column 9 = Z-COOR   |
Column 10= Spline Piece (Represents the spline piece that the point
was taken from).
Column 11= TVAL (Represents the T-value from a specific spline piece
identified in Column 10).  If this TVAL is substituted
into its corresponding spline piece (from Column 10 which
will look like At^3+Bt^2+Ct+D), this will give the
corresponding X-COOR, Y-COOR, and Z-COOR.

## Helix Restraint Potential (CONS HELIx)¶

Note

Questions and comments regarding CONS HELIx should be directed to Wonpil Im (wonpil@ku.edu); Jinhyuk Lee (mack97hyuk@gmail.com); Taehoon Kim (comboy94@gmail.com); Sunhwan Jo (sunhwanj@gmail.com) Center for Bioinformatics/Dept. of molecular biosciences, Univ. of Kansas

References:

1. Jinhyuk Lee and Wonpil Im, J. Comput. Chem., 28, 669(2007)
2. Jinhyuk Lee and Wonpil Im, Chem. Phys. Lett., 441, 132(2007)
3. C.Chothia, J.Mol.Biol. 145, 215(1981)

### Syntax¶

CONS { HELIx } DISTance <real> FORCe <real> -
{ BHG   } [SELE 1st-atom-selection END] [SELE 2nd-atom-selection END] -
UDISt <int> STEP <int>

CONS { HELIx } { [CROSs] [HINGe] } ANGLe <real> FORCe <real> -
{ BHG   } [SELE  1st-atom-selection END] [SELE 2nd-atom-selection END] -
UANG <int> STEP <int>

CONS { HELIx } { TilX } ANGLe <real> FORCe <real> -
{ BHG   } { TilY } [SELE atom-selection END] -
{ TilZ } UANG <int> STEP <int>

CONS { HELIx } ROTH { RotX } ANGLe <real> FORCe <real> REFA <int> -
{ BHG   }      { RotY } [SELE atom-selection END] -
{ RotZ } UANG <int> STEP <int>

Single selection - Tilt angle constraint or Rotation angle constraint
Double selection - Cross angle constraint or Hinge angle constraint

CROSs : default option - Crossing angle constraint
HINGe : Hinge angle constraint

HELIx : for helix
BHG   : for beta-hairpin

CONS HELIx RESEt     ! reset CONS HELIx

### Details of CONS HELIx commands¶

1. The DISTannce command

The CONS HELIx DISTance command will setup a helix-helix distance restraint between two selected helices. The detail formalizm and description are in J. Comput. Chem., 28:669-680(2007).

2. The CROSs/HINGe command

The CONS HELIx CROSs command will setup a helix-helix crossing angle restraint between two selected helices. The detail formalizm and description are in J. Comput. Chem., 28:669-680(2007).

The CONS HELIx HINGe command will setup a helix-helix hinge angle restraint between two selected helices.

3. The ANGLe command

The CONS HELIx ANGLe command will setup a helix tilt angle restraint of selected helix. The helix tilt (tau) is defined as the angle between helical principal axis and Z-axis (default). The reference axis can be changed by extra keywords: (TilX (X-axis),TilY (Y-axis), and TilZ (Z-axis)).

4. The ROTH ANGLe command

The CONS HELIx ROTH ANGLe command will setup a helix rotation angle restraint of selected helix. The helix rotation (rho) is defined as the angle between the perpendicular vector (rs) from the helical axis to the selected Ca atom (keyword: REFA) and the projection vector (zp) of the Z-axis (default) onto the plane made by the second and third principal axes (see Figure 1, Biophys. J., 99:175-183 (2010)). The default Z-axis can be changed by extra keywords: (RotX (X-axis), RotY (Y-axis), and RotZ (Z-axis)).

5. Energy related properties:

 ?echd Helix-helix distance restraint energy ?echa Helix-helix cross/hinge angle restraint energy ?echt Helix tilt restraint energy ?echr Helix rotation restraint energy
6. COOR HELIx substitution parameters

Since CONS HELIx incoperate with COOR HELIx command, the following substitution parameters are specified:

 ?mind Helix-helix distance ?omeg Helix-helix cross angle ?hang Helix-helix hinge angle ?tang Helix tilt angle ?rota Helix rotation angle
7. Examples of usage

1. To setup a restraint with a force constant of 200.0 kcal/(mol Ang^2) for a helix-helix distance of 10 angstroms between two helices and to print the distance to a file linked to a fortran unit 11 every 100 step during simulation:

define helixa sele segid PROA .and. type CA end
define helixb sele segid PROB .and. type CA end

open write card unit 11 name dist.dat

cons helix dist 10.0 force 100.0 select helixa end select helixb end -
udist 11 step 100
2. To setup a restraint with a force constant of 70.0 kcal/(mol rad^2) for a helix-helix crossing angle of 45 degree between two helices and to print the angle to a file linked to a fortran unit 11 every 100 step during simulation:

define helixa sele segid PROA .and. type CA end
define helixb sele segid PROB .and. type CA end

open write card unit 11 name dist.dat

cons helix cross 45.0 force 35.0 select helixa end select helixb end -
uang 11 step 100
3. To setup a restraint with a force constant of 6000.0 kcal/(mol rad^2) for a helix tilt angle of 45 degree respect to Z-axis (defalut) and to print the angle to a file linked to a fortran unit 11 every 100 step during simulation:

define helixa sele segid PROA .and. type CA end

open write card unit 11 name angle.dat

cons helix angle 45.0 force 3000.0 select helixa end -
uang 11 step 100
4. To setup a restraint with a force constant of 200.0 kcal/(mol rad^2) for a helix rotation angle of 30 degree using Ca atom in 10th residue as an internal reference (Biophys. J., 99:175-183 (2010)) and to print the angle to a file plinked to a fortran unit 11 every 100 step during simulation:

define helixa sele segid PROA .and. type CA end

open write card unit 11 name rotation.dat

cons helix roth angle 30.0 force 100.0 refa 10 select helixa end -
uang 11 step 100

Note

The helix restraint does not have one-half in the harmonic form, so the force constants must be a half of real value if a one-half harmonic form is considered for any post-analysis.