block (c49b1)

The commands described in this section are used to partition a
molecular system into "blocks" and allow for the use of coefficients
that scale the interaction energies (and forces) between these blocks.
This has a number of applications, and specific commands to carry out
free energy simulations with a component analysis scheme have been
implemented. The lambda-dynamics, an alternative way of performing
free energy calculations and screening binding molecules, has also been
implemented. Subcommands related to BLOCK will be described here. To
see how to output the results of a dynamics run, please see DYNAMICS
documentation (keywords are IUNLDM, NSAVL, and LDTITLE).
Please refer to PDETAIL.DOC for detailed description of the lambda
dynamics and its implementation.

BLOCK was recently modified so that it works with the IMAGE
module of CHARMM. As some changes to the documentation were necessary
anyways, it was decided to also improve the existing documentation.
The Syntax and Function section below are relatively unchanged; the
added documentation is in the Hints section (READ IT if you are using
BLOCK for the first time!). Comments/suggestions to Stefan Boresch.

BLOCK was modified so that it works with the Ewald (simple and PME)
method of CHARMM. The Syntax and Function of BLOCK module are unchanged.


* Syntax | Syntax of the block commands
* Function | Purpose of each of the commands
* Hints | Some further explanations/hints
* Limitations | Some warnings...

Top
Syntax of BLOCK commands


BLOCk [int]

Subcommands:

miscellaneous-command-spec ! see » miscom

CALL int atom-selection

LAMBda real

COEFficient int int real -
[BOND real] [ANGL real] [DIHEdral real] [ELEC real] -
[VDW real] [VDWA real] [VDWR real]

NOFOrce

FORCe

FREE_energy_evaluation [OLDLambda real] [NEWLambda real] -
FIRSt int [NUNIT int] [BEGIn int] [STOP int] [SKIP int] -
[TEMPerature real] [CONTinuous int] [IHBF int] [INBF int]
[IMGF int]

INITialize

CLEAr

Energy_AVeraGe [OLDLambda real] [NEWLambda real] -
FIRSt int [NUNIT int] [BEGIn int] [STOP int] [SKIP int] -
[CONTinuous int] [IHBF int] [INBF int] [IMGF int]

COMPonent_analysis DELL real NDEL int [TEMPerature real] -
FIRSt int [NUNIT int] [BEGIn int] [STOP int] [SKIP int]
[IHBF int] [INBF int] [IMGF] int

AVERage {DISTance int int}
{STRUcture}
[PERT] [TEMPerature real] [OLDLambda real] [NEWLambda real] -
FIRSt int [NUNIT int] [BEGIn int] [STOP int] [SKIP int]

EXCLusion int int [int int] [int int]

ADEXclusion int int

LDINitialize int real real real real [real]

RMBOnd RMANgle

LDMAtrix

LDBI int

LDBV int int int int real real int

THBV COLL [int|ALL] real real

THBV INDE [int|ALL] [real|AUTO]

LDRStart

LDWRite IUNL int NSAVL int

RMLAmbda {internal_energy_spec}
internal_energy_spec ::== BOND 12BOnd 13BOnd THETa|ANGLe PHI|DIHEd IMPHi|IMPR CMAP
SAVE

UNSAve

QLDM [THETa]

QLMC [MCTEmperature real] [FREQ int] [MCSTep int] [MAX real]

MCIN int {real .... real}

MCDI real

MCRS

MCLEar

MSLD [int_1 int_2 ... int_nblocks | NSITe int] { FNEXponential [real] }
{ FNXS [real_1 ... real_nsites] }
{ FNSIn }
{ F2Exponential }
{ F2Sin }
{ FFIX }
! note: int_1 must be 0, block 1 = environment = Site 0

BLASsign int_block int_site

MSMAtrix

LANG [TEMP real]

RSTP int real
" Dual-topology Softcore"
[PSSP] ! use soft core potentials for interactions in between
! blocks. This option is remembered. With
! the PSSP keyword, two parameters, ALAM and DLAM can
! be set.

[ALAM real] ! Separation parameter for elec. interaction (defaults to 5A^2)

[DLAM real] ! Separation parameter for LJ interaction (defaults to 5A^2)

[NOPSsp] ! Turn off use of soft core interactions.
NB! This requires FAST OFF and nonbond options SHIFT VSWITCH.
" -- H. Li and W. Yang

MCFRee EXFReq int FINI real FFIN real FLAT real

MCLAmd int LAMD0 real LAMD1 real ....... LAMD[int-1] real

HYBH real ! HYBrid Hamiltonan module (HYBH).

OUTH int ! HYBH

TSTH real [<update-spec>] ! HYBH

PRIN ! HYBH

PRDH ! HYBH

CLHH ! HYBH

SOFT [W14 | ON | OFF]

SOMM "CHARMM/OpenMM implementation of softcore"

PMEL [NN | EX | ON | OFF]

FLAM string int

SCAT [ON | K [real] | OFF]

CATS atom-selection

NSOB int [RALF real] [LEXP real] [BLEX real]

SOBO int atom-selection1 atom-selection2

RLFR [ON | OFF]


END

Top
1) BLOCk [int] enters the block facility. The optional integer is
only read when the block structure is initialized (usually the first
call to block of a run) to specify the number of blocks for space
allocation. If not specified, the default of three is assumed.

2) END exits the block facility. The assignment of blocks, the
coefficient weighting of the energy function, the force/noforce
option, etc. remain in place. For the terms of the energy function
that are supported, each call to ENERGY (either directly or through
MINIMIZE, DYNAMICS, etc. commands) results in an energy and force
weighted as specified. The matrix of interaction coefficients is
printed upon exiting.

3) CALL removes the atoms specified by "atom-selection" from their
current block and assigns them to the block number specified by the
integer. Initially all atoms are assigned to block 1. If atoms are
removed from any block other than block 1, a warning message is
issued. If blocks are assigned such that some energy terms (theta,
phi, or imphi) are interactions between more than two blocks, a
warning is issued when the END command is encountered. (Take such
warnings seriously; this is a severe error and indicates that
something is wrong. However, the problem might be not the CALL
statement (or the atom selection) itself; quite possibly your hybrid
molecule was generated improperly)

4) LAMBda sets the value of lambda to "real". This command is only
valid when there are three blocks active. Otherwise multiple COEF
commands may be used to set the interaction coefficients manually.
LAMBda x
is equivalent to (let y=1.0-x)
COEF 1 1 1.0
COEF 1 2 y
COEF 1 3 x
COEF 2 2 y
COEF 2 3 0.0
COEF 3 3 x

5) COEF sets the interaction coefficient between two blocks (represented
by the integers) to a value (the real number). When the block facility
is invoked, all of the atoms are initially assigned to block 1 and all
interaction coefficients are set to one. The required real value
(first specified) scales all energy terms expect those specific terms
which are named with alternative corresponding scale factors.

The name "VDWA" and "VDWR" correspond to the Attractive and Repulsive
terms in the Lennard-Jones potential respectively. That is they allow
one to independently scale the attractive (r^(6)) and repulsive terms (r^(12))
independently.

6) NOFOrce specifies that in subsequent energy calculations, the
forces are not required. This is economical when using the
post-processing commands (FREE,EAVG,COMP). Forces may be turned back
on with the FORCe command; this is necessary before running
minimizations and dynamics if there was a prior NOFO command.

7) FREE calculates a free energy change using simple exponential
averaging, i.e. the "exponential formula". If the old and new lambdas
(OLDL,NEWL) are specified (can only be done when three blocks are
active), the perturbation energy is calculated for these values (i.e.
FREE gives you the free energy difference between NEWLambda and
OLDLambda via perturbation from the lambda value at which your
trajectory was calculated. If not, the current coefficient matrix is
used (FREE should be used with three blocks, and the use of OLDL and
NEWL is recommended). FIRSt_unit, NUNIt, BEGIn, STOP, and SKIP
specify the trajectory/ies that is/are to be read (for a further
description see the TRAJ command elsewhere in the CHARMM
documentation). TEMPerature defaults to 300 K and gives the
temperature value to be used in k_B*T. CONTinuous specifies the
interval for writing cumulative free energies. A negative value
causes binned (rather than cumulative average) values to be written.
Be careful to make sure that you use correct non-bonded lists (see the
hints section!)

8) INITialize is called automatically when the BLOCK facility is
first entered and may also be called manually at some other point.
All atoms are assigned to block one and all interaction coefficients
are set to their initial value.

9) CLEAr removes all traces of the use of the BLOCK facility. The
next command should generally be END, and then CHARMM will operate
as if BLOCK had not ever been called.

10) EAVG The average value of the potential energy during a simulation
can be calculated with the EAVG (Energy_AVeraGe) command. The parsing
is very much like the FREE command above. The most frequent use of
this command is to calculate the average value of dV/dlambda during
the course of a simulation for use in thermodynamic integration.
CONTinuous specifies the interval for writing cumulative free
energies. A negative value causes binned (rather than cumulative
average) values to be written. Be careful to make sure that you use
correct non-bonded lists (see the hints section!) The command accepts
the OLDL / NEWL option, similarly to FREE, but for EAVG it is
recommended to set up the interaction matrix (using COEF commands)
yourself -- see the hints section.

11) [COMP] The COMP module is essentially a modified version of the
EAVG module which aside from calculating <dU/dl> = <U_1 - U_0> at a
given value of lambda l(i) will also give you expectation values of
this quantity at l(i+-1), l(i+-2) etc. based on perturbation theory.
COMP requires 4 blocks. Put the usual WT (reactant) in block 2 and
MUT (product) in block 3. Put the portion of the environment whose
contribution to the free energy change is desired into block 4 (this
can be everything else, or just a subset) (Note that the same can be
achieved easily with the EAVG command) You have to set up your own
coefficient matrix. Much of the parsing is like the EAVG command.
CONT is not supported. Two special subcommands (required) are DELL
and NDEL. The normal output of COMP is <U_1 - U_0> evaluated at the
lambda of the simulation. However, COMP also evaluates the same
ensemble averages perturbed to lambda = lambda +/-
{0,1,2,...NDEL}*DELL. This (sometimes) helps the quadrature in
thermodynamic integration. Note that NDEL must be at least 1, and
DELL should not be zero. (You have to specify these values; the
default values will lead to an invalid input, i.e. you bomb...) Be
careful to make sure that you use correct non-bonded lists (see the
hints section!) A word of warning: If your initial ensemble average
(at the lambda of the simulation) is not well converged, then your
perturbed values are most likely random numbers. The approach taken
by COMP is theoretically sound, but it should only be applied if
convergence has been established! The output format of COMP is
somewhat messy: COMP first prints <dU/dl> = <U_1 - U_0> at lambda =

lambda - NDEL*DELL
lambda - (NDEL-1)*DELL
...
lambda
lambda + DELL
...
lambda + NDEL*DELL;

then it prints an average (integral) value over these results. The
meaning of this last value is unclear to me. In earlier versions of
this documentation, COMP has been recommended over EAVG. In my
experience the opposite is true. There is little COMP can do which
you can't do with EAVG (aside from obtaining expectation values for
dU/dl). (Maybe the unclear output of the COMP module is the main
reason why I don't like it).

12) [AVER] The AVERage command is used to extract ensemble average
structural properties from a dynamics simulation. Features in this
implementation allow averages taken over ensembles that are perturbed
from that which the simulation corresponds to. This is particularly
useful for calculating the average structure expected at lambda=0.0
from a simulation run at lambda=0.1, for example. One may calculate
average structures [STRUcture] and average distances [DISTance int
int; where the two integers are the atom numbers between which the
average distance is requested], currently. The PERT keyword indicates
that a perturbed ensemble from the dynamics trajectory is desired,
with TEMPerature giving the temperature to use in the exponential for
the perturbation (defaults to 300 K), OLDLambda and NEWLambda are the
lambdas for which the simulation was run and for which the ensemble is
requested, respectively (only valid if three blocks are active; if
these are not specified, the perturbation energy is calculated with
the current coefficient matrix), and the remaining keywords are used
to specify the trajectory. NOTE: TO THE BEST OF MY KNOWLEDGE THIS
COMMAND HAS NOT BE MAINTAINED (so you are on your own if you use it!)

12a) [EXCL] The EXCLusion command allows you to create exclusions between
and within blocks, and thus eliminates the need to add them to the
residue/patch definitions in the rtf. For example, one can exclude
the non-bonded interactions between block i and blok j, as defined
by the block selections from call i {selection} and call j {selection},
with the block subcommand:
EXCL i j
where i and j are the integers corresponding to the blocks i and j,
respectively. This is, in principle, a powerful way to set up
interesting non-bonded exclusions, but was designed primarily for use
with multi-site lambda dynamics to eliminate the need to add the
long list of multiple-site exclusions to the rtf residue and patch residue
definitions. For examples of the use of this command, see:
c41test/blockexcl_test.inp and c41test/msld_test2.inp.

[ADEX] The ADEXclusion command adds to the list of exclusions created
with the EXCLusion command. (EXCLusion overwrites previous exclusions
when called a second time.) This enables the automated setup of
exclusions in a loop, when the number of exclusions is too large to
fit on a single charmm script input line.

13) LDINitialize specifies input parameters for running lambda
dynamics. It sets up the value of lambda**2, the velocity of
the lambda, its mass and reference free energy (or biasing potential).
E.g, the following input lines set up
parameters for the third lambda with [lambda(3)]**2 = 0.4,
lambdaV(3) = 0.0, lambdaM(3) = 20.0, and lambdaF(3)=5.0 (note that lambdaF(1)
should always be set to zero).

LDIN 3 0.4 0.0 20.0 5.0

For more details, see Node Hints, section "lambda-dynamics simulations".

14) LDMAtrix will automatically map the input lambda**2 values onto the
coefficient matrix of the interaction energies (and forces) between
blocks.

15) LDBI provides an option on applying biasing potentials on lambda
variables. The integer value specifies the total number of biasing
potentials to be used. E.g,

LDBI 3

will include total of 3 biasing potentials in the simulation.

16) LDBV sets up the specific form of the biasing potentials. At the
moment, the functional form is of power law and allows three different
classes (for details see "the actual simulations"). The input format is

LDBV INDEX I J CLASS REF CFORCE NPOWER

e.g.

LDBV 2 2 3 3 0.0 50.0 4

will assign the second biasing potential acting between lambda(2) and
lambda(3). The potential form belongs to the third class with reference
value of zero, the force constant of 50 kcal/mol and the power of four.

*) THBV uses theta biasing during MSLD theta dynamics to reduce the
amount of time spent sampling alchemical intermediates which allows
simulations with increased numbers of substituents. Two theta biases
are available, a collective bias (COLL)

nhigh(s) = sum((0.5*sin(theta(s,i))+0.5)**POWER,i)
nlow(s) = sum((-0.5*sin(theta(s,i))+0.5)**POWER,i)
V = 0.5*COEF*((nhigh(s)-1)**2+(nlow(s)-nsub(s)+1)**2)

where s and i are site and substituent indices, respectively; and an
independent bias (INDE)

V = sum(-b(-0.5*sin(theta(s,i))+0.5)^4,i)
with a default b coefficient of b=B*kT
B = 0.5*ln(0.125*pi*Ns^2*B)

The second argument of THBV chooses the collective bias or the independent
bias. The third argument specifies a site, by number, or if the keyword ALL
is used, will apply the bias to all sites. For the collecitve bias the
syntax

THBV COLL ALL COEF POWER

will set the coefficient to COEF, (kT is recommended), and will set the
power to POWER (2 is recommended).

For the independent bias, the syntax

THBV INDE ALL AUTO

will set the b value to the defalt value indicated above, and

THBV INDE ALL COEF

will set the coefficient to the real value given by COEF.


17) LDRStart is used to restart the lambda dynamics runs.


18) LDWRite specifies the FORTRAN output unit No. and the frequency
for writing lambda histogram by assigning an integer to IUNL and an
integer to NSAVL. (IUNL and NSAVL can be reset in DYNAmic command,
see » dynamc )

19) RMBOnd and RMANgle are used when no scaling of bond and angle energy
terms is desired.

20) RMLA is used when no scaling of bond, angle, proper torsion, and
improper torsion terms are desired. This option always works with block module.
The keywords: "RMBOnd" and "RMANgle" work only in lambda-dynamics.

COEF command can work in the same way when lambda-dynamics or hybrid-MC/MD are
not used.
e.g.
"RMLA BOND" = "COEF real BOND 1.0"

RMLA BOND removes scaling for both normal bond and Urey Bradley bond terms.
Use RMLA 12BOnd to remove bond scaling only and 13BOnd to remove Urey
Bradley scaling only.

21) SAVE saves the decomposed-energy file for post processing in the TSM
module. This command gives a choice for free energy calculation with
block module to get free energy without saving the trajectory file.
The condition and the name for the decomposed-energy file can be defined
in the dynamics module. (» dynamic keyword: IBLC, NBLC)

22) UNSAve removes the traces of the use of SAVE command shown above.

23) QLDM turns on lambda-dynamics option. LDIN command also turns on
the lambda-dynamics option only when QLMC turns off.

24) QLMC turns on hybrid-MC/MD option. If QLMC option is on, LDIN commands
do not activate the QLDM option.

In this version, we do not re-assign the velocity of the atoms when
chemical variables (lambda) are changed by MC method. Therefore, the kinetic
terms suddenly change into the different phase space. The stochastic dynamics
may diminish such artificial effects and help to reach the canonical ensemble.
QLMC and QLDM are exclusive and latest choice is active.
QLMC command should specify conditions for hybrid-MC/MD.

e.g.
QLMC MCTEmperature 300.0 FREQ 10 MCST 5 MAX 0.9

IN the above example, the temperature used for sampling the chemical space
by MC method is 300.0 [Kelvin]; MC sampling works every 10 molecular dynamics
steps (using for sampling of the atomic space); in one MC sampling, 5 trials
are examined; the scale factor (lambda^2) for the selected ligand is assigned
to 0.9 and the rest of ligands (L-1) have the scale factor 0.1/(L-1).
Different temperature can be defined in the lambda-dynamics and hybrid MC-MD
for atomic variables and chemical variables.

25) MCIN allows the intermediate states in which only two ligands have non-zero
lambda values in hybrid-MC/MD method.

e.g. (Three ligands system)

MCIN 5 0.0 0.25 0.5 0.75 1.0

5 means that each ligand may have one these five scalings:
0.0, 0.25, 0.5, 0.75, and 1.0.

In this condition, CHARMM recognizes the following chemical states:
(SCALE FACTOR)
STATE NO. LIG_A LIG_B LIG_C
1 1.0 0.0 0.0
2 0.0 1.0 0.0
3 0.0 0.0 1.0
4 0.25 0.75 0.0
5 0.75 0.25 0.0
6 0.25 0.0 0.75
7 0.75 0.0 0.25
8 0.0 0.25 0.75
9 0.0 0.75 0.25
10 0.5 0.5 0.0
11 0.5 0.0 0.5
12 0.0 0.5 0.5


26) MCDI (increment) specifies the step size to move in lambda chemical
movement. It allows intermediate states in which more than two ligands
can have non-zero lambda values in hybrid-MC/MD method. "MCDI" requires the
uniform interval for the definitions of the intermediate states.
Step size must satisfy:
Stepsize = 1.0/integer.
Example: Three ligands system

MCDI 0.25 ! 0.25 shows the step size to move in lambda chemical movement.

In this condition, CHARMM recognizes next chemical states.
(SCLE FACTOR)
STATE NO. LIG_A LIG_B LIG_C
1 1.0 0.0 0.0
2 0.0 1.0 0.0
3 0.0 0.0 1.0
4 0.25 0.75 0.0
5 0.75 0.25 0.0
6 0.25 0.0 0.75
7 0.75 0.0 0.25
8 0.0 0.25 0.75
9 0.0 0.75 0.25
10 0.5 0.5 0.0
11 0.5 0.0 0.5
12 0.0 0.5 0.5
13* 0.25 0.25 0.5
14* 0.25 0.5 0.25
15* 0.5 0.25 0.25

It is possible for MCDI to produce a state in which three ligands take
non-zero lambda values as shown with the asterisk (states 13, 14 and 15).
"MCDI" seems to be more general, but "MCIN" allows non-uniform
intervals. Thus, small step sizes can be assigned near end points.


27) MCRS ignores the force for lambda coming from the restraining potential
in lambda-dynamics. It also ignores the restraining potential energy when
chemical space is sampled by MC method. CMC/MD (Chemical Monte Carlo &
molecular dynamics) method can be carried out by combining this command
with QLMC.

28) MCLEar removes the traces of the use of QLMC command shown above.
BLOCK CLEAr command also removes the all traces of the use of QLMC.
MCLEar removes the traces of QLMC, while BLOCK CLEar removes all traces of the
BLOCK module.

29) LANG turns on the interaction between lambda variable and langevin
heatbath. In general, weak interaction between lambda variables and atoms
produced large deviations from the target temperature. Different temperatures
for lambda and atoms make nonequilibrium states and gave incorrect free
energies. Therefore, we recommend that LANG turn on in any lambda-dynamics
simulations. LEAP FROG integration method is required when using the LANG
option.

30) RSTP adds the restraining potential for the unbound states ligands
in lambda-dynamics and hybrid-MC/MD method to keep the physical low energy
states. The type of the restraining potential used with RSTP is;

R = alpha *(1 - lambda^2)* ( V - F )
i i i i

It disappears when this ligands is in bound state (lambda=1).

e.g.
REST 3 0.3
3 means the type of the restraining potential; 0.3 shows the alpha value.

There are three types for the restraining potential.
Type 1 Both environmental atoms and the ligands feel the restraining potential.
Umbrella sampling technique is used to remove the bias effect coming
from the restraining potential.
Type 2 The fixed average structure of the environmental atoms are assigned into
Block 2. The restraining potential was calculated Ri is defined as a
function of the fixed environmental atoms and the ligands.
When the system is flexible and the difference between the real
coordinates of the environmental atoms and fixed average coordinates
are considerably large, the convergence tends to slow.
Type 3 When the environmental atoms form the specific structure and vibrated
around the minimum, the fixed average structure of the environmental
atoms are similar to those of the real time coordinates.
Therefore, the force coming from the restraining potential can be
approximated zero as an average. If such a condition is satisfied,
the environmental atoms can be ignored the force coming from the
restraining potential and the ligands only feel the restraining
potential.This approximation may have a problem when we handle the
unstructured system like gas or liquid.

The utility program, post_ldm_mcmd.exe is prepared for calculating the free
energy differenes both without or with the restraining potential in
lambda-dynamics or hybrid-MC/MD method.

This program is saved in "support/post_analysis".

31) MCFRee EXFReq int FINI real FFIN real FLAT real is the main subcommand for
the definition of simulated scaling simulations. Here, EXFReq int is to set up
the frequency for Monte Carlo acceptance and rejection of the lambda space
move. FINI real is to set up the initial modification factor, usually as
2.71828 following the original Wang-Landau algorithm. FFIN real is to set up
the cutoff value for the final modification factor. FLAT real is to set up
the cutoff value for each cycle of flatness judgment.

Reference: Li, H., Fajer, M., and Yang, W. 2007. Simulated scaling method for
efficient localized conformational sampling and simultaneous alchemical free
energy simulation: A general method for MM, QM, and QM/MM simulations.
J. Chem. Phys. 126:024106.

32) MCLAmd int LAMD0 real LAMD1 real ...... LAMD[int-1] real is an additional
facility for the flexible usage of the simulated scaling method. Here, [int]
is to define the number of lambda values. LAMD0 is the first lambda value,
LAMD1 is the second one, ...., LAMD[int-1] is the last one.

33) HYBH , HYBrid_Hamiltonian module. Implementation of the truncation
scheme described in "Ensemble Variance in Free Energy Calculations by
Thermodynamic Integration: Theory, Optimal "Alchemical" Path, and
Practical Solutions", A.Blondel (2004) J.Comp.Chem 25, 985-993.
Details on the method should be sought therein. In brief, the
implementation is based on dual topology (although single topology
could be used under some conditions), the bonded terms (bond, angle
and Urey-Bradly) are kept unchanged, dihedral and impropers are
modified according to simple quadratic scheme (w_product=(3.l+1).l/4),
and electrostatic and van der Waals are treated together with a
truncation scheme reminiscent of soft-core vdw to minimize the
numerical fluctuations of the integrant (hence Optimal "Alchemical"
Path). Ewald sums and correction terms associated appeared soft
enough to be treated according to linear scaling of the charges,
allowing direct analytical calculation of dEwald/dl. A benefit of the
method, in addition to the fact that the integrant has limited
numerical fluctuations, is that it also produce a linear evolution of
the integrant along lambda (or l) in regular cases.

The implementation attempts to supports most of non-bonds, image
and Ewald sums options and warnings are made. Slow routines are not
currently supported. However, it is advised to test the results when
new combination of options are used. CMAP is not currently supported.

Associated commands are called from within the BLOCk module and are:

HBYH real: Switchs the module on and sets the lambda parameter.
Due to the theoretical properties of the method, evenly spaced
values should be sufficient (eg. l=(2i-1)/20). The product part
(bloc 3) is weighted according to l as explained above, and the
reactant part (bloc 2) is weighted according to (1-l) as explained
above.

OUTH int: Sets the output unit for the dE/dl terms.

TSTH real [<update-spec>]: Sets dl and tests the derivatives (dE/dl)
by finite differences (E(l+dl)-E(l-dl))/2/dl. None zero components
of the energy are printed.

PRIN : Prints dE/dl with the usual ENERGY printing format.

PRDH : Writes dE/dlambda components to outh unit. Replaces the
automatic writting performed during dynamics, for example, when
re-reading a trajectory for post-processing.

The current form of the output is formatted, two line per dynamic step.
R l dDIHEr dIMDIHEr dVDWr dELECr dEWKSUMr dEWSELFr d(EWEXCL+EWQCOR+EWUTIL)r
P l dDIHEp dIMDIHEp dVDWp dELECp dEWKSUMp dEWSELFp d(EWEXCL+EWQCOR+EWUTIL)p
Format: (a1,1x,f6.4,7(1x,1pg24.16e2))

CLHH: Clears the data structure for truncation scheme and switchs off
the module without changing the rest of the block setup. Note, the
BLOCk/CLEAr command also switchs off the module.

No analysis routine is currently supplied as careful convergence
analysis should be undertaken. It is advised that additions of the
terms be made at least in real*8 format as truncation errors might
be significant otherwise.

Testcases c35test/block_hybh.inp & block_hybh_ew.inp are provided.

34) MSLD invokes Multi-Site lambda-dynamics. The integers which follow
the keyword indicate the "Site" to which atoms within each block are
assigned. The first block must be assigned to Site 0 (the "environment"
atoms). Currently, QLDM THETA must be specified prior to invoking MSLD.

If there are too many blocks to assign each to a site in the MSLD
command, (due to CHARMM variable and line length limitations),
MSLD may be invoked with the NSITe option, e.g. "MSLD NSITe int",
where int specifies the number of sites, and blocks may be assigned
to sites individually later in the block section using
"BLASsign int_block int_site", which assigns block int_block to site
int_site.

Several different functional forms of lambda have been implemented. The
default functional form is FNEX 5.5. (Note: these functions are for
lambdas associated with all blocks except for block 1--ie. the environment
atoms at site 0.)

i) n-block normalized exponential: FNEX [c]
Note: Use FNXS [c1 c2 ... cnsites] to set a different c for each site
num(Site_a,sub_i) = exp(c*sin(theta(Site_a,sub_i))

lam(Site_a,sub_i) = num(Site_a,sub_i)
-------------------------
----
\
/ num(Site_a,sub_j)
----
all j

ii) n-block normalized sin: FNSI
num(Site_a,sub_i) = sin(theta(Site_a,sub_i))^2

lam(Site_a,sub_i) = num(Site_a,sub_i)
-----------------------------
----
\
/ num(Site_a,sub_j)
----
all j

iii) 2-block exponential: F2EX (based on the logistic function)
lam(Site_a,sub_1) = exp(theta(Site_a)) / [ 1.0 + exp(theta(Site_a)) ]

lam(Site_a,sub_2) = 1.0 / [ 1.0 + exp(theta(Site_a)) ]

iv) 2-block sin: F2SI (based on constant pH-MD and theta-dynamics)
lam(Site_a,sub_1) = sin(theta(Site_a))^2

lam(Site_a,sub_2) = 1.0 - sin(theta(Site_a))^2

v) Fixed lambdas: FFIX (lambda doesn't move from its starting value)
Useful for doing FEP or MBAR in systems set up for MSLD

The MSMA keyword is the Multi-Site lambda-dynamics equivalent to the
LDMAtrix command and will automatically map the input lambda values
onto the coefficient matrix of the interaction energies (and forces)
between blocks.

Assuming that groups of atoms have already been defined to correspond to
"site1sub1" etc., here is an example of a Multi-Site lambda-dynamics
setup in an input file.

BLOCK 7
Call 2 sele site1sub1 end
Call 3 sele site1sub2 end
Call 4 sele site2sub1 end
Call 5 sele site2sub2 end
Call 6 sele site2sub3 end
Call 7 sele site2sub4 end
qldm theta
lang temp 310.0
ldin 1 1.0 0.0 12.0 0.0 5.0
ldin 2 0.50 0.0 12.0 0.0 5.0
ldin 3 0.50 0.0 12.0 3.2 5.0
ldin 4 0.30 0.0 12.0 0.0 5.0
ldin 5 0.40 0.0 12.0 -0.5 5.0
ldin 6 0.15 0.0 12.0 8.5 5.0
ldin 7 0.15 0.0 12.0 15.1 5.0
rmla bond thet
msld 0 1 1 2 2 2 2 fnex 5.5
msma
END

After this setup, minimizations and dynamics can be invoked as usual. MSLD
is currently only compatible with the default dynamics routine (leapfrog
Verlet) and can be used with Langevin dynamics (LANG) using the LEAP
integrator.

Analysis of the generated lambda trajectories can be performed using
options in the trajectory command for multiple blocks at one or two Sites
(see TRAJ LAMB in dynamc.info). For hybrid molecules that have multiple
blocks at more than two Sites, we suggest running the TRAJ LAMB command
with the "print" option to write out lambda and theta values at each step.

Currently, Multi-Site lambda-dynamics is compatible with LDBI and
LDBV. However, the LDBV defined biases are not yet taken into
account in the TRAJ analysis routine.

Top
A warning is in order: the BLOCK module is quite user-unfriendly, AND
the user (=you) has to know what he/she is doing, otherwise you won't
get anywhere! (Of course, this could be a blessing in disguise) There
are two applications for BLOCK: (i) Mere use as an energy partitioning
facility, which may, e.g., very helpful as an alternative to the
INTEraction energy command and (ii) use in free energy simulations.
The focus here is on free energy applications. The following paragraphs
assume that you are familiar with the theory of free energy difference
simulations (e.g. Brooks et al. Advances in Chem. Physics, Vol. LXXI,
1988, chapter V); the emphasis here is to show how a rough tool as
BLOCK can be used to implement the theory in a program and (of course)
how to use it.

Using BLOCK in order to calculate a free energy difference consists
out of two rather dissimilar parts (as far as practical problems are
concerned): (i) Run your system at various values of lambda and save
trajectories. (ii) Postprocess the trajectories with the FREE or the
EAVG command (possibly COMP), use the quantities which these modules
give you to calculate the free energy difference.

(i) The actual simulations
==========================

It's probably easiest to use a concrete example, and the free energy
difference between ethane and methanol in aqueous solution is used for
that purpose. BLOCK is a so-called dual topology method (D. Pearlman,
JPC 1994, 98, 1487) i.e. one has to duplicate any atom that is
different with respect to any of its parameters. In the
ethane/methanol case this means that you have to run with a solute
which looks something like


H1
\ /H4
\ C1E ---- C2-H5
H2 = { } \H6
/ C1M --- OG
/ \HG1
H3


(and there is water.)

Conceptually, this system is divided into three regions:

environment: water, H1, H2, H3 (the region where nothing changes)
reactant: C1E, C2, H4, H5, H6 (ethane half)
product: C1M, OG, HG1 (methanol half),

where of course the role of reactant and product is interchangeable.

The steps involved to start running dynamics are as follows:

(1) set up the hybrid (generate psf). In principle straightforward,
but there is a practical pitfall: The autogenerate angles and
dihedrals option(s) may produce artificial dihedrals/angles between
the two/three parts of the system, e.g. you don't want angles
H1-C1E-OG etc. or dihedrals H3-C1M-C2-H4 etc. Also, make sure to
specify nonbonded exclusions between the reactant and product part,
otherwise you'll get endless distance warnings and may even bomb if
two atom positions coincide.

(2) Place the hybrid into water (stochastic or periodic boundary
conditions -- yes, IMAGE is now supported) as usual

(3) Partition the system, i.e. enter BLOCK
The following script fragment will do the trick:

block 3
call 2 sele <reactant> end
call 3 sele <product> end
end

(reactant and product have to be defined according to your system).
BLOCK 3 initializes the block module with 3 blocks, all atoms are in
block 1. The two CALL commands bring the reactant and product part of
the system into block 2 and 3 respectively.

(4) Run the necessary MD simulations. Let's assume that you decide to
use the following values of lambda, lambda = 0.1, 0.3, 0.5, 0.7, 0.9.
You want to start your simulation at lambda = 0.1 and you have already
partitioned your system as shown in (3). (This information is kept
within the same script between calls to block, but it is not saved in
restart files or the psf, i.e. you have to repeat this step (as well
as step (3)) in every input file). Enter block again, e.g.

block
lamb 0.1
end

From now on interactions between the 3 blocks will be scaled according
to the following matrix (lambda = l = 0.1 ==> 1-l = 0.9):

block | 1 2 3
------|--------------------
1 | 1.0 1-l l
2 | 1-l 1-l 0.
3 | l 0. l

Please note that BLOCK will first calculate an interaction, then check
to which block the two atoms belong and scale the energy (and forces)
appropriately. Therefore, if the distance between 2 atoms is zero
(e.g. in the ethane/methanol example I would define C1M and C1E on top
of each other!) then you need non-bonded exclusions, otherwise you
encounter a division by 0 error!

The LAMB command is a shortcut for the following sequence of COEF
commands, the following code fragment should be self-explanatory:

block
coef 1 1 1.0
coef 1 2 0.9
coef 1 3 0.1
coef 2 2 0.9
coef 2 3 0.0
coef 3 3 0.1
end

BLOCK only accepts and uses symmetric matrices, i.e. it doesn't
matter whether you specify COEF 1 2 or COEF 2 1.

Whenever you now call the energy routines, the energies/forces
returned from them will be scaled according to the matrix you have set
up. Minimizers and Dynamics can be used as always. So you are ready
to run dynamics, and for arguments sake say that you run at every
value of lambda 10,000 steps equilibration and 20,000 steps production
(i.e. you save coordinates to trajectories) You don't need to save
every step, every 5th to 20th step is probably more than enough. (If
you saved every step you'd obtain highly correlated data, i.e. you
have larger trajectories, but you won't gain anything in terms of
convergence.)

(ii) Post-processing -- how to obtain a free energy difference
==============================================================

At this point in our example, you would have five trajectories
corresponding to lambda = 0.1, 0.3, ..., 0.9 The BLOCK module now has
to be used to obtain the average quantities you need for either the
exponential formula (FREE) or thermodynamic integration (EAVG,COMP)
from the trajectories you generated in step (i)

(1) At this point, some issues regarding the non-bonded list have to
be considered. No special considerations were necessary while running
dynamics (aside from having some non-bonded exclusions where
necessary); you just set up list updates as usual. During
post-processing there are two considerations: (a) efficiency -- you
just want to calculate the necessary subset of interactions (otherwise
your post-processing run will take about as much time as the
simulation itself), and (b) proper list-updating.

(a) Efficiency: In none of the post-processing routines do you need
the interactions between particles that belong to the environment;
therefore you should avoid calculating them. This can be done easily
by specifying

cons fix sele <environment> end

Note that this is not necessary, but it will reduce the CPU time
necessary from hours to minutes (and results are identical!) However,
if you had atoms belonging to reactant or product or both FIXed during
the simulations in step (i), you MUST NOT FIX them now; otherwise
you'll omit contributions.

(b) List updating: While the efficiency considerations in principle
are optional, you have to follow one of the two strategies below
otherwise you'll get erroneous results. If you used IMAGE, you have
to use the second protocol! Originally, the BLOCK post-processing
commands would not do any list updating. This meant that you had to
have a nonbonded list which would include all possible interactions
before starting post-processing -- don't forget that you post-process
over, e.g., 20 ps and particles will move quite far. You can easily
create such a nonbonded list by specifying a CUTNB value of, e.g. 99.
or 999. Ang (surely, all possible interactions will be included). A

!set up system (psf, initial coordinates)
block
!partition system
end
cons fix sele <environment> end
==> energy cutnb 99. <all other options as during dynamics>
!open trajectories
block
!postprocessing
end

In this case, do not use the inbf, ihbf and imgf options of the
post-processing commands, they will default to 0, i.e. no update.
This approach, however, CANNOT work with IMAGES! Proper use of IMAGEs
requires that the minimum image convention is checked periodically,
i.e. particles have to be repartitioned between primary and image
region. As the BLOCK post-processing commands now understand INBF,
IHBF and IMGF, this doesn't pose a problem. However, the automated
update is not supported (if you specify a negative value, you'll get a
mild warning and the system will default to +1), and I recommend that
you use 1 for all frequencies (don't forget, the frames in your
trajectory are several steps apart, i.e. in general an update may be
necessary) The above scheme now looks like:

!set up system (psf, initial coordinates)
block
!partition system
end
cons fix sele <environment> end
! set up images if needed
==> energy <all options, incl. CUTNB, as during dynamics>
!open trajectories
block
eavg <other options> inbf 1 ihbf ? (imgf 1)
end

Unless you have explicit hbond terms, ihbf can of course be 0!
(Please note that there may or may not be problems with CRYSTAL, see
Limitations section)

(2) The actual post-processing commands. In the following I'll
explain how to set things up for FREE, EAVG and COMP (as well as why).
To speed up things further, you'll also want to specify the NOFOrce
option at some point.

FREE: This module allows you to calculate the necessary ensemble
average for the exponential formula. Using our example, you can for
example estimate the free energy difference between l=0.1 (a value at
which you ran a trajectory) and l=0.0, or, based on your l=0.1
trajectory the free energy difference between l=0.0 and 0.2 (double
wide sampling), i.e.

A(0.0)-A(0.1) = -k_B*T*ln <exp[-(U(l=0.0)-U(l=0.1))/kT]>_(l=0.1)

or

A(0.2)-A(0.0) = -k_B*T*ln <exp[-(U(l=0.2)-U(l=0.0))/kT]>_(l=0.1)

You should set up your system with 3 blocks and the usual environment,
reactant and product partitions. Before entering block to issue the
free command, you have to open the trajectory/ies.

! all the stuff shown above for non-bond lists
open file unit 10 read name dat01.trj
block
free oldl 0.1 newl 0.0 first 10 nunit 1 [temp 300. -
inbf 1 imgf 1]
end

or, for double wide sampling, the free line would be replaced by

free oldl 0.0 newl 0.2 first 10 nunit 1 [temp 300. -
inbf 1 imgf 1]

Here dat01.trj is the trajectory which contains your 20 ps of dynamics
at lambda = 0.1. Based on the oldl/newl values (which correspond to
A(newl) - A(oldl)), FREE generates the appropriate interaction matrix,
which it prints; I recommend that you try to understand why it
generates this matrix! FIRST is the unit number of the first
trajectory file (10 in our example), NUNIT is the number of
trajectories (1 in our example). These (and the other options
regarding the trajectories work as in any other post-processing
command in CHARMM, see e.g. the TRAJ command) The update frequencies
are optional depending on how you decided to handle your non-bonded
updates. temp defaults to T=300 K, cf. equations above.

If you specify CONT +n, you'll get a cumulative average every n steps;
in this case the last value equals the final result; if you specify CONT
-n, you'll get the average over every n frames, plus of course the
final result at the end.

Note that trajectories are not rewound after use; i.e. before any
subsequent FREE (or EAVG,COMP) command you have to rewind (or reopen)
them!

Once you have all the free energy pieces you need, you simply add them
up to obtain the free energy difference (beware of sign errors
depending on how you defined oldl/newl)

EAVG: The main use of this module lies in obtaining the required
ensemble averages for thermodynamic integration. The most significant
difference to EAVG is that you have to specify your own interactions
matrix. BLOCK uses linear coupling in lambda in the potential energy
function, i.e.

V(l) = V0 + (1-l)*V_reac + l*V_prod,

where V0 contains all the intra-environment terms, V_reac are the
intra-reactant and reactant-env. interactions, and V_prod are the
intra-product and product-env. interactions, respectively. The
quantity of interest in TI is dV/dl; for the above potential energy
function we have

dV/dl = V_prod - V_reac

It's very easy to obtain this quantity from EAVG. Use 3 blocks,
partition the system as before.

! all the stuff shown above for non-bond lists
open file unit 10 read name dat01.trj
block
coef 1 1 0.
coef 1 2 -1.
coef 2 2 -1.
coef 1 3 1.
coef 2 3 0.
coef 3 3 1.
eavg first 10 nunit 1 [inbf 1 imgf 1 cont +-n]
end

You will calculate the average interaction energy over all the frames
in the trajectory according to the following (symmetric) matrix

0.0
-1.0 -1.0
1.0 0.0 1.0;

i.e. it's easy to see that the above script will give you <V_prod -
V_reac>_(l=0.1). If you post-process the other trajectories (l=0.3,
0.5, ..,0.9) in an analogous fashion, you just have to approximate the
TI integral by the trapezoidal formula (for basic Newton Cotes
formulae (open and closed) see, e.g., Numerical Recipes), i.e. in this
case you would have

dA = 0.2 * (dV(0.1)+dV(0.3)+...+dV(0.9)),

where dV(0.1) = <V_prod - V_reac>_(l=0.1), etc.

The above is an example of the basic use of EAVG. You automatically
get the formal components according to interaction type. Cont +-n
works similarly to the FREE case. If you wanted to exclude the
intramolecular contributions from ethane and methanol you could set up
a slightly different coefficient matrix, i.e.

coef 1 1 0.
coef 1 2 -1.
coef 2 2 0.
coef 1 3 1.
coef 2 3 0.
coef 3 3 0.

and you'll get only the solute-solvent contributions. You can use
more blocks (m > 3) to extract only a subset of interactions, e.g.

block 1: environment - x
block 2: reactant
block 3: product
block 4: x,

where x is the region of interest, e.g. a specific sidechain in a
protein (but not the one that is mutated!)

Using EAVG with an appropriate coefficient matrix, e.g.

coef 1 1 0.
coef 1 2 0.
coef 1 3 0.
coef 1 4 0.
coef 2 2 0.
coef 2 3 0.
coef 2 4 -1.
coef 3 3 0.
coef 3 4 1.
coef 4 4 0.

will give you (after integration over lambda) the free energy
contribution of the interaction of sidechain x with the mutation site.
Note that such formal free energy components may be (strongly)
path-dependent. These last two examples have hopefully provided a
flavor of what can be done with the EAVG module.

COMP: This module is also used for thermodynamic integration. It
always operates with four (and only four) blocks, just as the advanced
example last given for EAVG, so it facilitates COMPonent analysis.
Here I want to focus on the second unique aspect of COMP, it's
capability to extrapolate additional datapoints, and so I consider in
the framework of our ethane/methanol example the "special" case where
I want the total free energy difference (as before in EAVG). In order
to do this, the system needs to be partitioned as follows

block 1: --
block 2: reactant
block 3: product
block 4: environment

Whereas EAVG gave us <V_prod - V_reac>_l only for those lambda values
at which we had actually done the simulations, COMP gives us
additional values via perturbation (see Bruce Tidor's thesis). Using

! all the stuff shown above for non-bond lists
open file unit 10 read name dat01.trj
block
coef 1 1 0.
coef 1 2 0.
coef 1 3 0.
coef 1 4 0.
coef 2 2 -1.
coef 2 3 0.
coef 2 4 -1.
coef 3 3 1.
coef 3 4 1.
coef 4 4 0.
comp first 10 nunit 1 [inbf 1 imgf 1] dell 0.06667 ndel 1
end

will now give us <V_prod - V_reac>_l at l=0.03334, l=0.1 and
l=0.16667. If we use the same script on the other trajectories, we
have 15 instead of 5 datapoints for the integration, i.e. we can
obtain dA as

dA = 0.06667 * (dV'(0.03334)+dV(0.1)+...+dV'(0.96667)),

where dV(0.1) = <V_prod - V_reac>_(l=0.1), etc. and the ' indicates
that this is a perturbed quantity. In principle, this
should give a better numerical integration; however, in practice
everything depends on how well your actual data (l=0.1, 0.3, ...,0.9)
are converged.

There is no check whether your ndel/dell combination is meaningful;
and you cannot run COMP without using the perturbation feature, i.e.
NDEL should be set to at least 1 (valid values are 1 through 5). The
defaults (if you don't specify ndel/dell) lead to an invalid input
(This should be fixed...)

(iii) Lambda-dynamics simulations
=================================

In an efforts to make the transition from using previous subcommands
to running the lambda dynamics as smoothly as possible, we purposely
parallel new syntax after the COEF subcommand. There are
total of eight new keywords for setting up new dynamics. They are
classified according to their functionality.

(a) LDINitialize and LDMAtrix

These two keywords are basic commands for starting the lambda
dynamics run. The correct use of them is tied together with the BLOCK
and CALL commands. Using the same example as the one given in "the
actual simulations", the input script fragment will be as following:

block 3
call 2 sele <reactant> end
call 3 sele <product> end
LDIN 1 1.0 0.0 20.0 0.0
LDIN 2 0.9 0.0 20.0 0.0
LDIN 3 0.1 0.0 20.0 0.0
LDMA
end

Here, the LDINitialize command models after the COEF command with
the format

LDIN INDEX LAMBDA**2 LAMBDAV LAMBDAM LAMBDAF

Several comments are in order. First, notice that [lambda(1)**2]
= 1.0 and [lambda(2)]**2 + [lambda(3)]**2 = 1.0. They are quite
similar to the inputs of COEF subcommand. However, since one
index instead of a pair is required here, only diagonal elements
of the interaction coefficient matrix are specified. To fill up
the matrix, LDMA is provided to finish the job automatically.
In general, if there is total of N blocks, the first one is
by default assumed to be the region where nothing changes.
Therefore, [lambda(1)**2] = 1.0 is always true. The condition

N
____
\
/ [lambda(i)**2] = 1.0 (1)
----
i = 2

has to be satisfied for the partion of the system Hamiltonian.
Due to some technical reasons in our implementation (details
see PDETAIL.DOC), we have used [lambda(i)**2] instead of lambda(i)
in our partion of the system Hamiltonian. Next, to make sure the above
condition is met at any given simulation step, we have also enforced a
condition containing velocities of the lambda variables

N
____
\
/ lambda(i)*lambdaV(i) = 0.0 (2)
----
i = 2

We used lambdaV(i) = 0.0 in the above script just to simplify the
input. As far as the mass parameter lambdaM is concerned, the minimum
requirement is that the value of mass has to be chosen such that the
time step (or frequency) of lambda variables is consistent with that
used for spatial coordinates x, y, z. Since the lambda variable is
introduced into the system by using extended Lagrangian,
considerations gone into the similar quantities, such as the
adjustable parameter Q in a Nose thermostat are applicable to the
choice of lambdaM. Some crude estimation can be made by examining
the derivative of the system Hamiltonian with respect to the
lambda, the curvature (simple harmonic approximation) or energy
difference between two end-point states (0 and 1). Our experience
has indicated that a conservative choice of the mass, i.e. a little
bit heavier mass than that of the crude estimate, serves us well
so far.

The biasing potential LAMBDAF has two functions: (1) In the screening
calculations LAMBDAF corresponds to the free energy difference of the
ligands in the unbound state. Such calculations can identify ligands
with favorable binding free energy and a ranking of the ligands can be
obtained from the probability of each ligand in the lambda=1 state;
(2) In precise free energy calculations, LAMBDAF corresponds to the best
estimate of free energy from previous calculations. Therefore the
estimate of free energy can be improved iteratively.


(b) LDBI and LDBV

In order to provide better control over simulation efficiency and
sampling space, an option of applying biasing (or umbrella)
potentials is furnished. LDBI specifies how many biasing
potentials will be applied and LDBV supplies all the details.
The general input format is

LDBV INDEX I J CLASS REF CFORCE NPOWER


Let us look at the following script

block
LDBI 3
LDBV 1 2 2 1 0.2 40.0 2
LDBV 2 3 3 2 0.6 50.0 2
LDBV 3 2 3 3 0.0 20.0 2
end

It states that there is total of 3 biasing potentials. The first one
(INDEX = 1) is acting on lambda(2) itself (I = J = 2), the second one
on lambda(3) and the third one is coupling lambda(2) and lambda(3)
together. At the moment, five different classes of functional forms
are supported:

CLASS 1:
__
| CFORCE*(lambda - REF)**NPOWER if lambda < REF
V =|
| 0 otherwise
|__


CLASS 2:
__
| CFORCE*(lambda - REF)**NPOWER if lambda > REF
V =|
| 0 otherwise
|__


CLASS 3:

V = CFORCE*[lambda(I) - lambda(J)]**NPOWER


CLASS 4:
__
| CFORCE*(1.0 - ((lambda - REF)**2)/REF**2) if lambda < REF
V =|
| 0 otherwise
|__


CLASS 5:

V = CFORCE*lambda(I)
note: the CLASS 5 biasing potential is the same as invoking the
biasing potential LAMBDAF in LDIN (except these biases will not
currently be taken into account in the TRAJ analysis routines).


CLASS 6:

V = CFORCE*[lambda(I) * lambda(J)]


CLASS 7:

V = CFORCE*[lambda(I) * (1 - lambda(I))]/[lambda(I) + REF]


CLASS 8:

V = CFORCE*[lambda(I) * lambda(J)]/[lambda(I) + REF]


CLASS 9:

V = CFORCE*[lambda(J) * (1 - ((lambda(I) + REF)/REF)**NPOWER)]


CLASS 10:

V = CFORCE*[lambda(J) * (1 - exp(REF*lambda(I)))]


(c) LDRStart

LDRStart is used only if for some reason, e.g. execution of EXIT command,
the logical variable QLDM for the lambda dynamics has been set to false.
In this case, to restart the dynamics, LDRStart can be used to reset
QLDM = .TRUE.. However, if LDIN is also being used in restarting the
dynamics, it will automatically reset QLDM. Therefore, LDRS does not
need to be called in this case.


(d) LDERite

LDWRite provides specifications for writing out lambda dynamics, i.e.
the histogram of the lambda variables, the biasing potential etc. The
integer variable IUNLdm is the FORTRAN unit on which the output data
(unformatted) are to be saved. The value of the integer NSAVL sets step
frequency for writing lambda histograms. IUNLdm is defaulted to -1 and
NSAVL is defaulted to 0. Both IUNLdm and NSAVl can be reset in DYNAmics
command (Please refer to » dynamc for details).

the following script will set IUNLdm with unit No. 8 and NSAVL equal to 10:

LDWRite IUNL 8 NSAVL 10


(e) RMBOnd and RMANgle

Since each energy term is scaled by lambda, RMBOnd and RMANgle can prevent
bond breaking caused by such scaling during dynamic simulations. Alternatively
one can fix bonds (and angles) using SHAKE. But is is not always possible.

(f) MSLD

Multi-Site lambda-dynamics is a generalized version of the original
lambda-dynamics. Greater numerical stability of the simulations
is acheived with the MSLD definitions of lambda which implicitly
satisfy the constraints a) that each lambda value varies between 0 and 1 and
b) that the lambda values for a given Site sum to 1 (see the functional
forms listed above). Any system set up for the original lambda-dynamics
(i.e. that has multiple blocks at only one Site) can be run using MSLD.
In this case, the system would be set up in BLOCK as before, but the LDMA
command would be replaced by the MSLD commands.

For example, the original lambda-dynamics, using the theta-dynamics option
(qldm test) setup would be:
BLOCK 4
Call 2 sele site1sub1 end
Call 3 sele site1sub2 end
Call 4 sele site1sub3 end
qldm theta
lang temp 310.0
ldin 1 1.0 0.0 12.0 0.0 5.0
ldin 2 0.50 0.0 12.0 0.0 5.0
ldin 3 0.20 0.0 12.0 3.2 5.0
ldin 4 0.30 0.0 12.0 -1.0 5.0
rmla bond thet
ldma ! use for original lambda-dynamics
END

and the MSLD setup would be:
BLOCK 4
Call 2 sele site1sub1 end
Call 3 sele site1sub2 end
Call 4 sele site1sub3 end
qldm theta ! required for MSLD
lang temp 310.0
ldin 1 1.0 0.0 12.0 0.0 5.0
ldin 2 0.50 0.0 12.0 0.0 5.0
ldin 3 0.20 0.0 12.0 3.2 5.0
ldin 4 0.30 0.0 12.0 -1.0 5.0
rmla bond thet
msld 0 1 1 1 fnex 5.5 ! use for MSLD
msma ! use for MSLD
END

Lambda trajectory files written by MSLD can be analyzed by TRAJ LAMB
commands. The header contains all the information required to process
the trajectory (e.g. number of blocks, which blocks are assigned to
which site etc.). The lambda trajectory files are specified in the
DYNAMICS commands using keywords:
IUNLDM unit ! where unit corresponds to the unit number of the
lambda trajectory file
NSAVL freq ! where freq corresponds to the frequency of writing
the lambda values

The TRAJ LAMB command will process the lambda trajectory file and print
out statistics related to individual sites ("single-site" statistics):
* the population of each block (population = the number
of snapshots in which each block(i) has lambda(i) = 1, or more
specifically, the number of snapshots in which each block(i) has
lambda(i) > threshold).
* the number of transitions at each Site (i.e. the number of times
the identity of the block with lambda(i) > threshold changes).
* and the relative free energies for each pair of blocks at each Site.
(without and with the correction for the fixed lambda biased invoked in
the LDIN command)

Output is provided for two threshold values (default 0.8 and 0.9) for
approximating lambda(i) = 1 to provide an estimate of the sensitivity of
the results to the specific threshold used:
lambda(i) = 1, if lambda(i) > threshold

For systems with more than one site (i.e. sites at which multiple blocks
are modeled), a complete physical ligand is present at a given snapshot
when there is a block with lambda > threshold at each Site. For a given
system, there are a total of N(site_1) x N(site_2) x ... N(site_n)
possible ligands where N(i) is the number of blocks at Site i.

For systems with two sites, in addition to the general "single-site"
statistics, the TRAJ LAMB command will account for all combinations of
the blocks and print out "multi-site" statistics:
* the populations of each "ligand" for two thresholds (population =
the number of snapshots in which each "ligand" exists, i.e. the
combination of blocks corresponding to the ligand each have lambda = 1)
* the number of transitions between these ligands * the relative free
energies of each pair of ligands (without and with the correction for
the fixed lambda biased invoked in the LDIN command)

For systems with more than two sites, it is recommended that you use
the TRAJ LAMB PRINT command to print out the lambda values for each
snapshot and perform the population analysis and compute the relative
free energies yourself.

See TRAJ LAMB in dynamcs.info for a complete list of options.
E.g.:
To read header information only:
open unit 24 read file name scratch/msld_prod.lmd
traj lamb query unit 24
close unit 24

To process the trajectory file and print out lambda values at each
timestep:
open unit 24 read file name scratch/msld_prod.lmd
traj lamb print first 24 nunit 1
close unit 24

While the trajectory is being processed, the following internal variables are
stored:
'TMIN' - Minimum number of transitions for any site in the system
'TMAX' - Maximum number of transitions for any site in the system
'FPL' - Fraction of the snapshots which represent full Physical Ligands
'POP#' - Population for the substituent associated with indicated BLOCK number
at the low threshold value (e.g. the ?pop2 contains the population for
substituent in BLOCK 2 given CUTLO threshold)
'DDG#_#' - Relative free energy between the first and second substituents
listed at the low threshold value (e.g. ?ddg2_5 is the relative free energy
between the substituents associated with BLOCKS 2 and 5).

If for any reason you wish to suppress the storage of internal variables
(for example, if you have many substituents in your system and alreadyt
many internal variables have been stored such that processing the MSLD
trajectory gives a fatal error indicative of too many variables) then
include the keyword "nosub" in the trajectory command, i.e.:
open unit 24 read file name scratch/msld_prod.lmd
traj lamb print first 24 nunit 1 nosub
close unit 24

Top
(1) Please be advised (again) that the AVERage command is unsupported,
and I would not be surprised if it does not work (anymore). Unless
someone who understands this module better than I do maintains it, I
recommend that we remove it.

(2) BLOCK now coexists with IMAGE "peacefully" and essentially
transperantly to the user. It works correctly for the case of a
periodic water-box (cf. the block3.inp testcase). I would, however,
check carefully whether things really work before I would use it on
something fancier like infinite alpha helices. Similarly, it is not
clear to me whether things work with the CRYSTAL facility. If one
modifies block3 as to use CRYSTAL instead of IMAGE things (seem to)
work. On the other hand, I know that I didn't support XTLFRQ in the
post-processing routines as I don't understand its meaning. I'll fix
things if someone is willing to help me with the bits and pieces I
don't understand.

(3) Bond and bond angle terms (including Urey-Bradleys). Be advised
that if you run a simulation at lambda = 0 or lambda = 1 you may
effectively remove bond (and bond angle terms) as they get scaled by
zero. In other words, you would have ghost particles that can move
freely through your systems, and this leads to all sorts of nasty
side-effects. Furthermore, this approach is not sound theoretically
(S. Boresch & M. Karplus, unpublished). So in general, avoid running
at lambda = 0 and 1. If you have your bonds constrained you're safe
as the constraint will keep things together (that won't take care of
angles however!) In order to avoid artifacts from noisy, diverging
bond and bond angle contributions throw them out during
post-processing, e.g. by using the SKIP BOND ANGL UREY command before
starting block post-processing. If you want to see what can go wrong,
look at the block2 test-case...

" Dual Topology Soft Core Potential"
The new commands PSSP/NOPSsp and the optional parameters ALAM and
DLAM control the interactions between soft core potentials and BLOCK,
which is essentially the same as the PSSP command in the PERT soft
core (» pert ). After you specify PSSP inside BLOCK, soft core
LJ and electrostatic interactions will be used inside block interactions.
For the atom based NBOND command (NBOND ATOM), the block coefficents
(lambda) of VDW and ELEC can be defined as the different values. For
the group based case (NBOND GROUP), they share the same lambda value
currently. The separation parameters for elec. and LJ interactions can
be set with the ALAM and DLAM options, the default of 5A^2 should be
reasonable. The option is memorized, i.e., after the first invocation
of PSSP, all further calls of EVDW will use soft core interactions.
To turn this off, please use the NOPSsp keyword inside BLOCK/END pair.
NB! Requires FAST OFF and nonbond options SHIFT VSWITCH." -- New by H. Li and W. Yang

"Multisite lambda Dynamics Soft Core Potential"
The SOFT directive turns soft cores a la Hayes et al JPC B (2017) on or
off. These soft cores are intended for use with multisite lambda dynamics
and domdec. Outside of domdec, the standard hard cores are used. OFF turns
soft cores off, ON turns them on for nonbonded interactions, W14 turns them
on for nonbonded and 1-4 interactions.

"CHARMM/OpenMM Soft Core Potential"
The SOMM directive turns on the CHARMM/OpenMM soft cores ONLY for the vdW interactions
a la Hayes et al JPC B (2017). To be used in running TI with BLOCK through the CHARMM/OpenMM
interface, where the energies, forces and dynamics are integrated through OpenMM for
post analysis of the trajectory to use TI, FEP or MBAR (preferred).

"Multisite lambda Dynamics PME Electrostatics"
The PMEL directive controls how MSLD treats long range electrostatics with
PME. The PME potential is modified slightly, as described in Huang, Chen,
Wallace, and Shen, JCTC (2016). PMEL is only compatible with domdec. To use
PME with MLSD, PMEL must be invoked inside the block directive, but PME must
also be invoked as described in ewald.info and domdec.info by appropriately
setting the nonbonded options and domdec options.

PMEL OFF does not use PME electrostatics. PMEL ON scales all charges by the
lambda of their particular block in the k-space and self energy terms
(energy terms EWKS and EWSE). PME exclusions (energy term EWEX) are scaled
by the product of lambdas for substituents at different sites, by zero for
different substituents at the same site, and by lambda for intrasubstituent
or substituent-environment interactions. PMEL EX scales all charges by
lambda just like PMEL ON, but the exclusions are treated differently:
specifically, since intrasubstituent interactions are scaled by lambda
squared in the k-space term, they are also scaled by lambda squared in the
exclusions term. All other exclusion scaling remains the same. PMEL NN
scales exclusions by the product of the two lambdas regardless.

"Saving lambda Forces"
In order to write effective test cases and charmm scripts, sometimes it is
necessary to be able to examine the forces on lambda. "FLAM string int"
saves the lambda force for the block specified by int to the CHARMM
parameter whose name is given in string, much like the set command (see
» miscom ). That lambda force can then be accessed
by name using @ like any other CHARMM parameter.

"Scaling Bonded Interactions of Constrained Atoms"
Sometimes when converting between two closely related scaffolds with MSLD
it is desirable to convert the atom in one substituent directly to the
analagous atom in the other substituent, especially if the changing atoms
are in the core of th molecule rather than on the periphery. Reasons
include avoiding exploring larger conformational spaces in the off state
and avoiding double counting of all the bonded interactions which can
result in errors due to differing strain in the two halves of the
thermodynamic cycle. While direct conversion of the atoms is not offered
by the BLOCK module, it is possible to effectively convert them by
constraining their positions to overlap (for example with CONS NOE), and
then scaling their bonded interactions (bond, angle, dihe, impr, etc...)
by lambda. The primary reason for not scaling bonded interactions with
the RMLA directive is to prevent the atoms from drifting of and exploring
large conformational spaces, so if they are localized in some manner,
scaling their interactions no longer causes poor sampling and avoids
artifacts mentioned by Liu, Wang, and Mobley in Journal of Chemical
Information and Modeling 55:727-735 (2015)

SCAT ON enables Scaling of Constrained AToms (SCAT). SCAT OFF turns them
back off. SCAT K [real] sets the spring force constant that restrains each
atom to the center of mass. (Yes, they are technically restraints, not
constraints.) You can also set K to zero and use restraints from the CONS
module. Scaling of constrained atoms is only tested within domdec. Once
scaling has been turned on, each group of constrained atoms may be
specified with "CATS atom-selection". Any bonded interaction which would
normally be unscaled due to RMLA will be scaled by lambda if all atoms are
constrained or are part of the environment or another block. If any of the
atoms are unconstrained, the scaling of the interaction is dictated by
RMLA.

"Soft Bonds"
Sometimes it is necessary to break a bond in an alchemical transformation,
e.g. when running simulations that involve core swaps or macrocycles, or
other perturbations that change the topology of the core. Soft bonds are
currently only implemented in domdec.

NSOB int [RALF real] [LEXP real] [BLEX real] turns on soft bonds if int is
greater than 0, and turns them off otherwise. The integer gives the number
of soft bonds that will be allocated. RALF is the saturation radius of all
soft bonds in angstroms and defaults to 1. See JCTC 13:6290-6300 (2017)
for the functional form, their "alpha"=RALF^-2. Set RALF to a negative
value to get a "hard" bond with RALF=infinity. LEXP is the exponent
applied to the lambda scaling, and also defaults to 1. All other bonded
interactions including angles and dihedrals which include both atoms of
the soft bond will also be scaled by lambda^LEXP, but currently maintain
their "hard" functional form, including the singularities in the forces.
This fact can be exploited to scale interactions for a particular ijk
angle by lambda^LEXP by declaring a soft bond between i and k even though
they are not bonded. If a different lambda scaling exponent is desired for
the bonds and ureys relative to the angles, dihedrals, and impropers,
BLEX may be used to specify the former while LEXP will apply to the
latter, otherwise LEXP will apply to both.

Once the number of soft bonds has been declared, individual soft bonds are
specified with "SOBO int atom-selection1 atom-selection2" where int is the
index of the soft bond from 1 to NSOB, and the two selections specify the
two atoms in the soft bond.

Sometimes, especially when running dynamics with FFIX, it may be desirable to
start a simulation with a new lambda value from a restart file with an old
lambda value. To do this, set "RLFR OFF" (Read Lambda From Restart),
otherwise, CHARMM will read lambda and theta from the restart file.

"Adaptive Integration (ADIN) Method for Hybrid MD/MC Simulation"
In order to overcome the trapped distribution at certain lambda value in the
chemical space hybrid MD/MC simulation, adaptive integration method was
implemented. In this method, the biasing free energy potential is derived
by linearly integrating the ensemble average of energy derivatives at various
lambda values. By adaptive integration method, free energy difference between
two end states can be quickly computed. It is noted that this technique works
well when free energy has linear relationship with lambda value. It can crash
when there is severe end point singularity problem. Its general efficiency is
lower than the simulated scaling method, which does not suffer from end point
singularity problems. - by Lianqing Zheng and Wei Yang

"Theta-dynamics"
This is an alternative method for the original lambda-dynamics. Lambda**2 is
replaced by sin(theta)**2 and (1-lambda**2) by cos(theta)**2. Theta, instead
of lambda, now is the variable for propagation. This implementation can avoid
the artifacts brought in by the constant external works in the Lagarangian
Multiplier boundary treatment. In the theta-dynamics, history dependent
approaches can work very nicely with no danger of being trapped at the end
points. - by Lianqing Zheng and Wei Yang

"Multi-Site lambda-dynamics" (MSLD)
This is a more generalized lambda-dynamics method that allows
multiple substituents on multiple Sites on a common framework to be
evaluated simultaneously. Different functional forms of lambda have been
implemented which inherently satisfy the constraints that each lambda
should vary between 0 and 1 and the sum of the lambda values at a given
Site must equal 1. This strategy reduces the need to use Lagrangian
Multipliers and renormalization schemes and, for most systems, the timestep
can be increased in dynamics to 2 fs when SHAKE is invoked.
- by Jennifer L. Knight and Charles L. Brooks III

Top
Here is an example of independently scaling the attractive
and repulsive terms in the Lennard-Jones interaction:

! scale the interaction parameters
block 2
call 2 sele segid heli end
coeff 1 1 0.0 ! turn off the interactions between atoms in set 1
coeff 1 2 1.0 vdwa 0 vdwr 1.0 ! scaling ratio to scale interactions
! between protein and other atoms
coeff 2 2 1.0 ! leave interactions within the protein unchanged
end

In this example we turn off the attractive term (vdwa) in the LJ interaction
and have only hard-core repulsion.