# gbim (c49b1)

Generalized Born Solvation Energy Module with Implicit Membrane

GBIM is a modification of the GENBORN module that includes

Implicit Membrane in the calculations of the electrostatic contribution

to solvation energy. The non-polar region of the membrane is approximated

as a planar dielectric slab having the same dielectric constant as inside

the molecule. It permits the calculation of the Generalized Born solvation

energy and forces following the formulation of the Qui & Still pairwise

GB approach in linearized version of B. Dominy and C.L. Brooks, III

(» genborn ).

The Generalized Born model with Implicit Membrane is described in

Spassov et al., 2002 (see below).

In the GBIM module the polarization energy is computed following the

equation:

q q

N N i j

G = -Cel(1/eps -1/eps ){1/2 Sum Sum ------------------------------------ }

pol m slv i=1 j=1 [r^2 + alpha *alpha * exp(-D )]^(0.5)

ij i j ij

eps_m is the dielectric constant of the reference medium and eps_slv is

the dielectric constant of the solvent.

If the membrane is present, the effective Born radii are calculated as:

C

el

alpha = - (1/eps_m -1/eps_slv) ----------

i 2G

pol,i

where

G = (1/eps_m -1/eps_slv) { GAM( Z(i),R(i), L, Lambda, Gamma )

pol,i

+ Sum {P2*V(j)/rij^4} + Sum {P3*V(j)/rij^4}

bonds angles

+ Sum {P4*V(j)*Cij/rij^4 }

non-bonded

The self term (1/eps_m -1/eps_slv)* GAM(i) approximates the polarization

energy of a single ion in the presence only of membrane. Z(i) is the

distance of the atom from the membrane midplane and L is the membrane

thickness.

slv cntr slv

GAM(i) = g + (g - g ) / {1 + exp[ Gamma * (Z(i) + R(i) - L/2)] }

i i i

where

slv

g = -Cel/(2*Lambda*R(i)) + P1*Cel/(2*R(i)^2

i

and

cntr Cel ln(2)

g = - ----------

i L

The rest of the variables are the same as in genborn.info.

The gradient of polarization energy is also computed so GBIM can be used

in energy minimization and dynamics.

The combined use of GBIM and ASPENRMB » aspenrmb can be used for

calculations of solvation energy in the frames of GBSA/IM

(Generalized Born - Surface Area model with Implicit membrane) approach.

REFERENCES:

V.Z. Spassov, L. Yan and S. Szalma. Introducing an Implicit Membrane in

Generalized Born / Solvent Accessibility Continuum Solvent Models.

J. Phys. Chem. B, 106,8726-8738 (2002)

* Syntax | Syntax of the GBIM commands

* Function | Purpose of each of the commands

* Examples | Usage examples of the GBIM module

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Syntax of the Generalized Born model with Implicit Membrane commands

[SYNTAX: GBIM commands]

GBIM { P1 <real> P2 <real> P3 <real> P4 <real> P5 <real>

[LAMBda <real>] [EPSILON <real>] [EPSMOL <real>]

[TMEMB <real>] [ZMDIR (or XMDIR or YMDIR) ] [CENTER <real>]

[CUTAlpha <real>] [WEIGht] [ANALysis] }

{ CLEAr }

Syntax of the Generalized Born model with Implicit Membrane commands

[SYNTAX: GBIM commands]

GBIM { P1 <real> P2 <real> P3 <real> P4 <real> P5 <real>

[LAMBda <real>] [EPSILON <real>] [EPSMOL <real>]

[TMEMB <real>] [ZMDIR (or XMDIR or YMDIR) ] [CENTER <real>]

[CUTAlpha <real>] [WEIGht] [ANALysis] }

{ CLEAr }

Top

Parameters of the Generalized Born Model with Implicit Membrane

P1-P6 The parameters P1, P2, ..., P5 specify the particular parameters

controlling the calculation of the effective Born radius for

a particular configuration of the biomolecule.

Alpha(i) = [ GAM( Z(i),R(i), L, Lambda, Gamma )

+ Sum {P2*V(j)/rij^4} + Sum {P3*V(j)/rij^4}

bonds angles

+ Sum {P4*V(j)*Cij/rij^4}]^(-1)*(-CCELEC)/2

non-bonded

with Cij = 1 when (rij^2)/(R(i)+R(j))^2 > 1/P5

and Cij = 1/4(1-cos[P5*PI*(rij^2)/(R(i)+R(j))^2])^2 otherwise.

Note: R(i), V(i) correspond to the vdW radius and volume respectively,

CCELEC is the conversion from e^2/A to kcal/mol, rij is the separation

between atom i and atom j.

slv

Lambda This is the scaling parameter for the vdW radius in the g term

of GAM function. It has the same meaning, as in genborn.info.

Note: The parameters P1-P5 and Lambda correspond to parameters for a

particular CHARMM parameter/topology set.

***The parameters P1-P5 and Lambda are required input***

EPSILON This is the value of the dielectric constant for the solvent medium.

The default value is 80.0

EPSMOL This is the value of the dielectric constant for the

reference medium. The default value is 1.0.

TMEMB Membrane thickness

ZMDIR Membrane normal is along Z axis (or XMDIR or YMDIR)

CENTER Position of membrane midplane ( Z coordinate, if ZMDIR)

Gamma Empiric parameter regulating the slope of GAM function

A good accuracy for the charmm19 force field is achieved

with Gamma = 0.55 [A^(-1)].

CUTAlpha This is a maximum value for the effective Alpha for any atom

during the calculation for a particular conformation of the

biomolecule. It is necessary because in some instances the

expression above for Alpha(i) can take on negative values

of numerical problems with the expression for very buried atoms

in large globular biopolymers. The default for this value is

10^6.

WEIGht This is a flag to specify that you want the vdW radii for the

atoms to be taken from the wmain array instead of the parameter

files (from Rmin values). The default is to use the parameter

values. These values are used for the R(i) and V(i) noted above.

ANALysis This flag turns on an analysis key that puts the atomic contributions

to the Generalized Born solvation energy into an atom array (GBATom)

for use through the scalar commands.

CLEAr Clear all arrays and logical flags used in Generalized Born

calculation.

Parameters of the Generalized Born Model with Implicit Membrane

P1-P6 The parameters P1, P2, ..., P5 specify the particular parameters

controlling the calculation of the effective Born radius for

a particular configuration of the biomolecule.

Alpha(i) = [ GAM( Z(i),R(i), L, Lambda, Gamma )

+ Sum {P2*V(j)/rij^4} + Sum {P3*V(j)/rij^4}

bonds angles

+ Sum {P4*V(j)*Cij/rij^4}]^(-1)*(-CCELEC)/2

non-bonded

with Cij = 1 when (rij^2)/(R(i)+R(j))^2 > 1/P5

and Cij = 1/4(1-cos[P5*PI*(rij^2)/(R(i)+R(j))^2])^2 otherwise.

Note: R(i), V(i) correspond to the vdW radius and volume respectively,

CCELEC is the conversion from e^2/A to kcal/mol, rij is the separation

between atom i and atom j.

slv

Lambda This is the scaling parameter for the vdW radius in the g term

of GAM function. It has the same meaning, as in genborn.info.

Note: The parameters P1-P5 and Lambda correspond to parameters for a

particular CHARMM parameter/topology set.

***The parameters P1-P5 and Lambda are required input***

EPSILON This is the value of the dielectric constant for the solvent medium.

The default value is 80.0

EPSMOL This is the value of the dielectric constant for the

reference medium. The default value is 1.0.

TMEMB Membrane thickness

ZMDIR Membrane normal is along Z axis (or XMDIR or YMDIR)

CENTER Position of membrane midplane ( Z coordinate, if ZMDIR)

Gamma Empiric parameter regulating the slope of GAM function

A good accuracy for the charmm19 force field is achieved

with Gamma = 0.55 [A^(-1)].

CUTAlpha This is a maximum value for the effective Alpha for any atom

during the calculation for a particular conformation of the

biomolecule. It is necessary because in some instances the

expression above for Alpha(i) can take on negative values

of numerical problems with the expression for very buried atoms

in large globular biopolymers. The default for this value is

10^6.

WEIGht This is a flag to specify that you want the vdW radii for the

atoms to be taken from the wmain array instead of the parameter

files (from Rmin values). The default is to use the parameter

values. These values are used for the R(i) and V(i) noted above.

ANALysis This flag turns on an analysis key that puts the atomic contributions

to the Generalized Born solvation energy into an atom array (GBATom)

for use through the scalar commands.

CLEAr Clear all arrays and logical flags used in Generalized Born

calculation.

Top

Examples

The examples below illustrate some of the uses of the generalized Born

model with charmm19. See also c31test/gbsaim.inp

Example (1)

-----------

Calculates the generalized Born solvation energy using atomic radii

from the wmain array (the example illustrates the useage but simply

uses the same radii as would be employed w/o the "Weight" option). The

membrane is present as a 30. Angstrom dielectric slab. The membrane

normal is along Z and membrane midplane has a coordinate Z = 0.

A value of 2.0 is used for the molecular & membrane dielectric constant

and 80. for the water solvent.

! Test use of radii from wmain array

scalar wmain = radii

! Now turn on the Generalized Born energy term using the param19 parameters

Gbim P1 0.415 P2 0.239 P3 1.756 P4 10.51 P5 1.1 Lambda 0.730 -

Epsilon 80.0 Epsmol 2. -

Tmemb 30. Zmdir Center 0.0 Gamma 0.55 Weight

! Now calculate energy w/ GB

energy cutnb 20 ctofnb 16 ctonnb 14

GBIM Clear

Example(2)

----------

Use of the ANALysis key to access atomic solvation energies.

Gbim P1 0.415 P2 0.239 P3 1.756 P4 10.51 P5 1.1 Lambda 0.730 -

Epsilon 80.0 Epsmol 2. -

Tmemb 30. Zmdir Center 0.0 Gamma 0.55 Analysis

energy cutnb 990

! What are the current Generalized Born Alpha, SigX, SigY, SigZ and T_GB

! and atomiuc solvation contribution (GBATom) values?

skipe all excl GbEnr

energy cutnb @cutnb

scalar GBAlpha show

scalar SigX show

scalar SigY show

scalar SigZ show

Scalar T_GB show

Scalar GBAtom show ! One can now use these individual contributions

GBIM Clear

Example(3)

----------

Do a minimization (could be dynamics too)

! Minimize for 1000 steps using SD w/ all energy terms.

skipe none

Gbim P1 0.415 P2 0.239 P3 1.756 P4 10.51 P5 1.1 Lambda 0.730 -

Epsilon 80.0 Epsmol 2. -

Tmemb 30. Zmdir Center 0.0 Gamma 0.55 Analysis

mini sd nstep 1000 cutnb 20 ctofnb 18 ctonnb 18 -

elec cdiel Eps 2 switch

Note, that Eps must be equal to Epsmol for consistent results!

Examples

The examples below illustrate some of the uses of the generalized Born

model with charmm19. See also c31test/gbsaim.inp

Example (1)

-----------

Calculates the generalized Born solvation energy using atomic radii

from the wmain array (the example illustrates the useage but simply

uses the same radii as would be employed w/o the "Weight" option). The

membrane is present as a 30. Angstrom dielectric slab. The membrane

normal is along Z and membrane midplane has a coordinate Z = 0.

A value of 2.0 is used for the molecular & membrane dielectric constant

and 80. for the water solvent.

! Test use of radii from wmain array

scalar wmain = radii

! Now turn on the Generalized Born energy term using the param19 parameters

Gbim P1 0.415 P2 0.239 P3 1.756 P4 10.51 P5 1.1 Lambda 0.730 -

Epsilon 80.0 Epsmol 2. -

Tmemb 30. Zmdir Center 0.0 Gamma 0.55 Weight

! Now calculate energy w/ GB

energy cutnb 20 ctofnb 16 ctonnb 14

GBIM Clear

Example(2)

----------

Use of the ANALysis key to access atomic solvation energies.

Gbim P1 0.415 P2 0.239 P3 1.756 P4 10.51 P5 1.1 Lambda 0.730 -

Epsilon 80.0 Epsmol 2. -

Tmemb 30. Zmdir Center 0.0 Gamma 0.55 Analysis

energy cutnb 990

! What are the current Generalized Born Alpha, SigX, SigY, SigZ and T_GB

! and atomiuc solvation contribution (GBATom) values?

skipe all excl GbEnr

energy cutnb @cutnb

scalar GBAlpha show

scalar SigX show

scalar SigY show

scalar SigZ show

Scalar T_GB show

Scalar GBAtom show ! One can now use these individual contributions

GBIM Clear

Example(3)

----------

Do a minimization (could be dynamics too)

! Minimize for 1000 steps using SD w/ all energy terms.

skipe none

Gbim P1 0.415 P2 0.239 P3 1.756 P4 10.51 P5 1.1 Lambda 0.730 -

Epsilon 80.0 Epsmol 2. -

Tmemb 30. Zmdir Center 0.0 Gamma 0.55 Analysis

mini sd nstep 1000 cutnb 20 ctofnb 18 ctonnb 18 -

elec cdiel Eps 2 switch

Note, that Eps must be equal to Epsmol for consistent results!