# umbrel (c49b1)

Order Parameters

The RXNCOR module in CHARMM was initially implemented by J. Kottalam in

December 1990 for molecular dynamics simulations with an umbrella potential.

The code and this documentation are currently being updated by Aaron R. Dinner

and co-workers for use in all situations in which sampling based on (single

or multiple) (scalar or vector) order parameters are desired. » tps

for additional notes.

* Syntax | Syntax of RXNCOR and its subcommands

* Examples | Examples of specifying a reaction coordinate in CHARMM and

interpreting the results

The RXNCOR module in CHARMM was initially implemented by J. Kottalam in

December 1990 for molecular dynamics simulations with an umbrella potential.

The code and this documentation are currently being updated by Aaron R. Dinner

and co-workers for use in all situations in which sampling based on (single

or multiple) (scalar or vector) order parameters are desired. » tps

for additional notes.

* Syntax | Syntax of RXNCOR and its subcommands

* Examples | Examples of specifying a reaction coordinate in CHARMM and

interpreting the results

Top

Syntax

All the commands invoking this module are prefixed by the keyword RXNCord.

The geometrical elements such as points, lines and planes are referenced by

names selected by the user.

[Syntax RXNCoor]

RXNCoor < set-spec | bas-spec | wri-spec | umbr-spec | defi-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 } (for TPS and/or SMD)

wri-spec ::= < WRITe [ UNIT unit (default is outu) ] |

TRACe name [ UNIT unit (default is outu) ] >

umbr-spec ::= UMBRella FORM form KUMB ku DEL0 del0 PERIod period SMDDel smddel

stat-spec ::= STATistics LOWDelta lowdel HIDElta hidel DELDelta deldel -

START start

defi-spec ::= DEFIne name geom-spec

geom-spec ::= POINt [MASS] atom_selection

DIREction point1 point2

direction1 direction2

LINE THROugh point1 THROugh point2

PARAllel_to line1

PERPend line1 PERP line2

NORMal_to plane1

PLANe THROugh point1 THRO point2 THRO point3

CONTaining line1

PERPendic line1

PARAllel line1 PARA line2

plane1

DISTance point1 point2

line

plane

ANGLe direction1 direction2 direction3

line1 line2 direction3

line1 plane2 direction3

plane1 plane2 direction3

CECM atom_selection atom_selection rsw dsw

RATIo distance1 distance2

COMBination name1 weight1 name2 weight2 ...

SCOMbination name1 mult1 name2 mult2 ...

VCOMbination name1 mult1 name2 mult2 ...

Notes on geom-spec:

A distance can be between two points or the perpendicular distance of a

point from a plane or a line. An angle can be between two (intersecting or

non-intersecting) lines and so on. Planes and lines are ultimately defined

in terms of points and points can be defined as the centres of geometry (or

mass) of a groups of atoms in the macromolecule. Thus we have in CHARMM a

general algorithm to define any order parameter (of the above form) in terms

of the cartesian coordinates of arbitrary sets of atoms.

The name immediately following the DEFIne keyword is the name of the object

being defined. Names referenced towards the right side are names of objects

already defined.

If the MASS keyword appears in the POINt definition, then the point is the

centre of mass, otherwise it is the centre of geometry.

The order of points in DIREction definition is important, unlike in DISTance

definition. When two directions are used to define a third direction, the

third direction is perpendicular to the other two.

The ANGLe is the one subtended by the first two arguments measured anti-

clockwise when viewed along direction3. The angle defined with a line and

plane is the one between the line and the plane normal, NOT the plane itself.

The CECM is the modified center of excess charge coordinate useful for studying

proton transfer reactions. It requires two selections, the first contains the heavy

atoms that can participate in proton transfers; the second contains hydrogen atoms. The

parameters rsw and dsw define the switching function used to define bond connectivity

during the proton transfers. The weights of the heavy atoms should be specified by

the WMAIN array. For more detailed discussions, see Koenig et al., J. Phys. Chem. A

110, 548-563 (2006). See test/c43test for a very simple example.

RATIo is distance1/distance2.

COMBination is the weighted mean of all names; SCOMbination is the simple

sum mult1*name1+mult2*name2...; VCOMbination is a vector analog of

SCOMbination, where three-dimensional vectors can be combined with arbitrary

weighting to define another vector.

The SET command sets a particular geometric element as the reaction coordinate.

This element must be already defined. If a name is referenced and not defined,

the program will stop. If a name is defined but not referenced, no message is

issued, but this will result in some unnecessary computations without affecting

the results.

Notes on umbr-spec:

The UMBR commad specifies the form and parameters for an umbrella potential:

form functional form of potential

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

1 ku*(delta-del0)**2

5 ku*(delta-del0)**2 + Ubias(delta)

In form 5, Ubias is a biasing potential, used in addition to the harmonic

restraining potential, to truncate high barriers of activated processes.

Ideally, Ubias(Rc) would be the negative of the potential of mean force g(Rc),

where Rc is the reaction coordinate. Ubias is implemented as a cubic spline

function based on a tabulated data to be read prior to the call of RXNC.

Order parameters can be periodic. To ensure correct calculation of the energy

and forces, set the PERIod keyword to a non-zero value.

Notes on stat-spec:

The STAT subcommand specifies the range of a coordinate and when to collect

statistics. Starting from the 'start'-th step of dynamics, the number of

occurences of delta (the value of each reaction coordinate) will be counted

in each interval 'deldel' long. This counting will be done in the range

'lowdel' to 'hidel'. The statistics collected by the STAT subcommand are

printed out at the end of dynamics when the WRITe subcommand has been invoked.

WRITe will print out a table without any header. The header is left out on

purpose to enable this file to be read by any plotting program. The meanings

of the numbers are therefore explained here. Recall that the STAT subcommand

essentially setup a range of the reaction coordinate (delta) and divided this

range into small pieces. For each piece the following information is printed

out in one line:

the midpoint of the delta interval

the free energy at this midpoint (after subtracting the umbrella potential)

the number of observations for which delta fell in this interval.

(One observation is made at every step of the dynamics)

Apart from the cumulative statistics, it may be useful to have a print out

of the delta values versus time. The time series of any quantity defined by

the DEFIne subcommand can be printed by using the TRACe subcommand. This

command should appear before the dynamics command.

Syntax

All the commands invoking this module are prefixed by the keyword RXNCord.

The geometrical elements such as points, lines and planes are referenced by

names selected by the user.

[Syntax RXNCoor]

RXNCoor < set-spec | bas-spec | wri-spec | umbr-spec | defi-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 } (for TPS and/or SMD)

wri-spec ::= < WRITe [ UNIT unit (default is outu) ] |

TRACe name [ UNIT unit (default is outu) ] >

umbr-spec ::= UMBRella FORM form KUMB ku DEL0 del0 PERIod period SMDDel smddel

stat-spec ::= STATistics LOWDelta lowdel HIDElta hidel DELDelta deldel -

START start

defi-spec ::= DEFIne name geom-spec

geom-spec ::= POINt [MASS] atom_selection

DIREction point1 point2

direction1 direction2

LINE THROugh point1 THROugh point2

PARAllel_to line1

PERPend line1 PERP line2

NORMal_to plane1

PLANe THROugh point1 THRO point2 THRO point3

CONTaining line1

PERPendic line1

PARAllel line1 PARA line2

plane1

DISTance point1 point2

line

plane

ANGLe direction1 direction2 direction3

line1 line2 direction3

line1 plane2 direction3

plane1 plane2 direction3

CECM atom_selection atom_selection rsw dsw

RATIo distance1 distance2

COMBination name1 weight1 name2 weight2 ...

SCOMbination name1 mult1 name2 mult2 ...

VCOMbination name1 mult1 name2 mult2 ...

Notes on geom-spec:

A distance can be between two points or the perpendicular distance of a

point from a plane or a line. An angle can be between two (intersecting or

non-intersecting) lines and so on. Planes and lines are ultimately defined

in terms of points and points can be defined as the centres of geometry (or

mass) of a groups of atoms in the macromolecule. Thus we have in CHARMM a

general algorithm to define any order parameter (of the above form) in terms

of the cartesian coordinates of arbitrary sets of atoms.

The name immediately following the DEFIne keyword is the name of the object

being defined. Names referenced towards the right side are names of objects

already defined.

If the MASS keyword appears in the POINt definition, then the point is the

centre of mass, otherwise it is the centre of geometry.

The order of points in DIREction definition is important, unlike in DISTance

definition. When two directions are used to define a third direction, the

third direction is perpendicular to the other two.

The ANGLe is the one subtended by the first two arguments measured anti-

clockwise when viewed along direction3. The angle defined with a line and

plane is the one between the line and the plane normal, NOT the plane itself.

The CECM is the modified center of excess charge coordinate useful for studying

proton transfer reactions. It requires two selections, the first contains the heavy

atoms that can participate in proton transfers; the second contains hydrogen atoms. The

parameters rsw and dsw define the switching function used to define bond connectivity

during the proton transfers. The weights of the heavy atoms should be specified by

the WMAIN array. For more detailed discussions, see Koenig et al., J. Phys. Chem. A

110, 548-563 (2006). See test/c43test for a very simple example.

RATIo is distance1/distance2.

COMBination is the weighted mean of all names; SCOMbination is the simple

sum mult1*name1+mult2*name2...; VCOMbination is a vector analog of

SCOMbination, where three-dimensional vectors can be combined with arbitrary

weighting to define another vector.

The SET command sets a particular geometric element as the reaction coordinate.

This element must be already defined. If a name is referenced and not defined,

the program will stop. If a name is defined but not referenced, no message is

issued, but this will result in some unnecessary computations without affecting

the results.

Notes on umbr-spec:

The UMBR commad specifies the form and parameters for an umbrella potential:

form functional form of potential

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

1 ku*(delta-del0)**2

5 ku*(delta-del0)**2 + Ubias(delta)

In form 5, Ubias is a biasing potential, used in addition to the harmonic

restraining potential, to truncate high barriers of activated processes.

Ideally, Ubias(Rc) would be the negative of the potential of mean force g(Rc),

where Rc is the reaction coordinate. Ubias is implemented as a cubic spline

function based on a tabulated data to be read prior to the call of RXNC.

Order parameters can be periodic. To ensure correct calculation of the energy

and forces, set the PERIod keyword to a non-zero value.

Notes on stat-spec:

The STAT subcommand specifies the range of a coordinate and when to collect

statistics. Starting from the 'start'-th step of dynamics, the number of

occurences of delta (the value of each reaction coordinate) will be counted

in each interval 'deldel' long. This counting will be done in the range

'lowdel' to 'hidel'. The statistics collected by the STAT subcommand are

printed out at the end of dynamics when the WRITe subcommand has been invoked.

WRITe will print out a table without any header. The header is left out on

purpose to enable this file to be read by any plotting program. The meanings

of the numbers are therefore explained here. Recall that the STAT subcommand

essentially setup a range of the reaction coordinate (delta) and divided this

range into small pieces. For each piece the following information is printed

out in one line:

the midpoint of the delta interval

the free energy at this midpoint (after subtracting the umbrella potential)

the number of observations for which delta fell in this interval.

(One observation is made at every step of the dynamics)

Apart from the cumulative statistics, it may be useful to have a print out

of the delta values versus time. The time series of any quantity defined by

the DEFIne subcommand can be printed by using the TRACe subcommand. This

command should appear before the dynamics command.

Top

As an example, consider the interconversion between the chair and boat

forms of cyclohexane. This process can be described in terms of three

rotation angles. These angles rotate carbons 2, 4 and 6 respectively about

the plane of carbons 1, 3 and 5.

Let us number the carbon atoms in cyclohexane as C1,...,C6. Consider the

plane of atoms c1, c3 and c5 and the plane of atoms c1, c2 and c3. Let us

call the angle between these two planes as a rotation angle. There are two

other rotation angles about the c1-c3-c5 central plane. The mean of these

three rotation angles serves as a reaction coordinate for the chair-boat

conversion.

rxncor: define c1 point select atom cycl 1 c1 end

rxncor: define c2 point select atom cycl 1 c2 end

rxncor: define c3 point select atom cycl 1 c3 end

rxncor: define c4 point select atom cycl 1 c4 end

rxncor: define c5 point select atom cycl 1 c5 end

rxncor: define c6 point select atom cycl 1 c6 end

rxncor: define d13 direction c1 c3

rxncor: define d35 direction c3 c5

rxncor: define d51 direction c5 c1

rxncor: define d12 direction c1 c2

rxncor: define d34 direction c3 c4

rxncor: define d56 direction c5 c6

rxncor: define norc direction d35 d13

rxncor: define nor1 direction d13 d12

rxncor: define nor2 direction d35 d34

rxncor: define nor3 direction d51 d56

rxncor: define alf1 angle norc nor1 d13

rxncor: define alf2 angle norc nor2 d35

rxncor: define alf3 angle norc nor3 d51

rxncor: define mean combi alf1 1.0 alf2 1.0 alf3 1.0

rxncor: set mean

An example of the use of FORM 5 is shown below:

...

rxncor: define RC distance PCC PCO

rxncor: set RC

open read unit 33 form name bias.pot

rxncor: bias unit 33

close unit 33

rxncor: umbrella kumb 20. del0 1.50 form 5

...

WHERE bias.pot contains:

* Trial Biasing Potential

* example, 1200

*

5 ! number of points (up to 25)

1.0 -28.0 ! Rc Ubias(Rc)

1.3 -18.0

1.4 -8.0

1.5 0.0

1.6 -2.0

END description of FORM 5 JG 12/00

In each case, dynamics is run by invoking the DYNAmics command. » tps

for notes on using RXNCOR with transition path sampling and steered molecular

dynamics.

To extract results from umbrella sampling simulations, return to the example

of cyclohexane

rxncor: trace alf1 unit 22

rxncor: trace alf2 unit 23

rxncor: trace alf3 unit 24

rxncor: trace mean unit 25

rxncor: umbrella kumb 15.0 form 1 del0 -0.4

rxncor: statistics lowdelta -0.6 hidelta -0.4 deldel 0.002 start 5000

dynamics rest nstep 15000 firstt 300.0 finalt 300.0 ihtfrq 0 -

teminc 0.0 iunwrite 19 kunit 20 iunread 17

rxncor: write unit 21

close unit 21

Here, the essential results are the first and second columns of the output

from the WRITe subcommand, which plot free energy versus the order parameter

in the covered range of the order parameter values (delta values). In order

to cover the full range of delta the procedure is repeated by constraining

delta around a particular value by using an umbrella potential centered at

that value.

For theory and practice of umbrella sampling, see Kottalam and Case in Journal

of American Chemical Society, 110, 7690 (1988)

As an example, consider the interconversion between the chair and boat

forms of cyclohexane. This process can be described in terms of three

rotation angles. These angles rotate carbons 2, 4 and 6 respectively about

the plane of carbons 1, 3 and 5.

Let us number the carbon atoms in cyclohexane as C1,...,C6. Consider the

plane of atoms c1, c3 and c5 and the plane of atoms c1, c2 and c3. Let us

call the angle between these two planes as a rotation angle. There are two

other rotation angles about the c1-c3-c5 central plane. The mean of these

three rotation angles serves as a reaction coordinate for the chair-boat

conversion.

rxncor: define c1 point select atom cycl 1 c1 end

rxncor: define c2 point select atom cycl 1 c2 end

rxncor: define c3 point select atom cycl 1 c3 end

rxncor: define c4 point select atom cycl 1 c4 end

rxncor: define c5 point select atom cycl 1 c5 end

rxncor: define c6 point select atom cycl 1 c6 end

rxncor: define d13 direction c1 c3

rxncor: define d35 direction c3 c5

rxncor: define d51 direction c5 c1

rxncor: define d12 direction c1 c2

rxncor: define d34 direction c3 c4

rxncor: define d56 direction c5 c6

rxncor: define norc direction d35 d13

rxncor: define nor1 direction d13 d12

rxncor: define nor2 direction d35 d34

rxncor: define nor3 direction d51 d56

rxncor: define alf1 angle norc nor1 d13

rxncor: define alf2 angle norc nor2 d35

rxncor: define alf3 angle norc nor3 d51

rxncor: define mean combi alf1 1.0 alf2 1.0 alf3 1.0

rxncor: set mean

An example of the use of FORM 5 is shown below:

...

rxncor: define RC distance PCC PCO

rxncor: set RC

open read unit 33 form name bias.pot

rxncor: bias unit 33

close unit 33

rxncor: umbrella kumb 20. del0 1.50 form 5

...

WHERE bias.pot contains:

* Trial Biasing Potential

* example, 1200

*

5 ! number of points (up to 25)

1.0 -28.0 ! Rc Ubias(Rc)

1.3 -18.0

1.4 -8.0

1.5 0.0

1.6 -2.0

END description of FORM 5 JG 12/00

In each case, dynamics is run by invoking the DYNAmics command. » tps

for notes on using RXNCOR with transition path sampling and steered molecular

dynamics.

To extract results from umbrella sampling simulations, return to the example

of cyclohexane

rxncor: trace alf1 unit 22

rxncor: trace alf2 unit 23

rxncor: trace alf3 unit 24

rxncor: trace mean unit 25

rxncor: umbrella kumb 15.0 form 1 del0 -0.4

rxncor: statistics lowdelta -0.6 hidelta -0.4 deldel 0.002 start 5000

dynamics rest nstep 15000 firstt 300.0 finalt 300.0 ihtfrq 0 -

teminc 0.0 iunwrite 19 kunit 20 iunread 17

rxncor: write unit 21

close unit 21

Here, the essential results are the first and second columns of the output

from the WRITe subcommand, which plot free energy versus the order parameter

in the covered range of the order parameter values (delta values). In order

to cover the full range of delta the procedure is repeated by constraining

delta around a particular value by using an umbrella potential centered at

that value.

For theory and practice of umbrella sampling, see Kottalam and Case in Journal

of American Chemical Society, 110, 7690 (1988)

Top

The RXNCOR module has been modified to make it possible to define

a "pseudoroll angle" for nucleic acids that correlates closely with the roll

angle between adjacent base pairs, as determined by programs such as 3DNA.

The modifications are enabled by compiling CHARMM with the ROLLRXNCOR

preprocessor key. The roll-angles.str stream file (in the support/stream

directory) can then be used to define the coordinate. The stream file assumes

that the nucleic acid occupies two segments labeled "A" and "B" and defines

the roll angle as Rn where n is the base pair step number. The script

requires two variables, "A1" and "B1", which are the residue numbers for

the first base pair of the roll angle for strands A and B, respectively.

For example to define the roll angle for the central base pair step of

a Drew-Dickerson dodecamer (12 base pairs total), use the following:

set a1 = 6

set b1 = 7

stream ~/charmm/c38a1/support/stream/roll-angles.str

rxncor set nrxn 1 r6

The pseudoroll angle defined in this way be used for adaptive umbrella

sampling (see

van der Vaart, JCTC 8, 2145 (2012).

The RXNCOR module has been modified to make it possible to define

a "pseudoroll angle" for nucleic acids that correlates closely with the roll

angle between adjacent base pairs, as determined by programs such as 3DNA.

The modifications are enabled by compiling CHARMM with the ROLLRXNCOR

preprocessor key. The roll-angles.str stream file (in the support/stream

directory) can then be used to define the coordinate. The stream file assumes

that the nucleic acid occupies two segments labeled "A" and "B" and defines

the roll angle as Rn where n is the base pair step number. The script

requires two variables, "A1" and "B1", which are the residue numbers for

the first base pair of the roll angle for strands A and B, respectively.

For example to define the roll angle for the central base pair step of

a Drew-Dickerson dodecamer (12 base pairs total), use the following:

set a1 = 6

set b1 = 7

stream ~/charmm/c38a1/support/stream/roll-angles.str

rxncor set nrxn 1 r6

The pseudoroll angle defined in this way be used for adaptive umbrella

sampling (see

**»**adumb ) as described in Spiriti andvan der Vaart, JCTC 8, 2145 (2012).