Generalized Born using Molecular Volume (GBMV) Solvation Energy and Forces Module - and - Surface Area Questions and comments regarding GBMV should be directed to Michael S. Lee c/o Charles L. Brooks, III (brooks@scripps.edu) * Menu: * Description:: Description of GBMV and related commands * Syntax:: Syntax of the GBMV Commands * Function:: Purpose of each of the commands * Examples:: Usage examples of the GBMV module

Background: The GBMV module is a Generalized Born method for mimicking the Poisson-Boltzmann (PB) electrostatic solvation energy. The PB method for obtaining solvation energies is considered a benchmark for implicit solvation calculations. However, the PB method is slow and the derivatives, i.e. forces, are ill-defined unless one changes the definition of the m olecular volume. The Generalized Born equation, as prescribed by Still, et. al. allows one to compute solvation energies very similar to the PB equations. As it is an analytical expression, forces are available as well: q q N N i j G = -C (1-1/eps){1/2 sum sum ------------------------------------ } pol el i=1 j=1 [r^2 + alpha *alpha exp(-D )]^(0.5) ij i j ij D = r^2 / (K_s * alpha * alpha ) ij ij i j where K_s = 4 for Still's original equation, or 8 for modified equation. The only problem is that one needs to calculate the alpha's, a.k.a. Born radii for each atom, accurately. There are various methods available, such as the GBORN, ACE, and PBEQ modules in CHARMM. The GBMV method obtains the Born radii very accurately, i.e, w/ greater than 0.99 correlation. It is available as three approaches: 1) grid-based (Most accurate) 2) analytical method I (Least accurate, fastest) 2) analytical method II (preferred for dynamics) approach and an analytical method. The analytical method has derivatives and thus can be used in molecular dynamics simulations. The grid-based method has no derivatives, however, is the most accurate and still can be used in energy ranking and Monte-Carlo methods. When should you use GBMV? Because the analytical and grid-based methods are quite accurate, the parameters change very little when optimized for a particular force-field. Hence, forcefields besides those of CHARMM can be used with GBMV with out refitting of parameters. The GBMV is slower than the other GB methods in CHARMM. However, GBMV can be made quite fast through the use of multiple time steps. GBMV is one the most accurate GB methods in the literature as of 2002. For PARAM22, GBMV is the best (only) choice as of version 29. However, for PARAM19, GBORN and ACE may suffice. Papers: M. S. Lee, F. R. Salsbury, Jr., and C. L. Brooks III. J. Chem. Phys., 116, 10606 (2002). M. S. Lee, M. Feig, F. R. Salsbury, Jr., and C. L. Brooks III. J. Comp. Chem., submitted (2002) Surface Area We have implemented a solvent accessible surface area (SASA) calculation within the GB module. It is relatively FREE compared to the GB calculation and 5 times faster than the exact calculation. It is accurate to within 1% of the exact SASA and is much more accurate than the SASA module.

Syntax of Generalized Born Molecular Volume (GBMV) Solvation commands [SYNTAX: GBMV commands] [method I: faster but less accurate] GBMV { P1 <real> P2 <real> LAMBda1 <real> DN <real> SHIFT <real> WATR <real> BETA <real> EPSILON <real> SA <real> SB <real> SCUT <real>} [WEIGHT] CORR <int> { ESHIFT <real> SHIFT <real> TT <real> (CORR = 0) } { SHIFT <real> SLOPE <real> (CORR = 1) } } [method II: slower but more accurate (recommended)] GBMV { [GEOM] [ARITH] [WEIGHT] [FIXA] BETA <real> EPSILON <real> DN <real> WATR <real> LAMBDA1 <real> TOL <real> BUFR <real> MEM <int> CUTA <int> HSX1 <real> HSX2 <real> ONX <real> OFFX <real> ALFRQ <int> EMP <real> P1 <real> P2 <real> P3 <real> P4 <real> P6 <real> SA <real> SB <real> SCUT <real> KAPPA <real> WTYP <int> NPHI <int> CORR <int> { ESHIFT <real> SHIFT <real> TT <real> (CORR = 0) } { SHIFT <real> SLOPE <real> (CORR = 1) } } [ modify alpha update frequency ] { UPDATE <int> } [ grid-based method ] GBMV GRID { [GEOM] [ARITH] [CONV] [WEIGHT] EPSILON <int> DN <real> WATR <real> P6 <real> KAPPA <real> WTYP <int> NPHI <int> CORR <int> { SHIFT <real> SLOPE <real> (CORR = 1) } { ESHIFT <real> SHIFT <real> (CORR = 0) } } } [ free-up memory and/or start over] GBMV CLEAr

--------------------------------------------------------------- Parameters of the Generalized Born using Molecular Volume Model common to all methods: --------------------------------------------------------------- WTYP Angular integration grid type: 0 - Dodecahedron 1 - Spherical polar 2 - Lebedev (DEFAULT) 3 - Alternating octahedron/cube NPHI Used when WTYP equals 1 or 2. When WTYP=1, it corresponds to number of phi angles. When WTYP=2, it corresponds to size of Lebedev grid, which can only have values of 6,26 (Default), and 38 at the present time. CUTA Extent of radial integration points in Angstroms. (Default 20) CORR Coloumb field correction method: 1 for R^7 method (default), 0 for R^5 method. The R^7 method using SHIFT/SLOPE. The R^5 method used SHIFT/ESHIFT. TT Multiplicative factor for correction term (CORR = 0 only). SHIFt The shifting factor of Alpha(i). CORR=0 or 1. MUST be set! ESHIft Energy shifting factor of the self-polarization energies: 1/Alpha(i). CORR=0 only. (Default 0.0) SLOPE Multiplicative factor of the Alpha(i). CORR=1 only. (Default 1) WATR The radius of the water probe. Usually this is set to 1.4 Angstroms. If this were changed, other parameters would have to be modified. EPSILON This is the value of the dielectric constant for the solvent medium. The default value is 80. KAPPA Debye-Huckel ionic term: Units of inverse length (Angs). Default is 0 (no salt). GEOM Select geometric cross-term in Still equation (default). ARITH Select arithmetic cross-term in Still equation. P6 Exponent in exponential of Still equation. Default is 4, for historical reasons. Value of 8 is RECOMMENDED for GEOM, 6.5 for ARITH. WEIGHT Use WMAIN array for radii. (Default uses vdW radii array) CLEAr Clear all arrays and logical flags used in Generalized Born calculation. Use command by itself. ----------------------------------------------------------- Parameters specific to GBMV I and II: ----------------------------------------------------------- FIXA Update alphas only if coordinates have changed more than expected for finite differences. Useful for static pka calculations. With FIXA keyword, finite-difference wouldn't work correctly, hence it must be specified. Not on by default. ALFRQ Update frequency of Born radii. For single points and minimizations, value of 1 is recommended. For dynamics, values of 5-10 may be used with Nose thermostatting (NOSE). One of LIMP,IMP, or EMP options must be selected. (Default 1) LIMP Use ALFRQ*(dE/dalpha)(dalpha/dx) part of GB force every ALFRQ steps. For ALFRQ <= 5. EMP Decay constant of the impulse force. Default is 1.5, which is meant for ALFRQ of 5. Generally, EMP ~= ALFRQ/4. For ALFRQ <= 10. (Recommended option) IMP Use (dE/dalpha)(dalpha/dx) part of GB force every ALFRQ steps. Any ALFRQ can be used. Only meant for equilibrium calculations. DN The cell width of the lookup grid. Larger values make program slower. Smaller values use up more memory. Default of 1.0 A is best compromise between speed and memory. BETA Smoothing factor for tailing off of volume. Values of around -100 are fine for GBMV I. Values of -20 to -50 are recommended to GBMV II. Value of -20 is necessary for stable dynamics in GBMV II. (Default -20) In general for GBMV I, larger values will make the calculation go faster but potentially introduce jumps in the potential energy surface. LAMBda The threshold value for the atomic volumes. In GBMV I, smaller values produces shorter Born radii and wide variance w/respect to accurate PB radii. Large values produce larger radii but smaller variance. In GBMV II, value should be kept at 0.5. BUFR Distance that any atom is allowed to move before lookup table is rebuilt. Larger values lead to less lookup table update but larger memory usage. Use 0.0 for static structure. Values between 0.2 and 1.0 Angstrom. (Default 0.5) MEM Percentage extra memory beyond hypothetical calculation of table size. (Default 10) TOL Accuracy of the switching function used to determine accuracy of the first derivatives, i.e. forces. (Default 1e-8) SA Surface area coefficient (KCAL/(MOL*A**2)). (Default 0.0) SASA Energy term shows up under EXTERN/ASP. SB Surface area constant (KCAL/MOL) (no effect on forces) (Default 0.0) SON The startpoint for the switching function of each hard sphere. (Default 1.2) Units in Angstroms SOFF The endpoint for the switching function of each hard sphere. (Default 1.5) ----------------------------------------------------------- Parameters specific to GBMV I: ----------------------------------------------------------- P1 The multiplicative factor for the exponent of the quartic exponential atomic function: Gamma(i) = P1 * log(lambda)/(Rad(i)^4) Parameters specific to GBMV II: P1,P2 Variables which affect the shape of the VSA atomic function in the region of R to R+2. F(x) = A^2 / (A + x^2 - R^2)^2 where A = P1 * R + P2 (Defaults: P1 = 1.25/P2 = 0.45) P3 Scaling factor of VSA function. Default = 0.7 P4 Scaling coefficient for correction term to Still's equation. (set to 0.0 for now) P5 Exponent to the Still correction term. (use default for now) HSX1/HSX2 Start and stop of hard-sphere tail with R(vdW) as origin. (Defaults: -0.125/0.25). ONX/OFFX Start and stop of VSA tail. Increasing values up to 2.8 A makes better accuracy, however slows calculation. Compromise of 1.9/2.1 is default. ----------------------------------------------------------- Parameters specific to Grid-based GBMV: ----------------------------------------------------------- ML Number of surface points to carve out re-entrant surface CONV Smear grid with cross-shaped blur function to improve accuracy

Usage Examples and Compatibility The examples below illustrate some of the uses of the generalized Born Molecular Volume (GBMV) module. See c29test/gbmvtest.inp for more examples. -------------------------------------- THERE ARE TWO REQUIREMENTS TO RUN GBMV -------------------------------------- 1) Coordinates MUST be defined for all atoms before invoking the GBMV keyword. Otherwise, "infinite" grid is established which uses too much memory. 2) CUTOFF Parameters MUST be defined. For non-infinite cutoffs, "switch" in nonbonded parameters is NECESSARY. Example 1 !To perform a single-point energy calculation w/infinite cutoffs using !GBMV I algorithm (any forcefield): scalar wmain = radii GBMV BETA -100 EPSILON 80 DN 1.0 WATR 1.4 TT 2.92 - SHIFT -0.5 ESHIFT 0.0 LAMBDA1 0.1 P1 0.44 - BUFR 0.5 Mem 20 CUTA 20 WTYP 0 - WEIGHT ! Radii from wmain ENERGY ctonnb 979 ctofnb 989 cutnb 999 Example 2 !To perform a single-point energy calculation w/infinite cutoffs using !the GBMV II algorithm (any forcefield): GBMV BETA -20 EPSILON 80 DN 1.0 watr 1.4 GEOM - TOL 1e-8 BUFR 0.5 Mem 10 CUTA 20 HSX1 -0.125 HSX2 0.25 - ALFRQ 1 EMP 1.5 P4 0.0 P6 8.0 P3 0.70 ONX 1.9 OFFX 2.1 - WTYP 2 NPHI 38 SHIFT -0.102 SLOPE 0.9085 CORR 1 ENERGY ctonnb 979 ctofnb 989 cutnb 999 GBMV CLEAR ! Clear GB arrays Example 3 !To perform a minimization w/ cutoffs using !the GBMV II algorithm: GBMV BETA -20 EPSILON 80 DN 1.0 watr 1.4 GEOM - TOL 1e-8 BUFR 0.5 Mem 10 CUTA 20 HSX1 -0.125 HSX2 0.25 - ALFRQ 1 EMP 1.5 P4 0.0 P6 8.0 P3 0.70 ONX 1.9 OFFX 2.1 - WTYP 2 NPHI 38 SHIFT -0.102 SLOPE 0.9085 CORR 1 MINI sd nstep 100 ctonnb 12 ctofnb 14 cutnb 16 vswitch switch !Then run some dynamics with multiple time step alpha update: GBMV UPDATE 5 DYNAMICS vver start timestep 0.001 nstep 1000 nprint 100 iprfrq 100 - firstt 298 finalt 298 ichecw 0 iasors 0 iasvel 1 isvfrq 1000 - ntrfrq 100 - !GB is not rotationally invariant due to finite int. grid tstruc 298 - !not a fixed water molecule NOSE RSTN TREF 298.0 QREF 10 NCYC 10 ! UPDATE 5 is not energy-conserving Example 4 !Minimal parameter specification (Analytical Method II): GBMV P6 8.0 SHIFT -0.102 SLOPE 0.9085 ENERGY ctonnb 979 ctofnb 989 cutnb 999 Example 5 !Grid-based GBMV: GBMV GRID EPSILON 80 DN 0.2 watr 1.4 GEOM P6 8.0 - WTYP 0 NPHI 10 SHIFT -0.007998 SLOPE 0.9026 CORR 1 CONV ENERGY ctonnb 979 ctofnb 989 cutnb 999 ---------------------------------------------------------------------- <Known Compatible with> - PARALLEL - CONS FIX - INTE - PHMD - VIBRAN (finite difference second derivatives) - MMFF (WEIGHT keyword must be used) <Known Incompatible with (so far)> - VIBRAN (no analytic second derivatives) - BLOCK (hence not compat. w/ PERT/PIMPLEM/PERTURB/REPLICA) - IMAGE/CRYSTAL - EWALD - multiple dielectric - QUANTUM* (single energy with original charges is ok) - FLUCQ - GAMESS - GENBORN - GRID - PRESSURE - SBOUND

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Modified, updated and generalized by C.L. Brooks, III

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