# facts (c47b2)

FACTS: Fast Analytical Continuum Treatment of Solvation

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

Questions and comments regarding FACTS should be directed to

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

Amedeo Caflisch (caflisch@bioc.uzh.ch)

Reference for FACTS:

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

[1]Haberthuer and Caflisch, J. Comput. Chem., 29(5): 701-715, 2008

DOI: 10.1002/jcc.20832

* Description | Description of FACTS

* Syntax | Syntax of the FACTS Commands

* Function | Description of the FACTS keywords and options

* Examples | Usage examples of the FACTS module

* Examples-II | Usage examples of the FACTS energy decomposition

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

Questions and comments regarding FACTS should be directed to

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

Amedeo Caflisch (caflisch@bioc.uzh.ch)

Reference for FACTS:

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

[1]Haberthuer and Caflisch, J. Comput. Chem., 29(5): 701-715, 2008

DOI: 10.1002/jcc.20832

* Description | Description of FACTS

* Syntax | Syntax of the FACTS Commands

* Function | Description of the FACTS keywords and options

* Examples | Usage examples of the FACTS module

* Examples-II | Usage examples of the FACTS energy decomposition

Top

FACTS is an efficient generalized Born implicit solvent model [1].Because

of its speed it is particularly useful for MD simulations. It is based on

the fully analytical evaluation of the volume and spatial symmetry of the

solvent that is displaced from around a solute atom by its neighboring

atoms. The two measures of solvent displacement are combined in empirical

equations to approximate the atomic (or self) electrostatic solvation

energy and the solvent accessible surface area. The former directly yields

the effective Born radius of each atom, which is used in the generalized

Born formula to calculate the screening of the pairwise interactions.

(Note that the effective pairwise interactions are the sum of

the low-dielectric Coulombic energy and the generalized Born energy.)

The solvent accessible surface area is used to approximate the non-polar

contribution to solvation. FACTS is only 3 to 5 times slower than using the

vacuum energy in molecular dynamics simulations of peptides and proteins.

1) Force field and further parameterization.

FACTS can be used with either force field "param19" or "param22/27".

!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IMPORTANT !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! FACTS with param22 should be used with the special GBSW CMAP parameter !

! file "par_all22_prot_gbsw.inp", which is in ~charmm/toppar/gbsw/ !

! The GBSW CMAP is necessary for a correct conformational equilibrium !

! of the peptide backbone. !

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

It is important to note that MD simulations of miniprotein folding

and peptide aggregation suggest (as of today, i.e., June 2011) that

param22 should be used with TEPS 1.0

and

param19 should be used with TEPS 2.0

(TEPS is the dielectric constant of the solute, see below).

FACTS parameters were derived for protein atoms only. Parameters for unknown

atom types can be interpolated from known ones with the "TAVW" option

(see below).

2) Periodic boundary conditions.

The FACTS module works with the IMAGE facility, the image setup should

precede the call to FACTS command.

3) Ionic strength.

The influence of salt can be taken into account on the Debye-Huckel

level based on the formalism described in [J. Srinivasan, M.W. Trevathan,

P. Beroza, and D.A. Case, Theor. Chem. Acc., 101, 426-434 (1999)].

The default is without salts.

4) Constraints and rigid atoms.

FACTS can correctly treat fixed atoms (CONS FIX). They are taken into account

as low dielectric region for the evaluation of the effective Born radii,

and for calculation of the accessible surface. Moreover, the screening of the

pairwise interactions between fixed and flexible atoms is taken into account

by the generalized Born formula.

5) Energy decomposition.

FACTS is compatible with the BLOCK module.

The INTE command can be used to evaluate FACTS energy between two

subsets of atoms.

The flag SLFO (SeLF-Only) calculates only the self-energy which is the

sum of electrostatic self-polarization (1st term on the right hand side of

Equation (8) in ref. [1]) and the non-polar solvation energy

(Sum_i GAMMa * SASA_i).

The flag SCRO (SCReen-Only) calculates only the electrostatic screening energy

(2nd term on the right hand side of Equation (8) in ref. [1]).

6) FACTS energy variables

The FACTS polar and non-polar energy of the latest energy evaluation can be

accessed with ?FCTP and ?FCTN, respectively.

7) Parallel code.

The FACTS algorithm has been parallelized in 2007 by F.Marchand

(fmarchand@bioc.uzh.ch).

FACTS is an efficient generalized Born implicit solvent model [1].Because

of its speed it is particularly useful for MD simulations. It is based on

the fully analytical evaluation of the volume and spatial symmetry of the

solvent that is displaced from around a solute atom by its neighboring

atoms. The two measures of solvent displacement are combined in empirical

equations to approximate the atomic (or self) electrostatic solvation

energy and the solvent accessible surface area. The former directly yields

the effective Born radius of each atom, which is used in the generalized

Born formula to calculate the screening of the pairwise interactions.

(Note that the effective pairwise interactions are the sum of

the low-dielectric Coulombic energy and the generalized Born energy.)

The solvent accessible surface area is used to approximate the non-polar

contribution to solvation. FACTS is only 3 to 5 times slower than using the

vacuum energy in molecular dynamics simulations of peptides and proteins.

1) Force field and further parameterization.

FACTS can be used with either force field "param19" or "param22/27".

!!!!!!!!!!!!!!!!!!!!!!!!!!!!! IMPORTANT !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! FACTS with param22 should be used with the special GBSW CMAP parameter !

! file "par_all22_prot_gbsw.inp", which is in ~charmm/toppar/gbsw/ !

! The GBSW CMAP is necessary for a correct conformational equilibrium !

! of the peptide backbone. !

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

It is important to note that MD simulations of miniprotein folding

and peptide aggregation suggest (as of today, i.e., June 2011) that

param22 should be used with TEPS 1.0

and

param19 should be used with TEPS 2.0

(TEPS is the dielectric constant of the solute, see below).

FACTS parameters were derived for protein atoms only. Parameters for unknown

atom types can be interpolated from known ones with the "TAVW" option

(see below).

2) Periodic boundary conditions.

The FACTS module works with the IMAGE facility, the image setup should

precede the call to FACTS command.

3) Ionic strength.

The influence of salt can be taken into account on the Debye-Huckel

level based on the formalism described in [J. Srinivasan, M.W. Trevathan,

P. Beroza, and D.A. Case, Theor. Chem. Acc., 101, 426-434 (1999)].

The default is without salts.

4) Constraints and rigid atoms.

FACTS can correctly treat fixed atoms (CONS FIX). They are taken into account

as low dielectric region for the evaluation of the effective Born radii,

and for calculation of the accessible surface. Moreover, the screening of the

pairwise interactions between fixed and flexible atoms is taken into account

by the generalized Born formula.

5) Energy decomposition.

FACTS is compatible with the BLOCK module.

The INTE command can be used to evaluate FACTS energy between two

subsets of atoms.

The flag SLFO (SeLF-Only) calculates only the self-energy which is the

sum of electrostatic self-polarization (1st term on the right hand side of

Equation (8) in ref. [1]) and the non-polar solvation energy

(Sum_i GAMMa * SASA_i).

The flag SCRO (SCReen-Only) calculates only the electrostatic screening energy

(2nd term on the right hand side of Equation (8) in ref. [1]).

6) FACTS energy variables

The FACTS polar and non-polar energy of the latest energy evaluation can be

accessed with ?FCTP and ?FCTN, respectively.

7) Parallel code.

The FACTS algorithm has been parallelized in 2007 by F.Marchand

(fmarchand@bioc.uzh.ch).

Top

Syntax of the FACTS Command

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

FACTs { TCPS < 19 | 22 > } { TEPS < 1.0 | 2.0 > }

[TKPS real] [GAMM real] -

[CONC real] [TEMP real] -

[TAVW] [TPSL] -

[TCIL real] [TCIC real] -

[ < SLFO | SCRO > ] -

[SLFU integer] [SCRU integer] [NPOU integer]

Syntax of the FACTS Command

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

FACTs { TCPS < 19 | 22 > } { TEPS < 1.0 | 2.0 > }

[TKPS real] [GAMM real] -

[CONC real] [TEMP real] -

[TAVW] [TPSL] -

[TCIL real] [TCIC real] -

[ < SLFO | SCRO > ] -

[SLFU integer] [SCRU integer] [NPOU integer]

Top

Description of the FACTS keywords and options

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

Keyword Default Purpose

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

TCPS 22 Choice of force field: all-atom (22) or polar hydrogens,

i.e., extended carbon and sulfur atoms (19).

Note that TCPS 22 also works

with param27, although only protein atoms are parameterized.

TEPS 1.0 Solute dielectric constant. One can specify only TEPS = 1.0

or TEPS = 2.0, since only these values were used as interior

dielectric constant for the finite-difference Poisson

calculation of atomic solvation energies which are the

reference values employed to parameterize FACTS.

TKPS 4.0 Kappa, the factor in the denominator of the exponential

function in the Generalized Born formula. It usually

ranges between 4.0 (Still's original equation) and 8.0.

GAMM 0.015 Nonpolar surface tension coefficients in [kcal/(molxA^2)].

Ideally one should start test simulations with different

values of GAMM (e.g., 0.0075, 0.010, 0.015, and 0.020)

but see also the values suggested in the examples below.

CONC 0.0 Monovalent salt concentration in [M].

TEMP 298 Temperature in [K] of the Debye-Huckel screening parameter

(only necessary with CONC).

TAVW false FACTS distinguishes atoms solely based on their VdW radius

and only atoms found in proteins are currently parameterized.

If a system contains atoms whose radii are not among those

already parameterized in FACTS, then the "TAVW" option will

interpolate new parameters from already parameterized atoms.

TPSL false Flag to print detailed information about the atomic

self-electrostatic contribution to the energy.

TCIC 7.5 {param 19} Cutoff for the SHIFT function of pairwise screening

12.0 {param 22} interactions. It corresponds to the CTOFNB of non-bond

interactions and must have the same value for

consistency.

TCIL 9.0 {param 19} Cutoff for the list of pairwise screening interactions.

14.0 {param 22} It corresponds to the CUTNB of non-bond interactions

and must have the same value for consistency.

Keywords for FACTS energy (post-)analysis and decomposition:

(more explanation in the example below)

SLFO false (SeLF-Only) Flag to compute self-energy (self-polarization)

and non-polar energy only. The electrostatic screening

energy (i.e., pairwise generalized Born term) is NOT computed.

Mutually exclusive with SCRO.

SCRO false (SCReen-Only) Flag to compute the electrostatic screening

energy. Note that this is the pairwise generalized Born term,

i.e., the 2nd term on the right hand side of Equation (8) in

ref. [1]. It is usually positive, i.e., unfavorable, because

it is dominated by pairs of charges of opposite sign

which have more favorable electrostatic interaction in vacuo

than in a high-dielectric solvent.

Self-energy and non-polar energy are NOT computed.

Mutually exclusive with SLFO.

SLFU -1 Fortran unit on which the atomic self-energy values are

written. Each line contains NATOM self-energy values

(order from 1 to NATOM).

SCRU -1 Fortran unit on which the "atomic sums" of screening energies

are written. Each line contains NATOM "atomic sum" values.

(order from 1 to NATOM).

NPOU -1 Fortran unit on which the atomic non-polar contributions are

written. Each line contains NATOM non-polar energies.

(order from 1 to NATOM).

Description of the FACTS keywords and options

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

Keyword Default Purpose

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

TCPS 22 Choice of force field: all-atom (22) or polar hydrogens,

i.e., extended carbon and sulfur atoms (19).

Note that TCPS 22 also works

with param27, although only protein atoms are parameterized.

TEPS 1.0 Solute dielectric constant. One can specify only TEPS = 1.0

or TEPS = 2.0, since only these values were used as interior

dielectric constant for the finite-difference Poisson

calculation of atomic solvation energies which are the

reference values employed to parameterize FACTS.

TKPS 4.0 Kappa, the factor in the denominator of the exponential

function in the Generalized Born formula. It usually

ranges between 4.0 (Still's original equation) and 8.0.

GAMM 0.015 Nonpolar surface tension coefficients in [kcal/(molxA^2)].

Ideally one should start test simulations with different

values of GAMM (e.g., 0.0075, 0.010, 0.015, and 0.020)

but see also the values suggested in the examples below.

CONC 0.0 Monovalent salt concentration in [M].

TEMP 298 Temperature in [K] of the Debye-Huckel screening parameter

(only necessary with CONC).

TAVW false FACTS distinguishes atoms solely based on their VdW radius

and only atoms found in proteins are currently parameterized.

If a system contains atoms whose radii are not among those

already parameterized in FACTS, then the "TAVW" option will

interpolate new parameters from already parameterized atoms.

TPSL false Flag to print detailed information about the atomic

self-electrostatic contribution to the energy.

TCIC 7.5 {param 19} Cutoff for the SHIFT function of pairwise screening

12.0 {param 22} interactions. It corresponds to the CTOFNB of non-bond

interactions and must have the same value for

consistency.

TCIL 9.0 {param 19} Cutoff for the list of pairwise screening interactions.

14.0 {param 22} It corresponds to the CUTNB of non-bond interactions

and must have the same value for consistency.

Keywords for FACTS energy (post-)analysis and decomposition:

(more explanation in the example below)

SLFO false (SeLF-Only) Flag to compute self-energy (self-polarization)

and non-polar energy only. The electrostatic screening

energy (i.e., pairwise generalized Born term) is NOT computed.

Mutually exclusive with SCRO.

SCRO false (SCReen-Only) Flag to compute the electrostatic screening

energy. Note that this is the pairwise generalized Born term,

i.e., the 2nd term on the right hand side of Equation (8) in

ref. [1]. It is usually positive, i.e., unfavorable, because

it is dominated by pairs of charges of opposite sign

which have more favorable electrostatic interaction in vacuo

than in a high-dielectric solvent.

Self-energy and non-polar energy are NOT computed.

Mutually exclusive with SLFO.

SLFU -1 Fortran unit on which the atomic self-energy values are

written. Each line contains NATOM self-energy values

(order from 1 to NATOM).

SCRU -1 Fortran unit on which the "atomic sums" of screening energies

are written. Each line contains NATOM "atomic sum" values.

(order from 1 to NATOM).

NPOU -1 Fortran unit on which the atomic non-polar contributions are

written. Each line contains NATOM non-polar energies.

(order from 1 to NATOM).

Top

Examples

--------

PARAM 19

--------

REMARK: It was observed that (for param19) FACTS performs better with

the solute dielectric constant (TEPS) set to 2.0 rather than to 1.0.

! ------------------------------------------------------------------

! large, globular systems (e.g., protein in folded state)

! epsilon=2.0 and GAMMa=0.025

set diele 2.0

nbond nbxmod 5 atom cdiel eps @diele shift vatom vdistance vshift -

cutnb 9.0 ctofnb 7.5 ctonnb 6.5 e14fac 0.4 wmin 1.5

scalar wmain = radius

scalar wmain set 1.0 selection (type h*) end

facts tcps 19 teps @diele gamm 0.025

! ------------------------------------------------------------------

! Reversible folding simulations of structured peptides

! epsilon=2.0 and GAMMa=0.015

set diele 2.0

nbond nbxmod 5 atom cdiel eps @diele shift vatom vdistance vshift -

cutnb 9.0 ctofnb 7.5 ctonnb 6.5 e14fac 0.4 wmin 1.5

scalar wmain = radius

scalar wmain set 1.0 selection (type h*) end

facts tcps 19 teps @diele gamm 0.015

! ------------------------------------------------------------------

! Unstructured peptides and peptide aggregation

! epsilon=2.0 and GAMMa=0.0075

set diele 2.0

nbond nbxmod 5 atom cdiel eps @diele shift vatom vdistance vshift -

cutnb 9.0 ctofnb 7.5 ctonnb 6.5 e14fac 0.4 wmin 1.5

scalar wmain = radius

scalar wmain set 1.0 selection (type h*) end

facts tcps 19 teps @diele gamm 0.0075

! ------------------------------------------------------------------

! Print detailed informations about the atomic self-electrostatic

! contributions to the energy with the 'TPSL' option

set diele 2.0

nbond nbxmod 5 atom cdiel eps @diele shift vatom vdistance vshift -

cutnb 9.0 ctofnb 7.5 ctonnb 6.5 e14fac 0.4 wmin 1.5

scalar wmain = radius

scalar wmain set 1.0 selection (type h*) end

facts tcps 19 teps @diele TPSL

! ------------------------------------------------------------------

PARAM 22

--------

REMARK: Use the special GBSW CMAP parameter file "par_all22_prot_gbsw.inp"

(~charmm/toppar/gbsw/par_all22_prot_gbsw.inp)

! ------------------------------------------------------------------

! epsilon=1.0 and GAMMa=0.015

! Interpolate parameters for non-parameterized

! radii with the 'TAVW' option

! read in the CMAP topology file (standard)

open read card unit 10 name @toppar/top_all22_prot_cmap.inp

read rtf card unit 10

close unit 10

!read in the parameter file that contains GBSW specific CMAP

open read card unit 11 name @topar/par_all22_prot_gbsw.inp

read para card unit 11

close unit 11

...

...

set diele 1.0

nbond nbxmod 5 atom cdiel eps @diele shift vatom vdistance vswitch -

cutnb 14.0 ctofnb 12.0 ctonnb 10.0 e14fac 1.0 wmin 1.5

scalar wmain = radius

facts tcps 22 teps @diele gamm 0.015 TAVW

! ------------------------------------------------------------------

See also: test cases ~/charmm/test/c35test/facts_p19.inp

~/charmm/test/c35test/facts_p22.inp

Examples

--------

PARAM 19

--------

REMARK: It was observed that (for param19) FACTS performs better with

the solute dielectric constant (TEPS) set to 2.0 rather than to 1.0.

! ------------------------------------------------------------------

! large, globular systems (e.g., protein in folded state)

! epsilon=2.0 and GAMMa=0.025

set diele 2.0

nbond nbxmod 5 atom cdiel eps @diele shift vatom vdistance vshift -

cutnb 9.0 ctofnb 7.5 ctonnb 6.5 e14fac 0.4 wmin 1.5

scalar wmain = radius

scalar wmain set 1.0 selection (type h*) end

facts tcps 19 teps @diele gamm 0.025

! ------------------------------------------------------------------

! Reversible folding simulations of structured peptides

! epsilon=2.0 and GAMMa=0.015

set diele 2.0

nbond nbxmod 5 atom cdiel eps @diele shift vatom vdistance vshift -

cutnb 9.0 ctofnb 7.5 ctonnb 6.5 e14fac 0.4 wmin 1.5

scalar wmain = radius

scalar wmain set 1.0 selection (type h*) end

facts tcps 19 teps @diele gamm 0.015

! ------------------------------------------------------------------

! Unstructured peptides and peptide aggregation

! epsilon=2.0 and GAMMa=0.0075

set diele 2.0

nbond nbxmod 5 atom cdiel eps @diele shift vatom vdistance vshift -

cutnb 9.0 ctofnb 7.5 ctonnb 6.5 e14fac 0.4 wmin 1.5

scalar wmain = radius

scalar wmain set 1.0 selection (type h*) end

facts tcps 19 teps @diele gamm 0.0075

! ------------------------------------------------------------------

! Print detailed informations about the atomic self-electrostatic

! contributions to the energy with the 'TPSL' option

set diele 2.0

nbond nbxmod 5 atom cdiel eps @diele shift vatom vdistance vshift -

cutnb 9.0 ctofnb 7.5 ctonnb 6.5 e14fac 0.4 wmin 1.5

scalar wmain = radius

scalar wmain set 1.0 selection (type h*) end

facts tcps 19 teps @diele TPSL

! ------------------------------------------------------------------

PARAM 22

--------

REMARK: Use the special GBSW CMAP parameter file "par_all22_prot_gbsw.inp"

(~charmm/toppar/gbsw/par_all22_prot_gbsw.inp)

! ------------------------------------------------------------------

! epsilon=1.0 and GAMMa=0.015

! Interpolate parameters for non-parameterized

! radii with the 'TAVW' option

! read in the CMAP topology file (standard)

open read card unit 10 name @toppar/top_all22_prot_cmap.inp

read rtf card unit 10

close unit 10

!read in the parameter file that contains GBSW specific CMAP

open read card unit 11 name @topar/par_all22_prot_gbsw.inp

read para card unit 11

close unit 11

...

...

set diele 1.0

nbond nbxmod 5 atom cdiel eps @diele shift vatom vdistance vswitch -

cutnb 14.0 ctofnb 12.0 ctonnb 10.0 e14fac 1.0 wmin 1.5

scalar wmain = radius

facts tcps 22 teps @diele gamm 0.015 TAVW

! ------------------------------------------------------------------

See also: test cases ~/charmm/test/c35test/facts_p19.inp

~/charmm/test/c35test/facts_p22.inp

Top

Keywords for FACTS energy (post-)analysis and decomposition:

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

Sometimes it is useful and informative to decompose the solvation energy

into its different contributions or to determine which part of a system

contribute most to a given process (for example, which groups of a ligand

contribute most to binding affinity). A serie of keywords was introduced

to decompose the FACTS solvation energy. Also, FACTS can now be used with

the INTEraction command. These keyword are designed for post-processing

(of MD trajectories for example) rather than dynamics or minimization.

The FACTS solvation energy is

dG = FCTPOL1 + FCTPOL2 + FCTNPL

with

FCTPOL1 = Sum of atomic self-energies (self-polarizations).

FCTPOL2 = Sum of pairs of screening interactions (usually positive because

dominated by pairs of charges of opposite sign).

FCTNPL = Sum of non-polar contributions (= Sum_i GAMMa * SASA_i ;

GAMMa is surface tension, SASA is the Solvent Accessible

Surface Area).

Note that FCTPOL1 and FCTPOL2 correspond to the first and second term,

respectively, on the right hand side of Equation (8) in ref. [1].

FCTPOL1 and FCTPOL2 are both electrostatic contributions and their sum is given

by the "FCTPOL>" field in CHARMM output. FCTNPL is given by the "FCTNPL>"

field. FCTPOL1 and FCTNPL are both atomic contributions, in contrast to

FCTPOL2 which is the pairwise screening.

It is important to note that

the effective electrostatic interaction (or screenED interaction) between two

atoms i and j is the sum of the vacuo Coulombic energy and the GB screening

interaction (FCTPOL2(i,j)). Contrary to the Coulombic interactions, the GB

screening interactions involve also the 1-2 and 1-3 pairs (i.e., pairs of

atoms separated by a single covalent bond or two covalent bonds).

Without them the hydration free energy (related to the transfer from vacuo

to water) would be far too favorable for any molecule. Note also that

with FACTS both the Coulombic and screening interactions

use a SHIFT cutoff function. The value of these cutoffs must be the same,

as they are with the default settings.

A detailed decomposition of the different contributions can be obtained by

using the INTE command.

Let's consider a system composed of two interacting segments, S1 and S2

which could be protein and small-molecule ligand, respectively.

Example 1:

----------

! Compute the screening interaction (i.e., the generalized Born term)

! between segments S1 and S2.

! The value will be returned in the "INTE FCTPOL>" field in the output

! (use SCRO and INTE command)

! FACTS command:

facts tcps 22 teps @diele gamm @gamma SCRO

...

open read file unit 21 name ./dcd/@dcdfile

trajectory query unit 21

set nstop ?nfile

traj iread 21 iwrite -1 nfile @nstop

! Starting frame

set n 1

label looptrj

traj read

! INTE command:

inte sele segid S1 end sele segid S2 end

incr n

if @n .le. @nstop goto looptrj

Example 2 (only the FACTS and INTE command are given):

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

! Compute the self-energy of segment S2 only (but still in the presence of

! segment S1). This will give the sum of atomic self-energies belonging

! only to segment S2 in the "INTE FCTPOL>" field and the sum of atomic

! non-polar contributions belonging only to segment S2 in the "INTE FCTNPL>"

! field.

! Note: by setting the surface tension (GAMMa) to 1.0 the "INTE FCTNPL>" value

! will be equal to the SASA (as approximated by FACTS)

! FACTS command:

facts tcps 22 teps @diele gamm @gamma SLFO

! INTE command:

inte sele segid S2 end sele segid S2 end

Example 3:

----------

! Compute the screening interactions within segment S2 only

! FACTS command:

facts tcps 22 teps @diele gamm @gamma SCRO

! INTE command:

inte sele segid S2 end sele segid S2 end

Example 4: (effective electrostatic interaction)

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

! Compute the effective electrostatic interaction between S1 and S2

! which is the sum of the low-dielectric Coulombic energy

! and the generalized Born energy:

! Effective(S1-S2) = Coulomb(S1-S2) + Screening(S1-S2)

! ELEC(S1-S2), FCTPOL2(S1-S2), and EFFECTIVE are all written to a file

! EFFECTIVE = ELEC(S1-S2) + FCTPOL2(S1-S2)

! ELEC(S1-S2) < 0.0 usually

! FCTPOL2(S1-S2) > 0.0 usually

! -----------------

...

facts tcps 22 teps @diele gamm @gamma SCRO

...

set seg1 S1

set seg2 S2

open write card unit 30 name ./data/@system.screen.@seg1.@seg2.dat

open read file unit 21 name ./dcd/@dcdfile

trajectory query unit 21

set nstop ?nfile

traj iread 21 iwrite -1 nfile @nstop

! Starting frame

set n 1

label looptrj

traj read

! INTE command:

inte sele segid @seg1 end sele segid @seg2 end

calc effect = ?elec + ?fctp

write title unit 30

* ?elec ?fctp @effect

*

incr n

if @n .le. @nstop goto looptrj

! -----------------

Example 5:

----------

Further, time series of atomic contributions can be written to files with the

SLFU, SCRU, and NPOU keywords:

! -----------------

! FACTS command:

facts tcps 22 teps @diele gamm @gamma SLFU 43 NPOU 44 SCRU 45

...

! The files are opened only here, as a line is written at

! each energy evaluation (twice during FACTS initialization)

open write card unit 43 name ./data/@system.self.dat

open write card unit 44 name ./data/@system.npl.dat

open write card unit 45 name ./data/@system.scr.dat

open read file unit 21 name ./dcd/@dcdfile

trajectory query unit 21

set nstop ?nfile

traj iread 21 iwrite -1 nfile @nstop

! Starting frame

set n 1

label looptrj

traj read

ener

incr n

if @n .le. @nstop goto looptrj

! --------------

The resulting files, *.self.dat, *.npl.dat, *.scr.dat will contain ?nfile lines

with NATOM fields (the atomic contributions for each frame).

For the atomic screening sums (SCRU), half of the screening interaction between

atom I and J is given to atom I and the other half to atom J. Thus, field I is

equal to half the sum all screening interactions involving atom I.

Example 6: (binding energy)

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

! Compute the binding energy between segment S1 and S2 (useful for docking).

! This can be done with the BLOCK module by setting the intra-block

! coefficients (S1-S1 and S2-S2) to 0.0 and the inter-block coefficients

! (S1-S2) to 1.0.

! The binding energy is the sum of VdW, Coulombic, and FACTS interactions

! between the two segments.

! The total FACTS/BLOCK interactions between segment S1 and S2 is the sum of

! 1) the changes of atomic self-energies due to the presence of the other

! segment

! 2) the GB screening interactions between segments S1 and S2

! 3) the changes in the GB screening interactions within segment S1 due to

! the presence of S2, and within segment S2 due to the presence of S1

! 4) the changes in the atomic non-polar contributions due to the presence

! of the other segment

! --------------

...

set seg1 S1

set seg2 S2

! Enter BLOCK module

! Define number of subsystems (2)

block 2

! Decompose the system into subsystems

call 2 sele segid @seg2 end

! Set the interaction coefficient matrix

coef 1 1 0.0

coef 1 2 1.0

coef 2 2 0.0

end

...

facts tcps 22 teps @diele gamm @gamma

...

open write card unit 30 name ./data/@system.inter.@seg1.@seg2.dat

open read file unit 21 name ./dcd/@dcdfile

trajectory query unit 21

set nstop ?nfile

traj iread 21 iwrite -1 nfile @nstop

! Starting frame

set n 1

label looptrj

traj read

ener

calc dgtot = ?vdw + ?elec + ?fctp + ?fctn

write title unit 30

* ?vdw ?elec ?fctp ?fctn @dgtot

*

incr n

if @n .le. @nstop goto looptrj

! --------------

Keywords for FACTS energy (post-)analysis and decomposition:

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

Sometimes it is useful and informative to decompose the solvation energy

into its different contributions or to determine which part of a system

contribute most to a given process (for example, which groups of a ligand

contribute most to binding affinity). A serie of keywords was introduced

to decompose the FACTS solvation energy. Also, FACTS can now be used with

the INTEraction command. These keyword are designed for post-processing

(of MD trajectories for example) rather than dynamics or minimization.

The FACTS solvation energy is

dG = FCTPOL1 + FCTPOL2 + FCTNPL

with

FCTPOL1 = Sum of atomic self-energies (self-polarizations).

FCTPOL2 = Sum of pairs of screening interactions (usually positive because

dominated by pairs of charges of opposite sign).

FCTNPL = Sum of non-polar contributions (= Sum_i GAMMa * SASA_i ;

GAMMa is surface tension, SASA is the Solvent Accessible

Surface Area).

Note that FCTPOL1 and FCTPOL2 correspond to the first and second term,

respectively, on the right hand side of Equation (8) in ref. [1].

FCTPOL1 and FCTPOL2 are both electrostatic contributions and their sum is given

by the "FCTPOL>" field in CHARMM output. FCTNPL is given by the "FCTNPL>"

field. FCTPOL1 and FCTNPL are both atomic contributions, in contrast to

FCTPOL2 which is the pairwise screening.

It is important to note that

the effective electrostatic interaction (or screenED interaction) between two

atoms i and j is the sum of the vacuo Coulombic energy and the GB screening

interaction (FCTPOL2(i,j)). Contrary to the Coulombic interactions, the GB

screening interactions involve also the 1-2 and 1-3 pairs (i.e., pairs of

atoms separated by a single covalent bond or two covalent bonds).

Without them the hydration free energy (related to the transfer from vacuo

to water) would be far too favorable for any molecule. Note also that

with FACTS both the Coulombic and screening interactions

use a SHIFT cutoff function. The value of these cutoffs must be the same,

as they are with the default settings.

A detailed decomposition of the different contributions can be obtained by

using the INTE command.

Let's consider a system composed of two interacting segments, S1 and S2

which could be protein and small-molecule ligand, respectively.

Example 1:

----------

! Compute the screening interaction (i.e., the generalized Born term)

! between segments S1 and S2.

! The value will be returned in the "INTE FCTPOL>" field in the output

! (use SCRO and INTE command)

! FACTS command:

facts tcps 22 teps @diele gamm @gamma SCRO

...

open read file unit 21 name ./dcd/@dcdfile

trajectory query unit 21

set nstop ?nfile

traj iread 21 iwrite -1 nfile @nstop

! Starting frame

set n 1

label looptrj

traj read

! INTE command:

inte sele segid S1 end sele segid S2 end

incr n

if @n .le. @nstop goto looptrj

Example 2 (only the FACTS and INTE command are given):

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

! Compute the self-energy of segment S2 only (but still in the presence of

! segment S1). This will give the sum of atomic self-energies belonging

! only to segment S2 in the "INTE FCTPOL>" field and the sum of atomic

! non-polar contributions belonging only to segment S2 in the "INTE FCTNPL>"

! field.

! Note: by setting the surface tension (GAMMa) to 1.0 the "INTE FCTNPL>" value

! will be equal to the SASA (as approximated by FACTS)

! FACTS command:

facts tcps 22 teps @diele gamm @gamma SLFO

! INTE command:

inte sele segid S2 end sele segid S2 end

Example 3:

----------

! Compute the screening interactions within segment S2 only

! FACTS command:

facts tcps 22 teps @diele gamm @gamma SCRO

! INTE command:

inte sele segid S2 end sele segid S2 end

Example 4: (effective electrostatic interaction)

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

! Compute the effective electrostatic interaction between S1 and S2

! which is the sum of the low-dielectric Coulombic energy

! and the generalized Born energy:

! Effective(S1-S2) = Coulomb(S1-S2) + Screening(S1-S2)

! ELEC(S1-S2), FCTPOL2(S1-S2), and EFFECTIVE are all written to a file

! EFFECTIVE = ELEC(S1-S2) + FCTPOL2(S1-S2)

! ELEC(S1-S2) < 0.0 usually

! FCTPOL2(S1-S2) > 0.0 usually

! -----------------

...

facts tcps 22 teps @diele gamm @gamma SCRO

...

set seg1 S1

set seg2 S2

open write card unit 30 name ./data/@system.screen.@seg1.@seg2.dat

open read file unit 21 name ./dcd/@dcdfile

trajectory query unit 21

set nstop ?nfile

traj iread 21 iwrite -1 nfile @nstop

! Starting frame

set n 1

label looptrj

traj read

! INTE command:

inte sele segid @seg1 end sele segid @seg2 end

calc effect = ?elec + ?fctp

write title unit 30

* ?elec ?fctp @effect

*

incr n

if @n .le. @nstop goto looptrj

! -----------------

Example 5:

----------

Further, time series of atomic contributions can be written to files with the

SLFU, SCRU, and NPOU keywords:

! -----------------

! FACTS command:

facts tcps 22 teps @diele gamm @gamma SLFU 43 NPOU 44 SCRU 45

...

! The files are opened only here, as a line is written at

! each energy evaluation (twice during FACTS initialization)

open write card unit 43 name ./data/@system.self.dat

open write card unit 44 name ./data/@system.npl.dat

open write card unit 45 name ./data/@system.scr.dat

open read file unit 21 name ./dcd/@dcdfile

trajectory query unit 21

set nstop ?nfile

traj iread 21 iwrite -1 nfile @nstop

! Starting frame

set n 1

label looptrj

traj read

ener

incr n

if @n .le. @nstop goto looptrj

! --------------

The resulting files, *.self.dat, *.npl.dat, *.scr.dat will contain ?nfile lines

with NATOM fields (the atomic contributions for each frame).

For the atomic screening sums (SCRU), half of the screening interaction between

atom I and J is given to atom I and the other half to atom J. Thus, field I is

equal to half the sum all screening interactions involving atom I.

Example 6: (binding energy)

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

! Compute the binding energy between segment S1 and S2 (useful for docking).

! This can be done with the BLOCK module by setting the intra-block

! coefficients (S1-S1 and S2-S2) to 0.0 and the inter-block coefficients

! (S1-S2) to 1.0.

! The binding energy is the sum of VdW, Coulombic, and FACTS interactions

! between the two segments.

! The total FACTS/BLOCK interactions between segment S1 and S2 is the sum of

! 1) the changes of atomic self-energies due to the presence of the other

! segment

! 2) the GB screening interactions between segments S1 and S2

! 3) the changes in the GB screening interactions within segment S1 due to

! the presence of S2, and within segment S2 due to the presence of S1

! 4) the changes in the atomic non-polar contributions due to the presence

! of the other segment

! --------------

...

set seg1 S1

set seg2 S2

! Enter BLOCK module

! Define number of subsystems (2)

block 2

! Decompose the system into subsystems

call 2 sele segid @seg2 end

! Set the interaction coefficient matrix

coef 1 1 0.0

coef 1 2 1.0

coef 2 2 0.0

end

...

facts tcps 22 teps @diele gamm @gamma

...

open write card unit 30 name ./data/@system.inter.@seg1.@seg2.dat

open read file unit 21 name ./dcd/@dcdfile

trajectory query unit 21

set nstop ?nfile

traj iread 21 iwrite -1 nfile @nstop

! Starting frame

set n 1

label looptrj

traj read

ener

calc dgtot = ?vdw + ?elec + ?fctp + ?fctn

write title unit 30

* ?vdw ?elec ?fctp ?fctn @dgtot

*

incr n

if @n .le. @nstop goto looptrj

! --------------