CHARMM

Table Of Contents

Previous topic

The HQBM Module of CHARMM

Next topic

The Internal Coordinate Manipulation Commands

This Page

Images

Original implementation by Bernard R. Brooks, 1983

CHARMM has a general image support system that allows the simulation of almost any crystal and also finite point groups (such as dimers and tetramers...). There is also a facility to introduce bond linkages (with additional energy terms including angles, dihedrals and improper dihedrals) between the primary atoms and image atoms. This allows infinite polymers, such as DNA to be studied. For infinite systems, an asymmetric unit may be studied because rotations and reflections are allowed transformations.

The IMAGE facility is invoked by reading an image transformation file. From this point, the images of the primary atoms will be included in any energy and force determinations for the remainder of the calculation. A null image file with the INIT keyword will disable this facility.

The simple periodic boundary code is underdevelopment by Charles L. Brooks, III at the Scripps Research Institute as of Spring 1995.

Image Transformation File

The image transformation file contains all of the information needed to define the position and orientation of all symmetric images of the primary atoms. The file is read in free field and may be passed parameters.

READ IMAGe  [UNIT integer] [INIT] [PRINT]

File Structure:

(title)

SCALE  xfactor  yfactor  zfactor
IMAGE  image_name                       ! start of a new transformation
DEFIne repeat( [INVErse] other_image )  ! define transformation from others
ROTAte xdir  ydir   zdir   angle        ! specify an axis and angle
TRANslate  xdir  ydir  zdir [distance]  ! specify a displacement
NEGAte                                  ! invert through origin
END                                     ! terminates transformation file

When an image file is read, any existing image transformations are discarded, but not any information regarding image patching. The INIT keyword on reading will remove ALL existing image data first. Rereading an image transformation file without the INIT keyword is useful when crystal parameters are to be modified, but the patching data is to be retained. The PRINt option, prints all data as it is read.

The image file starts with a standard CHARMM title. The remaining commands are processed sequentially.

The SCALe command gives three values which multiply all subsequent transformation specifications. The default values are unity.

The IMAGe command initiates a new image transformation. The transformation matrix is set to unity (no rotation, no translation). This transformation matrix is then modified by subsequent commands until another IMAGe commmand or the END command is found.

The DEFIne command multiplies the current transformation matrix by any of the previously defined images. The INVErse keyword proceeding the other transformation name, uses the inverse of this transformation. Any number of previous transformations may be listed with this command, but they are processed sequentially (just in case they don’t commute).

The ROTAte command causes the current transformation matrix to be operated with a rotation. Four real numbers must follow which define a rotation axis and an angle about this axis (in degrees).

The TRANslation command will translate the current transformation matrix. If three values are specified, then this is used as the translation vector. If four values are given, then the first three define a direction, and the fourth value defines a distance. Before operating on the transformation matrix, the elements of this vector are multiplied by the current scale factors (from last SCALe command).

The NEGAte command projects the current transformation through the origin. This operation changes the chirality of the system, and is not appropriate for macromolecules. This operation is required for simulations with glide planes.

The END command is used to terminate the IMAGE file. This is required if the file is read from the input stream.

Warning

One restriction on the transformations is that every transformation MUST have an inverse. There is a serious warning if this restriction is violated. This requirement is needed in defining the energy of the system. When computing the energy, the Hamiltonian is assumed to be symmetric, and only the lower half is generated. The result of having an image without a transformation is to remove the symmetry of the Hamiltonian. The considerations of program efficiency and memory requirements make this necessary. There may be examples where this is desired, such as for cases where no energy calculations are needed or for structural analysis. A transformation may be its own inverse as is the case when a transformation consists of only a 180 degree rotation.

The maximum number of allowed transformations is 100. This limit can easily be increased.

Image Writing and Printing

Several different types of image data may be written or printed. These are used for analysis and to check the operation of the program.

WRITE IMAGes  { TRANsformations   }  [UNIT integer]
              { PSF               }
              { FORCes            }

The TRANsformation option will list all image transformation matricies as well as what the inverse transformations are. For each transformation, there is given a 3 X 3 rotation matrix followed by the translation vector. For the use in this program the translation is done AFTER the rotation has been made.

The PSF option, lists information about the image atoms as well as list all primary-image internal coordinates (bonds, angles, dihedrals, and improper dihedrals).

The FORCe option, lists the total force and torque each image transformation applies on the primary atoms. This data may be used to estimate the pressure of a system, or to check if minimization is complete. At the end, the total force (vector sum) and torques are listed.

Image Updating

The crystal build procedure has to be done prior to image, nonbond or hydrogen bond updating with IXTFrq frequency - it can be also done manually by issuing Crystal Build command. Actually first time is has to be done manually to read parameters associated with crystal build command.

The image update procedure has several functions. This updating is done prior to any nonbond or hydrogen bond updating, because its results may affect those updates.

{                                                           } ! no change
{ IXTFrq int IMGFrq int [CUTIm real] [IMALl  ] [INVErse  ]  }
{                                    [IMBRief] [NOINverse]  }
{ IMGFrq  0                                      } ! suppress image updating

The absence of the IMGFrq keyword, maintains the current status of image updating. Specifying an IMGFrq value of zero, suppresses all image update functions, but does not modify the image lists in any way.

The IMGFrq integer value gives the frequency of image updating to use during dynamics or minimization. For setting up a single image update, any positive value may be used. When negative value was used, e.g., INBFRQ = -1, all lists are updated when necessary (heuristic test).

The CUTIm value gives the maximum allowable distance of any group to be included in the image atom lists. Normally, a group is included only if it belongs to a transformation whose inverse transformation is of a higher index than its own. This is because only the lower triangle of the Hamiltonian is computed and any image interaction between primary atoms and image atoms of a higher inverse index will already be computed. This efficiency consideration greatly reduces the required number of image atoms and the size of the image nonbond lists. This reduction is activated by the use of the IMBRief option (default). If on the other hand, one desires these groups for the purpose of analysis or for displays, the IMALL keyword may be used to generate all image atoms within the CUTIm distance.

The sequence of events in this update are;

  1. Save existing image atom lists (from the previous update).
  2. Process image centering if requested to replace far off groups of atoms by a closer image.
  3. Generate appropriate image atoms within the cutoff distance of the primary atoms.
  4. Remap internal coordinate energy list if the new image atom list differs from the previous one. Also remap the IC table and image exclusion lists.

The INVErse and NOINverse options are internal and neither should be specified under normal circumstances.

Image Structure File Patching

This command introduces bonding linkages between primary atoms and image atoms. This allows the simulation of infinite (or cyclic) polymers.

IMPAtch patch_residue repeat( image_name segid resid ) [SETUp] [WARN]

The patch_residue must be present in the topology file and the syntax of this patch residue is identical to ordinary patching (see Patch command to modify PSF), with the restrictions that the ATOM, DONOr, and ACCEptor specifications may not be used. Atom characteristics may not be modified with this command. The donor and acceptor status of any image atom must match that of the corresponding primary atom. The patching specifications that are recognized are; BOND, ANGLe, DIHEdral, IMPHi, and IC (internal coordinates)

A residue specification is required for each used in the PRES. These are specified by three names, (1) the image name (for primary atoms the name PRIM must be used), (2) the segid, and (3) the resid.

The SETUp keyword causes all PRES IC table entries to be added to the current IC table.

The WARN makes all errors nonfatal and lists errors.

Image Centering

There is a set of commands that allow for the centering of selected part of the PSF during an image update. This is primarily designed for solvent, but may be used in many ways.

IMAGE  { FIXEd        }  [ XCEN real ] [ YCEN real ] [ ZCEN real ]
       { BYSEgments   }                                 atom-selection
       { BYREsidues   }
       { BYGRoups     }
       { BYAToms      }

During dynamics, a particular water may become far from the rest of the primary structure. The centering features allows one of its image (the one closest to the primary space) to become the primary water.

It is also useful when setting up a crystal calculation. With a single update, the “best” image choice of all solvent molecules may be made. One example of this is the netropsin crystal where one of the published sulfate groups is quite far from the primary netropsin. This command is required for a pure solvent simulation where solvent can freely diffuse.

The execution of this command only sets up data used during the image update. There is only one value each for XCEN, YCEN, and ZCEN. If these values are not specified in any IMAGe command, then they are not modified (default 0.0).

For each atom, there is a flag specifying the manner of image centering to be used. Each invocation of the IMAGE command may modify these flags. The default is FIXEd (don’t center this atom). The BYSEgment option will center an entire segment as a group (providing it has no FIXED atoms). The remaining commands will allow certain other groups of atoms to be centered as a group. It wouldn’t work well if only one part of a molecule was centered (there is no checking for this!).

The command;

IMAGE FIXED SELE ALL END   - will turn off all centering
IMAGE BYRES SELE RESNAME ST2 END - will allow centering of all ST2's
IMAGE BYATOM SELE ALL END - will not work if there are any bonds

Warning

Image centering should be set after the PSF is completed. Any modification to the PSF with image centering active will nullify the image centering function and a warning message is issued. The IMAGE command will need to be reissued if image centering is desired.

Image Operation

The IMAGE routines in CHARMM can be classified into five sections.

These catagories are :

  • Set up images -IMREAD, REIMAG, INIMAG, IMPATC, IMATOM, IMSPEC
  • Update image arrays - UPIMAG, IMCENT, MKIMAT, IMMAP, MKIMNB
  • Set up energy lists - IMHBON, NEWHBL, IMHBFX, NBONDM
  • Compute image energy - EIMAGE, TRANSO, TRANSI
  • Print out - IMWRIT, IMPSFW

The first category involves reading the image file (IMREAD) and setting up the data structure (REIMAG, INIMAG). In the section are also the routines involving image patching and setting up the centering options.

The second category concerns itself with the selection of image groups are to be kept. This selection process is repeated each image update. Also done, is the centering, PSF remapping (if the atom list has changed), and the generation of the image exclusion lists.

The third category in addition to finding the energy terms codes, also generates the nonbond and hydrogen bond lists between primary and image atoms.

The fourth category is concerned with the computation of energy terms. For the actual computation of energy, standard routines are used (ENBOND, EHBOND, ENST2) with a modified calling sequence. The procedure used is:

  1. Compute coordinates for all image atoms
  2. Set up arrays for self energy terms (atom with its own image)
  3. Compute self terms, divide energy by 2, zero out image forces
  4. Compute remaining terms including forces on image atoms
  5. Transform forces on image atoms back into the primary space

Using a procedure where the forces on image atoms is kept, allows for a substantial reduction in the number of necessary image atoms. This results in the necessity that all transformations have an inverse. This procedure has the drawback that the self energy terms must be treated specially and that all Hbonds between image and primary atoms must be computed and then trimmed of any repeats.

Since there is no treatment of the second derivative of the energy for image atoms, The procedures involving Newton-Raphson minimizations and vibrational analysis should be avoided (see Energy Manipulations: Minimization and Dynamics).).

Simple periodic boundaries

This code was developed by William A. Shirley and Charles L. Brooks, III, Department of Molecular Biology, The Scripps Research Institute, during the spring of 1995.

Its purpose is to speed up calculations which use the periodic boundry conditions for A TRUNCATED OCTAHEDRAL BOX; A RHOMBIC DODECAHEDRAL BOX; A TWO AND THREE DIMENSIONAL RHOMBOIDAL BOX.

Reference:

    1. Allen and D. J. Tildesley, Computer Simulation of Liquids, Ch. 1.
BOUNd { CUBOUNdary } { BOXL <real>                            }  CUTNB <real>
      { TOBOUNdary } { XSIZe <real> YSIZe <real> ZSIZe <real> }
      { RDBOUNdary }
      { RHBOUNdary }

where
        TOBOUN =        TruncatedOctahedralBOUNd
        RDBOUN =        RhombicDodecahedralBOUNd
        RHBOUN = Two dimensional RHomboidalBOUNd
        CUBOUN =                      CUbicBOUNd

and BOXL <real> (or XSIZe) and CUTNB <real> are required. :chm:XSIZe, :chm:YSIZe, and :chm:ZSIZe are the edgelengths in the x, y, and z-directions. If YSIZe is not specified it is assumed to equal XSIZe (or BOXL), and if ZSIZe is not specified it is assumed to equal YSIZe.

Warning

Image centering and definition of the image transformations through the READ IMAGE and IMAGE centering must be used in conjunction with this command. Moving the commands to be available in other fast implementations, i.e., in vector codes, will follow shortly.

The basic code is implemented following the outline:

  1. Parse the control variables based upon the keyword BOUNd, which set the control flags to be set. These flags turn off the existing image generation code during run time. Control is passed back to the CHARMM level, and the program continues.
  2. Do not generate image atoms to add to the PSF. When UPIMage is called, skip MKIMat. Set the completion flag in NBONdm.
  3. During the generation of the nonbonded list use the MI in NBONdg to get correct pairs onto the list.
  4. During the calculation of the nonbonded energies in ENBFast, adjust the distances suing MI to get the correct VDW and Elec energies.