ATMForce

class ATMForce : public OpenMM::Force

The ATMForce class implements the Alchemical Transfer Method (ATM) for OpenMM. ATM is used to compute the binding free energies of molecular complexes and of other equilibrium processes. ATM and its implementation are described in the open access article:

Solmaz Azimi, Sheenam Khuttan, Joe Z. Wu, Rajat K. Pal, and Emilio Gallicchio. Relative Binding Free Energy Calculations for Ligands with Diverse Scaffolds with the Alchemical Transfer Method. J. Chem. Inf. Model. 62, 309 (2022) https://doi.org/10.1021/acs.jcim.1c01129

Refer to the publication above for a detailed description of the ATM method and the parameters used in this API and please cite it to support our work if you use this software in your research.

The ATMForce implements an arbitrary potential energy function that depends on the potential energies (u0 and u1) of the system before and after a set of atoms are displaced by a specified amount. For example, you might displace a molecule from the solvent bulk to a receptor binding site to simulate a binding process. The potential energy function typically also depends on one or more parameters that are dialed to implement alchemical transformations.

To use this class, create an ATMForce object, passing an algebraic expression to the constructor that defines the potential energy. This expression can be any combination of the variables u0 and u1. Then call addGlobalParameter() to define the parameters on which the potential energy expression depends. The values of global parameters may be modified during a simulation by calling Context::setParameter(). Next, call addForce() to add Force objects that define the terms of the potential energy function that change upon displacement. Finally, call addParticle() to specify the displacement applied to each particle. Displacements can be changed by calling setParticleParameters(). As any per-particle parameters, changes in displacements take effect only after calling updateParametersInContext().

As an example, the following code creates an ATMForce based on the change in energy of two particles when the second particle is displaced by 1 nm in the x direction. The energy change is dialed using an alchemical parameter Lambda, which in this case is set to 1/2:

ATMForce *atmforce = new ATMForce("u0 + Lambda*(u1 - u0)");
atm->addGlobalParameter("Lambda", 0.5);
atm->addParticle(Vec3(0, 0, 0));
atm->addParticle(Vec3(1, 0, 0));
CustomBondForce* force = new CustomBondForce("0.5*r^2");
atm->addForce(force);

Expressions may involve the operators + (add), - (subtract), * (multiply), / (divide), and ^ (power), and the following functions: sqrt, exp, log, sin, cos, sec, csc, tan, cot, asin, acos, atan, atan2, sinh, cosh, tanh, erf, erfc, min, max, abs, floor, ceil, step, delta, select. All trigonometric functions are defined in radians, and log is the natural logarithm. step(x) = 0 if x is less than 0, 1 otherwise. delta(x) = 1 if x is 0, 0 otherwise. select(x,y,z) = z if x = 0, y otherwise.

If instead of the energy expression the ATMForce constructor specifies the values of a series of parameters, the default energy expression is used:

select(step(Direction), u0, u1) + ((Lambda2-Lambda1)/Alpha)*log(1+exp(-Alpha*(usc-Uh))) + Lambda2*usc + W0;
usc = select(step(u-Ubcore), (Umax-Ubcore)*fsc+Ubcore, u), u);
fsc = (z^Acore-1)/(z^Acore+1);
z = 1 + 2*(y/Acore) + 2*(y/Acore)^2;
y = (u-Ubcore)/(Umax-Ubcore);
u = select(step(Direction), 1, -1)*(u1-u0)

which is the same as the soft-core softplus alchemical potential energy function in the Azimi et al. paper above.

The ATMForce is then added to the System as any other Force

system.addForce(atmforce);

after which it will be used for energy/force evaluations for molecular dynamics and energy optimization. You can call getPerturbationEnergy() to query the values of u0 and u1, which are needed for computing free energies.

In most cases, particles are only displaced in one of the two states evaluated by this force. It computes the change in energy between the current particle coordinates (as stored in the Context) and the displaced coordinates. In some cases, it is useful to apply displacements to both states. You can do this by providing two displacement vectors to addParticle():

atm->addParticle(Vec3(1, 0, 0), Vec3(-1, 0, 0));

In this case, u1 will be computed after displacing the particle in the positive x direction, and u0 will be computed after displacing it in the negative x direction.

This class also has the ability to compute derivatives of the potential energy with respect to global parameters. Call addEnergyParameterDerivative() to request that the derivative with respect to a particular parameter be computed. You can then query its value in a Context by calling getState() on it.

Public Functions

explicit ATMForce(const std::string &energy)

Create an ATMForce object.

Parameters

energy – an algebraic expression giving the energy of the system as a function of u0 and u1, the energies before and after displacement

ATMForce(double lambda1, double lambda2, double alpha, double uh, double w0, double umax, double ubcore, double acore, double direction)

Create an ATMForce object with the default softplus energy expression. The values passed to this constructor are the default values of the global parameters for newly created Contexts. Their values can be changed by calling setParameter() on the Context using the parameter names defined by the Lambda1(), Lambda2(), etc. methods below.

Parameters

  • lambda1 – the default value of the Lambda1 parameter (dimensionless). This should be a number between 0 and 1.

  • lambda2 – the default value of the Lambda2 parameter (dimensionless). This should be a number between 0 and 1.

  • alpha – the default value of the Alpha parameter (kJ/mol)^-1

  • uh – the default value of the Uh parameter (kJ/mol)

  • w0 – the default value of the W0 parameter (kJ/mol)

  • umax – the default value of the Umax parameter (kJ/mol)

  • ubcore – the default value of the Ubcore parameter (kJ/mol)

  • acore – the default value of the Acore parameter dimensionless)

  • direction – the default value of the Direction parameter (dimensionless). This should be either 1 for the forward transfer, or -1 for the backward transfer.

inline int getNumParticles() const

Get the number of particles managed by ATMForce.

This should be the same number of particles as the System

inline int getNumForces() const

Get the number of Forces included in the ATMForce.

inline int getNumGlobalParameters() const

Get the number of global parameters that the interaction depends on.

inline int getNumEnergyParameterDerivatives() const

Get the number of global parameters with respect to which the derivative of the energy should be computed.

const std::string &getEnergyFunction() const

Get the algebraic expression that gives the energy of the system

void setEnergyFunction(const std::string &energy)

Set the algebraic expression that gives the energy of the system

int addForce(Force *force)

Add a Force whose energy will be computed by the ATMForce.

Parameters

force – the Force to the be added, which should have been created on the heap with the “new” operator. The ATMForce takes over ownership of it, and deletes the Force when the ATMForce itself is deleted.

Returns

The index within ATMForce of the force that was added

Force &getForce(int index) const

return the force from index

int addParticle(const Vec3 &displacement1, const Vec3 &displacement0 = Vec3())

Add a particle to the force.

All of the particles in the System must be added to the ATMForce in the same order as they appear in the System.

Parameters

  • displacement1 – the displacement of the particle for the target state in nm

  • displacement0 – the displacement of the particle for the initial state in nm

Returns

the index of the particle that was added

void getParticleParameters(int index, Vec3 &displacement1, Vec3 &displacement0) const

Get the parameters for a particle

Parameters

  • index – the index in the force for the particle for which to get parameters

  • displacement1 – the displacement of the particle for the target state in nm

  • displacement0 – the displacement of the particle for the initial state in nm

void setParticleParameters(int index, const Vec3 &displacement1, const Vec3 &displacement0 = Vec3())

Set the parameters for a particle

Parameters

  • index – the index in the force of the particle for which to set parameters

  • displacement1 – the displacement of the particle for the target state in nm

  • displacement0 – the displacement of the particle for the initial state in nm

int addGlobalParameter(const std::string &name, double defaultValue)

Add a new global parameter that the interaction may depend on. The default value provided to this method is the initial value of the parameter in newly created Contexts. You can change the value at any time by calling setParameter() on the Context.

Parameters

  • name – the name of the parameter

  • defaultValue – the default value of the parameter

Returns

the index of the parameter that was added

const std::string &getGlobalParameterName(int index) const

Get the name of a global parameter.

Parameters

index – the index of the parameter for which to get the name

Returns

the parameter name

void setGlobalParameterName(int index, const std::string &name)

Set the name of a global parameter.

Parameters

  • index – the index of the parameter for which to set the name

  • name – the name of the parameter

double getGlobalParameterDefaultValue(int index) const

Get the default value of a global parameter.

Parameters

index – the index of the parameter for which to get the default value

Returns

the parameter default value

void setGlobalParameterDefaultValue(int index, double defaultValue)

Set the default value of a global parameter.

Parameters

  • index – the index of the parameter for which to set the default value

  • defaultValue – the default value of the parameter

void addEnergyParameterDerivative(const std::string &name)

Request that this Force compute the derivative of its energy with respect to a global parameter. The parameter must have already been added with addGlobalParameter().

Parameters

name – the name of the parameter

const std::string &getEnergyParameterDerivativeName(int index) const

Get the name of a global parameter with respect to which this Force should compute the derivative of the energy.

Parameters

index – the index of the parameter derivative, between 0 and getNumEnergyParameterDerivatives()

Returns

the parameter name

void updateParametersInContext(Context &context)

Update the per-particle parameters in a Context to match those stored in this Force object. This method should be called after updating parameters with setParticleParameters() to copy them over to the Context. The only information this method updates is the values of per-particle parameters. The number of particles cannot be changed.

virtual bool usesPeriodicBoundaryConditions() const

Returns whether or not this force makes use of periodic boundary conditions.

void getPerturbationEnergy(Context &context, double &u1, double &u0, double &energy)

Returns the current perturbation energy.

Parameters

  • context – the Context for which to return the energy

  • u1 – on exit, the energy of the displaced state

  • u0 – on exit, the energy of the non-displaced state

  • energy – on exit, the value of this force’s energy function

Public Static Functions

static inline const std::string &Lambda1()

Returns the name of the global parameter corresponding to lambda1. The value assigned to this parameter should be a number between 0 and 1.

static inline const std::string &Lambda2()

Returns the name of the global parameter corresponding to lambda2. The value assigned to this parameter should be a number between 0 and 1.

static inline const std::string &Alpha()

Returns the name of the global parameter corresponding to alpha. The value assigned to this parameter should be in units of (kJ/mol)^-1.

static inline const std::string &Uh()

Returns the name of the global parameter corresponding to uh. The value assigned to this parameter should be in units of (kJ/mol).

static inline const std::string &W0()

Returns the name of the global parameter corresponding to w0. The value assigned to this parameter should be in units of (kJ/mol).

static inline const std::string &Umax()

Returns the name of the global parameter corresponding to umax. The value assigned to this parameter should be in units of (kJ/mol).

static inline const std::string &Ubcore()

Returns the name of the global parameter corresponding to ubcore. The value assigned to this parameter should be in units of (kJ/mol).

static inline const std::string &Acore()

Returns the name of the global parameter corresponding to acore.

static inline const std::string &Direction()

Returns the name of the global parameter corresponding to direction. The value assigned to this parameter should be either 1 for the forward transfer, or -1 for the backward transfer.