SurfaceTetheredChain.h

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/**
 *  \file IMP/core/SurfaceTetheredChain.h
 *  \brief Score on surface-to-end distance of chain tethered to impenetrable surface
 *
 *  Copyright 2007-2021 IMP Inventors. All rights reserved.
 */

#ifndef IMPCORE_SURFACE_TETHERED_CHAIN_H
#define IMPCORE_SURFACE_TETHERED_CHAIN_H

#include <IMP/core/core_config.h>
#include <IMP/UnaryFunction.h>
#include <IMP/constants.h>

IMPCORE_BEGIN_NAMESPACE

//! Score on surface-to-end distance of chain tethered to impenetrable surface
/** When a flexible linker is represented by the freely jointed chain model with
    one end tethered to an impenetrable surface, the distance \f$ z \f$ of the
    free end from the surface follows the distribution
        \f[ p(z | \beta) = 2 \beta z \exp{(-\beta z^2)}, \f]
    where \f$ \beta = \frac{3}{2 N b^2} \f$, \f$ N \f$ is the number of links,
    and \f$ b \f$ is the average length of a single link. The score reaches its
    minimum value when \f$ z = \frac{1}{\sqrt{2 \beta}} \f$.

    See KA Dill, S Bromberg. Molecular Driving Forces. 2nd Edition. 2010.
    Eq 34.7.

    \note While the Gaussian approximation breaks down when \f$z > N b\f$, the
    score naturally increases as a harmonic restraint with force constant
    \f$2 \beta\f$.

    \note The resulting score blows up as the \f$ z \f$ approaches 0.
    Therefore, in this implementation, when \f$ z = .01 z_{min} \f$, where
    \f$ z_{min} \f$ is the value of \f$ z \f$ where the score is minimized,
    then the score increases linearly as \f$ z \f$ decreases.

    \see misc::FreelyJointedChain
    \see misc::WormLikeChain
    \see Harmonic
    \see SurfaceHeightPairScore
*/
class SurfaceTetheredChain : public UnaryFunction {

 private:
  void initialize() {
    double N = (double) N_;
    beta_ = 3. / 2. / N / b_ / b_;
    z_min_ = 0.01 / sqrt(2 * beta_);
    z_min_deriv_ = -141.4072141 * sqrt(beta_);
    z_min_int_ = 5.2585466 - std::log(beta_) / 2.;
  }

 public:
  SurfaceTetheredChain(int link_num, double link_length)
    : N_(link_num), b_(link_length) {
      IMP_USAGE_CHECK(N_ > 0, "Number of links must be positive.");
      IMP_USAGE_CHECK(b_ > 0, "Link length must be positive.");
      initialize();
    }

  virtual DerivativePair evaluate_with_derivative(
                  double feature) const IMP_OVERRIDE {
    if (feature < z_min_) {
      return DerivativePair(z_min_deriv_ * feature + z_min_int_,
                            z_min_deriv_);
    } else {
      return DerivativePair(beta_ * feature * feature -
                            std::log(2 * beta_ * feature),
                            2. * beta_ * feature - 1. / feature);
    }
  }

  virtual double evaluate(double feature) const IMP_OVERRIDE {
    return evaluate_with_derivative(feature).first;
  }

  IMP_OBJECT_METHODS(SurfaceTetheredChain);

  //! Get number of links in chain.
  int get_link_number() const { return N_; }

  //! Get length of each chain link.
  double get_link_length() const { return b_; }

  //! Set the number of links in chain.
  void set_link_number(int N) {
    N_ = N;
    IMP_USAGE_CHECK(N_ > 0, "Number of links must be positive.");
    initialize();
  }

  //! Set the length of each chain link.
  void set_link_length(double b) {
    b_ = b;
    IMP_USAGE_CHECK(b_ > 0, "Link length must be positive.");
    initialize();
  }

  //! Get the distance at which the score is at its minimum value.
  double get_distance_at_minimum() const {
    return 1. / sqrt(2 * beta_);
  }

  //! Get the average distance from the surface.
  double get_average_distance() const {
    return sqrt(PI / beta_) / 2.;
  }

 private:
  int N_;
  double b_;
  double beta_, z_min_, z_min_deriv_, z_min_int_;
};

IMPCORE_END_NAMESPACE

#endif /* IMPCORE_SURFACE_TETHERED_CHAIN_H */