1.  Gibbs

           Usage: gibbs [gibfile] [-O] -i gibin -o gibout
                             -p prmtop -c inpcrd -r restrt
                             -ref refc -x mdcrd -v mdvel -e mden
                             -inf mdinfo -ms micstat
                             -cm constmat -cs cnstscrt -a patnrg

      -O   Overwrite output files.

      1.1.  Introduction

           This  is a guide to gibbs, the AMBER module concerned with
      free energy calculations.  This module of the  AMBER  suite  of
      programs  calculates the free energy difference, G, between two
      states "0" and "1":

                                  G=G1-G0                         (1)

           In the prep/link/edit/parm modules, State 1 is defined  in
      the  PREP module and State 0 is defined in the PARM module.  In
      LEaP, State 1 is the default state and State 0  is  defined  by
      setting  the  perturbed  atom  parameters in the "Edit selected
      atoms" table in the xleap Unit Editor and using the  saveAmber-
      ParmPert  command to make the topology and coordinate files. In
      both types of setup, all the force field and topology  informa-
      tion for States 1 and 0 is contained in the topology file.

           The  free  energy  difference is calculated in a series of
      incremental steps which connect physical states 1 and 0 through
      a series of not-necessarily-physical intermediates. The charac-
      ter of the system  at  each  of  these  intermediate  steps  is
      related to a parameter lambda.

      1.2.  Free Energy Techniques Available in GIBBS

           There  are several techniques available in GIBBS/AMBER 4.0
      for evaluating the free energy difference between  two  states,
      all  based  on  various  statistical  mechanical relationships.
      These include:


       (1)   Free Energy Perturbation (FEP) Window Growth:  The  free
             energy  is  calculated  at discrete and uniformly spaced
             intervals of lambda using the formulae:

               G(i+1)-G(i)=-RTln<exp-[(V(i+1)-V(i))/RT]>(i)       (2)

                           G=G1-G0=iG(i+1)-G(i)                   (3)

             where G0 and G1 are the free energies of states 0 and 1,
             respectively,  Vlambda(i)  is the potential energy func-
             tion representative of state lambda (i), and <>lambda(i)
             means use the ensemble average of the enclosed quantity,
             representative of state lambda  (i).   The  ensemble  is
             evaluated  from an MD trajectory run with V = Vlambda(i)
             The user specifies the numbers of  equilibration  (NSTPE
             or  NSTMEQ)  and data collection (NSTPA or NSTMUL) steps
             for each lambda (i)->lambda (i+1) "window".

       (2)   Slow growth - the same as window growth,  except  lambda
             changes  by a small amount at every step. Lambda changes
             slowly enough that it is assumed the system  remains  in
             equilibrium  at every step (i.e. NSTPE=0, NSTPA=1). Thus
             the ensemble average in Equation (2) is replaced by  its
             instantaneous value at each step.

       (3)   Thermodynamic integration - instead of Equations (2) and
             (3), we use

                               G1-G0=0<V/>d                       (4)

             to calculate the free energy  difference.  In  practice,
             the  integral  is  approximated by a summation over dis-
             crete intervals in  lambda.   Thermodynamic  integration
             can use the particle-mesh-Ewald method of handling long-
             range interactions.  This option  is  discussed  in  the
             sander section of the manual.

       (4)   Dynamically  Modified  Windows - the equations of FEP (2
             and 3) are used as described for method  1  above.   But
             instead  of  using pre-chosen uniformly-spaced intervals
             of lambda, the width (delta  lambda  =  lambda  (i+1)  -
             lambda  (i)  )  of  each window is determined during the
             run, based on the recent value of the slope, partial G /
             partial  lambda,  of  the accumulated free energy versus
             lambda curve.  This allows the simulation to be run more
             "slowly"  when the free energy is changing very quickly,
             and more "quickly" when it is not.

       (5)   Dynamically Modified Thermodynamic  Integration  -  Uses
             the  same lambda adjustment algorithm as for FEP (method
             4), but the intervals in  correspond to  the  points  at
             which  the  integrand  in  Equation  (4) is evaluated to


             approximate the integral.

       (6)   Potential of Mean Force (PMF) Calculations  -  the  user
             can elect to constrain any chosen set of internals (dis-
             tances, angles, torsions) to a  chosen  lambda-dependent
             pathway.  By selecting the appropriate option (NCORC=1),
             the contribution to  the  free  energy  from  such  con-
             straints will be calculated. This constitutes a PMF cal-
             culation. PMF calculations can be carried out as part of
             either  a FEP Window Growth or Dynamically Modified Win-
             dows run (1 and 3 above).

      1.3.  Understanding the Output

           (a) Window growth, slow growth, dynamically modified  win-
      dows:  At  specified intervals during the simulation, the ener-
      gies calculated up to that point will be reported in  the  for-
      mat:

            Current Lambda =   0.850000
            Last F.E. update: Lambda =   0.800000  Step =    4000  Method = F.E.P.
            Accumulated "forward" quantities (Nonbond change)
               Lam+d_lam = 0.850000    F_energy  =   +0.64300
               ELEC =      0.000    NONB =     +0.643    14NB =      0.000
               14EL =      0.000    BADH =      0.000
            Accumulated "reverse" quantities (Nonbond change)
               Lam-d_lam = 0.750000    F_energy  =   -0.62130
               ELEC =      0.000    NONB =     -0.621    14NB =      0.000
               14EL =      0.000    BADH =      0.000

           When  the  free  energies  reported were last updated, the
      values of lambda and step number were as given  on  the  second
      line.  Note  that  the current values of lambda and Step may be
      different, if the free energies have not yet  been  updated  to
      reflect the ensemble now being generated.  Also reported on the
      second line is the method being used to calculate  free  energy
      differences:  F.E.P.   is Free Energy Perturbation (standard or
      Dynamically Modified Windows); T.I. is  Thermodynamic  Integra-
      tion (standard or Dynamically Modified Windows); Slow Growth is
      self explanatory.

           Both "forward" and "reverse" accumulated free energies are
      reported. By default, GIBBS carries out "double-wide sampling",
      which means that at every value of lambda we calculate the free
      energies  both  for going lambda->lambda + delta lambda and for
      going lambda->lambda - delta lambda.   The  values  "Lam+d_lam"
      and  "Lam-d_lam" which are reported were the values at the last
      free energy update.  If there were no sampling  errors  in  our
      calculations,   the  independent  sums  of  the  "forward"  and


      "reverse" values over the entire simulation would be the  same,
      except for sign. Their actual difference gives us a lower bound
      on the error. By convention, the "forward" energy always corre-
      sponds  to  the  energy  for  the process represented by lambda
      increasing 0->1.  Similarly, the "reverse"  energy  corresponds
      to  the  process represented by lambda decreasing 1->0. This is
      true regardless of the direction in which the actual simulation
      was run..

           Along  with  the  total  accumulated  free energies in the
      "forward" and "reverse" directions, a  component  breakdown  of
      the  energies is given.  Components listed include: ELEC (elec-
      trostatics, except 1-4's); NONB (non-bonds, except 1-4's); 14NB
      (1-4  nonbonds);  14EL  (1-4  electrostatics)  and BADH (bonds,
      valence angles and torsion angles).  Note that for Windows  and
      Dynamically  Modified  Windows, these components are only esti-
      mates. For slow growth and thermodynamic integration, they  are
      exact.

           If  PMF calculations are performed, a sixth component will
      be listed, CORC.  The procedure used to perform a PMF makes  it
      difficult  to  separate  contributions  due  to the constraints
      themselves from those due to non-bonded/electrostatic  interac-
      tions.  For  this  reason, in these cases CORC will reflect the
      sum total of all three types of contributions and the  individ-
      ual  non-bonded/electrostatic contributions will be reported as
      0's.

           (b) Thermodynamic integration: The output  is  similar  to
      that  described  above,  except  that,  because of the integral
      which must  be  evaluated  in  thermodynamic  integration  (TI)
      (Equation  4), double-wide sampling is not possible. Thus, only
      a "forward" set of energies is reported. Again, by  convention,
      these  value have the sign appropriate for the 0->1 conversion,
      regardless of the direction in which the simulation  was  actu-
      ally run.

           If  the calculation of individual entropy/enthalpy contri-
      butions is requested, these will also be included in  the  out-
      put, following the same forward/reverse conventions as above.

      1.4.    Defining  States  and  Obtaining  Appropriate  Starting
      Coordinates

           Using the "old"  AMBER  (prep/link/edit/parm),  the  state
      defined  in  PREP  is the lambda=1 state and the state given in
      the PARM is the lambda=0 state.  Using LEaP, the default  state
      is  lambda=1 and the state set in the xleap Unit Editor's "Edit
      selected atoms" table is lambda=0.

           The default state from which to start the perturbation  is
      usually  lambda=1,  because  the  coordinates which are carried


      from EDIT to PARM to SANDER to GIBBS  correspond  to  the  PREP
      state.   However,  you  can  equilibrate  at either lambda=1 or
      lambda=0 (or any arbitrary value of lambda) as follows:

           Set ISLDYN (line 14) to +-2 or +-3;
           Set NRUN (line 5) to 1;
           Set NSTLIM (line 8) to the number of steps  of  equilibra-
           tion desired;
           Set  ALMDA (line 14) to the value of lambda at which equi-
           libration is to take place;
           And set NSTMEQ (line 14) to any value greater than NSTLIM.

           The  program is capable of handling periodic boundary con-
      ditions with the solute in a solvent bath either with  constant
      volume  or constant pressure.  All the data required for bound-
      ary conditions is passed from the EDIT and PARM modules.  Addi-
      tionally, it is possible to decouple the free energy into elec-
      trostatic and van der Waals contributions, if desired.


      1.5.  Suggested introductory references

           The papers listed here emphasize the theory and experience
      with  the  AMBER programs; beyond listing "general reviews", we
      have not attempted to list the many other papers that would  be
      relevant to the field.

                             General Reviews:

       (1)   D.L. Beveridge and F.M. Di Capua (1989) "Free Energy Via
             Molecular  Simulation:  Applications  to  Chemical   and
             Biomolecular Systems."  Annu. Rev. Biophys. Biophys. 18,
             431-492.

       (2)   P.A. Kollman (1993) "Free Energy Calculations:  Applica-
             tions  to  Chemical  and  Biochemical Phenomena."  Chem.
             Rev. 93, 2395-2417.

             Discussion of issues pertinent to free energy perturbation:

       (3)   D.A. Pearlman and P.A. Kollman (1989) "Free Energy  Per-
             turbation  Calculations: Problems and Pitfalls Along the
             Gilded Road." In: Computer  Simulation  of  Biomolecular
             Systems:  Theoretical  and Experimental Applications (W.
             van Gunsteren and P.K. Weiner, eds.), pp. 101-119, Escom
             Science Publishers, Netherlands.

       (4)   W.F.  van  Gunsteren,  "Methods  for Calculation of Free
             Energies and Binding Constants: Successes and Problems,"
             ibid, pp.27-59.

       (5)   D.A.  Pearlman  and P.A. Kollman (1989) "The Lag Between
             the Hamiltonian and the  System  Configuration  in  Free
             Energy  Perturbation  Calculations."  J. Chem. Phys. 91,
             7831-7839.

       (6)   D.A. Pearlman and P.A. Kollman  (1991)  "The  Overlooked
             Bond-Stretching Contribution in Free Energy Perturbation
             Calculations." J. Chem. Phys. 94, 4532-4545.

       (7)   D.A. Pearlman (1994) "Free  energy  derivatives:  A  new
             method  for  probing  the  convergence  problem  in free
             energy calculations.", J. Comp. Chem. 15, 105-123.

       (8)   D.A.  Pearlman  (1994)  "A  comparison  of   alternative
             approaches to free energy calculations.", J. Phys. Chem.
             98, 1487-1493.

       (9)   R.J. Radmer and P.A. Kollman (1997) "Free energy  calcu-
             lation  methods:  A theoretical and empirical comparison
             of numerical errors and a  new  method  for  qualitative
             estimates  of  free energy changes."  J. Comp. Chem. 18,
             902-919.


                            Some Recent Applications:

       (10)  D.A.Pearlman and P.R. Connely  (1995)  "Deterimation  of
             the  Differential  Effects of Hydrogen Bonding and Water
             Release on the Binding  of  FK506  to  Native  and  Y82F
             FKBP-12  Proteins  Using  Free  Energy Simulations.", J.
             Mol. Biol. 148, 696-171.

       (11)  J.L. Miller and  P.A.Kollman,  (1996)  "Solvation  Freen
             Energies  of  the  Nulceic  Acid Bases.", J. Phys. Chem.
             100, 8587-8594.

       (12)  E.C. Meng,  J.W.  Caldwell,  and  P.A.  Kollman,  (1996)
             "Investigating the Anomalous Solvations Free Energies of
             Amines with a Polariazable Potential.", J.  Phys.  Chem.
             100, 2367-2371.

             Description and characterization of dynamically modified windows:

       (13)  D.A.  Pearlman and P.A. Kollman (1989) "A New Method for
             Carrying  Out  Free  Energy  Perturbation  Calculations:
             Dynamically   Modified  Windows."  J.  Chem.  Phys.  90,
             2460-2470.

                           Use of internal constraints:

       (14)  D.J. Tobias  and  C.L.  Brooks,  III  (1988)  "Molecular
             Dynamics with Internal Coordinate Constraints." J. Chem.
             Phys. 89, 5115-5127.

       (15)  D.A. Pearlman (1993) "Determining the  contributions  of
             constraints  in  free  energy calculations: Development,
             characterization, and recommendations", J.  Chem.  Phys.
             98, 8946-8957.

                       Generating potentials of mean force:

       (16)  D.A.  Pearlman  and  P.A. Kollman (1991) "Evaluating the
             Assumptions  Underlying  Force  Field  Development   and
             Application,  Using  Free Energy Conformational Maps for
             Nucleosides."  J. Am. Chem. Soc. 113, 7167-7177.

       (17)  C. Chipot, P.A. Kollman and D.A. Pearlman (1996) "Alter-
             native  approaches  to  potential of mean force calcula-
             tions: free  energy  pertubation  versus  thermodynamics
             integration.  Case study of some representative nonpolar
             interactions", J. Comp. Chem. 17, 1112-1131.

             In addition, it is strongly suggested that the user read
             the  discussion  which  follows  the  description of the
             input variables before using GIBBS.


      1.6.  Assigning files

           GIBBS incorporates a file  assignment  protocol  which  is
      easy to use, and which will work on all computers. In addition,
      on Unix machines, file assignments can optionally be  specified
      using flags on the command line, as in version 3A.

           For Unix machines, the program is invoked:

                 gibbs [gibfile] [-O] [-i PIN] [-p PPARM] [-c PINCRD]
                           [-o POUT] [-r PREST] [-inf PINFO] [-ms MICSTAT]
                           [-cm CONSTMAT] [-cs CNSTSCRT] [-a PATNRG]
                           [-x PCOORD] [-v PVEL] [-e PEN] [-ref PREFC]

      where  PIN,  PPARM,  etc. are replaced by the appropriate file-
      names to be assigned. The meanings of  the  various  files  are
      given below.

           If  "gibfile"  is  present,  it  must  be the first option
      given, and this file will be read to make the file assignments.
      In  this  case, any remaining flags are ignored. Otherwise, all
      assignments are made using command-line flags.  Any  flags  not
      specified  default  to the given name (e.g. if -o is not speci-
      fied, output would be in file POUT).

           For other machine types (and if gibfile is given on a Unix
      machine),  file  assignments  are  read at run-time from a file
      named "GIB.FILE" (non-Unix machines) or the file  specified  as
      "gibfile" (Unix machines).  GIB.FILE contains file assignments,
      one per line, in the following format:

             Filetype = Filename

      "Filetype" is the type of file, from the list of GIBBS I/O file
      assignments  listed  below. It must be given in upper case let-
      ters. Filename is the actual name to be used  in  opening  that
      file. E.g.

             POUT = test.out

      would  place  the  results  and  diagnostics  in  a  file named
      test.out.  The order in which files are defined is  not  impor-
      tant.  Any line that does not contain the "=" character will be
      considered a blank line.  The GIB.FILE file is opened and  read
      when the run is commenced, and then closed. Once the file defi-
      nitions have been read, the user is free to discard  or  change
      the GIB.FILE file (to e.g. start up a second Gibbs run).


                      +-----------------------------+
                      |GIBBS  I/O  FILE ASSIGNMENTS |
                      +-----------------------------+

           __________________________________________________________

            file    unit    purpose

           INPUT:

            PIN        5    Control data for the run (described below).

            PPARM      8    Topology file (created by PARM)

            PINCRD     9    Initial positions and (optionally) velocities.

            PREFC     10    Reference coordinates for optional position
                            restraints (only if NTR = 1)

           OUTPUT:

            POUT       6    Formatted results and diagnostics

            PREST     16    Restart coordinates and velocities.
                            For restarts, this file should be assigned to PINCRD.

            PINFO      7    Short file containing a summary of current energies.
                            For monitoring runs which are executing.

            MICSTAT   27    A concise summary of important energy information
                            for each window/interval.

            CONSTMAT  28    Contains data related to the matrix of free
                            energy data generated. Only used when IPER>0 for
                            one or more of the constraints/restraints defined
                            with INTR > 0 (see line 13).

            CNSTSCRT  42    Contains data required when generating
                            a matrix of free energies corresponding to two
                            independent sets of constraints (IPER>0 and INTR>0;
                            see line 13).

            PCOORD    12    Archived coordinate sets (if NTWX > 0)

            PVEL      13    Archived velocity sets (if NTWV > 0)

            PEN       15    Archived energy related data (if NTWE > 0)


      1.7.  Control parameters

           The  title  (line  1)  must  be the first line in PIN. All
      remaining standard flags are entered in the namelist &cntrl.

      TIMLIM      Time limit for the job  (in  seconds).   Default  =
                  999999.

      IREST       Flag to restart the run.

                     = 0   Normal start (default)

                     = 1   Job  to be restarted. The accumulated free
                           energies, current  value  of  lambda,  and
                           other  required  quantities  are read from
                           the end of the input coordinate file (PIN-
                           CRD).  This  file should be the PREST file
                           written by the simulation being restarted.

      IBELLY      Flag for belly type dynamics.

                     = 0   No  belly  run   (allow all atoms to move;
                           default).

                     = 1   Belly run.  The subgroups of  atoms  which
                           are  allowed  to  move  are read as groups
                           from file PIN.  See the section  on  GROUP
                           in the Appendices.

      ICHDNA      Option to modify the charge of end hydrogens during
                  in vacuo simulations.  Without this option, molecu-
                  lar   dynamics  calculations  on  nucleotides  will
                  result in bonding between the 5' and  3'  hydrogens
                  and the corresponding phosphate groups.

                     = 0   no charge modification (default)

                     = 1   modify charge

      IPOL        for  inclusion  of  polarizabilities  in  the force
                  field.

                     = 0   non polar calc (no  polarizabilities  read
                           from "prmtop"; default).


                     = 1   turn on polarization calculation.

      I3BOD       For 3-body terms with a polarization calc.

                     = 0   No 3-body terms to be defined.  Default.

                     = 1   Read  and  use  3-body interaction defini-
                           tions (see card 18).   3-Body  terms  only
                           have an effect when polarization is turned
                           on (IPOL=1).

      IEWALD      Set to 1 to invoke particle-mesh-Ewald  evaluation.
                  This  requires  additional lines of input after the
                  &cntrl  namelist.   See  the  sander  module  input
                  description  for  more  information.  Default is 0,
                  which disables the PME code.   PME  requires  extra
                  input  in  order  to  control the simulation. As in
                  sander, this input, consisting of  three  lines  of
                  free  format  numerical  input (not namelist input)
                  palced just after the regular namelist  and  before
                  any weight change information.

           LINE 1  Unit Cell parameters: BOXX,BOXY<BOXZ,ALPHA,BETA,GAMMA

                   BOXX,BOXY,BOXZ unit cell boxlengths in each dimension.

                   ALPHA,BETA,GAMMA unit cell angles, in usual crystallographic
                           setup. See sander documentation for more information.

           LINE 2  Interpolation and control information: NFFT1,NFFT2,NFFT3,
                   SPLINE_ORDER,ISCHARGED,VERBOSE

                   NFFT1,NFFT2,NFFT3
                           These give the size of the grid to interpolate the
                           charge onto, in each dimension. See the discussion in
                           the Sander manual

                   SPLINE_ORDER
                           Order of the spline interpolation. See the sander manual.

                   ISCHARGED
                           If ISCHARGED=0, the unit cell is neutralized by taking the
                           excess charge and spreading it uniformly across all atoms.

                           If ISCHARGED=1, a uniform neutralizing plasma is assumed.

                 Note that in Gibbs, these operations are applied to the
                           unit cell at both the beginning and ending states of the
                           perturbation. Note that in some cases the charge state of
                           unit cell may change during the simulation, such as when


                           calculating the free energy of charging an ion. In these
                           cases it is better to use ISCHARGED=1.

                   VERBOSE
                           Standard use is to set VERBOSE=0. Setting VERBOSE=1 will
                           print out direct, self, adjustment and reciprocal
                           components of the energy and virial. Setting VERBOSE=3
                           will in addition print out details of the nonbond list.

           LINE 3  The direct sum tolerance DSUM_TOL. See the discussion in Sander
                   manual.

                  Special  notes  about  the  PME  in GIBBS. (See the
                  Sander manual for additional such notes).  As  yet,
                  there is not much experience with the PME in Gibbs,
                  so it should be considered an experimental  option.
                  The  PME has only been implemented into the thermo-
                  dynamic integration module (IDIFRG=1), with the new
                  mixing  rules  (IOLEPS=0).  It has been tested only
                  with "standard" window growth  (ISLDYN  =  -3).  In
                  addition INTPRT must be >0 but not equal to 3. Thus
                  intra-pert group nonbond interactions  ARE  accumu-
                  lated.  The  PME  option  should be compatible with
                  constraint  forces  calculated  via  the  potential
                  forces  method (ITIMTH=0).  PME/gibbs will not work
                  with the 1991 force field if the  10-12  parameters
                  are changing during the perturbation.

      NTX         Option  to read the initial coordinates and veloci-
                  ties.

                           Options 1-3 are used when no set of start-
                           ing  velocities  is  available  (e.g. when
                           starting from a set of  minimized  coordi-
                           nates).   Options  4-5 are used when: 1) a
                           starting set of  velocities  is  available
                           (e.g.  after  MD equilibration or on an MD
                           RESTART); and 2)  The  coordinates/veloci-
                           ties  were  generated  with  MD run either
                           without periodic boundary  conditions,  or
                           with  constant  VOLUME  periodic  boundary
                           conditions. (Box dimensions, if  any,  are
                           taken  from  the  PARM file).  Options 6,7
                           are used  when  both  a  starting  set  of
                           velocities  are  available and the coordi-
                           nates/velocities were  generated  with  MD
                           run   using   constant  PRESSURE  periodic
                           boundary conditions.  Note: box dimensions
                           only  appear  in  coordinate files written
                           (as   PREST)   after   simulations   using


                           periodic   boundary  conditions  (constant
                           volume or constant pressure).

                     = 1   X is read; no  velocity  information  read
                           (Amber format); default

                     = 2   X  is  read;  no velocity information read
                           (unformatted)

                     = 4   X and V are read (unformatted)

                     = 5   X and V are read (Amber format)

                     = 6   X, V and BOX are read (unformatted)

                     = 7   X, V and BOX are read (formatted)

      NTXO        Option to write the final coordinates  and  veloci-
                  ties.

                     = 0   X,  V  and BOX are written to file 'PREST'
                           (unformatted)

                     = 1   X, V and BOX are written to  file  'PREST'
                           (Amber format); default.

      IG          The  seed  for the random number generator.  The MD
                  starting velocity is dependent on the random number
                  generator  seed.   The  generator works most effec-
                  tively when the seed is large and an odd or a prime
                  number (e.g. 71277, the default).

      TEMPI       Initial  temperature,  default  is 0.0.  If TEMPI >
                  1.0e-06, the velocities are taken from a maxwellian
                  distribution  with  TEMPI (K).  Choosing a low ini-
                  tial temperature (e.g. 10K) allows the  calculation
                  to reach the equilibrium conditions with the resid-
                  ual forces in the system during the initial  steps.
                  TEMPI is ignored if NTX > 3.

      HEAT        If  ABS(HEAT)  .GE. 1.0E-06, all the velocities are
                  multiplied by HEAT.  Default is 0.0.

      NTB         Flag for periodic boundary conditions.  If NTB .EQ.
                  0  then  the  boundary  conditions are NOT applied.
                  The periodic box may be rectangular  or  monoclinic


                  depending on the value of BETA.

                     = 0   no periodicity is applied; default.

                     = 1   constant volume

                     = 2   constant pressure.

      IFTRES      Flag  to  remove  the  nonbonded  cutoff  from  the
                  solute.

                     = 0   ALL solute - solute nonbonded interactions
                           are  calculated,  and  the boundary condi-
                           tions are not applied to the solute.   For
                           simulations of highly charged solutes in a
                           water bath, it can be useful to  calculate
                           ALL solute - solute nonbonded interactions
                           in order to reduce electrostatic problems.
                           Note  that  this  option  is  intended for
                           small solutes, and will generate many more
                           nonbonded  pairs than the normal method if
                           the solute is large.  This option is  use-
                           ful  for  DNA  and  counterions.  Note: if
                           counterions are added in edit,  then  they
                           are considered part of the solute.

                     = 1   Nonbondeds    are    evaluated   normally;
                           default.

                           Note: IFTRES will only have an effect when
                           periodic  boundary conditions are employed
                           (NTB > 0). When NTB=0,  IFTRES=1  behavior
                           (normal nonbond generation) always occurs.

      BOXX(1..3)  Lengths of the edges of the periodic box.  If IBXRD
                  >  0,  then the values specified here will be used.
                  Otherwise, the values specified  here  are  ignored
                  and the values in the PARM output file (if NTX < 7)
                  or the values in PINCRD (if NTX >= 7) will be used.

      BETA        Angle  between  the  x-  and  z- axes of the box in
                  degrees. The y- axis is assumed to be orthogonal to
                  the other axes. ( 0 < BETA < 180 ). The information
                  given for BOX(1..3) above applies to BETA as  well.
                  Non-orthogonal  systems  do not currently work cor-
                  rectly.  Therefore, if IBXRD > 1, BETA must be  set
                  to 90.0, which is the default.


      IBXRD       If IBXRD > 0, then the values of BOX(1..3) and BETA
                  specified here will be used. Otherwise, the  values
                  in  the  PPARM  or  PINCRD  file  will be used (see
                  above).

      NRUN        Number of MD-runs of NSTLIM steps to be  performed;
                  default  is  1.   Since the restart coordinates are
                  written only at the end of each run,  it  is  some-
                  times  desirable  to break a long run into a series
                  of shorter steps.   If NRUN is set > 1, one  should
                  ensure  that  the number of equilibration+data_col-
                  lection steps (if  performing  windows/TI)  divides
                  evenly   into  NSTLIM  (line  8).   The  number  of
                  picoseconds of molecular dynamics is equal  to  the
                  product of NRUN X NSTLIM X DT.

      NTT         Switch  for  temperature scaling. Note that several
                  of he temperature coupling options  available  here
                  are new to version 4 of GIBBS. Several of these are
                  rather ad-hoc, and may not result in a thermodynam-
                  ically relevant ensemble.  (They may be useful when
                  using MD strictly to sample conformational  space).
                  For free energy calculations, it is recommended you
                  stick with NTT = 0 (constant energy), NTT = 1 (con-
                  stant  temperature)  or  NTT = 5 (constant tempera-
                  ture, separate solute/solvent temperature scaling).

                     < 0   Re-assign  random  velocities whenever the
                           current temperature deviates by more  than
                           DTEMP  from  DTEMP0  (target temperature),
                           and every ABS(NTT) steps.  Velocities  are
                           assigned  in a Maxwellian distribution. By
                           default, velocities are are reset for  all
                           atoms. If NSEL > 0 (see below), NSEL atoms
                           are selected at random each time a  veloc-
                           ity  reassignment  is  to  take place, and
                           only those  atoms  have  their  velocities
                           reassigned.  (Be  sure  to set DTEMP0 to a
                           very large value if you  wish  to  disable
                           its action with this option).

                           Note  that  the  procedure  which  assigns
                           velocities makes the assignments as if all
                           particles   possessed   three  independent
                           degrees  of  translational  freedom.    If
                           SHAKE  is  used, this will not strictly be
                           the case, and  the  effective  temperature
                           immediately after velocity assignment will
                           be higher than the target temperature.  As
                           velocity     contributions    along    the


                           constrained directions are dissipated, the
                           temperature  will  rapidly  adjust towards
                           the target.

                     = 0   Classical dynamics. Never rescale/reassign
                           velocities  after  the  start.  [The total
                           energy (kinetic + potential) is conserved;
                           same as in older versions of GIBBS.]

                     = 1   Constant  temperature, using the Berendsen
                           coupling algorithm.  A single scaling fac-
                           tor  for  velocities  is  used (same as in
                           older versions of  GIBBS).   This  is  the
                           default.

                     = 2   Constant  temperature, using the Berendsen
                           coupling algorithm.  But only consider the
                           solute   temperature  in  determining  the
                           velocity scaling  on  each  step.    Could
                           result  in  solvent atoms having very high
                           temperature,  and  not  generally   recom-
                           mended.

                     = 3   Constant   temperature,   using  Berendsen
                           algorithm. But only rescale when  tempera-
                           ture  deviates  from  TEMP0  by  more than
                           TEMP0.  Single scaling factor.

                     = 4   When temperature deviates  from  TEMP0  by
                           more than DTEMP, do one quick scale of the
                           velocities to bring them  back  to  TEMP0.
                           Otherwise, do not scale.

                     = 5   Constant  temperature, using the Berendsen
                           coupling  algorithm,  and  with   separate
                           solute/solvent  velocity  scaling factors.
                           This option is recommended as  a  replace-
                           ment for NTT=1, and can help alleviate the
                           "cold solute/hot solvent" problem.

      TEMP0       Reference temperature at which the system is to  be
                  kept if NTT not = 0.  Default is 298.

      DTEMP       The  deviation  allowed in the constant temperature
                  MD-runs (read  but  ignored  if  NTT=0,1,2  or  5).
                  Default is 10.

      TAUTP       Temperature  relaxation time when NTT .gt. 0.  This
                  is a damping factor which prevents  abrupt  changes
                  in  the system, if the temperature exceed specified


                  deviations.  Generally, values for TAUTP should  be
                  in  the  range of 0.1-0.4.  Smaller values of TAUTP
                  result in "tighter" coupling.  Default is 0.1.

      TAUTS       If NTT=5, then TAUTP is the temperature  relaxation
                  time  for the solute, while TAUTS is the relaxation
                  time for the solvent.   If  is  specified  as  0.0,
                  TAUTS  is  set  equal  to  TAUTP.  Generally, TAUTS
                  should be in the range  of  0.1-0.4,  with  smaller
                  values   resulting   in   "tighter"  coupling.   If
                  NTT.NE.5, TAUTS is read but  ignored.   Default  is
                  0.1.

      ISOLVP      Only used if NTT = 2 or 5 (sep. solute/solvent temp
                  coupling)

                     = 0   default solvent atom pointer is  used.  If
                           periodic  boundary  conditions  are  being
                           used, this is the last solute atom.   Oth-
                           erwise,  it  will  be the last atom of the
                           system  (which  results  in  no   separate
                           solute/solvent coupling).  Note that coun-
                           terions are by default considered part  of
                           the _solute_.

                     > 0   Gives  the  number  of the last atom to be
                           considered part of  the  "solute".  ISOLVP
                           should  generally  be specified if NTT = 5
                           and NTB = 0.  ISOLVP only affects tempera-
                           ture scaling.

      NSEL        Only  used  if  NTT  < 0 (random velocity reassign-
                  ments)

                     = 0   When velocity  reassignment  takes  place,
                           velocities  for  all  atoms are reassigned
                           (default).

                     > 0   When velocity  reassignment  takes  place,
                           NSEL atoms are randomly selected, and only
                           the velocities for those atoms  are  reas-
                           signed.

      DTUSE       The  value of d_TEMP used in approximating the tem-
                  perature derivatives by finite  differences.  DTUSE
                  is  only used when individual enthalpy/entropy val-
                  ues are being calculated (ISANDE  =  1,  line  12).


                  DTUSE  should  generally  be  <= 1.0 (larger values
                  often  cause   floating   overflows/   underflows).
                  Default is 1.0.

      NTP         Flag  for  constant pressure dynamics.  This option
                  MUST be set to 1 or 2 when the  MD  calculation  is
                  done  with constant pressure periodic boundary con-
                  ditions (NTB=2, line 4).

                     = 0   Classical dynamics  without  any  Pressure
                           Monitoring (default)

                     = 1   MD with isotropic position scaling

                     = 2   MD  with  anisotropic  diagonal (x-,y-,z-)
                           position scaling

      NPSCAL      Flag for the type of scaling in  case  of  constant
                  pressure run.

                     = 0   Uniform coordinate Scaling (default)

                     = 1   Sub molecules Center of mass Scaling

      PRES0       Reference  pressure  at  which  the system is main-
                  tained (when NTP > 0) in units of bars, where 1 bar
                  ~ 1 atm. Default = 1.0.

      COMP        Inverse compressibility of the system when NTP > 0.
                  The unit is in 1.0E-06/bar (the  default  value  of
                  44.6 is recommended).

      TAUP        Pressure relaxation time when NTP .gt. 0 The recom-
                  mended value is between 0.1 and 1.0 ps-1.   Default
                  is 0.4.

      NDFMIN      Number  of  degrees  of  freedom  that will be sub-
                  tracted from the total number of degrees of freedom
                  to  account for center of mass removal, belly runs,
                  etc. (This will be a value between 0 and  6).    By
                  default  (if  NDFMIN.GE.0),  this value will be set
                  automatically.   For nearly  all  simulations,  you
                  should  accept the default calculated when NDFMIN =
                  0.  If you set  NDFMIN<0,  then  ABS(NDFMIN)  addi-
                  tional  degrees  of  freedom will be subtracted *in


                  addition to* the number  calculated  automatically.
                  This option is provided so that you can account for
                  systems containing  extended  linear  moities  that
                  reduce  the  true number of degrees of freedom from
                  that which would be calculated  by  a  simple  3N-6
                  determination.  For  example,  if you used a linear
                  triatomic molecule for your solvent, you would need
                  to set NDFMIN = -(number of solvent molecules).

      NTCM        Flag  for  the  removal  of translational and rota-
                  tional motion from the initial  velocities.   NOTE:
                  this flag is automatically set to 0 if belly option
                  is used.

                     = 0   The translational  and  rotational  motion
                           about  the  center  of mass is not removed
                           (default)

                     = 1   The above motion is removed  and  NTCM  is
                           reset to 0.  If velocities are being peri-
                           odically reassigned according to a  Boltz-
                           mann  distribution (NTT < 0) and NTCM = 1,
                           then center of mass motion will be removed
                           after each reassignment.

      NSCM        After  NSCM  steps the above motion will be removed
                  again if NTB .EQ. 0.  This flag should be set to -1
                  if  the belly option is used.  This results in NSCM
                  .EQ.  90 000 000 steps.  Default is -1.

      ISVAT       Residue-based  periodic  imaging  flag   ISVAT   is
                  ignored  when  periodic boundary conditions are not
                  used.

                     = 1   Residue-based periodic boundary conditions
                           are  used  (default).    For each residue,
                           imaging is determined based on  the  posi-
                           tion  of  the atom in the residue which is
                           closest to the residue's initial center of
                           mass.   Both  solute and solvent atoms are
                           imaged on a residue basis.  Each  atom  of
                           any  solute  or solvent residue "sees" the
                           same image of any interacting residue.

                     = 2   Same as 1, except that for  each  atom  of
                           the   _solute_,   different  whole-residue
                           images  on  interacting  residues  may  be
                           used.  Can be useful when a solute residue


                           is fairly long in one or more  dimensions.
                           The  code  required  to  implement ISVAT=2
                           does not vectorize, and may  result  in  a
                           substantial  hit  to performance on vector
                           machines. For this reason, ISVAT=1  should
                           be  used  except  where ISVAT=2 is clearly
                           required.

                     = 3   No residue-based periodic  imaging.  Sepa-
                           rate  imaging  is  done for each atom-atom
                           pair. This is the way imaging was done  in
                           versions  <= 3 of GIBBS (and MD). In typi-
                           cal operation, you would NOT want  to  use
                           this  option.   Setting  ISVAT<3  allows a
                           cutoff of as large as ~ 1/2  the  smallest
                           box  dimension  to  be  used. When ISVAT=3
                           with periodic boundary conditions, a  much
                           smaller cutoff/box ratio must be used.

      NSTLIM

                     > 0   Number  of  MD-steps  per  run  to be per-
                           formed.  NRUN such runs  will  be  carried
                           out.

                     = -1  Continue  simulation  until done, or until
                           TIMLIN is exceeded. This option  is  often
                           used  with dynamically modified procedures
                           (since we don't know  at  the  outset  how
                           many  total steps will be required).  This
                           is the default.

      INIT        Flag for different starting procedures.  If  option
                  NTX  is less than 5, INIT should be equal to 3.  If
                  option NTX is greater than  or  equal  to  5,  this
                  option should be equal to 4.

                     = 3   V(T-DT/2)   is   obtained  by  calculating
                           force(T); default.

                     = 4   Input V(T-DT/2) is used for  the  starting
                           velocity

      T           The  time  at  the  start (psec). Only for your own
                  use.  Not important for the simulation.  Default is
                  0.0.


      DT          The time step (psec); default is 0.001.  (Note that
                  in  the  special  case  where  window   growth   is
                  requested  by using the unrecommended flag combina-
                  tion (IFTIME = 0 and ISLDYN = 0; line  14),  DT  is
                  replaced by the value of DTA on line 15).

      VLIMIT      Limiting  velocity;  default  is 0.0.  If .ne. 0.0,
                  then any component of the velocity that is  greater
                  than  abs(VLIMIT)  will  be reduced to VLIMIT (pre-
                  serving the sign), and a warning  message  will  be
                  printed.   This  can  be  used  to avoid occasional
                  instabilities in molecular dynamics  runs.   VLIMIT
                  should generally be set (if at all) to a value like
                  20., which is well above the most probable velocity
                  in a Maxwell-Boltzmann distribution at room temper-
                  ature. Note that although it  is  anticipated  that
                  use of a liberal (large) value of vlimit should not
                  adversely affect the statistics accumulated  during
                  a  free  energy  simulation,  this has not yet been
                  definitively demonstrated.

      IVEMAX      Maximum times VLIMIT may be  exceeded.   If  IVEMAX
                  >0,  then  IVEMAX specifies the number of times the
                  limiting velocity VLIMIT can be exceeded in a simu-
                  lation.  If VLIMIT is exceeded >= IVEMAX times, the
                  simulation will stop.  If IVEMAX =0,  there  is  no
                  limit   on  the  number  of  times  VLIMIT  can  be
                  exceeded. Default is 0.

      NTC         Flag for SHAKE to perform bond length  constraints.
                  Constraining  the  bond lengths removes the highest
                  frequency  motions  from  the  system  and  usually
                  allows somewhat larger timesteps to be used.

                     = 1   SHAKE is not performed (default)

                     = 2   bonds  involving hydrogen are constrained.
                           No bonds which are part of the pert  group
                           are constrained.

                     = 3   all bonds are constrained

      TOL         Relative geometrical tolerance for bond constraints
                  in SHAKE.  Smaller values give tighter  tolerances.
                  The   (default)  recommended  value  is  <=  0.0005
                  Angstrom


      TOLR2       Relative geometrical tolerance for angle  and  tor-
                  sion  constraints  (radians).   Smaller values give
                  tighter  tolerances.   The  (default)   recommended
                  value is <= 0.0001 rad.

      NCORC       Constraint energy flag.

                     = 0   No  constraint  contributions  to the free
                           energy are calculated (default).

                     = 1   The contributions to the free energy  from
                           any  constraint  whose  equilibrium  value
                           changes with lambda  will  be  calculated.
                           This  includes:  A) Any constrained inter-
                           nals defined at the end of the input  (see
                           flag  INTR,  line 13); and B) any SHAKE-en
                           bonds (see NTC).

                           If NCORC=1 is specified, the program  will
                           determine  which  atoms of the system have
                           positions which are dependent on the  con-
                           straints,  and  all  of  these will effec-
                           tively  be  included  in  the   "perturbed
                           group".   This forces some time- consuming
                           calculations. If no constraints are chang-
                           ing with lambda, be sure to set NCORC=0.

                           The  procedure used to perform a PMF makes
                           it difficult to separate contributions due
                           to  the  constraints themselves from those
                           due to  non-bonded/electrostatic  interac-
                           tions.  For  this  reason,  in these cases
                           CORC will reflect the  sum  total  of  all
                           three types of contributions and the indi-
                           vidual non-bonded/ electrostatic contribu-
                           tions will be reported as 0's.

                           Note:  If  you  are  using  a "belly" with
                           NCORC=1, you must ensure that all residues
                           of  the  pert group are part of the moving
                           belly,   and   that,   additionally,   any
                           residues  sharing  constrained  bonds with
                           the pert group (if any) are  part  of  the
                           moving belly.

      ISHKFL      Flag  which  determines what the program will do in
                  the event of a SHAKE/internal constraint failure.


                     = 0   Program halts immediately.  This  is  what
                           the old versions of Amber did.

                     = 1   Program will write a restart file contain-
                           ing the coordinates before the failed call
                           to  the  constraint routine (+ velocities,
                           if  applicable).  The  program  will  then
                           halt.   >  1   The coordinates will not be
                           constrained on any iteration for which the
                           constraint  routine  fails.  If constraint
                           failure occurs on more than ISHKFL-1  con-
                           tiguous  steps,  the  program will stop as
                           described  for  ISHKFL=1.   This  is   the
                           default

      ITIMTH      Defines  which  method  should be used to calculate
                  constraint free energy contributions  when  NCORC=1
                  and the Thermodynamic Integration method (IDIFRG=1)
                  approach is being used.

                     = 0   Use  the  Potential  Forces  (PF)   method
                           (default).

                     = 1   Use the Constraint Forces (CF) method.

                     =-1   Use  the PF method, override program warn-
                           ings  about  constraints   within   closed
                           rings.

                           Two methods for determining the constraint
                           free energy contributions during  TI  have
                           been  derived  in the literature.   The PF
                           method appears to be more  efficient,  and
                           so  is  the  default.   However, PF method
                           cannot be used when any constraints of the
                           system which are changing with lambda (and
                           hence contribute to the free  energy)  are
                           part  of  a closed ring. In this case, the
                           CF method must be used.  The program  will
                           flag  any  constraints  of  the  perturbed
                           group which are part of a closed ring, and
                           will  stop  with  a  warning if TI is used
                           with PF in such a case. If none  of  these
                           constrained  bonds change with lambda, you
                           can still use  the  PF  method,  but  must
                           specify  ITIMTH=-1 here to ensure you have
                           considered whether this will be  appropri-
                           ate. It is suggested you NOT set ITIMTH=-1
                           automatically,  but  only  after  ensuring
                           that it will be appropriate.


      JFASTW      Fast  water definition flag. By default, the system
                  is searched for TIP3P waters, and special fast rou-
                  tines  are  used for these molecules. There are two
                  types of fast routines specific to TIP3P water:  1)
                  A  faster,  analytic  SHAKE  algorithm  for 3-point
                  water; 2) A faster routine to calculate  non-bonded
                  TIP3P-TIP3P water interactions.

                  In  normal  operation, the program defaults will be
                  acceptable.  However, in rare instances  (e.g.  for
                  debugging  purposes, or when the user has redefined
                  the definition of a TIP3P water), one may  wish  to
                  inhibit the use of these fast routines and/or rede-
                  fine the default definition used in Amber to define
                  TIP3P waters. This option makes this possible.

                     = 0   Normal  (default)  operation.  The default
                           AMBER definition of TIP3P water  is  used,
                           and the fast water routines are used where
                           appropriate.

                     = 1   Use the fast routines for water SHAKE  and
                           non-bonds, but redefine the names the pro-
                           gram uses to recognize TIP3P waters.   The
                           redefinition names are provided below.

                     = 2   Use  the  fast water routine for SHAKE. Do
                           not use the fast water  routine  for  non-
                           bonds.

                     = 3   Use  the  fast water routine for SHAKE. Do
                           not use the fast water  routine  for  non-
                           bonds. Redefine the names the program uses
                           to recognize TIP3P waters.  The  redefini-
                           tion names are provided below (line 17).

                     = 4   Do  not use fast water routines for either
                           SHAKE or non-bonds.

      NTF         Flag for force evaluation.  Typically  set  to  the
                  same value as NTC.

                     = 1   complete    interaction    is   calculated
                           (default)

                     = 2   bond interactions involving H-atoms  omit-
                           ted,  except  bonds in the perturbed group
                           (use  with  NTC  =  2,  see  above   SHAKE
                           options)


                     = 3   all the bond interactions are omitted (use
                           with NTC = 3)

                     = 4   angle involving H-atoms and all bonds  are
                           omitted

                     = 5   all  bond and angle interactions are omit-
                           ted

                     = 6   dihedrals involving H-atoms and all  bonds
                           and all angle interactions are omitted

                     = 7   all  bond, angle and dihedral interactions
                           are omitted

                     = 8   all bond, angle, dihedral  and  non-bonded
                           interactions are omitted

      NTID        Flag for solvent pairlist behavior.

                     = 0   only   the  first  atom  of  each  solvent
                           molecule is used when generating the  non-
                           bonded pairlist for a periodic system (for
                           water, this is the oxygen).  If this  atom
                           lies  within  the  specified  cutoff,  the
                           entire solvent molecule is included in the
                           non-bonded pairlist.  This can result in a
                           substantial speedup in non-bonded pairlist
                           generation,  and is recommended when using
                           water  as  the  solvent.   This   is   the
                           default.

                     =86   all  atoms  in a solvent molecule are con-
                           sidered  when  generating  the  non-bonded
                           pairlist  for  a  periodic system.  If any
                           atom of the solvent molecule  lies  within
                           the  specified  cutoff,  all  atoms of the
                           solvent molecule will be included  in  the
                           non-bonded  list.  This is the behavior of
                           versions of AMBER <= 3.0.

                           A value of NTID=0 is suggested for  calcu-
                           lations  using  water  as  a solvent.  For
                           calculations    using    larger    solvent
                           molecules,  one  should carefully consider
                           whether  using  only  the  first  atom  is
                           appropriate.   Regardless  of the value of
                           NTID, all atoms of the *solute*  are  con-
                           sidered when deciding whether to include a
                           second residue  in  the  interacting  non-
                           bonded  list for the solute residue.  NTID


                           will have no affect for non-periodic  sys-
                           tems.

      NTNB        Flag for non-bonded pair list generation.

                     = 0   no  pair  list will be generated (unlikely
                           you would choose this).

                     = 1   pair list will be generated (default)

      NSNB        After NSNB steps the non-bonded pair list  will  be
                  updated.  Default = 50.

      IDIEL       Type of dielectric function to be used.

                     = 0   distance   dependent  dielectric  function
                           (for in  vacuo  simulations  of  "aqueous"
                           systems).

                     = 1   constant  dielectric  function (always use
                           with  explicit   solvent,   e.g.   water);
                           default.

      IELPER      Flag  to  control the "electrostatic decoupling" of
                  the perturbation energy

                     = 0   Regular run; no  electrostatic  decoupling
                           (default).

                     = 1   Only the electrostatic contribution to the
                           free  energy  is  calculated  keeping  the
                           geometry and the VDW parameters pertaining
                           to LAMBDA = 1.

                     =-1   Only  the  non-electrostatic  (VDW,  etc.)
                           contributions  to the free energy are cal-
                           culated and the system changes  from  that
                           characteristic of LAMBDA = 1 to 0 (or from
                           that  characteristic  of  LAMBDA  =  0  to
                           LAMBDA  =  1  depending  on  the  signs of
                           IFTIME or ALMDEL).

                           In electrostatic decoupling, two runs have
                           to be performed, one for electrostatic and
                           the  other  for  VDW  etc.  contributions.
                           This  is  useful  when  a polar or charged


                           group is  being  established  or  removed.
                           However, the LAMBDA = 1 state must pertain
                           to the established group (the residue gen-
                           erated  by PREP) and the LAMBDA = 0 to the
                           removal of the group (as designated in the
                           PARM   input).   The  decoupling  MUST  go
                           through the following perturbation  cycle:
                           electrostatic   LAMBDA   =  1  ->  0  with
                           LAMBDA(vdw) = 1, followed by van der Waals
                           LAMBDA  =  1  ->  0.  If the simulation is
                           started at LAMBDA = 0,  then  reverse  the
                           above  procedure.   In  this  way, charges
                           never appear on atoms which do not possess
                           a  vdw radius which avoids very close con-
                           tacts due to charge-charge attractions.

                           Notes: (1) Two separate runs are needed to
                           fully  carry  out  the decoupling calcula-
                           tion.  (2) In  the  IELPER=+1  phase,  any
                           added restraints/constraints (if INTR > 0)
                           will be fixed at the values they have when
                           lambda=1.   (They   will   still  only  be
                           applied, however, over the  ranges  speci-
                           fied).   (3)  The free energy contribution
                           from internal constraints is never  calcu-
                           lated  during  the  IELPER=+1 phase (it is
                           calculated during the IELPER=-1 phase).

                  ---------------------------------------------------------
                    To summarize:

                     IELPER         internals/vdw      electrostatics
                        +1        fixed @ lambda=1         vary
                                  (non-pert) values

                        -1           vary               fixed @ lambda=0
                                                             (pert) values
                  ---------------------------------------------------------

      IMGSLT      Flag to control the Solute-Solvent  interaction  in
                  the case of PB simulation

                     = 0   The   Boundary  condition  is  applied  to
                           solute-solvent interactions (default)

                     = 1   No Solute-Solvent  imaging.   Solute  does
                           not see image solvent.   This assumes that
                           the solute is  centered  in  the  periodic
                           system,  and  is  not free to migrate.  Do
                           not use this with  mobile  solutes.   This


                           option is mainly useful for large solutes.

      IDSX0       Flag which controls how the  mixed  van  der  Waals
                  parameters  are calculated for atom pairs where one
                  atom vanishes (at  either  lambda=1  or  lambda=0).
                  (See Ref. 6).

                     = 0   r*(state   where   one  atom  vanishes)  =
                           r*(non-vanishing atom) (This  is  the  way
                           AMBER has done this in the past)  Default.

                     > 0   r*(lambda)  will  be  calculated  so  that
                           r*(state   where   one  atom  vanishes)  =
                           IDSX0/1000  r*(state  where   both   atoms
                           exist) = r*(A) + r*(B)

                     = -1  results  in  r*(state  where one atom van-
                           ished) = 0.0

      ITRSLU      During a periodic boundary  conditions  simulation,
                  controls  whether  SOLUTE  molecules which exit the
                  primary image box will be translated back into  the
                  central  box.    SOLVENT  molecules  which exit the
                  central image box are always translated  back  into
                  the  box.  A molecule is considered to have floated
                  out of the central box if the  first  atom  of  the
                  molecule exits the box.

                     = 1   Both  SOLUTE  and  SOLVENT molecules which
                           exit the primary image box will be  trans-
                           lated  back  into the box. The system will
                           be translated every 500 steps so that  the
                           center  of  geometry of the solute is cen-
                           tered in the primary image box.  (Default;
                           recommended for most systems).

                     = 2   Same  as  1,  except  that the system as a
                           whole is not  periodically  translated  to
                           keep  the  solute  centered in the primary
                           image box.

                     = 0   Only SOLVENT molecules will be  translated
                           back  into  the primary image box.  SOLUTE
                           molecules are not translated.

      IOLEPS      Controls how parameter mixing is performed for non-
                  bonded interactions.


                     = 0   Mixing  of  epsilon  (well-depth)  van der
                           Waals parameters done as

                              ()=*(mixed,=1)+(1-)*(mixed,=0)

                           Mixing of electrostatic interactions  done
                           as

                              q1q2()=*q1q2(=1)+(1-)*q1q2(=0)

                           This is the default

                     = 1   Mixing of epsilon done as

                                       ()=(i()j())

                           Mixing of electrostatics done as

                                     q1q2()=q1()q2()

                           Setting  IOLEPS=1 forces mixing to be done
                           as in older versions  (e.g.  3.0,  3A)  of
                           AMBER.  The "new" mixing scheme (IOLEPS=0)
                           has several  advantages,  including  A)  a
                           finite derivative for van der Waals inter-
                           actions involving an  atom  which  "disap-
                           pears"  at  one end point; and B) Interac-
                           tion between pairs of atoms where one/both
                           atoms "disappear" at both end points never
                           contribute to the energy. [One side- bene-
                           fit  of  this  is that it allows duplicate
                           topologies; thus one can perform perturba-
                           tions  using  the "CHARMM" methodology, if
                           desired].  Note that if IDIFRG = 1  (ther-
                           modynamic integration), the epsilon param-
                           eters are always mixed  as  described  for
                           IOLEPS = 0.

      INTPRT      Determines  which energies contribute to the calcu-
                  lation of the free energy change.

                     = 0   No  intra-perturbed  group  energies   are
                           accumulated (Default; same as pre-4.0 ver-
                           sions of AMBER)

                     = 1   intra-pert. group non-bond energies  accu-
                           mulated as well (but no 1-4's).

                     = 2   intra-pert.  group non-bond energies accu-
                           mulated (including 1-4's).


                     = 3   intra-pert group internal energies accumu-
                           lated (bonds, angles, torsions)

                     = 4   intra-pert  group  non-bond  and  internal
                           energies accumulated

                     = 5   intra-pert group non-bond, 1-4, and inter-
                           nal
                           energies accumulated

                           Note: If any PMF contributions  are  being
                           calculated (NCORC = 1, line 9), all intra-
                           perturbed group  non-bonded  contributions
                           will  be calculated if INTPRT = 1,2,4 or 5
                           (when NCORC=1, 1-4's are  not  broken  out
                           separately).

      ITIP        By  default (ITIP=0), GIBBS assumes that if you are
                  running a periodic boundary conditions (PBC)  simu-
                  lation  with solvent, the solvent is TIPNP water. A
                  special characteristic of  this  solvent  model  is
                  that  there  are  no  h-bond  (10-12)  interactions
                  between any pair of solvent molecules. A  potential
                  speedup  is  thus  obtained by skipping all such h-
                  bond interactions.  If you choose to use a  solvent
                  model where there should be h-bond (10-12) interac-
                  tions   calculated   between   pairs   of   solvent
                  molecules,  set  ITIP  to  any  value other than 0.
                  Note that in either case,  all  10-12  interactions
                  between  solvent and solute molecules will still be
                  determined normally.

      CUT         The primary  cutoff  distance  for  the  non-bonded
                  pairs. Default = 8.0.

      SCNB        The scale factor for 1-4 vdw interactions; if (SCNB
                  .EQ. 0.0) then SCNB = 2.0, which is the default.

      SCEE        The scale factor for 1-4 electrostatic interactions
                  There  is  no  namelist default, since the 1991 and
                  previous force fields  used  2.0,  while  the  1994
                  force field uses 1.2.

      DIELC       Dielectric  constant for the electrostatic interac-
                  tions; if  (DIELC  .LE.  0.0)  then  DIELC  =  1.0.
                  Default is 1.0.


      CUT2ND      An  (optional)  secondary  cutoff. If CUT2ND > 0.0,
                  then at every nonbonded update (every NSNB  steps),
                  the  energies and forces due to interactions in the
                  range CUT< Rij <= CUT2ND will be determined.  These
                  energies and forces will be added to the non-bonded
                  interactions within CUT distance at every timestep.
                  The  idea  is  that  long-range interactions change
                  more slowly than short range interactions, and thus
                  this  dual  cutoff  method  allows  one  to include
                  longer-range information at only a  moderate  addi-
                  tional cost.  Default is 0.0.

      CUTPRT      An  (optional)  alternative  cutoff  to be used for
                  interactions with the perturbed  group.  If  CUTPRT
                  and  CUT2ND  are  both defined, interactions in the
                  range CUTPRT < Rij <= CUT2ND  will  constitute  the
                  secondary  cutoff  range  for interactions with the
                  perturbed group.  Default is 0.0.

      NTPR        Flag for printing energy  related  quantities.  for
                  every  NTPR  steps these quantities will be output.
                  Default is 100.

      NTWX        Flag for packing the coordinates.  For  every  NTWX
                  steps  the  coordinates will be dumped through file
                  'PCOORD' in format (10F8.3). If NTWX=-1  (default),
                  no dumping will be performed.

      NTWV        For every NTWV steps the velocities will be written
                  in  file  'PVEL'  in  format  (8F8.4).  If  NTWV=-1
                  (default), no dumping will be performed.

      NTWE        Every  NTWE  steps  energy  info is written in file
                  'PEN' in formatted form. If NTWE=-1  (default),  no
                  dumping will be performed.

      NTWXM       After NTWXM steps the NTWX switch will be inactive.
                  Default is 999999.

      NTWVM       After NTWVM steps the NTWV switch will be inactive.
                  Default is 999999.

      NTWEM       After NTWEM steps the NTWE switch will be inactive.
                  Default is 999999.


      IOUTFM      Flag for format of velocity and coordinate sets

                     = 0   Formatted (default)

                     = 1   Binary

      ISANDE      Flag to output enthalpies and entropies, as well as
                  free energies. Note that these quantities are typi-
                  cally an order of magnitude or  more  less  precise
                  than free energy values, and will be much more sen-
                  sitive than free energies to  the  completeness  of
                  the  ensemble statistics collected. See the discus-
                  sion  following  the  input  description  for  more
                  information.   Setting  ISANDE  = 1 will also force
                  the printing of the integrand quantity  <V/>   when
                  Thermodynamic  Integration  is being performed (see
                  the IDIFRG flag, 14.6). This can be useful  if  the
                  user  wishes  to  apply  an alternative integration
                  algorithm. Default is 0.

      IPERAT      Request that free energy components or  derivatives
                  be  calculated.   Note  that free energy components
                  can be determined during any standard  free  energy
                  simulation.  Free  energy  derivatives  can only be
                  calculated in a  special  simulation  where  lambda
                  does not change.

                     = 0   No  free  energy components or derivatives
                           will be calculated (default).

                     = 1   Report free energy components.  Components
                           will  be  be  reported in file PATNRG on a
                           per-atom basis.

                     = 2   Report free energy components.  Components
                           will  be  be  reported in file PATNRG on a
                           per-residue basis.

                     = 3   Report free energy components.  Components
                           will  be  be  reported in file PATNRG on a
                           per-molecule basis.

                     = 4   Calculate/report free energy components or
                           derivatives  (depending  on  the flag ICM-
                           PDR). Values will be reported in file PAT-
                           NRG  for  the  atoms/groups defined at the
                           end of input using GROUP input.


                           For free energy components, free  energies
                           will  be  logged  as  defined by the GROUP
                           definition, subject to the condition  that
                           only  those  atoms  which  are part of the
                           perturbed group  or  which  move  with  an
                           added   CONstraint   will   ultimately  be
                           included.   All   atoms   not   explicitly
                           included in a group will be put in a final
                           single group.   For  free  energy  deriva-
                           tives, derivatives will be logged only for
                           those atoms included in  a  group  defini-
                           tion. Any atom of the system may be desig-
                           nated as part of any group (but each  atom
                           will  be  a  member of at most one group).
                           Typically, you will place individual atoms
                           in   their  own  groups  when  calculating
                           derivatives.

      IATCMP      If free energy components are  being  reported,  by
                  default    only   the   total   free   energy   per
                  atom/residue/molecule/ group is reported.  By  set-
                  ting IATCMP > 0, one can force the components to be
                  broken  down  into  electrostatic,  non-bonded  and
                  internal  contributions.  IATCMP has no affect when
                  free energy derivatives are being calculated.

                     = 0   Do not break free energy  components  into
                           contributions (default).

                     = 1   break free energy componenets into contri-
                           butions.

      NTATDP      Free energy  components/derivatives  will  only  be
                  reported  every  NTATDP  steps.   Note that if free
                  energy components are being logged, a  free  energy
                  report  will  occur  at  a  particular  multiple of
                  NTATDP steps only if the free  energy  accumulators
                  have been updated since the last report.   For free
                  energy derivatives, energies will be reported every
                  NTATDP  steps  in all cases.  If NTATDP = -1, it is
                  set to NTPR; default is 0.

      ICMPDR

                     = 0   no free energy derivatives (default).

                     = 1   If IPERAT=4, log the free  energy  deriva-
                           tives  with respect to charge and the non-
                           bonded parameters epsilon and r*.  If  the


                           contributions  of  constraints to the free
                           energy are being calculated (NCORC  =  1),
                           then  derivatives  with  respect  to  con-
                           straints in the perturbed group (and added
                           constraints) will also be calculated.

                           Free energy derivatives can only be calcu-
                           lated for lambda = 0 or lambda = 1.  It is
                           sufficient  to  define  a "null" perturbed
                           group in PARM if you simply wish to deter-
                           mine  the  non-bonded  free energy deriva-
                           tives of specified atoms.

      NCMPDR      If free energy  derivatives  are  being  calculated
                  (IPERAT=4 and ICMPDR=1), NCMPDR gives the number of
                  steps of effective "equilibration." After the first
                  NCMPDR  steps, the accumulators for the free energy
                  derivatives are  cleared  and  reset.  Free  energy
                  derivatives  reported  from this point forward will
                  only reflect averaging since the accumulators  were
                  cleared.  Some people prefer to use a post-process-
                  ing program to  analyze  free  energy  derivatives.
                  Such  programs can usually "remove" a given initial
                  portion of the free energy  derivative  information
                  from  subsequent  totals.  In  such a case, you may
                  wish  to  set  NCMPDR=0  here  (no  "equilibration"
                  phase),  and  pick the amount of data to discard in
                  the post-processing program.

      NTWPRT      Coordinate/velocity archive limit flag.  This  flag
                  can  be used to decrease the size of the coordinate
                  / velocity archive files, by  only  including  that
                  portion  of  the system of greatest interest. (E.g.
                  one can print only the solute and not the  solvent,
                  if so desired).

                     = 0   Coord/velocity  archives  will include all
                           atoms of the system (default).

                     < 0   Coord/velocity archives will include  only
                           the solute atoms.

                     > 0   Coord/velocity  archives will include only
                           atoms 1->NTWPRT.

      NTR         Flag for restraining specified atoms.


                     = 0   Classical MD (default)

                     =
                     MD with restraint of specified atoms

      NTRX        Flag for  reading  the  cartesian  coordinates  for
                  restraint  from  unit  PREFC.   Note:  the  program
                  expects coordinates for all atoms from which a sub-
                  set is selected by the GROUP input which follows.

                     = 0   binary form

                     = 1   formatted form (default)

      TAUR        The  relaxation  time for restraint. Default is 1.0
                  ps.

      INTR

                     = 0   No additional internal restraints or  con-
                           straints will be read (default).

                     > 0   Additional internal restraints/constraints
                           will be read following the  normal  input.
                           Storage will be allocated for a maximum of
                           INTR added restraints/constraints.   These
                           restraints/constraints  can  be  used  for
                           e.g. a PMF calculation.

      IBIGM       To calculate the free  energy  contributions  of  a
                  constraint   (if   NCORC=1),  the  free  energy  at
                  lambda+-d_lambda is evaluated by shifting the value
                  of the constraint to its value at lambda+-d_lambda.
                  This change in the value of the constraint  can  be
                  effected  either by performing half of the shift at
                  each end/side of the internal, or by performing the
                  entire shift at one end.

                     = 0   Half of the shift is performed at each end
                           of the internal.

                     = 1   The entire shift occurs at the end/side of
                           the  internal which results in fewer atoms
                           being moved. This is the default.

                           The number of atoms whose positions change
                           with  shifting  the constraint affects how


                           quickly the calculation can be  performed.
                           Setting  IBIGM = 1 can significantly speed
                           up some calculations (e.g. when rotating a
                           ring  about  a  constrained  torsion which
                           joins it to a protein), and  IBIGM  should
                           typically be set to 1 for in vacuo simula-
                           tions.  In  all  cases,  GIBBS  determines
                           which   interatomic   nonbonded  distances
                           depend  on  constraint  values,  and  only
                           these are recalculated when NCORC=1.

      ISFTRP      Causes the 6-12/10-12 functions used for non-bonded
                  interactions to be  replaced  by  "soft  repulsion"
                  terms of the form

                              RWELL*(r2-r*2)2

                  where   r*  is  the  optimal  interaction  distance
                  between a pair  of  atoms,  calculated  from  their
                  respective  van  der Waals radii.  This function is
                  sometimes  useful  in  structure  refinement,   but
                  should  *not* typically be used in free energy cal-
                  culations.  Atoms in the perturbed group are always
                  treated   by  normal  (6-12  or  10-12)  non-bonded
                  forces, regardless of the value of ISFTRP.

                     = 0   regular 6-12/10-12's. No  soft  repulsion.
                           Default.

                     = 1   replace 6-12's by soft repulsion.

                     = 2   replace  10-12's  by  soft  repulsion,  as
                           well.

      RWELL       Force constant (in kcal/mol) used for  soft  repul-
                  sion interactions.  Default is 5.0.

      IFTIME      Mutation  flag.   If  ISLDYN=0,  then if IFTIME = 0
                  (default) a standard Window Free  Energy  Perturba-
                  tion  will  be  carried  out. The perturbation will
                  start at lambda = ALMDA,  and  proceed  in  equally
                  spaced  intervals of delta(lambda) = ALMDEL until 1
                  (ALMDEL > 0) or 0 (ALMDEL < 0) is reached. At  each
                  value  of  lambda, NSTPE steps of equilibration and
                  NSTPA steps of data collection (see line  15)  will
                  be  performed,  and energy evaluated using Equation
                  2.  If IFTIME =+-1  A  "Slow  Growth"  perturbation
                  will  be carried out.  The simulation will start at
                  lambda = ALMDA, and will be run in either the  0->1


                  direction (IFTIME = +1) or 1->0 direction (IFTIME =
                  -1). CTIMT gives the number  of  psec  of  dynamics
                  which  would be used to perform the complete change
                  0->1 (or 1->0). The actual length of the simulation
                  will  depend  on  the  starting  value ALMDA.  NOTE
                  IFTIME is included for backwards compatibility with
                  input  files created for previous versions (< 4) of
                  AMBER.  However, it is  strongly  recommended  that
                  you use the ISLDYN flag to specify the type of sim-
                  ulation  desired.   If   ISLDYN.NE.0,   IFTIME   is
                  ignored.

      CTIMT       The  total length of the MD simulation (in psec) to
                  be carried out in performing a slow growth  simula-
                  tion  which transforms state lambda = 0 into lambda
                  = 1 (or vice-versa).   Note that this variable does
                  not control the number of steps which will actually
                  be run. For example, if CTIMT  =  10psec,  ALMDA  =
                  0.0,  ISLDYN = +1, and NRUN*NSTLIM*DT = 5psec, only
                  half of the desired  simulation  would  be  carried
                  out.  The remainder would have to be carried out by
                  a restart.  CTIMT is only used when ISLDYN = +-1 or
                  (IFTIME=+-1 and ISLDYN = 0). Default is 0.0.

      ALMDA       The  starting  value of lambda for this simulation.
                  The value can be on the  inclusive  interval  0.0->
                  1.0. Default is 1.0.

                  ALMDA  =  1  corresponds  to  the  "initial"  state
                  defined by the structure described in PREP. ALMDA =
                  0  corresponds  to the "final" state defined by the
                  structure described in PARM.  Intermediate "states"
                  are  defined by a linear combination of the parame-
                  ters representative of (lambda = 0) and  (lambda  =
                  1).   For  restart  simulations  (IREST=1, line 2),
                  ALMDA is read directly from the restart  file,  and
                  the value specified here is ignored.

      ALMDEL      For  _Standard_ (fixed width) Window and TI simula-
                  tions, ABS(ALMDEL) gives the width of  each  window
                  or  integration interval.   If double-wide sampling
                  is used with Window Growth (default), at each value
                  of  lambda,  the  free energies to both +ALMDEL and
                  -ALMDEL are evaluated. This results in "double wide
                  sampling"   (see   the   introductory   text).   If
                  (IFTIME=0 and ISLDYN=0), the sign of ALMDEL  deter-
                  mines  the  direction of the change. If ISLDYN=+-3,
                  the sign of ISLDYN determines the direction of  the
                  change.   ALMDEL  should be chosen so that the free
                  energy change over any interval is not  too  large.


                  It  has  been suggested (somewhat arbitrarily) that
                  as a rule the free energy change/window should  not
                  exceed  2RT.  ALMDEL is only used when ISLDYN = +-3
                  or (IFTIME=0 and ISLDYN = 0).  Default is 0.1.

      ISLDYN      Free Energy Method flag.  It  is  recommended  that
                  you  use  this flag exclusively, and ignore IFTIME.
                  Default is -3.

                     = +-1 Perform a Slow Growth simulation. The sim-
                           ulation  will  be  started  at  ALMDA, and
                           CTIMT psec will be  required  to  complete
                           the  conversion  to  the  end (0 or 1). If
                           ISLDYN = +1, the simulation will  be  car-
                           ried out in the direction 0-> 1.   If ISL-
                           DYN = -1, the simulation will  be  carried
                           out in the direction 1-> 0.

                     = +-2 Perform a Dynamically Modified Window sim-
                           ulation. The simulation will be started at
                           ALMDA and progress either in the direction
                           0-> 1 (if ISLDYN = +2) or 1-> 0 (if ISLDYN
                           =  -2).  The  numbers of equilibration and
                           data collection steps  performed  at  each
                           window  are given by NSTMEQ and NSTMUL (on
                           this line).  If IDIFRG  =  0,  the  energy
                           will  be  evaluated at each interval using
                           Equation 2 (FEP). If IDIFRG = 1, thermody-
                           namic  integration  will  be  carried  out
                           using Equation (4).

                     = +-3 Perform a "standard" Window Growth simula-
                           tion  (with fixed width lambda intervals).
                           The perturbation will start  at  lambda  =
                           ALMDA,   and  proceed  in  equally  spaced
                           intervals of delta(lambda)  =  abs(ALMDEL)
                           until  1 (ISLDYN > 0) or 0 (ISLDYN < 0) is
                           reached. At each value of  lambda,  NSTMEQ
                           steps of equilibration and NSTMUL steps of
                           data collection (see this  line)  will  be
                           performed.  If IDIFRG = 0, the energy will
                           be evaluated at each interval using  Equa-
                           tion 2 (FEP). If IDIFRG = 1, thermodynamic
                           integration will  be  carried  out,  using
                           Equation (4).

      IDIFRG      Thermodynamic integration flag.


                     = 0   No thermodynamic integration (default).

                     = 1   If windows or dynamically modified windows
                           have been specified, the  energy  will  be
                           calculated using thermodynamic integration
                           (TI) (Equation 4). The integrand  will  be
                           evaluated  at  the endpoints of each "win-
                           dow", and the integral  will  be  approxi-
                           mated  using the trapezoidal rule (see the
                           discussion following  the  input  descrip-
                           tion).  In addition to the integrated free
                           energy, if ISANDE is set  =  1  (see  flag
                           12.10),  the  value of <V/> will be output
                           at every energy  update,  so  a  different
                           integration  algorithm  can  be applied by
                           the user, if desired.  If slow growth  has
                           been  requested,  setting IDIFRG=1 has the
                           effect of performing the slow growth  sum-
                           mation  using the non-averaging equivalent
                           of the TI equation (4),  rather  than  the
                           FEP equation (2).

      NSTMEQ      number  of  steps  of  equilibration to be used for
                  each window if ISLDYN = +-2 or +-3.   (Note that if
                  windows are instead requested using the flag combi-
                  nation IFTIME = 0 and ISLDYN = 0, NSTPE  is  used).
                  Default is 2.

      NSTMUL      number  of  steps of data collection to be used for
                  each window if ISLDYN = +-2 or +-3.   (Note that if
                  windows are instead requested using the flag combi-
                  nation IFTIME = 0 and ISLDYN = 0, NSTPA  is  used).
                  Default is 2.

      NDMPMC      Every  NDMPMC windows, statistics will be dumped to
                  the statistics file (MICSTAT). The statistics  file
                  contains  a  condensed  format  record  of the free
                  energy for each window interval.  The MICSTAT  file
                  is  not  written  with slow growth, or if NDMPMC is
                  set < 0.   By  default  NDMPMC=100.  NDMPMC  cannot
                  exceed 100.

      IDWIDE      Allows  double-wide  sampling to be turned off with
                  FEP.

                     = 0   Double-wide sampling  performed  when  FEP
                           windows are being calculated (default).


                     = 1   Double-wide  sampling  turned off when FEP
                           windows are being calculated.

                           Double wide sampling means at  each  value
                           we  calculate  the free energy in both the
                           "forward" and  "reverse"  direction.  This
                           gives   an   intra-run  consistency  check
                           (lower bound on the error),  but  requires
                           we  calculate  every  interval  twice. The
                           simulation can be run in roughly half  the
                           time,  without the forward/reverse consis-
                           tency check,  by  setting  IDWIDE=1.   The
                           nature    of   thermodynamic   integration
                           (IDIFRG=1) is such that double  wide  sam-
                           pling  is never carried out. IDWIDE has no
                           effect for such calculations.

      IBNDLM      By default  (IBNDLM=0),  lambda+-d_lambda  is  con-
                  strained  to  the  range  0<lambda+-d_lambda<1.  If
                  IBNDLM=1,  then  lambda+-d_lambda  can  exceed  the
                  range  0->1.   Useful  when doing PMF-type calcula-
                  tions.  Ignored for regular slow growth.

      IAVSLP      The current dG/dLAMBDA slope will  be  approximated
                  by  a  linear  fit  to the Accumulated G vs. LAMBDA
                  data for the previous IAVSLP windows. Maximum value
                  = 1000; default is 8.

      IAVSLM      Until  IAVSLM windows have been collected, the win-
                  dow spacings will be fixed at  ALMDL0  (line  14c).
                  When  IAVSLM windows have been collected, the slope
                  will be  calculated  over  all  available  windows,
                  until  IAVSLP windows are available.  Default is 2.

                                i.e. #_windows < IAVSLM : dLAMBDA = ALMDL0
                                    IAVSLM <= #_windows < IAVSLP :
                                          dLAMBDA calculated from slope over #_windows
                                    #_windows >= IAVSLP :
                                          dLAMBDA calculated from slope over previous IAVSLP
                                          windows

                  If IAVSLM=-1, window widths will be fixed at ALMDL0
                  until IAVSLP windows are available.

      ISLP        Determines the direction in which the slope is cal-
                  culated.


                     = 0   (default) use  the  appropriate  value  of
                           ISLP (-1 or 1) to calculate the slope from
                           energies calculated in the same  direction
                           as the simulation (recommended).

                     = 1   the  slope  is calculated from the forward
                           (0->1) energy at each step.

                     =-1   the slope is calculated from  the  reverse
                           (1->0) energy at each step.

                     = 2   the  slope is calculated using the average
                           of the redundant free energy values  (from
                           double wide sampling) over the interval in
                           the direction opposite to the  simulation,
                           i.e.    G(reverse[curr  window]  -  G(for-
                           ware[prev  window])/2  or   G(forward[curr
                           window]  -  G(reverse[prev  window])/2 for
                           simulations run  0->1  and  1->0,  respec-
                           tively.   This  option  can be useful when
                           very few points are used to evaluate  each
                           slope (e.g. IAVSLP = 2).

                     = 3   the  slope is calculated using the average
                           of the forward  and  reverse  energies  at
                           each lambda.

                           For  best results in most cases, the slope
                           should be calculated in the same direction
                           as  the  simulation.  This  is the default
                           behavior  (ISLP=0).   With   thermodynamic
                           integration,  or when double-wide sampling
                           is defeated, ISLP  has  no  effect.   Only
                           options  ISLP=0 or ISLP=3 should typically
                           be used when AMXRST > 0.

      CORRSL      If the correlation coefficient for a linear fit  to
                  the previous IAVSLM windows is < CORRSL, the number
                  of windows over which the slope is calculated  will
                  be  halved  (for  this  determination  of the slope
                  only), and the slope calculated again. This process
                  continues  until  the  correlation coefficient is >
                  CORRSL. Default is 0.8.

      AMXMOV      The target free energy change per window. If  M  is
                  the  slope  over  the  previous IAVSLP windows, the
                  next value of dLAMBDA is chosen as dLAMBDA  =  AMX-
                  MOV/M  Note  that  when  double  wide  sampling  is
                  defeated (IDWIDE=1) while using a window FEP  tech-
                  nique  (IDIFRG=0), the free energy change at a win-
                  dow is defined as the total ("forward" + "reverse")


                  energy  change.  This  differs  from the definition
                  when double wide sampling is used, where  the  free
                  energy  change  at  a window is approximately 1/2 *
                  ("forward" + "reverse").  Thus,  AMXMOV  should  be
                  suitably  increased  when  IDWIDE  = 1.  Default is
                  0.1.

      IAVDEL      Number  of  windows  over  which  the  forward  and
                  reverse  energies will be compared. If IAVDEL<0, no
                  comparisons will  be  carried  out.  IAVDEL  should
                  always  be set <0 when thermodynamic integration is
                  used (IDIFRG = 1).  Maximum value =  1000;  default
                  is -1.

      IAVDEM      The relationship between IAVDEL and IAVDEM is anal-
                  ogous to that between IAVSLP and IAVSLM. Default is
                  2.

      AMXDEL      If  < ABS (DA(for)-DA(rev)) > .GT. ABS(AMXDEL) then
                  the next dLAMBDA will be scaled as [ < ABS (DA(for)
                  -  DA(rev))  > / AMXDEL ] **2 * dLAMBDA If AMXDEL <
                  0, then scaling occurs in all  cases.   Default  is
                  1.0.

      ALMDL0      Until  enough  intervals  have  been  calculated to
                  allow determination  of  dG/d_lambda  and  d_lambda
                  consistent  with  IAVSLP  and  IAVSLM,  an interval
                  width of ALMDL0 will be used. Default is 0.0001.

      DLMIN       The minimum  allowable  window  width.  Default  is
                  1.0D-6.

      DLMAX       The  maximum allowable window width Default is 0.1.

      AMXRST      If the free energy change, dG, over any  window  is
                  greater than AMXRST, then the data collection phase
                  for  that  window  will  be  re-performed  using  a
                  reduced  value of dLAMBDA. The new value of dLAMBDA
                  is determined as dLAMBDA(new) = (dLAMBDA(old)/dG) *
                  AMXMOV.  AMXRST should not be set too close to AMX-
                  MOV, or  too  many  windows  will  be  recalculated
                  (which     is     inefficient).      By    default,
                  AMXRST=5.*ABS(AMXMOV).


      NORSTS      If this is a restart run, and  NORSTS=1,  then  the
                  restart  information  relating to dynamically modi-
                  fied windows is not read (cold start for the dynam-
                  ically  modified  windows).   NORSTS  is ignored if
                  this is not a restart run.  Normally, NORSTS should
                  be set to the default of 0.

      NTSD        The  statistics  relating  to  dynamically modified
                  windows are written to file  POUT  every  NTSD.  If
                  NTSD=0,  then  NTSD is set equal to NTPR (line 12),
                  and these statistics will be output every time  the
                  standard  energy information is printed. Default is
                  0.

      ALMSTP(1)   Allows the values of AMXMOV, DLMIN, DLMAX,  AMXRST,
                  and  NTSD  to  be different for different ranges in
                  LAMBDA.

                     > 1 or < 0
                           the values defined in lines  14a-14c  will
                           remain in effect for the whole run.

                                   > 0  and
                                   <  1  the  values defined in lines
                           14b-14d will  remain  in  effect  for  the
                           range  of  LAMBDA  ALMDA->  ALMSTP(1).  In
                           this case, _additional line(s)_  are  read
                           with  the  values  of  the above variables
                           over various ranges of LAMBDA.   Each line
                           has the format

                                                AMXMOV, DLMIN, DLMAX, AMXRST, NTSD, ALMSTP(I)

                                                FORMAT(4F14.9,I5,F14.9)

                           These  lines  are read until ALMSTP(I) > 1
                           or ALMSTP(I) <  0.   Each  set  of  values
                           applies to the range in LAMBDA ALMSTP(I-1)
                           -> ALMSTP(I).  Note that the for the  last
                           line, ALMSTP(I) must be greater than 1, or
                           less than 0 (not equal to). This is  avoid
                           machine  precision  problems.   Note  also
                           that, at present, "namelist"-format  input
                           always assumes ALMSTP(1) < 0 (i.e. AMXMOV,
                           DLMIN, etc. remain fixed over  the  entire
                           run). If you wish to use the functionality
                           described above for ALMSTP(), you must use
                           formatted input.


      NSTPE       The  number  of  steps of Equilibration before col-
                  lecting the Free Energy Statistics.  For each  win-
                  dow  the  system  is  equilibrated for NSTPE steps.
                  (When ISDYN=+-2 or +-3, NSTMEQ serves the same pur-
                  pose). Default is 2.

      NSTPA       The number of steps for data collection.  The aver-
                  aging is performed over this number of steps. (When
                  ISLDYN=+-2 or +-3, NSTMUL serves the same purpose).
                  Default is 2.

      DTA         The time-step used for  window  runs  specified  by
                  IFTIME=0 and ISLDYN=0. All other runs use the time-
                  step specified on line 8. Default is 0.001

      IVCAP       Flag to control Cap Option.  The Cap option  is  to
                  solvate a spherical portion of a solute and to hold
                  the solvent from evaporating  through  a  half-har-
                  monic potential.

                     = 0   Cap will be in effect if it is passed from
                           the the parm module (default).

                     = 1   Cap will be activated except that the  Cap
                           atom pointer would be modified.

                     = 2   Cap will be inactivated.

      NATCAP      The  Cap  atom  pointer It is the last Non-Cap atom
                  number. If IVCAP.EQ.1 then the pointer passed  from
                  the PARM Module will be overwritten by this number.
                  Default is 0.

      FCAP        The Force Constants for the Cap Atoms.  Default  is
                  0.0

      WATNAM      The  residue  name  the  program  expects for TIP3P
                  waters. Default is "WAT".

      OWTNM       The atom name program expects for the TIP3P oxygen.
                  Default is "O   ".

      HWTNM1      The  atom name program expects for the TIP3P 1st H.
                  Default is "H1  ".


      HWTNM2      The atom name program expects for the TIP3P 2nd  H.
                  Default is "H2  ".

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

                     -- These card is read only if I3BOD.NE.0  --

                  This information must be provided in the formatted form given,
                  even if namelist format input is used above.

             - 18A-    1) N3B,  NION

                       FORMAT(2I5)

                   The number of 3body interactions to be defined, and the number
                   of ions in the system.

               == Include N3N cards 18B to define all 3-body interactions ==.

             - 18B-    1)AT1(I)  2)AT2(I)  3)ACON1(I)  4)BETA31(I)  5)GAMMA31(I)
                                           6)ACON0(I)  7)BETA30(I)  8)GAMMA30(I)

                       FORMAT(A4,A4,2X,6E10.3)

                   AT1(I):     The second atom in this 3-body interaction.
                   AT2(I):     The third atom in this 3-body interaction.
                   ACON1(I):   The pre-exponential factor for this 3-body
                               interaction for the lambda = 1 state.
                   BETA31(I):  The beta value for this 3-body interaction,
                               for the lambda = 1 state.
                   GAMMA31(I): The gamma value for this 3-body interaction,
                               for the lambda = 1 state.
                   ACON0(I):   The pre-exponential factor for this 3-body
                               interaction for the lambda = 0 state.
                   BETA30(I):  The beta value for this 3-body interaction,
                               for the lambda = 0 state.
                   GAMMA30(I): The gamma value for this 3-body interaction,
                               for the lambda = 0 state.

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

             - 19 -      IDENTIFICATION OF ATOMS WITH POSITION CONSTRAINTS
                              *** ONLY IF NTR = 1 ***

                   Constraint reference atoms are obtained by first reading
                   coordinates for the entire structure through file 'PINCRD'
                   or 'PREFC', then specific constraint atoms are selected by
                   group.  See the section on GROUP in the Appendices for format.
                   Does not support a namelist convention.


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

             - 20 -      IDENTIFICATION OF ATOMS FOR BELLY RUN
                            ***** ONLY IF IBELLY .GT. 0 *****

                   The belly atoms are loaded as groups. Consult the GROUP section
                   in the Appendices for a description of how to define a group.
                   The group definition immediately follows the end of the &cntrl
                   namelist. The GROUP input does not support a namelist convention.

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

             - 21 -      DEFINITION OF GROUP INPUT FOR FREE ENERGY COMPONENTS
                                     OR DERIVATIVES
                            ***** (ONLY IF IPERAT = 4) *****

                   For free energy components, free energies will be logged
                   as defined by the GROUP definition, subject to the condition
                   that only those atoms which are part of the perturbed group
                   or which move with an added CONstraint will ultimately
                   be included. All atoms not explicitly included in a group
                   will be put in a final single group.

                   For free energy derivatives, derivatives will be logged
                   only for those atoms included in a group definition. Any
                   atom of the system may be designated as part of any group
                   (but each atom will be a member of at most one group).
                   Typically, you will place individual atoms in their own groups
                   when calculating derivatives.

                   Note that in GIBBS, GROUP input supports two new features that
                   can be helpful in defining the input for free energy components
                   or derivatives. Both allow the creation of multiple single-atom
                   groups:

                        ATOM -IAT1 IAT2

                   (1st atom number negative) will place each atom from IAT1 to
                   IAT2 in its own group.

                        RES -IRES1 -IRES2

                   (both residue numbers negative) will place each atom of every
                   residue in the range IRES1->IRES2 in a separate group.

                   Group definition syntax is otherwise the same as described in
                   the manual.
           ----------------------------------------------------------------

             - 22 -      DEFINITIONS OF INTERNAL RESTRAINTS/CONSTRAINTS
                             *** ONLY IF INTR > 0 (line 13) ***

                   BRIEF DESCRIPTION:


                   Setting INTR > 0 allows the user to define here a series of
                   internal restraints and constraints whose force constants and
                   equilibrium values are a function of lambda.

                   Restraint/constraint definitions must be entered in the
                      formatted form shown below, not in a namelist.

                   Restraints/constraints are read in as pairs of lines:

                   line A: IAT1,IAT2,IAT3,IAT4,IUMB,IZE,ITOR,RLMDA1,RLMDA2
                           FORMAT (7(I5,1X),2F10.5)
                   line B: RKEQ1,REQ1,RKEQ2,REQ2,IPER,IPER2
                           FORMAT (4F10.5,2I5)

                   As many restraints/constraints may be defined as are desired.
                   A blank record signals the end of the input. This data must be
                   entered in the formatted form shown.
                   It does not support a namelist convention.

            INPUT VARIABLES
            ----- ---------
            IAT1-->IAT4:

                   The absolute atom numbers for the atoms defining the restraint.
                   If an atom number is <0, the absolute value of the atom number
                   is used (additional behavior for <0 values is defined when
                   IZE=1; see below).

                   IAT3 = IAT4 = 0    :  Bond restraints/constraints
                   IAT4 = 0           :  Angle restraints/constraints
                   IAT1->IAT4 non-zero:  Torsion restraints/constraints

            RLMDA1
            RLMDA2:The restraint/constraint will be applied only over the range in
                   lambda (RLMDA1, RLMDA2).

            RKEQ1
            REQ1  :The force constant in kcal/mol and equilibrium value,
                   respectively, for the restraint/constraint at lambda = RLMDA1.
            RKEQ2
            REQ2  :The force constant in kcal/mol and equilibrium value,
                   respectively, for the restraint/constraint at lambda = RLMDA2.

                   If RLMDA1=RLMDA2, the force constant and eq. value are fixed
                   at RKEQ1 and REQ1 (RKEQ2 and REQ2 are ignored).

                   RKEQ1 and RKEQ2 are ignored for constraints (ITOR=2).

                   If REQ1=999. or REQ2=999., the corresponding equilibrium value
                   is set to the current value of the internal coordinate (as
                   determined from the input set of coordinates PINCRD).

                   If ABS(REQ1) > 1000, the corresponding equilibrium value is set


                        REQ1 < 0:    REQ1 = current_value - [ABS(REQ1)-1000.]
                        REQ1 > 0:    REQ1 = current_value + [ABS(REQ1)-1000.]

                   If ABS(REQ2) > 1000, REQ2 is analogously reset.

                   Intermediate Keq() and Req()
                   are determined by linear interpolation between the force
                   constants and equilibrium values at RLMDA1 and RLMDA2.
                   No restraint/constraint is applied outside the range
                   (RLMDA1,RLMDA2).

            IZE:
            = 0    The restraint/constraint defined here is used _in addition to_
                   other parameters corresponding to this atom sequence from parm
                   (if any).

            = 1    The restraint parameters defined here _replace_ overlapping
                   parameters from parm (if any) for this atom sequence.

                   When IZE=1, any atom number IAT1->IAT4 which was specified as
                   < 0 has a special meaning: It allows a "wildcard" match to the
                   corresponding atom number when replacing parameters from parm.
                   For example, the sequence -1 3 8 -14 would result in a torsional
                   restraint which would replace parameters for all torsions
                   centered on the bond between atoms 3 and 8.

                   IZE is read but ignored when ITOR=2 (constraints).

            IUMB:  Determines the type of restraint.

            = 0    The restraint is to be considered part of the molecular force
                   field.  The free energy contribution from the restraint is
                   calculated by the standard formula (c.f. Equation 2).

            = 1    The restraint is considered to be an "umbrella" term. The
                   effects on the ensemble of the restraint are evaluated using
                   the following function in place of Equation 2:

             G=-RTln(<e-V/RTe/RT>V+/<e/RT>V+),

                   where  is the sum of all umbrella restraint terms and
                   V is as described for Equation 2.

                   IUMB is ignored for constraints (ITOR=2).
                   IUMB = 1 will not work correctly with slow growth or
                   thermodynamic integration.

            ITOR:  Functional form/constraint flag

            = 0    If this is a torsional restraint, a potential of the form

                         Ktor(-0)2


                   is used. This functional form is always used for bonds and
                   angles (ITOR = 0 has no effect for bonds/angles).

            = 1   If this is a torsional restraint, a potential of the form

                      Ktor(1-cos(-0))

                  is used. (ITOR = 1 has no effect for bonds/angles).

            = 2   Then a constraint, rather than restraint, is applied to the
                  corresponding internal coordinate. This is applicable to all
                  types of internal coordinates (distances, angles, torsions).
                  If NCORC = 1 (line 9), then an effective "potential of mean
                  force" (PMF) contribution to the free energy will be calculated
                  for this internal coordinate.
                  General "holonomic" internal constraints are used, as described
                  in Reference 7.

                  When ITOR = 2 (internal is being constrained), IZE is ignored,
                  and the following occurs:

                  For bonds and angles, if the constrained internal matches an
                      internal in the topology file, force constant parameters
                      for matching internal will be set to 0.

                  For torsions, if the constrained internal matches an internal
                      in the topology file, A) forces for all torsions centered on
                      the same bond will be omitted B) The contributions to the
                      free energy of all torsions centered on the same bond as the
                      constraint will be calculated. This is necessary because
                      several torsions can be centered on a central bond, and
                      there is no fixed relative arrangement for these torsions.

            IPER: IPER can be used to define a simulation where two internal
                  coordinates will be varied with two independent values of lambda.
                  Such a simulation can be used to generate a free energy
                  internal-internal map (sort of a free energy equivalent to a
                  Ramachandran map) to be generated.

                                      NOTE
                  The output of this option is somewhat complex, and
                  is intended for post-processing by a separate program. Any 2-D
                  run of value will necessarily be very compute-intensive, and a
                  number of issues must be considered before undertaking such a
                  simulation. This option should generally be avoided by the novice
                  user. If you are considering performing such a simulation, you
                  are urged to read Reference 8 (see above) first.

                  For use with the IPER flag, we define:

                    "primary" lambda: the "normal" lambda; that is, the lambda used
                                      in standard GIBBS runs to describe how the
                                      system varies between the initial and final


                                      states.

                  "secondary" lambda: a second lambda, which is translated from
                                      0->1 at each value of the "primary" lambda.

             = 0  This restraint will vary with the primary lambda; i.e. the
                  equilibrium value and force constant will be a function only of
                  the primary lambda. This is standard behavior.

             > 0  This restraint will vary with the secondary lambda; i.e. the
                  equilibrium value and force constant will be a function only of
                  the secondary lambda. Lambda will be varied from 0->1 for this
                  restraint in a series of IPER equally-spaced intervals (windows).

                  The "secondary" lambda is not used unless one or more restraints
                  are defined with IPER > 0.

                  The number of windows used for each "primary" restraint will
                  be the same, and the number used for each "secondary" restraint
                  will be the same. The first IPER(I) > 0 sets the number of
                  windows used for _all_ secondary restraints.

                  If secondary restraint(s) are requested, the value of IPER2 (see
                  below) corresponding to the first value of IPER(I) > 0 defines
                  the number of windows used for every primary restraint. Note
                  that any dynamically modified window or slow growth flags (card
                  14) will be defeated in this case.

                  When calculating PMF-type energies (if NCORC=1),
                  constraints will be applied in two cycles. First, dG will be
                  calculated for +-d(internal) for only those internals for which
                  IPER=0. Then a dG will be calculated +-d(internal) for only
                  those internals for which IPER>0.

                  Any parameters (other than constraints) that vary with lambda
                  will only change when lambda for the primary constraints changes.
                  You will typically define the "perturbed group" (see the PARM
                  module) to contain no atoms, when using "secondary" restraints/
                  constraints.

                  If IPER > 0, window or dynamically-modified window growth must
                  have been requested (line 14). IPER cannot be set > 0 with
                  slow growth or with thermodynamic integration (IDIFRG > 0).

                  The matrix of energies from a 2-D run is contained in file
                  CONSTMAT.  A matrix can be generated with either IDWIDE = 0 or
                  IDWIDE = 1, but it is strongly recommended that IDWIDE = 1
                  (no double-wide sampling) be used. In this case, five free
                  energy difference are evaluated from each ensemble,
                  corresponding to moves from (lam1, lam2) to
                  (lam1, lam2+d_lam2), (lam1, lam2-d_lam2), (lam1+d_lam1, lam2),
                  (lam1-d_lam1, lam2), (lam1-d_lam1, lam2-d_lam2). This set


                  allows the whole free energy map to be evaluated most
                  efficiently (see the Pearlman and Kollman reference [8] noted
                  above).

                  The "secondary" lambda always changes in the "forward" direction,
                  always starts at 0.0, and always ends at 1.0. After lambda has
                  gone from 0->1. The primary lambda is incremented one step, the
                  secondary lambda is reset to 0, and another cycle of secondary
                  lambda changes occurs. At the start of each cycle of changes in
                  the "secondary" lambda, the current coordinates are stored in
                  file CNSTSCRT.

            IPER2:If IPER > 0 for a particular restraint/constraint ("secondary"
                  restraints defined), IPER2 gives the number of "windows" used
                  in translating the "primary" lambda from 0 to 1. See the
                  description of IPER above. If IPER > 0, IPER2 fixed-width windows
                  will be used for the "primary" restraints, regardless of the
                  behavior requested by ISLDYN, etc. (lines 14-ff).


      1.8.  Choices Affecting Free Energy Calculations

                             David A. Pearlman
                     Dept. of Pharmaceutical Chemistry
          University of California, San Francisco, CA 94143-0446
                                   1/91

           The  development of ever-more-powerful computers, combined
      with the wide dissemination of modeling  packages  like  AMBER,
      puts the power to perform valuable calculations in the hands of
      an increasingly large number of scientists. It is  tempting  to
      say that, given the increasing sophistication of such programs,
      all one needs is the appropriate hardware and software to  per-
      form good experiments.

           But  this is not the case. As modeling programs have grown
      more sophisticated, they have sprouted an ever-increasing array
      of options-options which must be properly chosen, if worthwhile
      results are to be obtained. And even if the options are  appro-
      priately  set,  one  must  ensure  that the program is properly
      suited for the chosen application. Nowhere  in  AMBER  is  this
      more true than the GIBBS free energy module.

           Here we discuss several issues which impinge on developing
      an appropriate  GIBBS  input  file,  and  on  interpreting  the
      results produced. One is also strongly encouraged to review the
      literature referenced here and in the preface to the GIBBS pro-
      gram.

      1.8.1.   I.  What  method  should be used to calculate the free
      energy?

           GIBBS version 4.0 offers five choices of method for calcu-
      lating  the  free  energy  difference between two states. These
      include the general classes slow growth, free energy  perturba-
      tion,  and  thermodynamic  integration,  as well as dynamically
      modified variants of the latter two. These  were  described  in
      the  introduction  to GIBBS. As yet, it has not been shown con-
      clusively what method is "best"  for  any  particular  type  of
      problem.

       (1)   Slow  growth:  Some  early  studies  indicated that slow
             growth might be a  more  efficient  technique  for  free
             energy  calculation  than fixed-width windows [1].  More
             recent work [2] has indicated that the implicit  assump-
             tion  of  slow  growth-that lambda changes slowly enough
             that the system can be assumed to be in  equilibrium  at
             each  step-does  not  strictly hold. The consequences of
             this "Hamiltonian lag" have not been quantified.


       (2)   Window Growth: The equations of window growth,  or  Free
             Energy  Perturbation (FEP) are exact, and, in principal,
             if one has the computer resources to perform  sufficient
             sampling,  one  can  obtain  very  accurate results.  In
             practice, FEP suffers from two significant difficulties.
             The  first  is that, in reality, we do not always sample
             to convergence. Unfortunately, no reliable test to prove
             convergence  has been developed. The second problem with
             FEP is that Equation (2) requires  that  we  obtain  the
             ensemble  average of a quantity which relies of the dif-
             ference between the potential  functions  representative
             of  both  states  lambda  (i) and lambda (i+1).  But the
             average is evaluated from the ensemble of states visited
             when  MD  is  run using the potential function for state
             lambda (i). Thus, if states lambda (i) and lambda  (i+1)
             are  too dissimilar, it will be very difficult to obtain
             reliable statistics. Reducing the spacing between  adja-
             cent lambda states helps circumvent this problem, but at
             a significant additional cost. And even then we  do  not
             have  any  reliable methods for assuring the problem has
             been avoided [3].

       (3)   Thermodynamic Integration (TI): TI is appealing  because
             it    avoids    the   problem   in   sampling   V(lambda
             (i+1))-V(lambda (i)) described for FEP above. But TI has
             its  own problem: The driving equation of TI is an inte-
             gral (Equation 4), which in practice must be  calculated
             approximately  by  evaluating  the  integrand  at finite
             intervals of lambda.  Of course, TI is also  susceptible
             to errors when a simulation is not run sufficiently long
             to obtain a converged value  of  the  averaged  quantity
             which serves as the integrand.

             At  this  time, the relative rates of convergence of the
             averaged quantities required by FEP and TI,  which  will
             directly  impinge  on the reliabilities of the two tech-
             niques, have not been determined.

             Note that we approximate the integral using  the  trape-
             zoidal algorithm, i.e.

      Gi=G((i+1))+G((i))=(<V/>(i+1)-<V/>(i))((i+1)-(i))/2.        (5)

             This integration method should be reasonably accurate in
             most cases. But in case the user wishes to try their own
             integration scheme, setting ISANDE = 1 with TI will also
             force     reporting      of      the      values      of
             <partialV/partiallambda>lambda(i)   and   several  other
             averages at every evaluation  point  (the  other  values
             reported  relate to calculating the enthalpy/entropy, as
             described below).


       (4)   Dynamically Modified Windows (DMW): In dynamically modi-
             fied  windows [3], the delta lambda spacing between con-
             secutive windows in FEP or TI is  continually  changing,
             to  achieve a relatively constant free energy change per
             window. This should improve the efficiency of the calcu-
             lation, by focusing proportionately more simulation time
             on those ranges of  lambda  where  the  free  energy  is
             changing  more  rapidly.  We  have,  in fact, shown that
             dynamically modified windows significantly  improve  the
             sampling  efficiency  of  FEP simulations for model com-
             pounds [3].   The  biggest  drawback  to  DMW  is  that,
             because  we  do not know a priori the exact shape of the
             free energy versus lambda curve when we start a  simula-
             tion, we cannot predict with certainty how long the sim-
             ulation will take  to  go  to  completion.  This  caveat
             noted,  it  appears that DMW would be beneficial to most
             FEP and TI simulations.

      1.8.2.  II. Enthalpies and entropies

           GIBBS Version 4  allows  the  user  to  request  that  the
      enthalpy  and  entropy  changes  be reported in addition to the
      free energy (which is always reported). Two  different  schemes
      are  used  to calculate these quantities, depending on the free
      energy calculation  method.  Note  that  in  either  case,  the
      enthalpy and entropy are necessarily dependent on being able to
      reliably extract small differences between averages  of  (often
      large)  total  system  energies. In the case of free energy, on
      the other hand, we need only measure the average of a potential
      difference  or a derivative.  For this reason, enthalpy/entropy
      estimates are typically more than an order  of  magnitude  less
      accurate  than  their  free  energy counterpart.  One should be
      very cautious when interpreting them.

           For FEP, the approximate equations derived in Ref.  4  are
      used. These approximate the required temperature derivatives by
      a finite difference. The equations used are  derived  from  the
      FEP  expression,  and  the  sum  of  the  resulting (enthalpy -
      T*entropy) will equal the reported free energy.

           For TI, the  enthalpy  and  entropy  are  evaluated  using
      exact-form  integral  relationships  presented  in Ref. 5.  The
      (enthalpy - T*entropy) calculated by this method will not  nec-
      essarily  equal  the reported total free energy; the difference
      between the two quantities can be taken as a  crude  indication
      of  the  reliability of the enthalpy/entropy values.  The inte-
      grals are approximated by the trapezoidal  rule,  as  described
      above (Equation (5)).


      1.8.3.  III. Mixing rules for vanishing atoms

           By  default  (and  without  exception in older versions of
      Gibbs), the optimal interaction r*ij between two atoms i and  j
      is given by

                     r*ij()=r*i()+r*j()                           (6)

      This is fine when neither atom "vanishes" at either lambda end-
      point.  But now consider the case  where  atom  i  vanishes  at
      lambda=0.  Then

               r*ij(0)=r*i(0)+r*j(0)=r*j(0).                      (7)

      Thus,  r*ij  never  gets  smaller than r*j(0). At lambda=0, the
      mixed well depth, epsilon(0), will also be 0. But at any  value
      of  lambda  just slightly >0, epsilon!=0, and suddenly a steric
      "gap" between atoms i and j of r*j will be required.  This  can
      lead to sampling inefficiencies. A better solution is to shrink
      r*ij(lambda) to a user-chosen small value as one of  the  atoms
      "vanishes". This is the effect of variable IDSX0 (line 10).

      1.8.4.  IV. Using Dynamically Modified Windows

           The  theory of DMW, and some exploratory applications, are
      described in Ref. (3). A sample input for GIBBS is shown below,
      follow by a few important explanatory notes.

                  line
                  14     0  40.00000  0.00000  -0.02500  +2  0  100  100  0  0  0  0
                  14a    8    2   0   0.8000000   0.0100000
                  14b  -10   20   0.0001000
                  14c   1.0D-5  1.D-10   1.0D-2        0.10000000    0    0  -1.00

                  (format compressed to fit page)

      Line 14
      We  set  ALMDEL  = 0, ISLDYN=+2, IDIFRG=0, NSTMEQ=100, and NST-
      MUL=200. This results in dynamically modified window FEP,  with
      100 steps of equilibration and 100 steps of data collection per
      window.

      Line 14a:
      On the next line, we set IAVSLP = 8, IAVSLM=2, and  CORRSL=0.8.
      This  means  that,  at  most,  the  8  most recently calculated
      (lambda,  accumulated_free_energy)  points  will  be  used   in
      approximating  the  partial  G / partial lambda slope. IAVSLM=2
      means that as soon as 2 points are available, we will calculate
      the  slope from all available points, until the maximum of 8 is
      reached. If the best-fit line through the points fits the  data
      with  a  correlation coefficient (CC) < 0.8, then the number of


      points used in the current slope determination will be  halved,
      the  slope  and  CC  will  be  recalculated, and the comparison
      against CC will be performed again. A minimum of two points are
      always used to calculate the slope.

      AMXMOV, which is set to 0.01 here, is the target change in free
      energy per window we are aiming for. The delta lambda change on
      the next step is calculated as

                          =______                                 (8)

      Note  that  since  we  don't know a priori what the free energy
      versus lambda curve will look like, we do not know exactly  how
      many  steps  will  be required to complete the simulation.  The
      total number of MD steps required will depend  both  on  AMXMOV
      and  on NSTMEQ and NSTMUL (line 14). NSTLIM can be set to -1 on
      line 8 to  force  the  program  to  continue  until  the  total
      required  number  of  steps have been performed. Also note that
      the value of AMXMOV used will often depend on the magnitude  of
      the  total  anticipated  free  energy change.  For example, one
      would not typically want to  use  AMXMOV=0.01  and  NSTMEQ=NST-
      MUL=100  if  the total energy change is 50 or 100 kcal/mole, as
      it can be for certain electrostatic changes.

      line 14b:
      IAVDEL < 0, which means that the Gforward-Greverse  comparisons
      will  not be used in scaling the widths of lambda windows.  The
      viability and reliability of changes made using these types  of
      comparisons has not yet been established.

      line 14c:
      ALMDL0  is set to 1.0D-5. This means that the first IAVSLM win-
      dow steps (before we have enough points to calculate  a  slope)
      will  be made with this small step size. This step is chosen to
      be small in case the energy is changing quickly in this region.

      DLMIN  is  set  to 1.0D-10. Typically, a value of DLMIN such as
      this would have no effect, since it is unlikely that the  slope
      and  AMXMOV  would  be such to require a step this small in the
      first place. At any rate, steps calculated to be  smaller  than
      DLMIN  are  reset to DLMIN. DLMIN can be valuable in some cases
      when one wishes to limit how slowly a simulation can  progress.

      DLMAX  is set to 1.0D-2. Setting an appropriate value for DLMAX
      is important. If the G versus lambda curve has  any  points  of
      inflection,  we  might  calculate a slope of approximately 0 at
      one or more points. In this case, the simple  formula  used  to
      determine  the  next step size would indicate a very large step
      (as large as 1.0, the whole simulation length). This  would  be
      incorrect,  as the slope could clearly turn significantly non-0
      in a future range of lambda.  DLMAX bounds the change  in  such
      cases.


      AMXRST  is  set  to  0.10.  The  slope  we calculate is only an
      approximation of the "true" instantaneous slope, and  the  cur-
      rent  slope  is  only  an  estimate  of the slope over the next
      lambda interval (window).  Thus, it is possible  that  when  we
      calculate  the  actual free energy change over the next window,
      it will be an unacceptable amount larger than the target value.
      In  such  a  case, we may want to decrease the lambda step size
      for this window and  re-evaluate  the  energy.  AMXRST  is  the
      largest allowable energy for a step. If the energy is > AMXRST,
      the delta lambda stepsize is reduced, and the  energy  for  the
      window recalculated. Note that setting AMXRST too close to AMX-
      MOV will result not only in too many windows being  reevaluated
      (inefficient), but can also lead to biased sampling.

      ALMSTP(1)  is set to -1.0. If 0 < ALMSTP(1) < 1.0, one can pre-
      scribe that the values of AMXMOV, DLMIN, DLMAX and AMXRST  vary
      over different ranges in lambda, as described in the input dis-
      cussion.

      1.8.5.  V. Potential of Mean Force (PMF) calculations

           It is often of interest to determine the free energy  dif-
      ference between two states which differ in conformation, rather
      than in composition. For example, one might  be  interested  in
      the free energy profile for rotation about a ring in a protein.
      Such a profile can be determined by performing  a  PMF  simula-
      tion.  To perform such a simulation, one must be able to define
      conformation as a function of lambda within the context  of  an
      otherwise  free  MD  simulation. Fortunately, methods have been
      developed which allow selected internal coordinates to be  con-
      strained  to  chosen  values,  while otherwise affecting the MD
      trajectory only minimally. The best known of these is the SHAKE
      method for bond constraints. The methods of SHAKE have recently
      been extended to be generally applicable to angles and torsions
      [6].  one can calculate the free energy changes that accumulate
      as the internal constraints are translated from  those  of  the
      initial  state  to  those of the final state. If one graphs the
      free energy changes as a function of the restraint target  val-
      ues (themselves a function of lambda), one gets the free energy
      profile for conformational changes.

           Any constraint with a target value which is itself a func-
      tion  of  lambda  will  contribute to the free energy as lambda
      changes. This means that if SHAKE is used to constrain bonds of
      the  perturbed group, and any of those bonds "grow" or "shrink"
      during the simulation, there will be a corresponding  contribu-
      tion to the free energy. In earlier work, this contribution has
      been overlooked, but we have shown that it must be included  to
      reliably calculate free energies using the FEP method [7].  The
      contribution in such a case can be calculated simply by setting
      NCORC=1.


           Constraints  other  than  SHAKE-en bonds can be defined by
      setting INTR > 0 (line 14) and providing the definitions  after
      the  standard input (see above). Any internal coordinate can be
      used; Be aware, however, that any internal coordinate which  is
      part  of  a  closed  ring  will present a special set of (often
      tricky) considerations (see below).  In typical use, no  compo-
      sitional  (or topological) change is performed when a PMF simu-
      lation is being carried out. A GIBBS-format  topology  file  is
      still  required  from  PARM  or  LEaP,  though.  An appropriate
      topology file with no atoms in the  "perturbed  group"  can  be
      generated  by  using the PERT option in PARM, but with no atoms
      defined in the pert group; i.e.

           Title: Generic PERT topology with no atoms changing
           BIN FOR STDA    PERT
               0    0    0
               0    0    0    0
           PERTURBATION
           No atoms change
           END
           END

      Similarly, in LEaP, one does not define any per-atom  perturba-
      tions  ("edit  molecule"  /  Selection / Edit selected atoms to
      turn per-atom pert on/off) and does a

           > saveamberparmpert molecule nullpert.top nullpert.crd

           In general, PMF calculations within GIBBS may be performed
      with  any method - FEP, TI or slow growth. (Before version 4.1,
      only FEP could be used for PMF calculations.) Note  that  there
      is  one  scenario  where only the TI (with "constraint forces")
      method may be used: when any constrained internals whose target
      values  change  with  lambda lie within a closed loop. The loop
      can either be part of the molecular topology, or as a result of
      the  added  topology  of  the constraint(s).  To understand why
      neither FEP nor TI with "potential forces" can be used in  such
      a  case, you must recognize that for these latter methods, part
      of  the  procedure  for  calculating  constraint  contributions
      requires  that  we  determine  which  atoms  of  the system are
      affected by a rigid body translation/rotation  about  the  con-
      strained internals. But the requisite set of atoms is not unam-
      biguously defined when the  constraint  lies  within  a  closed
      loop.  Fortunately, the "constraint force" implementation of TI
      doesn't require that we make such a determination.

           It is important to note that PMF  calculations  are  typi-
      cally  very  compute-intensive.  For  FEP, Gibbs will determine
      which non-bonded  pairs  have  an  interatomic  distance  which
      varies  with  one  or  more constraints, and only these are re-
      evaluated in determining V(i+1). This helps reduce  the  amount
      of  computer  time  required for a FEP simulation, although the


      total amount of time can remain high. The additional cpu  over-
      head  for calculating constraint energies with TI is negligible
      in all cases.

           While we have a good error check for some torsional  PMF's
      (the free energy values after rotating 360 should be the same),
      we typically have no reliable way of determining that for other
      simulations enough sampling has carried out to determine a con-
      verged PMF curve. Our best guard against  spurious  results  is
      careful  consideration of the specific problem and the inherent
      relaxation timescales of the surroundings.

      1.8.6.  VI. Error estimates and convergence

           One of the thorniest issues related to free energy  calcu-
      lations  is estimating the error in the results [7-9].  At pre-
      sent, this error is typically estimated in one of four ways:

       (1)   Two separate free energy simulations  can  be  run,  one
             with  lambda  progressing  from  0->1,  the  second with
             lambda progressing from  1->0.  These  two  calculations
             should yield the same free energy value, and the differ-
             ence between them (the "hysteresis") gives a lower bound
             on  the  estimate  in the calculation. Errors derived in
             this way often underestimate the actual error [7].

       (2)   The difference between "forward" and  "backward"  values
             for  a  single  run.   As described in the introduction,
             when FEP or slow growth is performed,  double-wide  sam-
             pling can be carried out. This ultimately results in two
             pseudo-independent values for the free energy, one  cal-
             culated from the sum of all the lambda (i)->lambda (i+1)
             energies, and the other calculated from the sum  of  all
             the  lambda  (i)->lambda  (i-1).   If  the  results were
             exact, these values would be the same. In practice, they
             will  not  be,  and their difference gives a crude lower
             bound on the inherent error. Error estimates derived  in
             this  manner  tend  to  be even less reliable than those
             estimated using method (1), and  are  usually  worthless
             for slow growth type runs [8].

       (3)   Two  or  more  simulations  are run under equivalent but
             different conditions.  For example, staring with differ-
             ent  randomly  assigned sets of velocities.  The differ-
             ence between the free energies provide  an  estimate  to
             inherent errors. These estimates are subject to the same
             problems as (1) above.

       (4)   A series of simulations  is  run  which  differ  in  the
             respective  amounts of sampling done. For example, simu-
             lation 1 might use 100 steps of  equilibration  and  100
             steps   of   data   collection  at  each  window,  while


             simulation 2 used 200 steps of each. If the  value  from
             the  shorter simulation was accurate, the value from the
             second simulation should be acceptably close to  it.  If
             it  is  not,  the  simulation must be run even longer to
             confirm convergence. This method probably  provides  the
             best insurance that convergence has been reached, but it
             is not definitive, and it is also the most costly.

           It must be understood  that  none  of  the  above  methods
      allows a completely reliable error estimate. At best, they pro-
      vide a lower bound on the error. A large apparent  error  is  a
      good indication that the results obtained are not appropriately
      converged.  But a low apparent error does not necessarily indi-
      cate a converged and accurate simulation. This is clearly shown
      in Reference (7).

      1.8.7.  VII. Changing parameters versus dual topologies

           In "standard" operation, free energy changes in GIBBS  are
      effected  by transforming the potential representative of state
      1 to that representative of state 2. The topology of the system
      does  not  change.  To make atoms non-interacting at one of the
      endpoints, they are assigned zeroed non-bond and  electrostatic
      parameters at this endpoint.

           The  improved mixing rules which can be used in GIBBS Ver-
      sion 4 (IOLEPS = 0, line 10) allow a second method to be  used.
      One  result  of  these  new mixing rules is that if any pair of
      atoms "exist" only at mutually exclusive endpoints (e.g. atom i
      exists  in  state  1 but not state 2; atom j exists in state 2,
      but not in state 1), then effectively  no  non-bonded  interac-
      tions  are  ever  calculated  between them. This means that, in
      lieu of the "standard" method which uses a single topology,  we
      can define dual topologies, one corresponding to the lambda = 0
      endpoint, and the other corresponding to the lambda  =  1  end-
      point. For the former topology, all non-bonded parameters would
      be defined to be 0 in the lambda = 1 state. Similarly, all non-
      bonded  parameters for the latter topology would be 0 at lambda
      = 0.  The two topologies would then never "see" each  other  at
      intermediate  values  of  lambda.  Defining dual topologies can
      aid in performing free energy calculations where  bond  connec-
      tivities  must  change.  Dual topologies is the method incorpo-
      rated into the "CHARMM" program.

           On an efficiency basis, the relative  merits  of  the  two
      methods have not been established. Additional discussion of the
      two methods can be found in Ref. (7).


      1.9.  References

      (1)
        Straatsma, T.P., Berendsen, H.J.C. & Postma, J.P.M. (1986) J.
        Chem. Phys. 85, 6720.

      (2)
        Pearlman, D.A. & Kollman, P.A. (1989) J. Chem. Phys. 91, 7831

      (3)
        Pearlman, D.A. & Kollman, P.A.  (1989)  J.  Chem.  Phys.  90,
        2460.

      (4)
        Fleischman,  S.H.  &  Brooks,  C.L. (1987) J. Chem. Phys. 87,
        3029.

      (5)
        Yu, H.-A. & Karplus, M. (1988) J. Chem. Phys. 89, 2366.

      (6)
        Tobias D.J. & Brooks, C.L. III  (1988)  J.  Chem.  Phys.  89,
        5115.

      (7)
        Pearlman,  D.A.  &  Kollman,  P.A.  (1991) J. Chem. Phys. 94,
        4532.

      (8)
        Pearlman, D.A. & Kollman, P.A. (1989) In: Computer Simulation
        of Bimolecular Systems: Theoretical and Experimental Applica-
        tions (van Gunsteren, W. and  Weiner,  P.K,  eds.),  p.  101,
        Escom Science Publishers, Netherlands; van Gunsteren

      (9)
        van Gunsteren, W., ibid, p 27.