CHARMM c42b2 mc.doc



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                               Monte Carlo

The Monte Carlo commands in CHARMM have been designed to allow construction 
and use of an almost arbitrary move set with only a few atom selections.  
This goal is accomplished by providing a pre-defined set of move types which 
can be combined to specify the allowed movements of an arbitrary CHARMM 
molecule.  Speed and flexibility are gained by separating the bookkeeping 
associated with a move (MOVE subcommands) from the actual application of 
that move to the molecule (MC).

* Menu:

* Syntax::              Syntax of MOVE and MC commands
* Description::         Description of MOVE and MC commands
* Examples::            Examples of MOVE and MC commands
* SA-MC simulations::   How to use the SA-MC algorithm with this module
* Data Structures::     Data structures shared by the MOVE and MC commands
* Shortcomings::        Known problems and limitations
* References::          Some references of use



File: mc -=- Node: Syntax
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                      Syntax for MOVE and MC commands

[Syntax MOVE < ADD | DELEte | EDIT | READ | WRITe | LINK > ]

MOVE ADD  1{ MVTP move-type } nsele{ SELE...END } -
           [ WEIGht  1.0 ] [ DMAX      1.0 ] [ TFACtor     1.0  ] -
           [ FEWEr   0/1 ] [ NLIMit      1 ] [ LABEL move-label ] -
           [ opt-spec    ] [ mini-spec     ] [ hmc-spec         ]
           [ samc-spec   ]

           where nsele, the number of SELE...END statements, 
           depends on move-type

move-type (nsele)::= < RTRN rig-unit ( 1 ) |   ! Rigid translations
                       RROT rig-unit ( 1+) |   ! Rigid rotations
                       CART          ( 1 ) |   ! Single atom displacements
                       TORS          ( 2 ) |   ! Simple torsion rotations
                       CROT [PIMC]   ( 1+) |   ! Concerted torsion rotations
                       HMC           ( 1 ) |   ! Hybrid Monte Carlo
                       VOLU rig-unit ( 1 ) >   ! Volume scalings

rig-unit ::= < BYREsidue | BYALl | BYHEavy | BYATom >

opt-spec ::= [ ARMP   -1.0 ] [ ARMA      0.0 ] [ ARMB        0.0 ] -
             [ DOMCf  -1.0 ] [ ANISotropic 0 ] 

mini-spec::= [ MINI                      < SD (default) | CONJ > ] -
             [ NSTEps    0 ] [ NPRInt      0 ] [STEP         0.2 ] -
             [ TOLEner 0.0 ] [ TOLGrad   0.0 ] [TOLStep      0.0 ] -
             [ INBFrq   -1 ] 

hmc-spec ::= [ NMDSteps  0 ] [ TIMEstep  0.0 ] -
             [ MEUPdate  0 ] [ MEFActor  0.0 ] [ MEWEight 0.0 ]

samc-spec::= [ SAMC        ] [ WEPSilon  0.0 ] -
             [ MEPSilon  0 ] [ NEPSilon  0   ]

MOVE DELEte < MVINdex move-index | LABEL move-label > -

MOVE EDIT   < MVINdex move-index | LABEL move-label > -
            [ WEIGht prev  ] [ DMAX        prev ] [ TFACtor prev ] -
            [ NLIMit  prev ] [ opt-spec         ] [ mini-spec    ] -
            [ hmc-spec     ]

prev ::= previous value

MOVE WRITE [UNIT -1]

MOVE READ  [UNIT -1] [APPEnd 1]

MOVE LINK  < MVI1 move-index  |  LAB1 move-label > -
           [ MVI2 move-index ] [ LAB2 move-label ] [ GCMC ]

[Syntax MC]

MC [ NSTEps          0 ] [ ISEEd   prev ] [ IACCept   0 ] [ PICK      0 ] -
   [ TEMPerature 300.0 ] [ PRESsure 0.0 ] [ VOLUme prev ] [ ACECut 0.01 ] -
   [ INBFrq          0 ] [ IMGFrq     0 ] [ IECHeck   0 ] -
   [ IUNCrd         -1 ] [ NSAVc      0 ] [ IMULti   -1 ] -
   [ RESTart           ] [ IUNRead   -1 ] [ IUNWrite -1 ] [ ISVFrq    0 ] -
   [ IARMfrq         0 ] [ IDOMcfrq   0 ] [ gcmc-spec   ] [ wl-spec     ] -
   [ samc-opt          ]

gcmc-spec ::= [ GCBF  0.0 ] [ MUEX  0.0 ] [ DENSity 0.0 ] [ NGCTry 0 ] -
              [ GCCUt 0.0 ] [ NOTBias 1 ] [ RGRId  -1.0 ] [ INSPhere ] -
              [ INSX  0.0 ] [ INSY  0.0 ] [ INSZ    0.0 ] [ INSR 0.0 ] -
              [ XMIN  0.0 ] [ YMIN  0.0 ] [ ZMIN    0.0 ] -
              [ XMAX  0.0 ] [ YMAX  0.0 ] [ ZMAX    0.0 ] 

wl-spec   ::= [ IWLRead -1 ] [ IWLWrite  -1 ] [ NWLFrq  0 ] [ WLINcr 0.0 ] -
              [ WLTOl  0.0 ] [ WLUPdate 0.0 ]

samc-opt   ::= [ SAMC ] [ UNB ] [ IUNB -1 ]



File: mc -=- Node: Description
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                                   MOVE                               

     The MOVE subcommands are associated with construction of the move set.  

     The primary MOVE subcommand is MOVE ADD, which determines all of the 
locations in a subset of atoms to which a move type can be applied.   For 
each location (or "move instance"), MOVE ADD also determines the rotation 
axes and centers, the moving atoms, and the relevant bonded terms.  Thus, 
each call of MOVE ADD results in a group of move instances of the same move 
type (the number of instances is stored in the substitution variable ?NMVI).  
By repeatedly calling the MOVE ADD command, the user can employ several 
different types of moves in conjunction, which typically yields the most 
efficient and complete sampling.

     The available pre-defined move types are rigid translations (RTRN), rigid 
rotations (RROT), single atom displacements (RTRN), rotations of individual 
torsions (TORS), concerted rotation of seven (or, in the case of a chain end, 
six) torsions (CROT) to deform the system locally (Dinner, 2000; Dinner, 1999; 
Go and Scheraga, 1970; Dodd et al., 1993; Leontidis et al., 1994), hybrid 
Monte Carlo propagations (HMC) (Duane et al., 1987; Mehlig et al., 1992),
and volume scaling moves for constant pressure simulations (Eppenga and 
Frenkel, 1984).  Each of these can be applied to an arbitrary subset of atoms 
using standard CHARMM SELE...END statements.  

     MVTP rig-unit nsele Description
     ---- -------- ----- -----------
     RTRN BYALl       1  The entire atom selection is rigidly translated.

     RTRN BYREsidue   1  The residue containing each selected atom is 
                         rigidly translated.  If more than one atom in 
                         a residue is selected, each counts as a separate 
                         move instance.

     RTRN BYHEavy    1   Each heavy atom and its associated hydrogen atoms
                         are rigidly translated.

     RTRN BYATom     1   Each instance is a displacement of a single atom by
                         a random vector distributed uniformly in an ellipsoid
                         (see the description of the ANISotropic keyword).
                         For historic reasons, the CART keyword is a synonym 
                         for RTRN BYATom, but use of the former is discouraged 
                         since the moves are not actually based on Cartesian 
                         coordinates.

     RROT BYALl     1-2  The entire first atom selection specifies the rigid
                         body of atoms to be rotated, and each of the atoms in
                         the second atom selection is an allowed rotation 
                         center.  The second selection need not be a subset of
                         the first, so rotations around atoms outside the
                         rigid body can occur.  If no second atom selection is 
                         given (or one is given, but no atoms are selected),
                         the rotations are made around the center of mass of
                         the first atom selection.

     RROT BYREsidue  1   There is only a single atom selection, and each 
                         selected atom is a center of rotation (around a 
                         randomly selected axis) for its residue.  If more
                         than one atom in a residue is selected, each counts 
                         as a separate move instance.

     RROT BYHEavy    1   The hydrogens attached to a heavy atom are rigidly
                         rotated around the heavy atom.  If the FEWEr keyword
                         is set to 1 (the default), a move instance is counted 
                         for each selected heavy atom with at least one hydrogen 
                         atom attached (whether or not the hydrogens are selected 
                         does not matter).  If the FEWEr keyword is set to 0,
                         all heavy atoms are counted to permit straightforward 
                         linking with RTRN BYHEavy move groups.

     TORS            2   The two selections define the middle atoms (JK in
                         IJKL) of the rotatable torsions.  If the FEWEr keyword
                         is set to 1 (default is 0), the directionality of the 
                         selection will be ignored and each rotatable bond will 
                         be included only once in the move set (such as to rotate
                         the end with fewer atoms).  Otherwise, each rotatable 
                         bond will be included either once or twice depending on
                         whether the atom selections match the bond in only one 
                         direction (JK) or both (JK and KJ).  Only torsions in 
                         the PSF are enumerated.

     CROT            1+  The first atom selection defines the "backbone" 
                         along which the 7 (or in the case of a chain end, 6)
                         dihedrals lie.  Each additional pair of selections 
                         defines non-rotatable bonds.  The first bond in a set 
                         of 6 or 7 is the driver torsion.  Non-rotatable bonds 
                         are not allowed at the third or fifth bonds following 
                         the driver (counting only rotatable ones).  Note that 
                         there is no checking for whether bonds selected to be 
                         rotatable are indeed so.  NLIMit is the number of 
                         torsions in addition to the driver torsion that are 
                         restricted by the maximum rotation (DMAX); values of
                         0 to 5 are possible.  In general, setting NLIMit 
                         greater than or equal to 1 is recommended since it 
                         speeds up the root finding process and moves with large 
                         changes to the torsions tend to be rejected anyway.  
                         Concerted rotations of path integral "polymers" require 
                         the PIMC keyword.

     HMC              1  The selected atoms are propagated with the specified 
                         TIMEstep for NMDSteps molecular dynamics steps.  The 
                         change in total energy is used for the acceptance 
                         criterion.  SHAKE constraints are respected.  The 
                         standard fixed atom list is ignored, but note that,
                         in the present implementation, selections that move 
                         only small parts of the system will be inefficient.  
                         The non-bond list update during dynamics is separate 
                         from that used in MC and is controlled by a common 
                         variable set by the DYNAmics command.  To suppress
                         updates of the non-bond list, it is necessary to 
                         issue a dummy dynamics statement prior to MC:
                         DYNAmics NSTEps 0 INBFrq 0 NSAVC 0.  
 
                         If IACCept=2, the dynamics take place on a transformed
                         potential (Andricioaei and Straub, 1996; Andricioaei
                         and Straub, 1997); use of the Tsallis method with HMC
                         requires that the TSALLIS keyword be included in
                         pref.dat  during compilation.

                         If IACCept=0, sampling can be enhanced using the
                         method introduced in Andricioaei et al. (2003)
                         by setting MEFAactor, MEUPdate, and MEWEight to
                         non-zero values.  MEFActor is the csi multiplicative
                         factor above Eq. 18 in the above paper, MEUPdate is
                         the frequency of updating the bias vector, and
                         MEWEight is the weight each new dynamics step carries
                         in the bias vector (dt/tl, where dt is the timestep
                         and tl is the averaging period).

     VOLUme rig-unit  1  Volume scaling moves.  Changes in ln V are selected
                         uniformly from the allowed range, and the scaling is
                         around the image center.  The possible rigid units 
                         are the same as for RTRN and RROT.  If a "mixed"
                         scaling move is desired (e.g., solvent atoms are
                         scaled by residue while solute atoms are scaled 
                         individually), it is necessary to couple two or more
                         "pure" scaling moves (see MOVE LINK).

     GCMC             1  Insertion and deletion moves for grand canonical
                         Monte Carlo.  Move instances are identified in the 
                         same way as RTRN BYREsidue above.  In other words, 
                         there is one instance per selected atom in a grand 
                         canonical molecule (which must be a single residue); 
                         selecting more than one atom in a residue will waste
                         memory.  Moreover, translation and rotation moves of 
                         grand canonical molecules should be linked to the
                         GCMC move group to avoid wasting time moving inactive
                         atoms (see MOVE LINK).  See MC and the Examples
                         section below for further details on grand canonical
                         Monte Carlo.

     In addition, MOVE ADD associates with each group of move instances a set 
of parameters.  

     The values of the following parameters are used in all MC calls. 

     WEIGht       The relative weight of that group of move instances in 
                  the complete move set.  The probability of picking a 
                  group of move instances with weight w_i is w_i/(sum_j w_j)
                  where (sum_j w_j) is the total of all the WEIGht values.

     DMAX         The initial maximum displacement of each instance in a 
                  group.  Translations are in angstroms and rotations are in
                  degrees.  In cases where anisotropic automatic optimization 
                  is to be performed, the initial assignment is isotropic.

     TFACtor      A multiplicative factor to scale the TEMPerature in the 
                  acceptance criterion.  TFACtor is not used in assigning
                  the initial velocities in HMC moves.

     LABEL        An optional tag for the group of move instances.
                  Only the first four characters are retained.  All sets of
                  move instances are also given an integer index which can
                  be used instead.

     The following optional parameters are associated with automatic 
optimization of the volumes from which individual move instances are chosen
(the timestep in HMC moves).  The two available methods are the Acceptance 
Ratio Method (ARM) and Dynamically Optimized Monte Carlo (DOMC); both are 
described in detail by Bouzida et al.  (1992).  The latter has the advantage 
that it allows optimization of anisotropic volumes.

     ARMP         ARM target probability of move instance acceptance.

     ARMA, ARMB   Parameters to avoid taking the logarithm of zero in ARM:
        
                  DMAX(new) = DMAX(old)*ln(ARMA*ARMP+ARMB)/ln(ARMA*obsP+ARMB)
 
                  where obsP is the observed probability of accepting that
                  move instance.  
     
     DOMCF        The F factor in DOMC:

                  DMAX(new) = DOMCF*SQRT[(d2ave*TEMP)/Eave]
 
                  where d2ave is the observed average square of the
                  displacement and Eave is the observed average change in 
                  energy (both averages are done over all moves, not just those
                  accepted).  DOMCF is used for the anisotropic version of
                  this equation as well.   In the event that the square 
                  root of a negative number must be taken, the routine 
                  branches to ARM optimization, so ARMA, ARMB, and ARMP 
                  should be set even if one plans on using DOMC.

     ANISotropic  DOMC anisotropic optimization of the volume from which the 
                  moves are chosen.  If ANISotropic is 0, it is off (isotropic)
                  and, if ANISotropic is non-zero, it is on.  At present, 
                  only 3D translation moves (RTRN and CART) allow anisotropic 
                  optimization.

     The parameters NSTEps, NPRInt, STEP, TOLEner, TOLGrad, TOLstep, and 
INBFrq are associated with minimization prior to application of the acceptance 
criterion (Li and Scheraga, 1987) and have the same meanings as for
MINImization (see minimiz.doc).  Note that the INBFrq used for minimization
(set in MOVE) is distinct from that used for Monte Carlo (set in MC) even
though the command-line keywords are the same; moreover, INBFrq and NPRInt
access common variables associated with minimization directly and thus are
not stored with the rest of the move set by MOVE WRITE.  During the
minimization phase of a move, all atoms that have not been constrained with
CONS FIX are considered mobile.  At present, the minimization algorithms
available are steepest descents (SD) and conjugate gradients (CONJ);
in the case of CONJ, the following parameters are fixed: NCGC = 100,
PCUT = 0.9999, and TOLIter = 100.  It is important that the user keep in
mind that MC with minimization does not satisfy the detailed balance 
condition (microscopic reversibility) and thus should be used only for 
conformational searching, not calculating equilibrium averages.  Minimization
following HMC moves is not allowed.

     The optional parameters SAMC, WEPSilon, MEPSilon and NEPSilon, are used for Spatial 
Averaging MC simulations (SA-MC) (Refs): see the section 'SPATIAL AVERAGING SIMULATIONS'
below for more details. For each move instance the user can decide to enable 
the SA-MC algorithm by putting the SAMC keyword, and then precise the 3 parameters 
WEPSilon, MEPSilon, and NEPSilon.

     MOVE DELEte allows the user to delete a group of move instances.   The 
group to be deleted is the first that matches the four-character tag specified 
by LABEL or the integer specified by MVINdex; if there is a conflict, the 
LABEL is used.

     MOVE EDIT allows one to change the values of the parameters associated 
with a group of move instances.   The matching rules are the same as those for 
MOVE DELEte (as a result, the LABEL parameter itself cannot be changed with 
MOVE EDIT).  Any parameter not specified retains its current value.  If a 
positive value is specified for DMAX, all move instances will be reset to 
that (isotropic) value; if a negative value (default) is specified, the 
maximum displacements retain their current values.  If DMAX is not specified 
and the ANISotropic flag changes such that anisotropy is no longer allowed 
(when it was previously), the maximum displacements are assigned as the 
geometric mean of the eigenvalues of the matrix used to calculate the allowed 
ellipsoid from the unit sphere.

    MOVE WRITe writes out the current move set to a formatted file opened
with OPEN WRITe CARD.

    MOVE READ reads in a move set.  If APPEnd is 0, existing moves
are eliminated; otherwise they are preserved and the new moves are appended.  
MOVE ADD calls can follow to expand the move set further.

    MOVE LINK links two existing moves such that they are always performed 
together before applying the acceptance criterion.  For example, one might
wish to perform both a rigid body translation and a rigid body rotation of 
a butane molecule in the same MC step.  The first move group [specified by 
either its label (LAB1) or index (MVI1)] remains "active", while the second 
move group becomes "slaved" to the first.  In other words, a move from the 
second group can no longer be selected by itself (as a result, only the WEIGht
parameter of the first move group matters).  At present, move instances within
the groups are matched by indices, so the two move groups must have the same 
numbers of instances.  MOVE LINK can be called repeatedly to create a chain 
of moves.  In the example mentioned above, one might also want to change the 
central dihedral of the butane molecule in the same MC step.  In the second 
MOVE LINK call, the second move group from the first call would become the 
first move group, and the new move group would be the second:

    MOVE LINK LAB1 RTRN LAB2 RROT   !Resulting chain is RTRN->RROT
    MOVE LINK LAB1 RROT LAB2 DIHE   !Resulting chain is RTRN->RROT->DIHE

Moves can be decoupled (in the reverse order by which they were linked) by 
specifying only a single move label (LAB1) or index (IND1):

    MOVE LINK LAB1 RROT             !Resulting chain is RTRN->RROT
    MOVE LINK LAB1 RTRN             !All moves are treated separately

If minimization before applying the acceptance criterion is desired, it must 
be associated with the first move group in the chain (RTRN in the example); 
other minimization parameters will be ignored.  By the same token, only the 
TFACtor for the first move group will be used.  Linking is not allowed with 
Hybrid Monte Carlo moves (HMC).  

The GCMC keyword is used to specify that a move group involves changes to 
the coordinates of molecules that are inserted and deleted during grand 
canonical simulations.  MOVE LINK GCMC suppresses moving "ghost" molecules,
and thus saves simulation time.  In contrast to other calls to MOVE LINK, 
no chain of move groups is constructed, and the non-GCMC move group is still 
active (not slaved).  

Please note that the MOVE LINK command is presently under development.  
Consequently, the syntax might change in future versions.  Moreover, its 
compatibility with certain other features, such as automatic optimization 
of the move limits, is not guarranteed.



                                     MC


     The MC command performs the loop over the appropriate number of Monte 
Carlo steps.  Each step consists of (1) randomly picking a group of move 
instances (weighted), (2) randomly picking an instance from that group 
(unweighted), (3) calculating the energetic contribution of the moving 
atoms and their images, (4) applying the move, (5) calculating the energetic 
contribution in the new configuration, (6) applying the acceptance criterion, 
(7) if necessary updating the statistics for automatic optimization of the 
move limits, and finally (8) performing any desired I/O (at present, only 
trajectory writing is enabled).

     NSTEps       The number of loop iterations.  Each pick of a single move
                  instance and subsequent application of the acceptance 
                  criterion counts.

     ISEEd        The seed for the random number generator.  If it is not
                  specified, it is unchanged, so that a script can be seeded
                  once initially and then loop over an MC command and yield
                  different behavior with each call.

     TEMPerature  The absolute temperature in degrees Kelvin.

     PRESsure     The pressure in atmospheres.

     VOLUme       The starting volume for constant pressure simulations.
                  It is only necessary to specify if the images are created
                  by an IMAGe TRANsformation rather than the CRYStal command.

     INBFrq       The non-bond list update frequency.

                  If INBFrq = 0, the list is not updated.
                  If INBFrq < 0, a heuristic is applied every -INBFrq steps;  
                  the list is updated if any atom during a checking step moved 
                  more than 0.5*(CUTNB - CTOFNB). 

                  Note that a call to ENERgy or UPDAte must be made before 
                  MC to initialize parameters for non-bond list generation.

     IMGFrq       The image list update frequency.  

                  An image update will force a non-bond list update.  
                  If IMGFrq = 0, the list is not updated.
                  If IMGFrq < 0, the list is updated if a heuristic non-bond
                  list update is done; this option should be used only if
                  INBFrq is also negative.

     IECHeck      The total energy check frequency.
                  If IECHeck = 0, the energy is not checked.
                  If IECHeck < 0, the energy is checked if a heuristic non-bond
                  list update is done; this option should be used only if
                  INBFrq is also negative.

                  The difference between the MC running total and the current
                  total is printed in the Delta-E column of the table.  

     NSAVc        The frequency of writing out the trajectory.
                  If NSAVc is 0, no coordinates are written.

     IUNCrd       The I/O unit for trajectory writing.

     RESTart      If present, this keyword indicates that the run is a restart.

     IUNRead      The I/O unit from which to read  the restart information.

     IUNWrite     The I/O unit to which to write the restart information.

     ISVFrq       The frequency of writing the restart information.

     IARMfrq      The frequency of updating the move size by ARM.   Note that
                  this counter runs separately for each move instance.
                  If IARMfrq is 0, the move size is not updated.

     IDOMcfrq     The frequency of updating the move size by DOMC.  Note that
                  this counter runs separately for each move instance.
                  If IDOMcfrq is 0, the move size is not updated.

                  If both IARMfrq and IDOMcfrq are non-zero, IARMfrq takes 
                  priority.

     PICK         Flag for method of selecting moves from the move set:
                       0 = Random move group and random instance (default)
                       1 = Try each move group and instance sequentially
                       2 = Random move group but sequential instances within 
                           a group
                  At present, the PICK flag is considered to be an unsupported
                  feature and may be changed without backwards compatibility in
                  future versions.  

     IACCept      The acceptance criterion to be used.  
                  If IACCept is 0, Boltzmann (Metropolis) weighting is used.
                  If IACCept is 1, multicanonical (constant entropy) weighting
                       is used (in which case TEMPerature is ignored).
                  If IACCept is 2, Tsallis (generalized) weighting is used.
                  If IACCept is 3, Wang-Landau version of the multicanonical 
                     algorithm is used (recommended over IACCept=1).
                  If IACCept is 4, Spatial Averaging (SA-MC) can be used.
                     see the dedicated section below for more details.

     The following optional parameters are specific to particular non-canical 
acceptance criteria.

     EMIN         The estimated minimum energy of the system in Tsallis MC.

     QTSAllis     The Tsallis q parameter (see Andricioaei and Straub, 1997).

     IMULti       The I/O unit for reading in the multicanonical weights.
                  The file format (subject to change) is:

                       CHARMM title
                       Emin  Emax   Nbin
                       i     E_i    ln[n(E_i)]   
                              .
                              .
                              .
                       Nbin  E_Nbin ln[n(E_Nbin)]

                  Note that MC closes this file, so that it must be reopened
                  before each MC call with multicanonical weighting.

     IWLRead      The I/O unit from which to read the initial guesses of the
                  histogram and free energy for Wang-Landau MC.  The file must
                  begin with a CHARMM title (lines starting with "*") followed
                  by the data in three columns:  (1) the indices of the arrays 
                  holding the accumulated histogram and free energy surface,
                  (2) minus the free energy divided by kT (-bF), and (3) the 
                  accumulated histogram (n).  In other words,

                       CHARMM title
                       i     -bF_i    n_i   
                               .
                               .
                               .
                       Nbin  -bF_Nbin n_Nbin

     IWLWrite     The I/O unit to which to write the histogram and free energy
		  for Wang-Landau MC. The format for the result file is similar
		  to that for the initial guess, except that it does not have a
		  title section.

     NWLFrq       The frequency of checking the flatness of the histogram for
		  Wang-Landau MC.  A value on the order of 100000 is recommended.

     WLINcrement  The initial value of the amount added to the free energy at 
		  each step of a Wang-Landau MC simulation. It will be halved 
		  automatically when the criterion specified by WLUPdate is met.

     WLUPdate     The criterion for checking if the accumulated histogram is 
                  flat.  CHARMM MC compares this number with the ratio of 
                  the standard deviation of the accumulated histogram to its 
                  average.  A smaller WLUP will give more accurate results for 
                  the free energy but will require more simulation time.  
                  Reasonable choices are typically between 0.01 and 0.05.

     WLTOlerance  If WLIN reaches WLTO, a Wang-Landau simulation is considered 
		  converged and will stop prior to reaching the specified number
                  of MC steps.  A value on the order of 10^(-8) is recommended.

     The following optional parameters are associated with grand canonical 
Monte Carlo simulations.  Two algorithms for facilitating insertions can 
be used. The cavity bias method (Mezei, 1980) generates a set of candidate 
insertion positions at each GCMC step randomly, determines the ratio P_N = 
cavity sites/total sites, and picks a cavity site for insertion.  The 
acceptance probability is adjusted based on the average of P_N to satisfy 
detailed balance.  Alternatively, one can keep track of the cavities with 
a grid (Mezei, 1987).  The grid-based method is more memory intensive and 
slower at lower density but is generally more efficient at higher density 
and in confined geometries such as within the binding pocket of a protein.  
See Woo et al. (2004) for a discussion of the methods.

     MUEX         Excess chemical potential.

     DENSity      Desired density.

     GCBFactor    B = mu/kT + ln<N>, which sets the excess chemical potential.
                  If DENSity is greater than zero, GCBFactor will be calculated
                  from MUEX and DENSity.

     NGCTry       Number of points to generate in cavity-biased simulations
                  that do not employ a grid.  Simple cavity bias is used
                  automatically if NGCTry is greater than zero.

     GCCUt        Cutoff distance used for evaluating whether a point in space 
                  corresponds to a cavity in cavity-biased simulations.

     RGRId        The grid spacing for grid-based cavity-biased insertion.  
                  Grid-based insertion is used automatically if RGRId is
                  greater  than zero

     INSPhere     Restrict insertion to a sphere of radius INSR centered on 
                  INSX, INSY, INSZ.  Otherwise, insertions are made in the box
                  spanning XMIN < X < XMAX, YMIN < Y < YMAX, and
                  ZMIN < Z < ZMAX.

     NOTBias      The number of orientations to attempt when inserting.

     The parameter ACECut allows approximation of the ACE screening energy 
term to accelerate MC simulations which employ the ACE/ACS solvation model.  
In calculating the total screening energy, as in molecular dynamics, one 
performs two summations:  the first determines the Born radii (b_i) and self 
energies of the atoms and the second determines the screening energy given 
the Born radii.  In MC, this scheme becomes inefficient.  One typically moves 
only a small part of the system in each step, but one must update all the 
pairwise interactions (between atoms i and j) in which b_i, b_j, or both 
change (even if the distance between i and j remains the same).  In CHARMM, 
this problem is overcome by neglecting the contribution to the change in 
screening energy from atom pairs in which both S_i and S_j are less than 
ACECut, where S_i = Sum_k.ne.i [E_ik^self/(tau*q_i^2)] (see equations 22, 28, 
and 31 of Schaefer and Karplus, 1996).  For peptides, a choice of ACECut = 
0.01/Angstrom has been found to yield close to the maximum increase in speed
with errors of less than 0.001 kcal/mol/step.  Note that HMC moves and moves 
involving minimization employ the standard ACE energy routines and thus 
calculate the ACE energy exactly.

     The following optional parameters are associated with Spatial Averaging 
simulations (SA-MC), see the detailed section below for more details.

     SAMC         Keyword enabling the use of the SA-MC algorithm.

     UNB          Keyword enabling storage of the unbiasing factor.

     IUNB         The unit of the file to which the unbiasing factor is stored.
                  (1 column text file previously opened by the user).



File: mc -=- Node: Examples
Up: Top -=- Next: SA-MC simulations -=- Previous: Description


                   EXAMPLE OF A STANDARD MC SIMULATION

     No special actions must be taken during PSF generation to run an MC 
simulation.  Essentially, input files set up for dynamics can be turned into 
MC input files by replacing the DYNAmics call with a series of MOVE ADD calls 
(or a MOVE READ call) followed by a MC call.  For example, to simulate a 
peptide in water, one could add to the CHARMM script:

           .
           .
           .
      
     ! Standard PSF generation and coordinate input above

     ! Create the MC move set
     ! Allow waters to move by rigid translations and rotations.
     ! Allow anisotropic optimization of the volume from which the 
     !     translation vectors are chosen.
     MOVE ADD MVTP RTRN BYREsidue WEIGht 2.0 DMAX 0.10 SELE (TYPE OH2) END -
              ARMP 0.2 ARMA 0.8 ARMB 0.1 DOMCF 2.0 ANISo 1
     MOVE ADD MVTP RROT BYREsidue WEIGht 2.0 DMAX 30.0 SELE (TYPE OH2) END -
              ARMP 0.2 ARMA 0.8 ARMB 0.1 DOMCF 2.0 ANISo 0
     ! Allow all torsions to move by simple rotations
     MOVE ADD MVTP TORS WEIGht 0.1 DMAX 30.0 FEWEr 1 -
              SELE ALL END SELE ALL END 
     ! Allow the backbone to move by concerted rotations with non-rotatable
     ! peptide bonds and N-CA proline bonds.  If disulfides are present, the 
     ! cysteine phi and psi should be restricted too.
     MOVE ADD MVTP CROT WEIGht 0.5 DMAX 10.0 NLIMit 1 LABEL PEPTide -
              SELE ((TYPE N).OR.(TYPE CA).OR.(TYPE C)) END -
              SELE (TYPE C) END  SELE (TYPE N) END -
              SELE (RESNAME PRO .AND. TYPE CA) END -
              SELE (RESNAME PRO .AND. TYPE  N) END 

     ! Seed the generator (for this example, this could be done below)
     MC ISEEd 391004

     OPEN WRITE UNFOrmatted UNIT 32 NAME example.trj
     ! Do 20000 steps at 300 K, writing energy 100 steps. 
     ! Update the non-bonded list every 200 and 
     !     the maximum displacements every 5 picks of that move instance
     MC IACCept 0 NSTEp 20000 TEMP 300 -
        INBFrq 200 IECHeck 400 IMGFrq 400 IDOMcfrq 10 -
        IUNC 32 NSAVc 100

     In this example, there are four groups of move instances (one for 
each MOVE ADD call).  

     It should be mentioned that it is also possible to use moves in MC 
apart from those which can be generated by MOVE ADD since the MOVE READ 
command does not do any checking as it reads in the necessary move set 
information.  For example, it is straightforward to make rigid rotations 
around a pseudo-dihedral simply by changing the pivot and moving atom lists
of a dihedral rotation.  An understanding of the following section 
(Data Structures) will aid in manual move creation.

                      GRAND CANONICAL SIMULATIONS

Some additional actions are necessary for grand canonical Monte Carlo
simulations.

     Grand canonical atoms are designated as active through the GCMCon
array, which can be manipulated with the SCALAR command.  A value 
of 1 indicates that an atom is active and a value of 0 indicates
that an atom is inactive.  It is suggested that there be roughly twice
as many grand canonical molecules as anticipated will be active on
average to accomodate fluctuations.

     Atoms that block grand canonical insertions in the cavity-based
schemes described above are also initialized through a SCALAR array,
GCBLocker.  A value of 1 indicates that an atom is a blocker, and 
a value value of 0 indicates that it is not.  Time can be saved by
excluding hydrogens.

           .
           .
           .
      
     ! Generate PSF allowing for extra molecules.
     READ SEQUENCE TIP3 432
     GENERATE MAIN SETUP NOANGLE NODIHEDRAL

     ! Read coordinates of starting structure (216 molecules here).  
     OPEN READ CARD UNIT 1 NAME tip216.crd
     READ COOR CARD UNIT 1
     CLOSE UNIT 1

     ! Copy coordinates to uninitialized atoms.  This is important for
     ! molecular liquids to define the internal structure.
     COOR DUPLicate SELEct IRES 1:216 END SELEct IRES 217:432 END

     ! Set the active and blocking atoms
     SCALar GCMC      SET 1.0 SELEct IRES   1:216 END
     SCALar GCMC      SET 0.0 SELEct IRES 217:432 END
     SCALar GCBLocker SET 1.0 SELEct TYPE OH2     END
     ENERGY

     ! Create the MC move set
     ! Rigid translations
     MOVE ADD MVTP RTRN BYREsidue WEIGht 1.0 DMAX 0.25 -
              SELE (TYPE OH2) END LABEl DISP
     ! Rigid rotations
     MOVE ADD MVTP RROT BYREsidue WEIGht 1.0 DMAX 30.0 -
              SELE (TYPE OH2) END LABEl ROTA
     ! Insertion and deletion
     MOVE ADD MVTP GCMC WEIGht 1.0 SELE (TYPE OH2) END LABEl GCMC

     ! Link the GCMC moves to the rotations and displacements to avoid moving
     ! inactive molecules.
     MOVE LINK GCMC LAB1 GCMC LAB2 DISP
     MOVE LINK GCMC LAB1 GCMC LAB2 ROTA

     ! Link the translations and rotations to each other for greater efficiency
     MOVE LINK      LAB1 DISP LAB2 ROTA

     OPEN WRITE UNFOrmatted UNIT 32 NAME gcmc.trj
     ! Do 1000000 steps at 298 K, writing energy 1000 steps. 
     ! Grid-based insertions with 10 attempted orientations are used.
     MC NSTEp 1000000 TEMPerature 298.0 ISEEd 302430 -
        INBFrq 100 IECHeck 1000 IMGFrq 100 IUNC 32 NSAVc 1000 -
        MUEX -5.8 DENS 0.03342 -
        RGRId 0.25 GCCUt 2.5 NOTB 10 -
        XMIN -18.856 YMIN -18.856 ZMIN -18.856 -
        XMAX  18.856 YMAX  18.856 ZMAX  18.856 

     The trajectory saved contains all of the grand canonical molecules.
The inactive coordinates are set to the initialization flag (9999.0D0) before 
being written.  When using the trajectory file, read the trajectory and then 
delete the inactive molecules:  

     DELEte ATOM SELEct .BYRES. PROP X .GT. 9998.0 END

The list of active atoms is common, and thus GCMC can be combined readily with
other CHARMM features such as dynamics.  In addition, it is worth noting that
the marriage of GCMC and images is not an entirely happy one; errors arising
from insufficiently frequent image updates will be minimized by making the
region in which insertion is allowed well within the primary system.



File: mc -=- Node: SA-MC simulations
Up: Top -=- Next: Data Structures -=- Previous: Examples


                      SPATIAL AVERAGING SIMULATIONS

     Spatial averaging (SA-MC) is an efficient algorithm dedicated
to the study of rare-event problems: at the heart of this method is the 
realization that from the equilibrium density a related, modified probability 
density candidate can be constructed through a suitable transformation. This new 
density is more highly connected than the original density which increases the 
probability for transitions between neighboring states which in turn speeds up
the sampling. Practically, several new configurations are generated at each step
as following :

(1) Starting from a trial configuration X_0 of the system, a Gaussian distribution
of MEPSilon sets of NEPSilon configurations with standard deviation WEPSilon, 
centered around X_0 is generated.

(2) The randomly chosen MC MOVE --- such as translation or rotation --- is then
applied to all MEPSilon*NEPSilon configurations and the corresponding energies 
are estimated.

(3) A modified acceptance criterion (see Refs) is calculated by using those 
energies.

So SA-MC uses a biased acceptance criterion: if the user is interested in some 
thermodynamic properties the results have to be unbiased. Two optional parameters 
(LUNB and IUNB) are used for storing in a given text file an unbiasing ratio which 
can be used in a later post processing and unbiasing step (see SA-MC reference below).

     Enabling SA-MC is a two steps procedure: first, for all or some of the move 
instances in the input file, the user can enable SA-MC by adding the SAMC keyword, 
and then give a value for WEPSilon (Gaussian width), MEPSilon (number of sets) and 
NEPSilon (number of configurations):

           .
           .
           .
      
! Create the MC move set by a series of calls to MOVE ADD
MOVE ADD MVTP RTRN BYATom WEIGht 1.0 DMAX 0.15 LABEL TR -
    ARMP 0.40 ARMA 0.4 ARMB 0.4 DOMCf 3.0 -
    SAMC WEPS 0.5 MEPS 10 NEPS 10 -
    SELE ALL END

MOVE ADD MVTP TORS WEIGht 1.0 DMAX 25.0 FEWEr 1 LABEL DIHE -
    ARMP 0.20 ARMA 0.4 ARMB 0.4 DOMCf 5.0 -
    SAMC WEPS 0.25 MEPS 5 NEPS 5 -
    SELE ALL END SELE ALL END

           .
           .
           .

     Then on the main "MC [...]" command line the user needs to set the 
IACCept parameter to 4, and to add the SAMC keyword once more time. If the UNB 
keyword is also added, unbiasing data is stored in the unit file IUNB 
(note that this unit has to be opened before, see the following example):

           .
           .
           .
           
OPEN WRITE UNFOrmatted UNIT 2  NAME test.dcd
OPEN WRITE FORMatted   UNIT 10 NAME unbiasing.dat

MC TEMPerature 300.0 NSTEps 1000 IECHeck 1 IACC 4 PICK 0 -
    ISEED 9921142 222455522 11142255 6221444 -
    IUNCrd 2 NSAVc 1 ACECut 0.0 -
    IDOM 10 -
    SAMC UNB IUNB 10
    
           .
           .
           .

Compatibility of the SA-MC implementation with features of the MC module (Jan. 2014):

Moves:
RTRN                    YES
RROT                    YES
TORS                    YES
CROT                    NO
HMC                     NO
VOLU                    NO
GCMC                    NO
MOVE LINK feature       NO

Move limits optimisations
ARM and DOM optim.      YES
ANISotropic optim.      NO

Ensembles :
NVT (default)           YES
NPT (with PRES)         NO
Wang-Landau             NO



File: mc -=- Node: Data Structures
Up: Top -=- Next: Shortcomings -=- Previous: SA-MC simulations


                                Data Structures

     MOVE ADD establishes each of the following pointers for all move types.
Each is a pointer to a dynamically allocated array that is n-instance elements
long, where n-instance is equal to the number of move instances in that group.
In all cases, if the array does not apply to a particular move, it is not
allocated.
     
     MDXP       This array contains the information about the limits of the
                move.  For isotropic or one-dimensional moves, it is simply
                an n-instance-long array of REAL*8 elements containing the 
                maximum displacement.  If the displacements are to be drawn 
                from an anisotropic volume, the array is a list of pointers, 
                each of which points to an array of 9 REAL*8 elements which
                make up the matrix that transforms the unit sphere into the 
                appropriate ellipsoid.

     IBLSTP     A list of n-instance pointers, each of which points to
                the list of bonded terms changing under that move instance.  
                For each element in the four-element array QBND (bonds=1, 
                angles=2, dihedrals=3, impropers=4) that is true, there is 
                an element listing the index of the final element containing
                indices of that bonded term type followed by the list of 
                terms themselves.  This list is then followed by a similar 
                one for the next bonded term type with QBND(i) set to true.  

                For example, if bonds 3, 8, and 10 and angles 16 and 17 
                were changing, the QBND array would contain (T T F F) and the 
                list would contain (4 3 8 10 7 16 17).

                Urey-Bradley terms are handled with the lists generated for
                angle terms, so do not get their own entries.

     IPIVTP     This array keeps track of any pivot or special atoms.
                If there is only one pivot atom, then it is stored in the
                array.  If there are multiple (e.g., 2 for a TORS move
                and 14 for a CROT move), the list stores a pointer to 
                a list containing the pivot atoms.

     IMVNGP     This array contains a compact list of the moving atoms.
                Each element contains a pointer to a list of the following
                form.  The first element in the list is 1 more than the 
                number of rigid groups (NG).  Elements 2 to NG contain the
                index of the last array element with information about that
                rigid group.  The atoms in a rigid group are stored as 
                the first and last atoms in a contiguous range of atom indices.

     In addition, it is worth commenting on the CHARMM fixed atom list (IMOVE)
here.  MC does NOT use the fixed atom list in selecting atoms to move; rather,
atoms are held in place by judicious construction of the move set.  However, 
CONS FIX can be used to save memory because MC constructs the symmetrized 
non-bonded list that it uses for energy calculations from the standard (upper
triangle) non-bonded list.  Care must be exercised when using this feature to
avoid errors arising from moving atoms in the fixed atom list since no checking
is done.



File: mc -=- Node: Shortcomings
Up: Top -=- Next: References -=- Previous: Data Structures


                                Shortcomings

     In the interest of computational efficiency, Monte Carlo calls specific
energy routines directly, rather than through the main ENERGY routine.  As a
result, not all energy terms are supported.  Those that are supported are
bonds, angles, Urey-Bradley, dihedrals, impropers, vdw, electrostatic, 
image vdw, image electrostatic, QM/MM (MOPAC only), path integral, asp-EEF1, 
asp-ACE/ACS, NOE constraints, and user (also note that the user must edit 
both usersb.src and mcuser.src for the user energy to work correctly).  All 
non-bonded calculations can be either atom- or group-based.  Terms not listed 
above are not included in the present implementation.

Only atom-based non-bonded lists can be used in grand canonical simulations.

     No warnings are printed for attempts to move a bonded (or patched)
residue by rigid translation and rotation.

     Attempts to move cross-linked residues will break MOVE ADD if 
MVTP is CROT.  If there is a large drift in the bond energies when
bonds lengths and angles are fixed, it is probably because a non-rotatable
bond (for example, the N-CA bond in proline) is being rotated by CROT.
Someday, a flag might be provided to choose between automatic elimination 
of such moves and CROT-type relaxation of the cross-link (correct Jacobian 
weighting is necessary to meet the detailed balance condition in the latter),
but such a flag is not on the immediate agenda of the MC developer.




File: mc -=- Node: References
Up: Top -=- Previous: Shortcomings



                                REFERENCES

All studies that employ the MOVE and MC commands should reference:

Hu, J., Ma, A. and Dinner, A. R. (2006) Monte Carlo simulations of 
     biomolecules: The MC module in CHARMM. J. Comp. Chem. 27, 203-216.


In addition, studies that employ the CROT moves should reference:

Dinner, A. R. (2000) Local deformations of polymers with nonplanar rigid 
     main chain internal coordinates.  J. Comp. Chem., 21, 1132-1144.


Grand canonical simulation studies should reference:

Woo, H.-J., Dinner, A. R. and Roux, B. (2004) Grand canonical Monte Carlo
     simulation of water in protein environments.  J. Chem. Phys., in press.


Studies that employ the momentum-enhanced hybrid MC should reference:

Andricioaei, I., Dinner, A. R. and Karplus, M. (2003) Self-guided enhanced 
     sampling methods for thermodynamic averages. J. Chem. Phys., 118, 
     1074-1084.


Studies that employ Wang-Landau MC should reference:

Ma, A., Nag, A. and Dinner, A. R. (2006) Dynamic coupling between coordinates
in a model for biomolecular isomerization. J. Chem. Phys. 124, 144911.

Calvo, F. (2002) Sampling along reaction coordinates with the Wang-Landau
method. Mol. Phys. 100, 3421-3427.

Wang, F. and Landau, D. P. (2001) Efficient, multiple-range random walk 
algorithm to calculate the density of states. Phys. Rev. Lett. 86, 2050-2053.


Studies that employ SA-MC should reference:

Doll, J. D., Gubernatis, J. E., Plattner, N., Meuwly, M., Dupuis, P., Wang, H. (2009)
A spatial averaging approach to rare-event sampling. J. Chem. Phys., 131

Plattner, N., Doll, J. D., Meuwly, M. (2010) Spatial averaging for small molecule 
diffusion in condensed phase environments. J. Chem. Phys., 133 .

Hedin, F., Meuwly, M., Plattner, N., Doll, J. D. (2014) Spatial Averaging: Sampling 
Enhancement for Exploring Configurational Space of Atomic Clusters
and Biomolecules. JCTC, DOI: 10.1021/ct500529w


The following references may also be of interest:

Andricioaei, I. and Straub, J. (1997) On Monte Carlo and molecular dynamics
     methods inspired by Tsallis statistics:  Methodology, optimization, and
     application to atomic clusters.  J. Chem. Phys. 107, 9117-9124.

Andricioaei, I. and Straub, J. (1996) Generalized simulated annealing
     algorithms using Tsallis statistics:  Application to conformational 
     optimization of a tetrapeptide.  Phys. Rev. E 53, R3055-R3058.

Berg, B. A. and Neuhaus, T. (1992) Multicanonical ensemble:  A new approach 
     to simulate first-order phase transitions.  Phys. Rev. Lett. 68, 9-12.

Bouzida, D., Kumar, S. and Swendsen, R. H. (1992) Efficient Monte Carlo
     methods for the computer simulation of biological molecules.  
     Phys. Rev. A 45, 8894-8901.

Dodd, L. R., Boone, T. D. and Theodorou, D. N. (1993) A concerted 
     rotation algorithm for atomistic Monte Carlo simulation of polymer 
     melts and glasses.  Mol. Phys. 78, 961-996.

Duane, S., Kennedy, A. D., Pendleton, B. J. and Roweth, D. (1987) Hybrid 
     Monte Carlo.  Phys. Lett. B 195, 216-222.

Eppenga, R. and Frenkel, D. (1984) Monte Carlo study of the isotropic and
     nematic phases of infinitely thin hard platelets.  Mol. Phys. 52, 
     1303-1334.

Go, N. and Scheraga, H. A. (1970) Ring closure and local conformational
     deformations of chain molecules.  Macromolecules 3, 178-187.

Leontidis, E., de Pablo, J. J., Laso, M. and Suter, U. W. (1994)
     A critical evaluation of novel algorithms for the off-lattice Monte Carlo 
     simulation of condensed polymer phases.  Adv. Polymer Sci. 116, 285-318.

Lee, J. (1993) New Monte Carlo algorithm:  Entropic sampling.  
     Phys. Rev. Lett. 71, 211-214.

Li, Z. and Scheraga, H. A. (1987) Monte Carlo-minimization approach to the 
     multiple-minima problem in protein folding.  Proc. Natl. Acad. Sci. USA
     84, 6611-6615.

Mehlig, B., Heermann, D. W. and Forrest, B. M. (1992) Hybrid Monte Carlo 
     method for condensed-matter systems.  Phys. Rev. B 45, 679-685.

Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and
     Teller, E. (1953) Equation of state calculations by fast computing
     machines.  J. Chem. Phys. 21, 1087-1092.

Mezei, M. (1980) A cavity-biased (T, V, mu) Monte Carlo method for the
     simulation of fluids.  Mol. Phys. 40, 901-906.

Mezei, M. (1987) Grand-canonical ensemble Monte Carlo study of dense liquid
     Lennard-Jones, soft spheres and water.  Mol. Phys. 61, 565-582.

Okamoto, Y. and Hansmann, U. H. E. (1995) Thermodynamics of helix-coil 
     transitions studied by multicanonical algorithms.  J. Phys. Chem. 99,
     11276-11287.

Schaefer, M. and Karplus, M. (1996) A comprehensive analytical treatment of
     continuum electrostatics.  J. Phys. Chem. 100, 1578-1599.

Tsallis, C. (1988) Possible generalization of Bolzmann-Gibbs statistics.
     J. Stat. Phys. 52, 479-487.

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