ReferenceObc.cpp

/* Portions copyright (c) 2006-2009 Stanford University and Simbios.
 * Contributors: Pande Group
 *
 * Permission is hereby granted, free of charge, to any person obtaining
 * a copy of this software and associated documentation files (the
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 * permit persons to whom the Software is furnished to do so, subject
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 *
 * The above copyright notice and this permission notice shall be included
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#include <string.h>
#include <stdlib.h>
#include <sstream>
#include <cmath>
#include <cstdio>

#include "ReferenceForce.h"
#include "ReferenceObc.h"

using namespace OpenMM;
using namespace std;

/**---------------------------------------------------------------------------------------

    ReferenceObc constructor

    obcParameters      obcParameters object
    
    --------------------------------------------------------------------------------------- */

ReferenceObc::ReferenceObc(ObcParameters* obcParameters) : _obcParameters(obcParameters), _includeAceApproximation(1) {
    _obcChain.resize(_obcParameters->getNumberOfAtoms());
}

/**---------------------------------------------------------------------------------------

    ReferenceObc destructor

    --------------------------------------------------------------------------------------- */

ReferenceObc::~ReferenceObc() {
}

/**---------------------------------------------------------------------------------------

    Get ObcParameters reference

    @return ObcParameters reference

    --------------------------------------------------------------------------------------- */

ObcParameters* ReferenceObc::getObcParameters() const {
    return _obcParameters;
}

/**---------------------------------------------------------------------------------------

    Set ObcParameters reference

    @param ObcParameters reference

    --------------------------------------------------------------------------------------- */

void ReferenceObc::setObcParameters( ObcParameters* obcParameters) {
    _obcParameters = obcParameters;
}

/**---------------------------------------------------------------------------------------

   Return flag signalling whether AceApproximation for nonpolar term is to be included

   @return flag

   --------------------------------------------------------------------------------------- */

int ReferenceObc::includeAceApproximation() const {
    return _includeAceApproximation;
}

/**---------------------------------------------------------------------------------------

   Set flag indicating whether AceApproximation is to be included

   @param includeAceApproximation new includeAceApproximation value

   --------------------------------------------------------------------------------------- */

void ReferenceObc::setIncludeAceApproximation(int includeAceApproximation) {
    _includeAceApproximation = includeAceApproximation;
}

/**---------------------------------------------------------------------------------------

    Return OBC chain derivative: size = _obcParameters->getNumberOfAtoms()

    @return array

    --------------------------------------------------------------------------------------- */

vector<RealOpenMM>& ReferenceObc::getObcChain() {
    return _obcChain;
}

/**---------------------------------------------------------------------------------------

    Get Born radii based on papers:

       J. Phys. Chem. 1996 100, 19824-19839 (HCT paper)
       Proteins: Structure, Function, and Bioinformatcis 55:383-394 (2004) (OBC paper)

    @param atomCoordinates     atomic coordinates
    @param bornRadii           output array of Born radii

    --------------------------------------------------------------------------------------- */

void ReferenceObc::computeBornRadii(const vector<RealVec>& atomCoordinates, vector<RealOpenMM>& bornRadii) {

    // ---------------------------------------------------------------------------------------

    static const RealOpenMM zero    = static_cast<RealOpenMM>(0.0);
    static const RealOpenMM one     = static_cast<RealOpenMM>(1.0);
    static const RealOpenMM two     = static_cast<RealOpenMM>(2.0);
    static const RealOpenMM three   = static_cast<RealOpenMM>(3.0);
    static const RealOpenMM half    = static_cast<RealOpenMM>(0.5);
    static const RealOpenMM fourth  = static_cast<RealOpenMM>(0.25);

    // ---------------------------------------------------------------------------------------

    ObcParameters* obcParameters                = getObcParameters();

    int numberOfAtoms                           = obcParameters->getNumberOfAtoms();
    const vector<RealOpenMM>& atomicRadii         = obcParameters->getAtomicRadii();
    const vector<RealOpenMM>& scaledRadiusFactor  = obcParameters->getScaledRadiusFactors();
    vector<RealOpenMM>& obcChain                  = getObcChain();

    RealOpenMM dielectricOffset                 = obcParameters->getDielectricOffset();
    RealOpenMM alphaObc                         = obcParameters->getAlphaObc();
    RealOpenMM betaObc                          = obcParameters->getBetaObc();
    RealOpenMM gammaObc                         = obcParameters->getGammaObc();

    // ---------------------------------------------------------------------------------------

    // calculate Born radii

    for (int atomI = 0; atomI < numberOfAtoms; atomI++) {
      
       RealOpenMM radiusI         = atomicRadii[atomI];
       RealOpenMM offsetRadiusI   = radiusI - dielectricOffset;

       RealOpenMM radiusIInverse  = one/offsetRadiusI;
       RealOpenMM sum             = zero;

       // HCT code

       for (int atomJ = 0; atomJ < numberOfAtoms; atomJ++) {

          if (atomJ != atomI) {

             RealOpenMM deltaR[ReferenceForce::LastDeltaRIndex];
             if (_obcParameters->getPeriodic())
                 ReferenceForce::getDeltaRPeriodic(atomCoordinates[atomI], atomCoordinates[atomJ], _obcParameters->getPeriodicBox(), deltaR);
             else
                 ReferenceForce::getDeltaR(atomCoordinates[atomI], atomCoordinates[atomJ], deltaR);
             RealOpenMM r               = deltaR[ReferenceForce::RIndex];
             if (_obcParameters->getUseCutoff() && r > _obcParameters->getCutoffDistance())
                 continue;

             RealOpenMM offsetRadiusJ   = atomicRadii[atomJ] - dielectricOffset; 
             RealOpenMM scaledRadiusJ   = offsetRadiusJ*scaledRadiusFactor[atomJ];
             RealOpenMM rScaledRadiusJ  = r + scaledRadiusJ;

             if (offsetRadiusI < rScaledRadiusJ) {
                RealOpenMM rInverse = one/r;
                RealOpenMM l_ij     = offsetRadiusI > FABS(r - scaledRadiusJ) ? offsetRadiusI : FABS(r - scaledRadiusJ);
                           l_ij     = one/l_ij;

                RealOpenMM u_ij     = one/rScaledRadiusJ;

                RealOpenMM l_ij2    = l_ij*l_ij;
                RealOpenMM u_ij2    = u_ij*u_ij;
 
                RealOpenMM ratio    = LN((u_ij/l_ij));
                RealOpenMM term     = l_ij - u_ij + fourth*r*(u_ij2 - l_ij2)  + (half*rInverse*ratio) + (fourth*scaledRadiusJ*scaledRadiusJ*rInverse)*(l_ij2 - u_ij2);

                // this case (atom i completely inside atom j) is not considered in the original paper
                // Jay Ponder and the authors of Tinker recognized this and
                // worked out the details

                if (offsetRadiusI < (scaledRadiusJ - r)) {
                   term += two*(radiusIInverse - l_ij);
                }
                sum += term;

             }
          }
       }
 
       // OBC-specific code (Eqs. 6-8 in paper)

       sum                  *= half*offsetRadiusI;
       RealOpenMM sum2       = sum*sum;
       RealOpenMM sum3       = sum*sum2;
       RealOpenMM tanhSum    = TANH(alphaObc*sum - betaObc*sum2 + gammaObc*sum3);
       
       bornRadii[atomI]      = one/(one/offsetRadiusI - tanhSum/radiusI); 
 
       obcChain[atomI]       = offsetRadiusI*(alphaObc - two*betaObc*sum + three*gammaObc*sum2);
       obcChain[atomI]       = (one - tanhSum*tanhSum)*obcChain[atomI]/radiusI;

    }
}

/**---------------------------------------------------------------------------------------

    Get nonpolar solvation force constribution via ACE approximation

    @param obcParameters parameters
    @param bornRadii                 Born radii
    @param energy                    energy (output): value is incremented from input value 
    @param forces                    forces: values are incremented from input values

    --------------------------------------------------------------------------------------- */

void ReferenceObc::computeAceNonPolarForce(const ObcParameters* obcParameters,
                                      const vector<RealOpenMM>& bornRadii,
                                      RealOpenMM* energy,
                                      vector<RealOpenMM>& forces) const {

    // ---------------------------------------------------------------------------------------

    static const RealOpenMM zero     = static_cast<RealOpenMM>(0.0);
    static const RealOpenMM minusSix = -6.0;
    static const RealOpenMM six      = static_cast<RealOpenMM>(6.0);

    // ---------------------------------------------------------------------------------------

    // compute the nonpolar solvation via ACE approximation

    const RealOpenMM probeRadius          = obcParameters->getProbeRadius();
    const RealOpenMM surfaceAreaFactor    = obcParameters->getPi4Asolv();

    const vector<RealOpenMM>& atomicRadii   = obcParameters->getAtomicRadii();
    int numberOfAtoms                     = obcParameters->getNumberOfAtoms();

    // the original ACE equation is based on Eq.2 of

    // M. Schaefer, C. Bartels and M. Karplus, "Solution Conformations
    // and Thermodynamics of Structured Peptides: Molecular Dynamics
    // Simulation with an Implicit Solvation Model", J. Mol. Biol.,
    // 284, 835-848 (1998)  (ACE Method)

    // The original equation includes the factor (atomicRadii[atomI]/bornRadii[atomI]) to the first power,
    // whereas here the ratio is raised to the sixth power: (atomicRadii[atomI]/bornRadii[atomI])**6

    // This modification was made by Jay Ponder who observed it gave better correlations w/
    // observed values. He did not think it was important enough to write up, so there is
    // no paper to cite.

    for (int atomI = 0; atomI < numberOfAtoms; atomI++) {
        if (bornRadii[atomI] > zero) {
            RealOpenMM r            = atomicRadii[atomI] + probeRadius;
            RealOpenMM ratio6       = POW(atomicRadii[atomI]/bornRadii[atomI], six);
            RealOpenMM saTerm       = surfaceAreaFactor*r*r*ratio6;
            *energy                += saTerm;
            forces[atomI]          += minusSix*saTerm/bornRadii[atomI]; 
        }
    }
}

/**---------------------------------------------------------------------------------------

    Get Obc Born energy and forces

    @param atomCoordinates     atomic coordinates
    @param partialCharges      partial charges
    @param forces              forces

    The array bornRadii is also updated and the obcEnergy

    --------------------------------------------------------------------------------------- */

RealOpenMM ReferenceObc::computeBornEnergyForces(const vector<RealVec>& atomCoordinates,
                                           const vector<RealOpenMM>& partialCharges, vector<RealVec>& inputForces) {

    // ---------------------------------------------------------------------------------------

    static const RealOpenMM zero    = static_cast<RealOpenMM>(0.0);
    static const RealOpenMM one     = static_cast<RealOpenMM>(1.0);
    static const RealOpenMM two     = static_cast<RealOpenMM>(2.0);
    static const RealOpenMM three   = static_cast<RealOpenMM>(3.0);
    static const RealOpenMM four    = static_cast<RealOpenMM>(4.0);
    static const RealOpenMM half    = static_cast<RealOpenMM>(0.5);
    static const RealOpenMM fourth  = static_cast<RealOpenMM>(0.25);
    static const RealOpenMM eighth  = static_cast<RealOpenMM>(0.125);

    // constants

    const int numberOfAtoms = _obcParameters->getNumberOfAtoms();
    const RealOpenMM dielectricOffset = _obcParameters->getDielectricOffset();
    const RealOpenMM cutoffDistance = _obcParameters->getCutoffDistance();
    const RealOpenMM soluteDielectric = _obcParameters->getSoluteDielectric();
    const RealOpenMM solventDielectric = _obcParameters->getSolventDielectric();
    RealOpenMM preFactor;
    if (soluteDielectric != zero && solventDielectric != zero)
        preFactor = two*_obcParameters->getElectricConstant()*((one/soluteDielectric) - (one/solventDielectric));
    else
        preFactor = zero;

    // ---------------------------------------------------------------------------------------

    // compute Born radii

    vector<RealOpenMM> bornRadii(numberOfAtoms);
    computeBornRadii(atomCoordinates, bornRadii);

    // set energy/forces to zero

    RealOpenMM obcEnergy                 = zero;
    vector<RealOpenMM> bornForces(numberOfAtoms, 0.0);

    // ---------------------------------------------------------------------------------------

    // compute the nonpolar solvation via ACE approximation
     
    if (includeAceApproximation()) {
       computeAceNonPolarForce(_obcParameters, bornRadii, &obcEnergy, bornForces);
    }
 
    // ---------------------------------------------------------------------------------------

    // first main loop

    for (int atomI = 0; atomI < numberOfAtoms; atomI++) {
 
       RealOpenMM partialChargeI = preFactor*partialCharges[atomI];
       for (int atomJ = atomI; atomJ < numberOfAtoms; atomJ++) {

          RealOpenMM deltaR[ReferenceForce::LastDeltaRIndex];
          if (_obcParameters->getPeriodic())
              ReferenceForce::getDeltaRPeriodic(atomCoordinates[atomI], atomCoordinates[atomJ], _obcParameters->getPeriodicBox(), deltaR);
          else
              ReferenceForce::getDeltaR(atomCoordinates[atomI], atomCoordinates[atomJ], deltaR);
          if (_obcParameters->getUseCutoff() && deltaR[ReferenceForce::RIndex] > cutoffDistance)
              continue;

          RealOpenMM r2                 = deltaR[ReferenceForce::R2Index];
          RealOpenMM deltaX             = deltaR[ReferenceForce::XIndex];
          RealOpenMM deltaY             = deltaR[ReferenceForce::YIndex];
          RealOpenMM deltaZ             = deltaR[ReferenceForce::ZIndex];

          RealOpenMM alpha2_ij          = bornRadii[atomI]*bornRadii[atomJ];
          RealOpenMM D_ij               = r2/(four*alpha2_ij);

          RealOpenMM expTerm            = EXP(-D_ij);
          RealOpenMM denominator2       = r2 + alpha2_ij*expTerm; 
          RealOpenMM denominator        = SQRT(denominator2); 
          
          RealOpenMM Gpol               = (partialChargeI*partialCharges[atomJ])/denominator; 
          RealOpenMM dGpol_dr           = -Gpol*(one - fourth*expTerm)/denominator2;  

          RealOpenMM dGpol_dalpha2_ij   = -half*Gpol*expTerm*(one + D_ij)/denominator2;
          
          RealOpenMM energy = Gpol;

          if (atomI != atomJ) {

              if (_obcParameters->getUseCutoff())
                  energy -= partialChargeI*partialCharges[atomJ]/cutoffDistance;
              
              bornForces[atomJ]        += dGpol_dalpha2_ij*bornRadii[atomI];

              deltaX                   *= dGpol_dr;
              deltaY                   *= dGpol_dr;
              deltaZ                   *= dGpol_dr;

              inputForces[atomI][0]    += deltaX;
              inputForces[atomI][1]    += deltaY;
              inputForces[atomI][2]    += deltaZ;

              inputForces[atomJ][0]    -= deltaX;
              inputForces[atomJ][1]    -= deltaY;
              inputForces[atomJ][2]    -= deltaZ;

          } else {
             energy *= half;
          }

          obcEnergy         += energy;
          bornForces[atomI] += dGpol_dalpha2_ij*bornRadii[atomJ];

       }
    }

    // ---------------------------------------------------------------------------------------

    // second main loop

    const vector<RealOpenMM>& obcChain            = getObcChain();
    const vector<RealOpenMM>& atomicRadii         = _obcParameters->getAtomicRadii();

    const RealOpenMM alphaObc                   = _obcParameters->getAlphaObc();
    const RealOpenMM betaObc                    = _obcParameters->getBetaObc();
    const RealOpenMM gammaObc                   = _obcParameters->getGammaObc();
    const vector<RealOpenMM>& scaledRadiusFactor  = _obcParameters->getScaledRadiusFactors();

    // compute factor that depends only on the outer loop index

    for (int atomI = 0; atomI < numberOfAtoms; atomI++) {
       bornForces[atomI] *= bornRadii[atomI]*bornRadii[atomI]*obcChain[atomI];      
    }

    for (int atomI = 0; atomI < numberOfAtoms; atomI++) {
 
       // radius w/ dielectric offset applied

       RealOpenMM radiusI        = atomicRadii[atomI];
       RealOpenMM offsetRadiusI  = radiusI - dielectricOffset;

       for (int atomJ = 0; atomJ < numberOfAtoms; atomJ++) {

          if (atomJ != atomI) {

             RealOpenMM deltaR[ReferenceForce::LastDeltaRIndex];
             if (_obcParameters->getPeriodic())
                ReferenceForce::getDeltaRPeriodic(atomCoordinates[atomI], atomCoordinates[atomJ], _obcParameters->getPeriodicBox(), deltaR);
             else 
                ReferenceForce::getDeltaR(atomCoordinates[atomI], atomCoordinates[atomJ], deltaR);
             if (_obcParameters->getUseCutoff() && deltaR[ReferenceForce::RIndex] > cutoffDistance)
                    continue;
    
             RealOpenMM deltaX             = deltaR[ReferenceForce::XIndex];
             RealOpenMM deltaY             = deltaR[ReferenceForce::YIndex];
             RealOpenMM deltaZ             = deltaR[ReferenceForce::ZIndex];
             RealOpenMM r                  = deltaR[ReferenceForce::RIndex];
 
             // radius w/ dielectric offset applied

             RealOpenMM offsetRadiusJ      = atomicRadii[atomJ] - dielectricOffset;

             RealOpenMM scaledRadiusJ      = offsetRadiusJ*scaledRadiusFactor[atomJ];
             RealOpenMM scaledRadiusJ2     = scaledRadiusJ*scaledRadiusJ;
             RealOpenMM rScaledRadiusJ     = r + scaledRadiusJ;

             // dL/dr & dU/dr are zero (this can be shown analytically)
             // removed from calculation

             if (offsetRadiusI < rScaledRadiusJ) {

                RealOpenMM l_ij          = offsetRadiusI > FABS(r - scaledRadiusJ) ? offsetRadiusI : FABS(r - scaledRadiusJ);
                     l_ij                = one/l_ij;

                RealOpenMM u_ij          = one/rScaledRadiusJ;

                RealOpenMM l_ij2         = l_ij*l_ij;

                RealOpenMM u_ij2         = u_ij*u_ij;
 
                RealOpenMM rInverse      = one/r;
                RealOpenMM r2Inverse     = rInverse*rInverse;

                RealOpenMM t3            = eighth*(one + scaledRadiusJ2*r2Inverse)*(l_ij2 - u_ij2) + fourth*LN(u_ij/l_ij)*r2Inverse;

                RealOpenMM de            = bornForces[atomI]*t3*rInverse;

                deltaX                  *= de;
                deltaY                  *= de;
                deltaZ                  *= de;
    
                inputForces[atomI][0]   -= deltaX;
                inputForces[atomI][1]   -= deltaY;
                inputForces[atomI][2]   -= deltaZ;
  
                inputForces[atomJ][0]   += deltaX;
                inputForces[atomJ][1]   += deltaY;
                inputForces[atomJ][2]   += deltaZ;
 
             }
          }
       }

    }

    return obcEnergy;
}