tps (c46b2)

Transition Path Sampling

The Transition Path Sampling (TPS) methods introduced by Chandler and
co-workers to sample rare events (see References) are implemented as
extensions of the RXNCoor, DYNAmics, and USER commands in CHARMM. The
TPS keyword must be included in pref.dat for the code to be compiled.


* Syntax | Syntax required to invoke TPS
* Description | Description of TPS specific keywords
* References | Some references of use


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Syntax required to invoke TPS

[Syntax RXNCoor]

RXNCoor [ standard RXNCoor keywords ] [ set-spec ] [ bas-spec ] [wri-spec]

set-spec ::= SET [ NRXN 1 ] NRXN{ name }

where NRXN{ name } is an NRXN-long list of the names of
the order parameters to calculate.

bas-spec ::= BASIn NRXN{ name alo ahi blo bhi }

wri-spec ::= TPUNit NRXN{ name unit }

[Syntax DYNAmics]

DYNAmics [ RTRJ ] [ standard DYNAmics keywords ] -
PATH [ mod-spec ] [ tps-spec ] [ sht-spec ] [ trj-spec ] [ hsa-spec ]

mod-spec ::= [ ISVFrequency 0 ]

tps-spec ::= [ NTPAth 0 ] [ NSAVP 0 ] [ NPRAccept 0 ] -
[ ITPRint 0 ] [ ITPUnit STDOUT ] [ ACCU STDOUT ] -
[ USER 0 ] [ PSHOot 1.0 ] [ IMXShift 1 ]
[ SDUNit 0 ] [ SDINit 0 ]

sht-spec ::= [ VFRAction 0.0 ] [ TFRAction 1.0 ] [ NTFRaction NTPAth ] -
[ IFSHoot -1 ] [ IRST 0 ] [ PHALf 0 ] -
[ ISLO 0 ] [ ISLN 0 ]

trj-spec ::= [ NUNIt 1 ] [ FIRStu -1 ] [ VFIRst FIRStu+NUNIt ] -
[ BEGIn 0 ] [ SKIP -1 ] [ STOP 0 ] -
[ PNSAve NSTEP / NSAVC + 1]

hsa-spec ::= [ HSAM 0 ] [ IHUN STDOUT ] [ IHFR 0 ] -
[ NHSV -1 ] [ IHPR 1 ] [ NHST 0 ]



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RXNCoor

The RXNCoor command has been modified to facilitate the definition of the
basins that constrain the endpoints of the path.

Multiple order parameters can be specified using the NRXN keyword
following the SET keyword (» umbrel for a description of the
latter). However, note that the tree structure associated with the
RXNCoor command is not dynamically allocated, so that MAXNOD in
rxncom.fcm must be increased with for larger numbers of order parameters.

The BASIn keyword is used to specify the boundaries of the basins (A
and B). For each order parameter, one must give the name followed by
four real numbers: alo, ahi, blo, and bhi (the order is important).
Here, alo (blo) is the lower bound for basin A (B) and ahi (bhi) is
the upper bound for basin A (B).

The TPUNit keyword designates units to which values of the order
parameters are written. Values are written for each saved trajectory.
A unit number less than 1 suppresses writeout.

In addition, a steered molecular dynamics (SMD) has been implemented
through RXNCOR and integrated with transition path sampling (TPS) to allow
generation of reactive trajectories de novo. In this bias-annealing method,
SMD allows transitions between basins (defined in the RXNCOR module) of the
reaction coordinates where symmetric (harmonic) biasing potentials are
advanced in a ratchet-like manner. TPS shooting moves can then be made with
progressively milder biasing potentials until unbiased reactive trajectories
could be obtained. This facility is activated by including the SMDDel keyword
(along with a non-zero KUMB value) in the UMBRella subcommand. This facility
can be used with DYNAmics without TPS so long as the basins are defined.


DYNAmics

The DYNAmics command has been modified to provide a looping structure to
calculate multiple trajectories (paths). TPS is invoked by including the PATH
keyword.

The additional keywords that are specific to TPS are:

NTPAth The number of paths to calculate.

NSAVP The frequency of saving paths to the trajectory and velocity
files.

USER Whether to user USERSB to calculated the order parameters
used to determine the stable states.

ITPRint The frequency with which to write order parameter values
at basin evaluations.

ITPUnit The unit number on which to write order parameter values
at basin evaluations.

SDUNit The unit number to which to write random number generator
seeds for TPS with Langevin dynamics.

SDINit The unit number from which to read random number generator
seeds for TPS with Langevin dynamics.

NPRAccept The frequency of printing acceptance statistics.

ACCUnit The unit number to which to write acceptance statistics
as a function of saved structure. The columns are the same
as those printed by TPSACC to the CHARMM output file.

PSHOot The fraction of moves that are shooting moves.

IMXShift The maximum number of saved phase space points by which to
reptate the path in a shifting move. In other words, a
shift can be up to IMXS*NSAVC molecular dynamics steps long.

VFRAction The amount to perturb the velocities in shooting moves. A
random vector is chosen from a Gaussian (Maxwell-Boltzmann)
distribution and then scaled by VFRAction. The scaled vector
is added to the current velocity vector and the result is
scaled to conserve kinetic energy after correcting for SHAKE
if necessary. This procedure has the effect of rotating the
3N-dimensional velocity vector without changing its magnitude.

TFRAction The amount by which to scale the kinetic energy in each
shooting move if annealing is desired.

NTFRaction The number of ACCEPTED shooting moves in which to scale the
kinetic energy by TFRAction.

IFSHoot The first point from which to shoot in units of NSAVC. A
value of -1 indicates that IFSHot is chosen randomly if RTRJ
is specified and it is set to the middle of the path
if shooting from a structure.

IRST The saved phase space point to save to the restart file. It
is best if IRST is chosen to be close to the transition state.
Otherwise, numerical errors can prevent one from regenerating
a valid path using the saved phase space point.

PHALf The probability of shooting half a trajectory. A stochastic
element should be included if PHALf is greater than
zero. For example, see discussion about Langevin dynamics.

ISLO The lowest saved structure from which to shoot.

ISLN The number of saved structures from which to shoot (i.e.,
the last saved structure shot from is ISLO + ISLN - 1).

RTRJ If this keyword is present (in place of STARt or RESTart),
an entire trajectory is read at the beginning of a restart.
The keywords BEGIn, SKIP, and STOP have their usual meaning.

NUNIt The number of trajectory files to read if RTRJ is specified.

IFIRst The first trajectory file to read if RTRJ is specified.

VFIRst The first velocity file to read if RTRJ is specified.

PNSAve Allow TPS to read shorter trajectories into longer ones in
order to lengthen the allowed transition time. PNSAve specifies
the number of phase points in the short trajectories (default
is the number of phase points to be saved in the new trajectories).

HSAMple If this keyword is present, paths are accepted if they
start in basin A and ever go through basin B. Also, the
probability that the system is in basin B as a function of
time is calculated [<h_B(t)>].

NHSTart The path at which to start calculating <h_B(t)>.

IHUNit The unit number to which to write <h_B(t)>.

IHFRequency The frequency with which to write <h_B(t)>.

NHSV The frequency of evaluating whether the path is in
basin B (h_B[x(t)]). A value of -1 sets NHSV to NSAVC.

IHPRint h_B[x(t)] is printed every IHPRint*NHSV steps.



In addition, note that the meaning of the ISVFrequency keyword is changed
during TPS. It refers to the number of PATHS, not the the number of
molecular dynamics steps, between writes to the restart file.

Note that if PHALf is greater than 0, shooting moves are carried out in
which the path is only updated in one direction. In this case a stochastic
element should be included in the integration, such as Langevin dynamics.
It is possible to apply Langevin integration to only the periphery of the
simulation using the RBUF keyword. When using Langevin dynamics with TPS,
the random number seed used to generate the random forces is recorded for
every saved structure. This is necessary to regenerate the appropriate
displacement vectors from the coordinates and velocities in 2-step dynamics
during a shooting move. When writing and reading trajectories, these seeds
can be written/read as designated by the keywords SDUNit and SDINit. If
seeds are not read in with a trajectory, seeds are generated randomly for
the initial shooting move, which results in a different displacement vector
than in the original structure. If SHAKe is used in conjunction with Langevin
dynamics, the new displacement vectors have some velocity components along
the constrained bond. These components are zeroed, and the overall kinetic
energy will be reduced for that step. Also note that, if SHAKe is used,
there is a small error in the regeneration of displacement vectors for
atoms that have different values of FBETA and are connected by a shaken bond.


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REFERENCES

All studies that employ TPS in CHARMM should reference:

Hagan, M. F., Dinner, A. R., Chandler, D. and Chakraborty, A. K. (2003)
Atomistic understanding of kinetic pathways for single base-pair binding
and unbinding in DNA. Proc. Natl. Acad. Sci. USA 100, 13922-13927.

In addition, studies that employ SMD based on RXNCOR should reference:

Hu, J., Ma, A. and Dinner, A. R. (2006) Bias annealing: A method for obtaining
transition paths de novo. J. Chem. Phys., submittted.

Additional references on TPS:

Dellago, C., Bolhuis, P., Csajka, F. and Chandler, D. (1998)
Transition Path Sampling and the Calculation of Rate Constants.
J. Chem. Phys . 108, 1964.

Dellago, C., Bolhuis, P. and Chandler, D. (1998) Efficient
Transition Path Sampling: Application to Lennard-Jones Cluster
Rearrangements. J. Chem. Phys. 108, 9236.

Dellago C., Bolhuis, P. G., Geissler, P. L. (2002) Transition path
sampling. Adv. Chem. Phys. 123, 1.

Bolhuis, P. G., Chandler, D., Dellago, C. and Geissler, P. (2002)
Transition Path Sampling: Throwing ropes over mountain passes, in
the dark. Ann. Rev. Phys. Chem. 59, 291.