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// -*- Mode: C++; tab-width: 2; -*-
// vi: set ts=2:
//
// $Id: generalizedBornCase.C,v 1.3.10.1 2007/03/25 22:00:32 oliver Exp $
//
#include <BALL/SOLVATION/generalizedBornCase.h>
// #include "generalizedBornCase.h"
#include <BALL/SYSTEM/path.h>
#include <BALL/SYSTEM/timer.h>
#include <BALL/KERNEL/forEach.h>
#include <BALL/FORMAT/parameters.h>
#include <BALL/COMMON/exception.h>
#include <BALL/KERNEL/residue.h>
#include <BALL/KERNEL/bond.h>
using namespace std;
#define UNITED_ATOMS
// #define TSUI true
namespace BALL
{
const String GeneralizedBornModel::Option::VERBOSITY = "verbosity";
const String GeneralizedBornModel::Option::LAMBDA = "lambda";
const String GeneralizedBornModel::Option::DELTA = "delta";
const String GeneralizedBornModel::Option::KAPPA = "kappa";
const String GeneralizedBornModel::Option::RHO_0 = "rho_0";
const String GeneralizedBornModel::Option::DC_SOLVENT = "dc_solvent";
const String GeneralizedBornModel::Option::DC_SOLUTE = "dc_solute";
const String GeneralizedBornModel::Option::FILENAME = "filename";
const Size GeneralizedBornModel::Default::VERBOSITY = 10;
const float GeneralizedBornModel::Default::LAMBDA = 1.4f;
const float GeneralizedBornModel::Default::DELTA = 0.15f;
const float GeneralizedBornModel::Default::KAPPA = 0.1f;
const float GeneralizedBornModel::Default::RHO_0 = 0.09f;
const float GeneralizedBornModel::Default::DC_SOLVENT = 80.0f;
const float GeneralizedBornModel::Default::DC_SOLUTE = 2.0f;
const String GeneralizedBornModel::Default::FILENAME = "solvation/gb_scaling.ini";
/*
const Size GeneralizedBornModel::Default::VERBOSITY = 10;
const float GeneralizedBornModel::Default::LAMBDA = 1.0f;
const float GeneralizedBornModel::Default::DELTA = 0.00f;
const float GeneralizedBornModel::Default::KAPPA = 0.1f;
const float GeneralizedBornModel::Default::RHO_0 = 0.00f;
const float GeneralizedBornModel::Default::DC_SOLVENT = 80.0f;
const float GeneralizedBornModel::Default::DC_SOLUTE = 2.0f;
const String GeneralizedBornModel::Default::FILENAME = "solvation/GB.ini";
*/
GeneralizedBornModel::GeneralizedBornModel()
: ac_(0),
born_radii_(),
pair_list_(),
pair_distances_(),
pair_charges_(),
dc_solute_(0.0f),
dc_solvent_(0.0f),
scaling_factors_(),
scaling_factor_filename_(""),
lambda_(0.0f),
delta_(0.0f),
kappa_(0.0f),
rho_0_(0.0f)
{
// set the default values for the parameters
lambda_ = Default::LAMBDA;
delta_ = Default::DELTA;
kappa_ = Default::KAPPA;
rho_0_ = Default::RHO_0;
dc_solvent_ = Default::DC_SOLVENT;
dc_solute_ = Default::DC_SOLUTE;
// Compute the factor for converting values to kJ/mol
// Multiply charge unit
to_kJ_mol_ = Constants::e0 * Constants::e0;
// Divide by vacuum permittivity
to_kJ_mol_ /= Constants::VACUUM_PERMITTIVITY;
// Divide by length unit (Angstrom)
to_kJ_mol_ /= 1e-10;
// Divide by 1000 in order to resturn kJ/mol
to_kJ_mol_ /= 1e3;
// Now multiply with N_A for obtaining molar values
to_kJ_mol_ *= Constants::AVOGADRO;
// Divide by 4\pi
to_kJ_mol_ /= (4.0f * Constants::PI);
}
GeneralizedBornModel::~GeneralizedBornModel()
{
}
void GeneralizedBornModel::clear()
{
// Clear the AtomContainer pointer
ac_ = 0;
// Don't clear the scaling factors, although this is a clear() function.
// This is obviously inconsistent, but should make sense in this case.
// Maybe we should rename this method�
// Clear all the lists we built for fast calculations
atoms_.clear();
scaling_factor_.clear();
pair_list_.clear();
pair_distances_.clear();
pair_charges_.clear();
squared_distances_.clear();
}
bool GeneralizedBornModel::setup(const AtomContainer& ac)
{
Timer timer;
timer.start();
// save the AtomContainer
clear();
ac_ = const_cast<AtomContainer*>(&ac);
// Set the filename for the scaling factors
if (scaling_factor_filename_ == String(""))
{
scaling_factor_filename_ = Default::FILENAME;
}
// Go through the atoms of the molecule and find those charged
// hydrogens which have to be condensed on heavy atoms, because they
// bear partial charges without havin a radius.
// Note: Condensing hydrogens may lead to single atoms (NHx)!
// Store the atoms that have to be removed after condensation in a hash
// set.
HashSet<Atom*> remove_me;
// Iterate over the system
AtomIterator it = ac_->beginAtom();
for (; +it; ++it)
{
String resid;
if (it->getResidue() != 0)
{
resid = it->getResidue()->getID() + ":";
}
else
{
resid = "";
}
// DEBUG
/*
Log.info() << resid << it->getFullName() << "@"
<< it->getPosition() << " (r=" << it->getRadius() << ", c="
<< it->getCharge() << ", e=" << it->getElement().getSymbol() << ")"
<< endl;
*/
// DEBUG
if (it->getRadius() == 0.0 && it->getCharge() != 0.0)
{
if (it->getElement() != PTE[Element::H])
{
Log.error() << "Found non-hydrogen atom with non-zero charge and zero radius, aborting."
<< endl;
Log.error() << it->getResidue()->getID() << ":" << it->getFullName()
<< "@" << it->getPosition() << " (r=" << it->getRadius() << ", c="
<< it->getCharge() << ", e=" << it->getElement().getSymbol() << ")"
<< endl;
return(1);
}
else
{
Log.info() << "Found charged hydrogen with zero radius: "
<< it->getFullName() << endl;
#ifdef UNITED_ATOMS
Atom* hydrogen_partner = it->getBond(0)->getPartner(*it);
Log.info() << "Condensing it onto the bound heavy atom "
<< hydrogen_partner->getFullName() << endl;
hydrogen_partner->setCharge(hydrogen_partner->getCharge()
+ it->getCharge());
it->setCharge(0.0);
remove_me.insert(&*it);
#else
cout << "Setting radius to 1.30 A" << endl;
it->setRadius(1.30f);
#endif
}
}
}
// Now remove the atoms from the system
HashSet<Atom*>::Iterator remove_it = remove_me.begin();
for (; +remove_it; ++remove_it)
{
Atom* ptr = *remove_it;
delete(ptr);
}
Log.info() << "United atoms: Removed " << remove_me.size()
<< " atoms from the system" << endl;
if (ac_->countAtoms() < 2)
{
Log.error() << "Need at least two atoms for this method!"
<< endl;
}
// if there are scaling factors stored here, we're fine. If not, try to
// load them from the default file
if (scaling_factors_.size() == 0)
{
// Read scaling factors from standard INIfile
if (!readScalingFactors(scaling_factor_filename_))
{
return(false);
}
}
// Set scaling factor for each atom
AtomConstIterator it1;
for (it1 = ac_->beginAtom(); +it1; ++it1)
{
atoms_.push_back(&*it1);
float S_j = 0.0f;
if (scaling_factors_.has(it1->getElement().getSymbol()))
{
S_j = scaling_factors_[it1->getElement().getSymbol()];
}
else
{
Log.warn() << "Unknown element " << it1->getElement().getSymbol()
<< ". Using unscaled radius for calculating eff. Born radius."
<< std::endl;
S_j = 1.0f;
}
scaling_factor_.push_back(S_j);
}
Size N = atoms_.size();
// Allocate memory
pair_list_.resize(N*N / 2 + 1);
pair_distances_.resize(N*N / 2 + 1);
pair_charges_.resize(N*N / 2 + 1);
squared_distances_.resize(N);
// Build pair list and calculate distances
Size k = 0;
for (Size i = 0; i < N; ++i)
{
// Allocate memory
squared_distances_[i].resize(N);
for (Size j = 0; j < i; ++j)
{
float distance = atoms_[i]->getPosition().getDistance(atoms_[j]->getPosition());
if (distance < 0.1f)
{
Log.warn() << "Atoms too close: "
<< atoms_[i]->getResidue()->getFullName()
<< ":" << atoms_[i]->getResidue()->getID()
<< ":" << atoms_[i]->getName()
<< " - "
<< atoms_[j]->getResidue()->getFullName()
<< ":" << atoms_[j]->getResidue()->getID()
<< ":" << atoms_[j]->getName()
<< std::endl;
}
pair_list_[k] = std::pair<Size, Size>(i, j);
pair_distances_[k] = distance;
// DEBUG
// cout << "pair_distances_[" << k << "]: " << pair_distances_[k] << endl;
// /DEBUG
pair_charges_[k] = atoms_[i]->getCharge() * atoms_[j]->getCharge();
squared_distances_[i][j] = squared_distances_[j][i]
= distance * distance;
// DEBUG
/*
cout << i << " " << j << " " << k << " "
<< (Size) (i/2.0f * (i-1) + j) << endl;
*/
// /DEBUG
// increase index counter
++k;
}
}
timer.stop();
Log.info() << "setup(): " << timer.getCPUTime() << "s" << std::endl;
return(true);
}
void GeneralizedBornModel::calculateBornRadii_()
{
born_radii_.clear();
born_radii_.resize(atoms_.size());
for (Size i = 0; i < atoms_.size(); ++i)
{
// This is what we want to know for atom i
float effective_born_radius = 0.0f;
// This variable is used for summing up the actual contributions to the
// coulomb integral approximation
float tmp = 0.0f;
// The actual "radius" of atom i
float radius = atoms_[i]->getRadius();
Size n = atoms_.size();
for (Size j = 0; j < n; ++j)
{
if (j != i)
{
Size k;
if (i > j)
{
k = (Size) (i/2.0f * (i-1) + j);
}
else
{
k = (Size) (j/2.0f * (j-1) + i);
}
// DEBUG
// cout << i << " " << j << " --> " << k << endl;
// /DEBUG
// sum up the contribution of every atom of the system
tmp += coulombIntegralApproximation_(pair_distances_[k],
scaling_factor_[j] * (atoms_[j]->getRadius() - rho_0_),
radius - rho_0_);
}
}
// DEBUG
// float one_over_B = 1.0f / (radius - rho_0_) - 0.5f * tmp;
// std::cout << "HCT radius = " << (1.0f / one_over_B) << std::endl;
// /DEBUG
#ifdef TSUI
// These are the original calculations
// See Tsui et al.,
float S = 1.0f / ( radius - rho_0_ ) - 0.5f * lambda_ * tmp;
effective_born_radius = 1.0f / S - delta_;
// DEBUG
// std::cout << "reduced HCT radius = " << effective_born_radius << std::endl;
// /DEBUG
#else
// In Proteins 55:383-394, 2004 Onufriev et al. propose another term
// OBC I
float alpha = 0.8f;
float beta = 0.0f;
float gamma = 2.91f;
// OBC II
/*
float alpha = 1.0f;
float beta = 0.8f;
float gamma = 4.85f;
*/
float psi = 0.5f * (radius - rho_0_) * tmp;
float psi2 = psi * psi;
float psi3 = psi2 * psi;
float S = 1.0f / ( radius - rho_0_ )
- 1.0f / radius * tanhf( alpha * psi - beta * psi2 + gamma * psi3 );
effective_born_radius = 1.0f / S;
// DEBUG
// std::cout << "OCB I radius = " << effective_born_radius << std::endl;
// /DEBUG
#endif
// DEBUG
// cout << "born_radii_[" << i << "]: " << born_radii_[i] << endl;
// /DEBUG
born_radii_[i] = effective_born_radius;
}
}
float GeneralizedBornModel::calculateEnergy()
{
// We have to calculate Born radii every time we do the calculation of
// the energy because the distances between atoms does influence the
// effedctive radii. This could be done more sophisticated in order to
// speed up the calculation, no doubt.
Timer timer;
timer.start();
calculateBornRadii_();
timer.stop();
Log.info() << "calculateBornRadii_(): " << timer.getCPUTime()
<< "s" << std::endl;
return(calculateTransferEnergy_() + calculateCreationEnergy_());
}
float GeneralizedBornModel::calculateSolvationEnergy()
{
// We have to calculate Born radii every time we do the calculation of
// the energy because the distances between atoms does influence the
// effective radii. This could be done more sophisticated in order to
// speed up the calculation, no doubt.
Timer timer;
timer.start();
calculateBornRadii_();
timer.stop();
Log.info() << "calculateBornRadii_(): " << timer.getCPUTime()
<< "s" << std::endl;
// Solvation energy is just the transfer energy with an internal
// dieelectric constant of 1. The Coulomb part is constant and vanishes
// in the difference.
setSoluteDC(1.0f);
return(calculateTransferEnergy_());
}
bool GeneralizedBornModel::readScalingFactors(const String& filename)
{
Path path;
String tmp = path.find(filename);
if (tmp == "") tmp = filename;
Parameters gb_parameter_file(tmp);
GeneralizedBornModel::GBParameters gb_parameters;
if (!gb_parameters.extractSection(gb_parameter_file, "ScalingFactors"))
{
Log.error() << "Error reading paramters" << std::endl;
return(false);
}
scaling_factors_ = gb_parameters.getScalingFactors();
dc_solute_ = gb_parameters.getSoluteDC();
dc_solvent_ = gb_parameters.getSolventDC();
kappa_ = gb_parameters.getKappa();
return(true);
}
float GeneralizedBornModel::calculateCreationEnergy_()
const
{
Timer timer;
timer.start();
// This is just a simple Coulomb-Calculation.
float energy = 0.0f;
// iterate over all atom pairs
for (Size i = 0; i < pair_list_.size(); i++)
{
float contribution = 0.0f;
float c = pair_charges_[i];
if (c != 0.0f) contribution = c / pair_distances_[i];
energy += contribution;
}
// The pair list delivers every pair only once! So we don't
// have to divide by two like given in the formula
/*
$$
W = \frac{1}{2} \frac{1}{4 \pi \varepsilon_0 \varepsilon_r}
\sum_{i \neq j} \frac{q_i q_j}{r_{ij}}
$$
*/
// Divide relative permittivity
energy /= dc_solute_;
// Convert to the correct dimension kJ/mol
energy *= to_kJ_mol_;
// DEBUG
cout << "calculateCreationEnergy_(): " << energy << endl;
// /DEBUG
timer.stop();
Log.info() << "calculateCreationEnergy_(): " << timer.getCPUTime()
<< "s" << std::endl;
return(energy);
}
float GeneralizedBornModel::calculateTransferEnergy_()
const
{
Timer timer;
timer.start();
// This is a standard Generalized Born (see Still et al.) plus the salt
// effect calculations developed by Srinivasan et al. (Theor. Chem.
// Acc. 101:426-434, 1999)
float energy = 0.0f;
// inverse dcs
float inv_dc_solute = 1.0f/dc_solute_;
float inv_dc_solvent = 1.0f/dc_solvent_;
// First calculate those terms considering different atoms
for (Size k = 0; k < pair_list_.size(); ++k)
{
Size i = pair_list_[k].first;
Size j = pair_list_[k].second;
float c = pair_charges_[k];
if (c != 0.0)
{
// Calculate the evil f term and the resulting energy
// contribution
float f_GB = f_GB_(i, j);
float e = c / f_GB;
// DEBUG
// cout << "e: " << e << endl;
// /DEBUG
// Include salt effects if necessary
// Maybe this could be done more efficiently
if (kappa_ != 0.0f)
{
e *= (inv_dc_solute - inv_dc_solvent * exp(-kappa_ * f_GB));
}
energy += e;
}
}
// Now calculate self energies
for (Size i = 0; i < atoms_.size(); ++i)
{
float c = atoms_[i]->getCharge();
if (c != 0.0f)
{
float e = c * c / born_radii_[i];
// DEBUG
// cout << "e self: " << 0.5f * e << endl;
// /DEBUG
energy += 0.5f * e;
}
}
// This is the simple term without salt effects
if (kappa_ == 0.0f)
{
energy *= (inv_dc_solute - inv_dc_solvent);
}
// Change sign (this contribution is negative) and Convert to the unit
// of kJ/mol
energy *= - to_kJ_mol_;
// DEBUG
cout << "calculateTransferEnergy_(): " << energy << endl;
// /DEBUG
timer.stop();
Log.info() << "calculateTransferEnergy_(): " << timer.getCPUTime()
<< "s" << std::endl;
return(energy);
}
float GeneralizedBornModel::f_GB_(Size i, Size j) const
{
// we need the effective Born radii for computing this smooth volume
// function
float R_iR_j = born_radii_[i] * born_radii_[j];
// we need the squared distance
float squared_distance = squared_distances_[i][j];
// This is the term derived by Still et al. (JACS 112:6127-6129, 1990)
float result = sqrt(squared_distance
+ R_iR_j * exp(-squared_distance / (4.0f * R_iR_j)));
// There are other terms possible. Onufriew et al. propose
// (J Comput Chem 23:1297-1304, 2002) several other terms:
/*
float beta = 0.0f;
float S;
S = 1.0f / (1 + squared_distance/(4.0f * R_iR_j));
S = 1.0f / sqrt(1 + squared_distance/(4.0f * R_iR_j));
S = 1.0f / (1 + log(1.0f + squared_distance/(4.0f * R_iR_j)));
result = sqrt(squared_distance
+ beta * sqrt(R_iR_j)
+ R_iR_j * S);
*/
// DEBUG
// cout << "f_GB_(" << i << ", " << j << "):" << result << endl;
// /DEBUG
return(result);
}
float GeneralizedBornModel::coulombIntegralApproximation_(float r_ij,
float scaled_radius_j, float radius_i) const
{
// This is the approximation by Hawkins, Cramer, Truhlar (based on the
// calculations of Schaefer and Froemmel
//
// Hawkins et al,, Chem Phys Lett 246:122-129, 1995
// Hawkins et al., J Phys Chem 100:19824-19839, 1996
// Schaefer and Froemmel, J Mol Biol 216:1045-1066, 1990
// helper variables
float L_ij;
float U_ij;
float r_plus_Salpha = r_ij + scaled_radius_j;
float r_minus_Salpha = r_ij - scaled_radius_j;
if (r_plus_Salpha <= radius_i)
{
L_ij = 1.0f;
U_ij = 1.0f;
}
else
{
if (r_minus_Salpha <= radius_i)
{
L_ij = radius_i;
}
else
{
L_ij = r_minus_Salpha;
}
U_ij = r_plus_Salpha;
}
// Difference of the squared limits
float D = 1.0f / ( L_ij * L_ij ) - 1.0f / ( U_ij * U_ij );
float tmp
= 1.0f / L_ij
- 1.0f / U_ij
+ r_ij / 4.0f * -D
+ 1.0f / ( 2.0f * r_ij ) * log( L_ij / U_ij )
+ ( scaled_radius_j * scaled_radius_j )
/ ( 4.0f * r_ij ) * D;
return(tmp);
}
void GeneralizedBornModel::setScalingFactorFile(const String& filename)
{
scaling_factor_filename_ = filename;
}
void GeneralizedBornModel::setSolventDC(float solvent_dc)
{
dc_solvent_ = solvent_dc;
}
void GeneralizedBornModel::setSoluteDC(float solute_dc)
{
dc_solute_ = solute_dc;
}
void GeneralizedBornModel::calculatePotential(HashMap<const Atom*,
float>& p_hash) const
{
p_hash.clear();
AtomConstIterator it = ac_->beginAtom();
for (; +it; ++it)
{
p_hash[&*it] = calculatePotential(*it);
}
}
float GeneralizedBornModel::calculatePotential(const Atom& atom_i) const
{
Timer timer;
timer.start();
// We have to find the index of the atom in question
Index index = -1;
for (Size i = 0; i < atoms_.size(); ++i)
{
if (atoms_[i] == &atom_i) index = i;
}
if (index < 0)
{
Log.error() << "calculatePotential(): Could not find atom index!"
<< std::endl;
return(0.0f);
}
// the potential
float potential = 0.0f;
// inverse dcs
float inv_dc_solute = 1.0f/dc_solute_;
float inv_dc_solvent = 1.0f/dc_solvent_;
// Now iterate over all atoms and calculate the potential at the
// position of atom_i
for (Index j = 0; (Size) j < atoms_.size(); ++j)
{
// Get the charge of the atom
float c = atoms_[j]->getCharge();
// compute potential contribution only if charge is not zero
if (c != 0.0)
{
// Calculate the evil f term and the resulting energy
// contribution
float f_GB;
// If this is the self-energy part, take the effective Born radius
// which is equal to f_GB_(i, i). Otherwise compute f_GB_().
if (index == j)
{
f_GB = born_radii_[index];
}
else
{
f_GB = f_GB_(index, j);
}
// Add up this contribution to the potential.
float p = - c / f_GB;
// DEBUG
// cout << "p: " << p << " c: " << c << " f_GB: " << f_GB << endl;
// /DEBUG
// Include salt effects if necessary
// Maybe this could be done more efficiently
if (kappa_ != 0.0f)
{
p *= (inv_dc_solute - inv_dc_solvent * exp(-kappa_ * f_GB));
}
potential += p;
// pc is the coulomb part of the potential
float pc = 0.0f;
// Compute the Coulomb part of the potential
if (index != j)
{
pc = inv_dc_solute * c / sqrt(squared_distances_[index][j]);
potential += pc;
// DEBUG
// cout << "pc: " << pc << endl;
// /DEBUG
}
}
}
// Multiply with DC effect term. This is the simple term without salt
// effects.
if (kappa_ == 0.0f)
{
potential *= (inv_dc_solute - inv_dc_solvent);
}
// Multiply charge unit
potential *= to_kJ_mol_ / Constants::e0;
// Stop timer
timer.stop();
/*
Log.info() << "calculatePotential(): " << timer.getCPUTime()
<< "s" << std::endl;
*/
return(potential);
}
GeneralizedBornModel::GBParameters::~GBParameters()
{
}
GeneralizedBornModel::GBParameters::GBParameters()
: ParameterSection(),
scaling_factors_()
{
}
const StringHashMap<float>& GeneralizedBornModel::GBParameters::getScalingFactors() const
{
return(scaling_factors_);
}
float GeneralizedBornModel::GBParameters::getSoluteDC() const
{
return(dc_solute_);
}
float GeneralizedBornModel::GBParameters::getSolventDC() const
{
return(dc_solvent_);
}
float GeneralizedBornModel::GBParameters::getKappa() const
{
return(kappa_);
}
bool GeneralizedBornModel::GBParameters::extractSection(Parameters&
parameters, const String& section_name)
{
if (!parameters.isValid())
{
Log.error() << "Parameters are invalid." << std::endl;
return(false);
}
ParameterSection::extractSection(parameters, section_name);
if (!hasVariable("factor"))
{
Log.error() << "Missing variables" << std::endl;
return(false);
}
Size number_of_keys = getNumberOfKeys();
Index factor_index = getColumnIndex("factor");
// clear the HashMap and fill it with the new values
scaling_factors_.clear();
for (Size i = 0; i < number_of_keys; ++i)
{
String element_symbol = getKey(i);
if (scaling_factors_.has(element_symbol))
{
Log.error() << "Duplicate scaling factor for element "
<< element_symbol << std::endl;
return(false);
}
// DEBUG
std::cout << "inserting " << element_symbol << " with factor "
<< getValue(i, factor_index).toFloat() << std::endl;
// /DEBUG
scaling_factors_[element_symbol] = getValue(i, factor_index).toFloat();
}
if (options.has("dc_solute"))
{
dc_solute_ = options.getReal("dc_solute");
Log.info() << "Setting solute dc to " << dc_solute_ << std::endl;
}
if (options.has("dc_solvent"))
{
dc_solvent_ = options.getReal("dc_solvent");
Log.info() << "Setting solvent dc to " << dc_solvent_ << std::endl;
}
if (options.has("lambda"))
{
lambda_ = options.getReal("lambda");
Log.info() << "(still disabled) Setting lambda to "
<< lambda_ << std::endl;
}
if (options.has("delta"))
{
delta_ = options.getReal("delta");
Log.info() << "(still disabled) Setting delta to "
<< delta_ << std::endl;
}
if (options.has("kappa"))
{
kappa_ = options.getReal("kappa");
Log.info() << "Setting kappa to "
<< kappa_ << std::endl;
}
if (options.has("rho_0"))
{
rho_0_ = options.getReal("rho_0");
Log.info() << "(still disabled) Setting rho_0 to "
<< rho_0_ << std::endl;
}
valid_ = true;
return(true);
}
}
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