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
(see genborn.doc).
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.doc.
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.doc) 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)
* Menu:
* Syntax:: Syntax of the GBIM commands
* Function:: Purpose of each of the commands
* Examples:: Usage examples of the GBIM module
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 }
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.doc.
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.
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!
NIH/DCRT/Laboratory for Structural Biology
FDA/CBER/OVRR Biophysics Laboratory
Modified, updated and generalized by C.L. Brooks, III
The Scripps Research Institute