dims (c46b2)

Dynamic Importance Sampling (DIMS)


Dynamic Importance Sampling (DIMS) is a method that generates transitions
between a given initial and final state. Typically, those states are
experimental structures in two different functional states. What sets DIMS
apart from other methods is that no reaction coordinate needs to be defined in
advance and that the quality of a transition can be assessed with a score
during the simulation. The theory of the method is described in the articles
by Woolf et al (*note References::).


* Syntax | Syntax of the DIMS command and related commands.
* Description | Detailed description of DIMS and parameters.
* Restrictions | Restrictions, Known Bugs, and possible pitfalls.
* Examples | Example DIMS invocation and output.
* References | Articles and contact information.
* Developer notes | Notes on compiling Charmm with DIMS and source code
access.


Top
Syntax of DIMS Commands

The main command is DIMS but a few other commands also have DIMS-related
options. Those options are documented here extensively and their main
documentation links here.


Main DIMS command:

------------------------------------------------------------------------
DIMS { DBNM [HARD] }
[DCAR] }
[TMD] } dims-specs bhes-specs atom-selection
[HALT] } [bnm-atom-selection]
DIMS { HARD }
{ DCARtesian } dims-common-specs atom-selection


DBNM|HARD|DCAR biasing mode ('flavor')


bhes-specs Block Normal Mode parameters
(see » vibran Block normal mode
method.)

dims-specs ::= dims-common-specs [dims-nm-specs]

atom-selection atoms to which the DIMS bias is applied;
select )

bnm-atom-selection ::= atom-selection
(atoms for which the normal modes are computed. This
MUST contain all atoms of the protein)


dims-common-specs ::= COFF real SCAV int DSUNit int

( Common DIMS parameters::)


dims-nm-specs ::= DOFF real DSCAle real
NBIAs int SKIP int BSKIp int
NBESt int COMBinations int NWINdow int
ORIEnt int
NMPRint int UNIT unit
TMD HARD DCAR
DFIX
MTRA int NMUNit unit

( DIMS-NM parameters::)


Extensions to other commands:

------------------------------------------------------------------------
READ NM UNIT unit See also » io Other files.

------------------------------------------------------------------------
COORdinates COPY DIMS simple coordinate
» corman Simple. for a
description of the new DIMS set.

------------------------------------------------------------------------
DYNAMICS ... OMSC Compute the *note Onsager-Machlup score::
during dynamics.

?OMSCORE After the DIMS run, this energy variable
holds the trajectory's *note
Onsager-Machlup score::

?DSCORE DIMS score *note DIMS score::

?LDSCORE logarithmic DIMS score

------------------------------------------------------------------------
ENTEr <name> OMSC ETA <friction>
*note Onsager-Machlup score:: score as a CORREL
timeseries. See also
» correl Enter.


Top
Description of DIMS Commands


DIMS has a rather large number of options implemented and it can access
several other parameters from other functions that it uses. DIMS can use
different 'flavors' to bias the transition. (We use 'flavors' in favor of
'modes' in order to avoid confusion with normal modes.):

DBNM
DIMS-NM or DIMS-Block Normal Modes goes from the origin toward the target
by displacing atoms on the conformational space, using collective motion
information---the normal modes---as bias
dims References.)
This algorithm produces the best transitions but close to the target the
bias may not be strong enough to reach the target. At this point one can
have DIMS use a different algorithm to reach the target.

The algorithm employs the *note Block Normal Mode routines:
» vibran Block normal mode method. by *note Li and
» dims References.

DIMS defaults to DBNM.

HARD
Atoms are pulled from the origin towards the target based on the distance
and the remaining time steps.
dims References.) It is
guaranteed to reach the target state in a given number of steps but the
transitions can necessarily become forced with rather low quality scores.

DCARtesian
DIMS-Cartesian accepts moves that go toward the target
dims References.) and uses bias
moves towards the target with an acceptance function of the form:

2
P (DeltaPsi) = exp[ |DeltaPsi/DeltaPsi| ] if DeltaPsi < 0,
acc otherwise P (DeltaPsi)=1
acc

where P_acc(DeltaPsi) is the selected order parameter (*note RMSD
score::. or, for instance, the *note Interatomic distance::. score.)

This gently moves the system toward the target without a restriction on
the total time. If the barrier height is not high enough under some
conditions this algorithm will not converge. When the barriers to
conformation change is small this approach will converge with a better
DIMS or OM score.


* Common DIMS parameters | Parameters that are always needed for DIMS.
* DIMS-NM parameters | Parameters needed for DBNM with mode
combinations and/or mode avoidance.
* DIMS-NM algorithm | Description of DIMS-NM.
* Progress scores | How to measure progress along the transition.
* Trajectory scores | How to measure the quality of the trajectory.


Top
Common DIMS parameters

The common parameters are:

SCAV int
Number of dims scores to include in the computation of the scaling
factor, default: 5. The scaling factor is computed as the average
of the first SCAV scores, afterwards each new score is multiplied
by this scaling factor.

DSUNit int
Unit number to store DIMS score for the current run. default: -1.
NOTE: The unit must be open before calling DIMS or Charmm will crash.

atom-selection
The bias is applied to the *note selection of
» select Syntax. A sensible choice is all heavy atoms or
the back bone. Note that an atom selection must be provided or Charmm
bombs.



Top
DIMS-NM parameters

DIMS-NM is signified by the DBNM keyword. In this mode, the transition is
biased by using a combination of normal modes. The normal modes are computed
using the» vibran Block normal mode method.

Near the target configuration the energy landscape becomes rather soft and
normal modes are often not sufficient to drive the transition to the exact
target configuration. For this case DIMS-NM includes the 'Last-Mile-Hard'
option which allows it to exactly reach the target by using the DIMS-hard
mode. The switch to DIMS-hard occurs once the progress threshold COFF has
been reached.

The default score to measure the transition progress is RMS distance to the
target ( RMSD score::.), although in principle it can use any *note
Progress scores::.

In order to increase the variety in an ensemble of transition trajectories
DIMS-NM can use the *note Mode self-avoidance:: algorithm.

The syntax of the DIMS-NM command is

DIMS DBNM { [HARD] }
{ [DCAR] } dims-specs bhes-specs atom-selection
{ [TMD] } [bnm-atom-selection]
{ [HALT] }

The » vibran Block normal mode
method. defines the set of atoms for which the block normal modes are
computed. It defaults to the first selection. Its main use is when
simulations with explicit solvent are performed. In this case the
normal modes should only be computed for the protein (although the
Hessian is built from all interactions, including the solvent). If the
DIMS bias should only be applied to, say, the backbone, then the
bnm-atom-selection MUST contain the whole protein, including all
hydrogens as otherwise the normal modes would be calculated wrongly.


DIMS-NM supports the following options:

COFF real
This option tells DIMS-NM when to stop biasing based on the proximity to
the target (measured by the progress score, which is by default the RMS
distance from the target in Angstrom. Default value: 1.0

Depending on the options given, DIMS uses different approaches for the
remaining steps after the COFF threshold has been reached:

(no keyword, the default)
After COFF has been reached, the remaining NSTEP steps will be run
with unbiased MD. The trajectory is not guaranteed to exactly reach the
target.

HALT
After COFF has been reached the run stops.

DCARtesian
DCARtesian accepts moves that go toward the target and uses bias
moves towards the target with an acceptance function. Biasing
on the cartesian coordinates is being done using 'soft-ratcheting;
it is not guaranteed to reach the target.

HARD
The "Last-Mile-Hard" version is used (which is equivalent to running
'DIMS HARD') and the target will be reached by forcing the atoms to go
towards the target during the remaining steps. This can be important for
trajectory annealing schemes.

TMD
If targeted molecular dynamics (TMD) is enabled in Charmm and
the TMD flag is set then a last-mile TMD approach will be
run. This is equivalent to stopping your simulation at a given
cutoff and then running regular TMD from that final state
towards the target. TMD has to be configured via the regular TMD
commands (see » tmd Top. prior to the DIMS
call as DIMS does not handle any of the TMD parameters in any
way except for the target array orientation (if enabled).

DOFF
After the cutoff has been reached sometimes the structure tends to go back
thus increasing the order parameter. 'DOFF ("DynCutOff") prevents this by
re-computing the collective motions and forcing the structure to stay
within certain distance to the target. This option must be used with
caution as it might lead to undesired impulses in the dynamics.

DSCAle real
This is the NM-vector scaling. The force of the bias highly depends on
this parameter. The bias is applied for NBIAs steps. It is gradually
switched on with a sigmoidal function (over 1/3 NBIAS), set to a constant
DSCAle for 1/3 NBIAS, and switched off gradually over the remaining 1/3
NBIAs steps. Reasonable values range from 2.5*10^-2 to 2.5*10^-3

NBIAs int
The bias is applied for NBIAs steps.

SKIP int
Recompute the normal modes every SKIP steps. This is computationally
expensive so it is prudent to use a large SKIP value and a small BSKIP
value (see BSKIp). In this case, SKIP should be a multiple of BSKIp.

BSKIp int
The bias is applied every BSKIp steps for the next NBIAs steps. The
default value of BSKIP is the value of SKIP, which means that by default
the normal modes are recomputed every BSKIP steps. However, it is more
efficient (and seems to lead to more natural transitions) to only
recompute the normal modes every few thousand steps and reuse the same set
of normal modes for many cycles of biasing and relaxation. For example, if
SKIP 5000, BSKIP 40, and NBIAS 21, then every 5000 steps the Hessian is
diagonalized and the normal modes are recomputed. Every 40 steps, the bias
is applied for 21 steps, then for 19 steps the system evolves without
bias.

NBESt int
make a list of the NBESt "best" normal modes, where "best" means that
moving the system along this mode improves the progress score (by default
the RMSD) in the direction of the target structure.

COMB int
From the NBEST modes build combinations of up to COMB modes and evaluate
those combinations. E.g. if COMB 3 then singlets, doublets and triplets of
modes will be evaluated and ranked.

ORIEnt int
Re-orient the target every ORIEnt steps. If set to -1 then the structure
is not reoriented. Reorientation of the target does not need to be done
very frequently unless large changes happen quickly. A value of the order
of 1000...10,000 is probably appropriate.

NMPR int
Write the selected normal modes to the unit defined by UNIT every
NMPR steps.

UNIT unit
UNIT number to write the normal modes.

NWIND int
In order to generate variety in the transition, avoid the same combination
of modes as a bias within a window of +/-NWIND steps around the current
time step. The sequence of modes used must have been saved within a
previous run using the NMUN keyword and then read with READ NM UNIT unit.

MTRA int
MTRA is the number of NM bias-sequences stored in the file read with READ
NM UNIT unit.

NMUN unit
Unit to write the sequence of normal modes used as bias. This is used in
subsequent runs to avoid re-using the same modes
("self-avoidance"). Setting NMUN -1 disables writing of normal mode
combinations.

DFIX
This option enables DynFix which automatically sets to zero the
contribution to the motion from regular-MD for the steps in which the bias
from the collective motions is included. The system evolves exclusively
along the normal modes chosen as bias. NOT RECOMMENDED FOR STANDARD USE.
Default setting: OFF.

The command

READ NM UNIT unit

reads the sequence of normal mode combinations that were used in previous
DIMS-NM runs. It is used in conjunction with the MTRA, NWIND, and NMUN
keywords to compute an ensemble of trajectories with
*note Mode self-avoidance:Mode self-avoidance.

Also note that DIMS makes use of the Block Normal Mode subroutine implemented
by Dr. Guohui Li. Convergence also depends on those parameters; for further
information please refer to » vibran Block normal mode
method. and his paper on BNM
dims References. )

The main features of DIMS-NM are described in more detail in their
own entries:

* Mode self-avoidance | more on using the 'mode self-avoidance' algorithm
* Mode combinatorics | more on combining modes and how it interacts with
self-avoidance
* DIMS-NM algorithm::


Top
Mode self-avoidance in DIMS

To estimate transition rates a diverse ensemble of trajectories is
required. In order to increase diversity, one can calculate trajectories
sequentially and use information from the previous runs to avoid recreating
very similar trajectories.

We employ an approach inspired by self-avoiding random walks: DIMS-NM can
ignore modes or mode combination that were used in previous run at a given
time step (or window around a time step). Here the assumption is that modes
with the same mode number are the same mode and hence ignoring a given mode
forces the system to evolve in a different direction. Of course, this
assumption is not strictly true. In practice we found that this approach does
lead to an increased spread in trajectory space.

The 'mode self-avoidance' algorithm requires the use of a new files. This file
is used to store the modes that were used during a run. On subsequent runs if
is read with READ NM, and new modes are appended to it. The modes must be read
using the READ NM command,

open read unit 1 card name nmavoid.dat
read nm unit 1
close unit 1
open append card unit 10 name nmavoid.dat
dims ... nmun 10 ... mtraj 2


The write unit must be passed to DIMS using the NMUN keyword. If a unit other
than -1 is specified then the self-avoidance feature is active.

The MTRA parameter specifies how many trajectories are included in the
file.

DIMS can also avoid normal modes previously used within an specified window
with the NWIND keyword: If the mode (or mode combination) already occurred in
a previous trajectory within +/-NWIND steps of the current step then those
modes are ignored.


Top
Mode combinatorics in DIMS

By default DIMS-NM will only use one normal mode to bias the
transition. From all NMOD modes it uses the one which results in the
largest change towards the target (measured by the progress score).

However, it can be beneficial to combine normal modes for the biasing
step, say a combination of three modes. This is implemented as
'combinatorial normal mode DIMS' and signified with the parameter COMB
having a value larger than 1. COMB gives the maximum number of modes
to be combined. For instance, if COMB = 3, then at each biasing step
DIMS looks for the best singlet, doublet, or triplet of modes to use as
a bias. To speed up the combinatorical search it is prudent to
restrict the initial mode space from NMOD to the NBESt singlet modes.

Our tests show that the combinatorial version (COMB>1)
gives better transitions than the singlet version (COMB=1).

* Mode self-avoidance file | Details on the file used to record
normal modes and how to modify it when
changing COMB between runs.


Top
The mode self-avoidance file

When using self avoidance DIMS in combination with the combinatorial
version, DIMS will avoid a number COMB of combinations of normal
modes. One can not directly mix normal modes obtained for a simulation
with different COMB values. If this is desired then one will have to
pre-process the input NM file to match the file format expected for
the new COMB value.

For example, suppose a simulation was run with COMB=1 and self
avoidance so the normal modes at each NMPR steps were written to
NMUNit. Since COMB=1 is being used, DIMS will save just one mode for
each step. For the second simulation we want to increase the
combinatorics to three, i.e. COMB=3, but still avoid the modes
previously used. This is not a straightforward procedure as DIMS will
be expecting to see a file with triplets of nodes instead of singlets
from the first simulation, thus the NM file must be pre-processed
externally. Two skip modes must be added for each step in the
modes file. A skip mode is symbolized by -1. Examples should
make this clear:

Example file for COMB 1 (the ####### symbolizes a new trajectory):

** TITLE
** My normal modes singlets
*
2
33
21
#######

Example file for COMB 3 but based on a previous COMB 1 run:

** TITLE
** My modified normal modes -> triplets
*
8
-1
-1
33
-1
-1
21
########
-1
-1


Top
Outline of the DIMS-NM algorithm with
mode combinations and mode self-avoidance

DIMS-NM uses normal modes to bias the transition. Two additional
features increase the quality and diversity of trajectories: linear
combinations of normal modes and mode self-avoidance. The two main
ideas are:

(1) To not only use the best normal mode but combinations of modes.
(2) To increase diversity in an ensemble of trajectories by remembering
which modes were used at or near the same time step in previous
trajectories and then choosing different modes to bias the dynamics.

The basic algorithm for DIMS-NM that incorporates (1) and (2) reads thus:

1. Every SKIP steps, diagonalize the Hessian and compute the first
NMOD normal modes.

2. Rank those modes individually by how much they move the current
structure towards the target; the "best" mode is the one that
moves the structure closest towards the target as measured by
the progress variable and is ranked first.

3. Choose the top NBES best modes.

4. From those best modes, compute the possible change in progress
variable for all combinations of 2, 3, ... up to COMB modes.
Select that combination of modes that reduces the progress
variable most.

5. If self-avoidance is selected check if this combination has already been
used at this step in a previous run (or within a window of +/-NWIN steps
around the current step). If this is the case forget this combination
and try the next one (step 4).

6. Apply the bias (scaled by the factor DSCAle) along the mode(s)
for the next NBIAS steps during the dynamics.

7. Run unbiased dynamics for the remaining SKIP - NBIAS steps.

8. Check if the RMSD to the target has reached the cut-off distance
COFF (in Angstrom).
* If this is the case, switch to the hard DIMS version or TMD-DIMS
to move directly to the target.


Top
Measures of progress of the transition

To evaluate the conformational transition a progress variable must
be specified. For our current purposes we select an order parameter
based on RMS. Any other variable that attributes the transition
progress can be used. An example is a set of pairwise distances or
a vector RMS between two structures.

Other measures can be implemented in Charmm. As an example,
Interatomic distance was also implemented.

* RMSD score | configuration space root mean square distance
* Interatomic distance::


Top
Root mean square distance score

Root mean square deviation in configuration space (RMSD) is the default
score. It is measured in Angstrom. Small values mean that a given configuration
is close to the target.

For the calculation of the RMSD, the target configuration must be repeatedly
reoriented with respect to the evolving configuration of the molecule in the
trajectory. This is accomplished by setting the ORIEnt parameter to the DIMS
command.


Top
Interatomic distance score

NOTE: currently not enabled by default, requires ANNLIB.
Developer notes::.

The interatomic distance score is based on the distances between a
predetermined set of atoms during the simulation. Two set of atoms are
required for this approach: The first set, called the data set is
composed of the atoms/points whose distance to a second set, the query
set, is computed. These pair of sets can be equal or have
common elements, there are not restrictions as on what to put on
them. Note that both set of points dynamically evolve during the
simulation, the only things that are kept fixed are the atoms/points
indexes. Let C0 be the set of the k-nearest-neighbors in the data set
for every point in the query set for the target structure. Let I0 be
the atom indexes for the atoms in C0. The atomic distances between the
elements of C0 and the ones from the query set are then stored in D0
for the target structure. After a simulation step new coordinates are
obtained and both the data set and the query set are updated. Now the
set C is the set of atoms that belong to the data set that are indexed
by I0. The distances between the atoms in C and the ones in the query
set are then stored in D. The progress score is then defined as
ABS(D-D0). Therefore the score is positive definite and a lower score
means a closer match and 0 for identical. This approach is called
using the keyword IATD and an integer (k) and the two selection of
atoms:

dims ... IATD 3 sele type N end sele type CA end ! Compute the score from
! the distance between the three nearest N and each CA

The second approach also uses the data and query sets concept, however it
doesn't use the k-NNs and is slightly different from the previous one.
Two molecular descriptors are needed to compute the score. Each descriptor
contains the first three moment of the distance distribution for each query
point. The score is computed as the Manhattan distance between two molecular
descriptors. To use this metric we use the keyword adist plust two selection
of atoms:

dims ... ADIST sele all end sele type CA end ! all-Atom distribution about CAs


Top
Trajectory scores

Trajectory scores are used to rank trajectories in an
ensemble. Higher-ranked ('better') trajectories are the ones which are
more likely to occur without bias.

* Onsager-Machlup score | Onsager-Machlup action as a score
* DIMS score | The (approximated) DIMS score.


Top
Onsager-Machlup Score

The Onsager-Machlup score (OM score) is an action, computed along the
whole trajectory. The smaller this number is the more the (biased)
transition resembles a transition that could have naturally occurred.

The step score s(t) is the Onsager-Machlup action for the given time
step,

N_atom / x_i(t) - x_i(t-dt) F_i \ 2
s(t) := Sum |------------------- - ------- |
i=1 \ dt m_i*eta/

The cumulative OM score S(t) is

t
S(t) := Sum dt * s(t')
t'=0

The OM score S_OM of a trajectory of length t_traj is the cumulative
OM score of the last frame,

S_OM = S(t_traj)

After the DIMS run, the energy variable ?OMSCORE holds the
trajectory's Onsager-Machlup score. If the trajectory is continued
with another DIMS run, one can simply add the two scores for the score
of the combined trajectory.

With the OMSC keyword to DYNAMics (*note Langevin
» dynamc Syntax.) the OM score is computed during the
simulation and printed out. It is the sum of all the step scores over
the whole trajectory so far.


The normalized-cumulative-score

S*(t) := S(t)/s(0)

is computed with the *note OMSC time series:» correl Enter.


Top
DIMS score

The simplified DIMS score is described in
» dims References. It approximates a rigorous score
based on transition probabilities as a ratio of Boltzmann probabilities of the
unbiased and the biased movement of the system.

The single step score R_i^s at step i is:

s exp(-DeltaE_Q/kT)
R = -----------------
i exp(-DeltaE_D/kT)

where DeltaE_Q is the change in total energy if the system evolves unbiased
(according to the distribution Q) and DeltaE_D is the change in energy under
the bias D.

The DIMS score is the product along the trajectory

N S
S = Product R
i=1 i

A trajectory close to a naturally occurring one should have single step scores
close to 1 and a DIMS score close to 1. In practice, the DIMS score almost
always becomes very small and eventually underflows.

The logarithmic DIMS score ln S is slightly more robust in this respect.

In order to calculate reaction rates only relative scores between trajectories
are important so it is only necessary to record a non-vanishing score. Thus,
it is not a problem per se if the score is much smaller than 1.

The final DIMS score is available in the energy variable ?DSCORE and is also
written to the file designated by DSUNIT. The logarithmic DIMS score is
provided in ?LDSCORE. During a run, DIMS writes those score to the standard
output as well ( DIMS output::).


Top
Restrictions when using DIMS

The DIMS code is currently (December 2007) in alpha release. Feedback is very
welcome. References:: for contact details.

DIMS
* Mostly tested with DYNAMICS Langevin.
* No good default values - most parameters are probably system dependent.
* DIHEdral bias currently not implemented.
dims References.)
* PSF for initial and final state must be the same.
* DCAR runs in parallel as an MPI version but DBNM or HARD cannot be run
in parallel.
* The interatomic distances progress score is not enabled by
default because it requires an additional library.

CORREL OMSC
* OMSC is incompatible with RMS because they both use the same reference
array for different things (RMS stores the comparison structure, OMSC
the previous frame to compute velocities X(t) - X(t-1).) To be safe,
only use a single ENTER name OMSC .. time series per CORREL command.


Top
DIMS examples

It is recommended to read through the examples in sequence as important setup
steps are only shown in the first example. Further options are then added in
the other examples.

(See also the scripts in the test directory.)

The basic work flow with DIMS is simple:

1. Load structures; the target is stored in the DIMS coordinates set using
COOR COPY DIMS

2. Setup DIMS using the DIMS command.

3. Run dynamics.

If the 'mode self-avoidance' is used, also save the modes (see the second
example below) and repeat 3 to generate an ensemble or
trajectories. Alternatively one can also use an ensemble of initial and final
structures (e.g. from short MD) and/or different random seeds for initial
velocity assignment and Langevin random forces.

* NM DIMS example | Normal modes are used to drive the transition.
* DCAR DIMS example | DIMS-cartesian are used to drive the transition.
* NM DIMS + self-avoidance example:: Normal modes and self-avoidance to
increase diversity.
* Explicit solvent example: DIMS with water (and using SSBP).
* TMD last mile example:: Using DIMS-NM and TMD to reach the target.
* Choosing parameters | Initial guidance on how to choose appropriate
values for the many DIMS options.
* DIMS output | DIMS diagnostics explained.


Top
Example 1a:
Normal Mode-biased DIMS

DIMS with normal mode bias (mode keyword DBNM) tends to produce better
transitions than the cartesian or dihedral-based schemes. In this example we
combine up to 3 normal modes (COMB 3) out of the 15 best normal modes (NBES
15).

The following Charmm script fragment is not complete but shows the most
important steps.


! generate psf (same for start and target structure)
OPEN READ CARD UNIT 1 NAME start.crd
READ SEQUENCE COOR UNIT 1
GENERATE prot SETUP FIRST NTER LAST CTER ! PSF for initial and final
! states must be the same

! target configuration
OPEN READ UNIT 1 CARD NAME target.crd
READ COOR CARD UNIT 1
CLOSE UNIT 1

COOR COPY DIMS ! target must be copied to DIMS set

! starting configuration
OPEN READ UNIT 1 CARD NAME start.crd
READ COOR CARD UNIT 1
CLOSE UNIT 1


DEFINE mydims SELECT all END ! atoms to apply bias to

DIMS DBNM - ! set up NM-DIMS
DSCALE 8e-3 SKIP 500 BSKIP 50 NBIAS 27 SCAV 10 - ! dims options
SERL GENR SCAL 0.5882 TMEM 420 MEMO 20 MEMA 350 NMOD 50 - ! BNM options
COFF 0.8 HARD ORIENT 400 - ! Lastmile / Orient
COMB 3 NBES 15 - ! Combinatorics
MTRA 0 NMUN -1 NWIND 0 DSUNit 11 - ! Self Avoidance
SELE mydims END ! DIMS atom selection

SCALAR fbeta SET 50.0 ! friction coefficient in 1/ps

! run Langevin dynamics (in implicit solvent)
DYNA LEAP LANGEVIN START ... -
OMSC ... - ! compute *note Onsager-Machlup score::


Top
Example 1b:
DIMS-CARTESIAN-biased DIMS

open read.... ! Read input similar to that of NM DIMS example

DEFINE mydims SELECT all END ! atoms to apply bias to

DIMS DCAR 1e-7 - ! set up DCAR-DIMS
orient 10 ! re-orient at every 10 nstep
SELE mydims END ! DIMS atom selection
COFF 0.6 halt ! stop biasing when target is 0.6 A from target

SCALAR fbeta SET 25.0 ! friction coefficient in 1/ps

! run Langevin dynamics (in implicit solvent)
DYNA LEAP LANGEVIN START ... -
OMSC ... - ! compute *note Onsager-Machlup score::


Top

Normal Mode-biased DIMS with self avoidance of modes

DIMS is capable of avoiding previously used normal modes. On the first run,
save the normal modes:

open write card unit 10 name nmavoid.dat
dims ... nmun 10 ... mtraj 2

For subseqent runs, load the modes and append new ones by
using the READ NM command (» io Other files.):

open read unit 1 card name nmavoid.dat
read nm unit 1
close unit 1
open append card unit 10 name nmavoid.dat
dims ... nmun 10 ... mtraj 2

The write unit must be passed to DIMS using the NMUN keyword; using NMUN=-1
does not save the modes. One can also specify how many trajectories are
included in the file with the MTRA keyword. DIMS can also avoid normal modes
previously used within an specified window with the NWIND keyword.


DEFINE mydims SELECT all END ! atoms to apply bias to

DIMS DBNM -
DSCALe 0.1 SKIP 500 BSKIP 50 NBIAs 27 - ! dims options
SERL GENR SCAL 0.5882 TMEM 420 MEMO 20 MEMA 400 NMOD 30 - ! BNM options
COFF 2.0 HARD - ! NM Hard Cutoff
ORIEnt 20 - ! Orient every 20th
SELE mydims END - ! selection
COMB 3 NBES 15 - ! Store 15 best modes and then group them
- ! by 1, 2 and 3 for each try.
NWINDow 12 - ! Avoid normal modes previously used within
- ! a window of 12 modes
MTRA @I NMUNit 10 - ! @i trajectories per file, write output to unit 10
DSUNit 11 - ! Use unit 11 to store dims score


Top
Example 3:
Normal Mode-biased DIMS with explicit solvent

In this example, we will use DIMS on a peptide in water. The system is
simulated using the Spherical Solvent Boundary Potential *note
» mmfp

! read psf (peptide + water)
...

DEFINE solute SELECT SEGID pept END ! only the peptide
DEFINE mydims SELECT solute END ! DIMS on the whole peptide but not water

! read target coordinates
...
COOR COPY DIMS SELECT mydims END ! setup DIMS target structure (no solvent!)

! read starting structure
...


! non bonded interactions
NBONDS EXTEND GRAD QUAD GROUP SWITCH CDIE EPS 1.0 -
VDW VSWITCH -
CUTNB 12.0 CTOFNB 12.0 CTONNB 12.0 WMIN 1.2 WRNMXD 1.2

!------------------------------------------------------------
! SSBP & restraints
!------------------------------------------------------------
COOR STAT SELECT solute END
SET xcen = ?XAVE
SET ycen = ?YAVE
SET zcen = ?ZAVE

MMFP
! Use Stochastic Boundary Potential to constrain water
! (flexible boundary which adjusts shape). Leave out KIRKWOOD for
! faster, less accurate simulations
SSBP KIRKWOOD ANGU HSR EMPI CAVITY select type OH2 end

! keep peptide at centre; otherwise it may diffuse to the
! SSBP interface
GEO RCM SPHERE XREF @xcen YREF @ycen ZREF @zcen -
HARMONIC FORCE 5.0 -
SELECT solute END
END

!------------------------------------------------------------
! brief minimization
!------------------------------------------------------------
! should be on water only
CONS HARM FORCE 50.0 SELECT solute END
MINI SD NSTEP 100
CONS HARM FORCE 0 SELECT all END ! free solute


!------------------------------------------------------------
! DIMS
!------------------------------------------------------------
DIMS DBNM DSCALE 8e-3 SKIP 1000 BSKIP 40 NBIAS 21 - ! dims options
SERL GENR SCAL 0.5882 TMEM 420 MEMO 20 MEMA 350 NMOD 50 - ! NM options
COFF 0.5 HARD ORIENT 100 COMB 3 NBES 15 SCAV 10 -
MTRA 0 NMUN -1 NWIND 0 DSUN -1 -
SELECT mydims END - ! DIMS selection
SELECT mydims END ! BNM selection (optional)

!------------------------------------------------------------
! dynamics
!------------------------------------------------------------
SCALAR fbeta SET 5.0 SELECT .NOT. TYPE H* END
SHAKE BONH PARA

OPEN WRITE FILE UNIT 52 NAME dims.dcd ! trajectory

set TEMPERATURE = 300
set Nstep = 10000

! Run with Langevin dynamics
! (frequent output for testing)
PRNLEV 4 ! verbose DIMS output
DYNAMICS start nstep @Nstep timestp 0.002 iprfrq 100 -
nprint 100 echeck 10000.0 -
iasvel 1 -
firstt @TEMPERATURE finalt @TEMPERATURE tstruc @TEMPERATURE -
langevin tbath @TEMPERATURE -
inbfrq 10 imgfrq -1 ihbfrq 0 ilbfrq 0 -
nsavcrd 50 isvfrq 0 -
iunread -1 -
iunwrite -1 iuncrd 52 -
omsc ! DIMS Onsager-Machlup score


Top
NM-DIMS, using Targeted MD for the 'last mile'

Close to the target the normal modes may not be specific enough to drive the
transition completely to the target. If this is desired, other methods can be
used to close the transition. The simplest approach is to use targeted MD once
the RMSD becomes smaller than COFF = 0.9 Angstrom.

COOR COPY dims ! for DIMS
COOR COPY targ ! import for TMD calculations

TMDInitialize sele all end sele all end inrt 10 dincr 0.00025 ! Initialize TMD

DIMS DBNM DSCALE 0.08 SKIP 500 BSKIP 50 NBIAS 27 - ! dims options
SERL GENR SCAL 0.5882 TMEM 900 MEMO 30 MEMA 700 NMOD 50 - ! BNM options
COFF 0.9 TMD - ! NM TMD Cutoff
ORIENT 400 - ! Orient every 400th
COMB 3 NBES 15 MTRA 0 NMUN -1 NWIND 0 DSUN 11 - ! NM comb options
SELE mydims END ! selection


TMD pulls the structure linearly. It is also possible to employ the HARD
flavor of DIMS for a more natural transition. Note that CHARMM must be
compiled with TMD support (not enabled by default).


Top
Choosing parameters for DIMS-NM

Initial testing shows that a suitable choice of parameters can be rather
system dependent. The following is meant as a rough guideline to find
appropriate parameters.

* Use DBNM (the Block Normal Modes version) in conjunction with a
last-mile option. Typical DSCALE values are on the order of 1.0*10^-2
to 1.0*10^-5.

* Optimize BSKIp, SKIP, and NBIAs so that a transition close to the target
is achieved, say within COFF 0.5 Å (just using DBNM).

* Start with a reasonable number of dynamics steps, e.g. NSTEp 100,000 and
a time step of 1-2 fs (SHAKE can be used).

* Look at the Onsager-Machlup score (should rise as slowly as possible)
and the per-step DIMS score (should be as close to 1 as possible).

o The total DIMS score will eventually decay to 0; that's a current
limitation. A logarithmic DIMS score is displayed as well.
o To get a feeling for the OM score, compute it for your system when
running free Langevin MD (use the new OMSC time series). Note that
the OM score depends on the step size (ie your trajectory SKIP
value).
o The aim is to produce a variety of trajectories with low OM
scores. This may require running the dynamics for longer (larger
NSTEp) to bias the system more gradually.

* Analyze the transition:
o Plot RMSD (or more generally, the progress score) over steps.
o Plot total potential energy over steps.
o Plot the OM-score over time. (This is a cumulative measure and the
last frame's score is the score for the trajectory. It is also
available in the energy variable ?OMSCORE.)


Top
Explanation of the DIMS output

------------------------------------------------------------------------------
(1) Regular DIMS output

DIMS> DIMS Score: 0. -28164.3312 -28159.1454 2.34808744 0.00559546636 3 2
| | | | | | |
DIMS_averaged-----+ | | | | | |
Energy_unbiased------+ | | | | |
Energy_biased---------------------+ | | | |
Normalization_constant------------------------+ | | |
current_move_score----------------------------------------+ | |
dims_counter------------------------------------------------------------+ |
number of steps over which normalization constant was computed------------+

DIMS> DIMS LogScore: 0.28724E+04
|
Log(DIMS)-----------+

If the store goes to zero then the best way to monitor the dims score is to
save the scores to a file (using DSUN) and post-process them.

------------------------------------------------------------------------------
(2) At prnlev 3

When running NM-DIMS the Progress Score is printed ; by default the progress
score is the RMSD to the target (lower is better).

DIMS> Progress Score0: 1.58859248
DIMS> Move accepted:
1.57390
8.01332 36
3.88053 30
11.78028 46

Progress Score0
RMSD from target before DIMS: previous DIMS and MD

Move accepted
DIMS found a move along normal modes. After the move the new RMSD is given
(here: 1.57390). The modes are listed below in the format

frequency mode_number

Note that this triple (because COMB 3) of modes is the "best" combination
of modes out of all NBES 15 modes in the list. (Note: all combinations of
modes are checked and the best one is used, which may be a single mode or
only a combination of two, even if COMB 3.)

------------------------------------------------------------------------------
(3) At prnlev 4

* score of every combination

------------------------------------------------------------------------------
(4) At prnlev 6

* lots of output - only useful for debugging


Top
References for DIMS:

1. T. B. Woolf, Path corrected functionals of stochastic
trajectories: Towards relative free energy and reaction
coordinate calculations, Chemical Physics Letters 289(5-6)
(1998) 433-441.

2. D.M. Zuckerman and T. B. Woolf, Dynamic reaction paths and
rates through importance-sampled stochastic dynamics, J Chem
Phys 111 (1999) 9475-9484.

3. D. M. Zuckerman, T.B. Woolf, Rapid Determination of Multiple Reaction
Pathways in Molecular Systems: The Soft-Ratcheting Algorithm.
arxiv:physics/0209098 (2002)

4. H. Jang and T. B. Woolf, Multiple pathways in conformational
transitions of the alanine dipeptide: An application of dynamic
importance sampling, Journal of Computational Chemistry 27(11)
(2006) 1136-1141.

5. J. R. Perilla, A. Nagarajan, E. J. Denning, J. M. Johnston, O. Beckstein,
T.B. Woolf, Sampling macromolecular transitions with dynamic
importance sampling. (in preparation)

NM-DIMS uses the Block Normal Mode routines in Charmm so
please also cite

6. Li G and Cui Q. A coarse-grained normal mode approach for
macromolecules: an efficient implementation and application to
Ca(2+)-ATPase. Biophys J 2002 Nov; 83(5) 2457-74.

Ref 6 describes in more detail how to choose blocks for the BNM approach:

7. Tama F, Gadea FX, Marques O, and Sanejouand YH. Building-block approach
for determining low-frequency normal modes of macromolecules. Proteins
2000 Oct 1; 41(1) 1-7

Targeted Molecular Dynamics (TMD option):

1. J. Schlitter, M. Engels, P. Krueger, E. Jacoby and A. Wollmer,
Targeted Molecular Dynamics Simulation of Conformational
Change-Application to the T --> R Transition in Insulin
Mol. Sim. 10 (1993) 291-308.


Authors and Contact details:

Please direct feedback (questions, bug reports, suggestions) to

Tom Woolf <twoolf@jhmi.edu>
Juan Roberto Perilla <jrperillaj@jhu.edu>
Oliver Beckstein <orbeckst@jhmi.edu>


Top
Remarks (for developers):

Necessary flags for compiling with DIMS:

DIMS

Optional flags:

TMD # targeted MD for the 'last mile'
ARPK # see ARPACK section below
ANNLIB # see ANNLIB section below. Required to activate IATD and ADIST.

External libraries:

ANNLIB - A Library for Approximate Nearest Neighbor Searching.
http://www.cs.umd.edu/~mount/ANN/
ARPK - ARPACK is designed to solve large scale eigenvalue problems.
http://www.caam.rice.edu/software/ARPACK/


Testcase files for DIMS can be found in the c35test directory:

dims.inp
dims_nm.inp


(Email Thomas B. Woolf <twoolf@jhmi.edu> or Juan Roberto Perilla
<jrperillaj@jhu.edu> with questions or feature requests.)