# ace (c41b1)

Analytical Continuum Solvent (ACS) Potential

Purpose: calculate solvation free energy and forces based on

a continuum description of the solvent, in particular the analytical

continuum electrostatics (ACE) potential.

Please report problems to Michael Schaefer at schaefer@piaf.u-strasbg.fr

WARNING: The module is still being developed and may change in the future.

!======================================================================!

! Note on ACE2: the version 2 of ACE as of Jan 2002 is not yet fully !

! parameterized; it yields reasonably stably MD trajectories of native !

! proteins when using param19 (united atom parameters), but is !

! unreliable with all-hydrogen parameters. !

!======================================================================!

REFERENCES:

M. Schaefer & M. Karplus (1996) J. Phys. Chem. 100, 1578-1599.

M. Schaefer, C. Bartels & M. Karplus (1998) J. Mol. Biol. 284, 835-847.

N. Calimet, M. Schaefer & T. Simonson, (2001) Proteins 45, 144-158

M. Schaefer, C. Bartels, F. Leclerc& M. Karplus (2001),

J. Comp. Chem. 22, 1857-1879.

* Syntax | Syntax of the ACE specifications

* Defaults | Defaults and Recommended values

* Function | Purpose of each of the specifications

* Examples | Usage examples of the ACE module

Purpose: calculate solvation free energy and forces based on

a continuum description of the solvent, in particular the analytical

continuum electrostatics (ACE) potential.

Please report problems to Michael Schaefer at schaefer@piaf.u-strasbg.fr

WARNING: The module is still being developed and may change in the future.

!======================================================================!

! Note on ACE2: the version 2 of ACE as of Jan 2002 is not yet fully !

! parameterized; it yields reasonably stably MD trajectories of native !

! proteins when using param19 (united atom parameters), but is !

! unreliable with all-hydrogen parameters. !

!======================================================================!

REFERENCES:

M. Schaefer & M. Karplus (1996) J. Phys. Chem. 100, 1578-1599.

M. Schaefer, C. Bartels & M. Karplus (1998) J. Mol. Biol. 284, 835-847.

N. Calimet, M. Schaefer & T. Simonson, (2001) Proteins 45, 144-158

M. Schaefer, C. Bartels, F. Leclerc& M. Karplus (2001),

J. Comp. Chem. 22, 1857-1879.

* Syntax | Syntax of the ACE specifications

* Defaults | Defaults and Recommended values

* Function | Purpose of each of the specifications

* Examples | Usage examples of the ACE module

Top

Syntax

[SYNTAX ACE functions]

Syntax: The ACE specifications can be specified any time the nbond

specification parser is invoked, e.g.,

ENERgy [other-spec] [ace-spec]

ace-spec::=

[ ACE ] [ IEPS real ] [ SEPS real ] [ ALPHa real ]

[ SIGMa real ] [ IDEAl | CURRent ] [FVSCaling real]

[ ACE2 [ MXBSolv real ] [TBSOlv real ] [ TBSHydrogens real ]]

Syntax

[SYNTAX ACE functions]

Syntax: The ACE specifications can be specified any time the nbond

specification parser is invoked, e.g.,

ENERgy [other-spec] [ace-spec]

ace-spec::=

[ ACE ] [ IEPS real ] [ SEPS real ] [ ALPHa real ]

[ SIGMa real ] [ IDEAl | CURRent ] [FVSCaling real]

[ ACE2 [ MXBSolv real ] [TBSOlv real ] [ TBSHydrogens real ]]

Top

The defaults for the ACE potential are:

IEPS 1.0

SEPS 80.0

ALPHa 1.3

SIGMa 0.0

IDEAl true

FVSCa 1.0

The additional defaults for the ACE2 potential are:

MXBSo 14.0

TBSOl 8.4

TBSHy 3.85

In the current implementation, ACE should be used with united atom parameters,

ALPHa set equal to 1.3, the standard PARAM19 parameter file param19.inp and

Voronoi volumes as given in acepar19.inp (toppar and test/data).

The defaults for the ACE potential are:

IEPS 1.0

SEPS 80.0

ALPHa 1.3

SIGMa 0.0

IDEAl true

FVSCa 1.0

The additional defaults for the ACE2 potential are:

MXBSo 14.0

TBSOl 8.4

TBSHy 3.85

In the current implementation, ACE should be used with united atom parameters,

ALPHa set equal to 1.3, the standard PARAM19 parameter file param19.inp and

Voronoi volumes as given in acepar19.inp (toppar and test/data).

Top

0. Introduction

The analytical continuum solvent (ACS) potential is introduced to

perform molecular dynamics/minimization calculations with a continuum

approximation of the solvent.

Two solvent contributions to the effective (free) energy of a solute

are included: the electrostatic solvation free energy, and the

non-polar (i.e., non-electrostatic) solvation free energy.

The first (electrostatic) contribution (G_el) is calculated using an

analytical approximation to the solution of the Poisson-equation

called ACE (from: analytical continuum electrostatics).

The non-polar solvation free energy (G_np) is approximated by a pairwise

potential which yields results that are very similar to the well-known

surface area approximations of the hydrophobic (solvation) energy

(e.g., Wesson and Eisenberg, Prot. Sci. 1 (1992), 227--235; see

the ASP potential in CHARMM).

Restriction:

The ACE solvation potential has to be used together with no cutoff or with

atom based switching.

Compatibility:

1. ACE can be used with BLOCK (but: the diagonal elements of the BLOCK

matrix MUST NOT be zero).

2. ACE can be used with fixing atoms (CONS FIX); the resulting energy and

forces are an approximation, because all the interaction-dielectric terms

of the potential (eq (47) in Schaefer & Karplus, JPC 100 (1996), 1578)

which involve two fixed atoms are neglected, despite the fact that they

exist and that they are not invariant!

Meaning of the ACE parameters:

1. IEPS

Dielectric constant for the space occupied by the atoms that are treated

explicitly, e.g., the space occupied by the protein.

2. SEPS

Dielectric constant for the space occupied by the solvent that is treated

as a continuum (i.e., the complement of the space occupied by the protein).

3. ALPHa

The volumes occupied by individual (protein) atoms are described by

Gaussian density distributions. The factor ALPHa controls the width of these

Gaussians. The net volume of the individual atom Gaussian distributions is

defined in the volume table in the parameter file acepar19.inp.

The volumes in the acepar19.inp file are expected to work best

for an ALPHa of 1.3.

4. SIGMa

The ACE solvation potential includes a hydrophobic contribution

which is roughly proportional to the solvent accessible surface area.

The factor SIGMa scales the hydrophobic contribution. For peptides

with about 10-15 residues, a SIGMa factor of 3.0 results in hydrophobic

contributions that are approximately equal to the solvent accessible

surface area multiplied by 8 cal/(mol*A*A).

4. IDEAl | CURRent

As of c29a2, the ACE potential considers the distances between atoms

in the nonbonded exclusion list as invariant. This is consistent with

the assumption that the forces involving these atoms are governed by

the internal energy terms (bond, angle, and some 1-4 atom pairs in

aromatic ring systems). Note that solvation forces still apply to

pairs of these atoms, considered as a polar group.

With the IDEAl option (default), ACE calculates the nonbonded exclusion

list distances from ideal bond length and angles where possible; the

distances for 1-4 atom pairs in the exclusion list are calculated

from the current atom positions at the first ACE energy call.

With the CURRent option, all the distances between atoms in

the nonbonded exlusion list are calculated from the current

coordinates of the atoms. These distances are considered invariant

for all subsequent energy calls, during minimization and dynamics.

Recalculation of the nb-exclusion list atom pair distance is

enforced only when toggling IDEAl on/off, fixing/unfixing atoms,

or a change of the psf (e.g., REPLica).

4. FVSCal

One major problem with ACE1 (and gneralized Born methods in general)

is the overestimation of the desolvation by the pairwise de-screening

function ESELFIK (see ace.src). One way to reduce the impact of this

systematic error is to reduce the volume that is assigned to the atoms

by a constant factor FVSCal < 1 as proposed in Calimet et al., Proteins

45 (2001), 144-158. The default value for FVSCal is 1.0, though a value

of 0.9 appears reasonable in conjunction with param19 and volumes

in acepar19, using the ACE1 potential (work in progress). Note that

the modified treatment of the self energy (de-screening) potential

in ACE2 is aimed at fixing the overestimation problem of ESELFIK

such that the re-scaling of volumes becomes obsolete (work in progress).

4. ACE2

The ACE2 keyword implies ACE (no need to specify both). It invokes

a modified treatment of the Born solvation radii which are limited

by un upper bound --- MXBSolv (see below). This takes account of the

overestimation of the desolvation of charges by the pairwise de-screening

potential in ACE1.

4. MXBSolv

The Born solvation radii of all atoms (charges) are limited

by the upper bound parameter MXBSolv (default 14.0 Angstrom).

4. TBSOl

In the ACE2 potential, the conventional conversion of the atomic

solvation to the Born solvation radii is applied until a Born radius

of TBSOlv is obtained ("turning point"). After that, atomic solvation

energies (i.e., the de-solvation) is converted in a way that prevents

the Born solvation radii from exceeding the imposed maximum.

Details will be given in an upcoming publication.

4. TBSHyd

This parameter has the same meaning as TBSOl, but applies

to hydrogens, which are most susceptible to an overestimation

of the desolvation by neighboring atoms (volumes). The smaller

the TBSOl and TBSHyd, the more the over-desceening is counter-

acted (parametrization in progress).

0. Introduction

The analytical continuum solvent (ACS) potential is introduced to

perform molecular dynamics/minimization calculations with a continuum

approximation of the solvent.

Two solvent contributions to the effective (free) energy of a solute

are included: the electrostatic solvation free energy, and the

non-polar (i.e., non-electrostatic) solvation free energy.

The first (electrostatic) contribution (G_el) is calculated using an

analytical approximation to the solution of the Poisson-equation

called ACE (from: analytical continuum electrostatics).

The non-polar solvation free energy (G_np) is approximated by a pairwise

potential which yields results that are very similar to the well-known

surface area approximations of the hydrophobic (solvation) energy

(e.g., Wesson and Eisenberg, Prot. Sci. 1 (1992), 227--235; see

the ASP potential in CHARMM).

Restriction:

The ACE solvation potential has to be used together with no cutoff or with

atom based switching.

Compatibility:

1. ACE can be used with BLOCK (but: the diagonal elements of the BLOCK

matrix MUST NOT be zero).

2. ACE can be used with fixing atoms (CONS FIX); the resulting energy and

forces are an approximation, because all the interaction-dielectric terms

of the potential (eq (47) in Schaefer & Karplus, JPC 100 (1996), 1578)

which involve two fixed atoms are neglected, despite the fact that they

exist and that they are not invariant!

Meaning of the ACE parameters:

1. IEPS

Dielectric constant for the space occupied by the atoms that are treated

explicitly, e.g., the space occupied by the protein.

2. SEPS

Dielectric constant for the space occupied by the solvent that is treated

as a continuum (i.e., the complement of the space occupied by the protein).

3. ALPHa

The volumes occupied by individual (protein) atoms are described by

Gaussian density distributions. The factor ALPHa controls the width of these

Gaussians. The net volume of the individual atom Gaussian distributions is

defined in the volume table in the parameter file acepar19.inp.

The volumes in the acepar19.inp file are expected to work best

for an ALPHa of 1.3.

4. SIGMa

The ACE solvation potential includes a hydrophobic contribution

which is roughly proportional to the solvent accessible surface area.

The factor SIGMa scales the hydrophobic contribution. For peptides

with about 10-15 residues, a SIGMa factor of 3.0 results in hydrophobic

contributions that are approximately equal to the solvent accessible

surface area multiplied by 8 cal/(mol*A*A).

4. IDEAl | CURRent

As of c29a2, the ACE potential considers the distances between atoms

in the nonbonded exclusion list as invariant. This is consistent with

the assumption that the forces involving these atoms are governed by

the internal energy terms (bond, angle, and some 1-4 atom pairs in

aromatic ring systems). Note that solvation forces still apply to

pairs of these atoms, considered as a polar group.

With the IDEAl option (default), ACE calculates the nonbonded exclusion

list distances from ideal bond length and angles where possible; the

distances for 1-4 atom pairs in the exclusion list are calculated

from the current atom positions at the first ACE energy call.

With the CURRent option, all the distances between atoms in

the nonbonded exlusion list are calculated from the current

coordinates of the atoms. These distances are considered invariant

for all subsequent energy calls, during minimization and dynamics.

Recalculation of the nb-exclusion list atom pair distance is

enforced only when toggling IDEAl on/off, fixing/unfixing atoms,

or a change of the psf (e.g., REPLica).

4. FVSCal

One major problem with ACE1 (and gneralized Born methods in general)

is the overestimation of the desolvation by the pairwise de-screening

function ESELFIK (see ace.src). One way to reduce the impact of this

systematic error is to reduce the volume that is assigned to the atoms

by a constant factor FVSCal < 1 as proposed in Calimet et al., Proteins

45 (2001), 144-158. The default value for FVSCal is 1.0, though a value

of 0.9 appears reasonable in conjunction with param19 and volumes

in acepar19, using the ACE1 potential (work in progress). Note that

the modified treatment of the self energy (de-screening) potential

in ACE2 is aimed at fixing the overestimation problem of ESELFIK

such that the re-scaling of volumes becomes obsolete (work in progress).

4. ACE2

The ACE2 keyword implies ACE (no need to specify both). It invokes

a modified treatment of the Born solvation radii which are limited

by un upper bound --- MXBSolv (see below). This takes account of the

overestimation of the desolvation of charges by the pairwise de-screening

potential in ACE1.

4. MXBSolv

The Born solvation radii of all atoms (charges) are limited

by the upper bound parameter MXBSolv (default 14.0 Angstrom).

4. TBSOl

In the ACE2 potential, the conventional conversion of the atomic

solvation to the Born solvation radii is applied until a Born radius

of TBSOlv is obtained ("turning point"). After that, atomic solvation

energies (i.e., the de-solvation) is converted in a way that prevents

the Born solvation radii from exceeding the imposed maximum.

Details will be given in an upcoming publication.

4. TBSHyd

This parameter has the same meaning as TBSOl, but applies

to hydrogens, which are most susceptible to an overestimation

of the desolvation by neighboring atoms (volumes). The smaller

the TBSOl and TBSHyd, the more the over-desceening is counter-

acted (parametrization in progress).

Top

Examples

To set up simulations/minimizations with the ACE solvation potential,

read the standard CHARMM topology and parameter files and the corresponding

ACE parameter file using

read ACEParameters card unit IUN

e.g., the file acepar19.inp with param19 parameters.

The following energy call is expected to be adequate for most cases,

including proteins:

ENERgy ATOM ACE2 IEPS 1.0 SEPS 80.0 ALPHa 1.3 SIGMa 2.5 SWITch -

VDIS VSWI CUTNB 13.0 CTONNB 8.0 CTOFNB 12.0

When you run molecular dynamics or minimization with ACE, you get

two more lines in the log file printout with energy terms, e.g.,

DYNA DYN: Step Time TOTEner TOTKe ENERgy TEMPerature

DYNA PROP: GRMS HFCTote HFCKe EHFCor VIRKe

DYNA INTERN: BONDs ANGLes UREY-b DIHEdrals IMPRopers

DYNA EXTERN: VDWaals ELEC HBONds ASP USER

DYNA PRESS: VIRE VIRI PRESSE PRESSI VOLUme

DYNA ACE1: HYDRophobic SELF SCREENing COULomb

DYNA ACE2: SOLVation INTERaction

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

DYNA> 0 0.00000 -3423.29671 0.00000 -3423.29671 0.00000

DYNA PROP> 4.45310 -3423.12228 0.52327 0.17442 -532.70519

DYNA INTERN> 6.58717 60.43092 0.00000 56.00750 7.32144

DYNA EXTERN> -380.26218 -3173.38156 0.00000 0.00000 0.00000

DYNA PRESS> 0.00000 355.13679 0.00000 0.00000 0.00000

DYNA ACE1> 109.04469 -3829.20991 2750.59427 -2203.81062

DYNA ACE2> -1078.61564 546.78365

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

and the same during minimization (MINI...) or after

an energy calculation (ENER...).

The terms in lines with ACE1 and ACE2 are:

HYDRophobic: Hydrophobic potential, equivalent to a surface based

solvation term proportional to the sigma input parameter;

SELF: Self contribution to electrostatic solvation free energy,

Delta-E_self, first term of eq(8) (i.e., sum over all atomic

solvation energies, Delta-E_self_i, eq(28));

SCREENing: Interaction contribution to electrostatic solvation free energy,

i.e., screening of Coulomb interactions, eq(38) (sum over all

atom pairs, including bonded and 1-3 atom pairs!);

COULomb: Coulomb energy with constant dielectric of EPSI (sum over

all atom pairs for the first term in eq(36) -- excluding

bonded and 1-3 atom pairs, and 1-4 atom pair contributions

scaled with E14FAC);

SOLVation: Electrostatic (!) solvation free energy, sum of SELF and

SCREENing;

INTERaction: Electrostatic interaction, sum of SCREENing and COULomb

(eq(36), but taking account of the bonded, 1-3, and 1-4

exclusion in the Coulomb term, see above).

The term "ELEC" in line "DYNA EXTERN>..." is the total electrostatic energy:

ELEC: Sum of SELF, SCREENing, COULomb.

Equation numbers refer to Schaefer & Karplus, J. Phys. Chem. 100 (1996), 1578.

See also: test cases c27test/ace1.inp and c29test/ace_v2.inp.

Examples

To set up simulations/minimizations with the ACE solvation potential,

read the standard CHARMM topology and parameter files and the corresponding

ACE parameter file using

read ACEParameters card unit IUN

e.g., the file acepar19.inp with param19 parameters.

The following energy call is expected to be adequate for most cases,

including proteins:

ENERgy ATOM ACE2 IEPS 1.0 SEPS 80.0 ALPHa 1.3 SIGMa 2.5 SWITch -

VDIS VSWI CUTNB 13.0 CTONNB 8.0 CTOFNB 12.0

When you run molecular dynamics or minimization with ACE, you get

two more lines in the log file printout with energy terms, e.g.,

DYNA DYN: Step Time TOTEner TOTKe ENERgy TEMPerature

DYNA PROP: GRMS HFCTote HFCKe EHFCor VIRKe

DYNA INTERN: BONDs ANGLes UREY-b DIHEdrals IMPRopers

DYNA EXTERN: VDWaals ELEC HBONds ASP USER

DYNA PRESS: VIRE VIRI PRESSE PRESSI VOLUme

DYNA ACE1: HYDRophobic SELF SCREENing COULomb

DYNA ACE2: SOLVation INTERaction

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

DYNA> 0 0.00000 -3423.29671 0.00000 -3423.29671 0.00000

DYNA PROP> 4.45310 -3423.12228 0.52327 0.17442 -532.70519

DYNA INTERN> 6.58717 60.43092 0.00000 56.00750 7.32144

DYNA EXTERN> -380.26218 -3173.38156 0.00000 0.00000 0.00000

DYNA PRESS> 0.00000 355.13679 0.00000 0.00000 0.00000

DYNA ACE1> 109.04469 -3829.20991 2750.59427 -2203.81062

DYNA ACE2> -1078.61564 546.78365

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

and the same during minimization (MINI...) or after

an energy calculation (ENER...).

The terms in lines with ACE1 and ACE2 are:

HYDRophobic: Hydrophobic potential, equivalent to a surface based

solvation term proportional to the sigma input parameter;

SELF: Self contribution to electrostatic solvation free energy,

Delta-E_self, first term of eq(8) (i.e., sum over all atomic

solvation energies, Delta-E_self_i, eq(28));

SCREENing: Interaction contribution to electrostatic solvation free energy,

i.e., screening of Coulomb interactions, eq(38) (sum over all

atom pairs, including bonded and 1-3 atom pairs!);

COULomb: Coulomb energy with constant dielectric of EPSI (sum over

all atom pairs for the first term in eq(36) -- excluding

bonded and 1-3 atom pairs, and 1-4 atom pair contributions

scaled with E14FAC);

SOLVation: Electrostatic (!) solvation free energy, sum of SELF and

SCREENing;

INTERaction: Electrostatic interaction, sum of SCREENing and COULomb

(eq(36), but taking account of the bonded, 1-3, and 1-4

exclusion in the Coulomb term, see above).

The term "ELEC" in line "DYNA EXTERN>..." is the total electrostatic energy:

ELEC: Sum of SELF, SCREENing, COULomb.

Equation numbers refer to Schaefer & Karplus, J. Phys. Chem. 100 (1996), 1578.

See also: test cases c27test/ace1.inp and c29test/ace_v2.inp.