Spring Shooting in OpenPathSampling

Authors: Sander Roet

This module implements the spring shooting method in OpenPathSampling

Purpose of Module

Transition path sampling is most efficient when paths are generated from the top of the free energy barrier. However, complex (biomolecular) activated processes, such as nucleation or protein binding/unbinding, can have asymmetric and peaked barriers. Using uniform selection on these type of processes will not be efficient, as it, on average, results in selected points that are not on the top of the barrier. Paths generated from these points have a low acceptance probability and accepted transition paths decorrelate slowly, resulting in a low overall efficiency. Spring shooting was developed to increase the efficiency of path sampling of these types of barriers, without any prior knowledge of the barrier shape. The spring shooting algorithm uses a shooting point selector that is biased with a spring potential. This bias pulls the selection of points towards the transition state at the top of the barrier. The paths that are generated from points selected by this biased selector therefore have an increased acceptance probability and decorrelation between accepted transition paths is also increased. This results in a higher overall efficiency. The spring shooting algorithm is described by Brotzakis and Bolhuis (http://dx.doi.org/10.1063/1.4965882).

In summary, the spring shooting selection algorithm is a selector for the one-way shooting method for transition path sampling, which uses a bias. This bias is of the shape \min[1, e^{s\kappa\Delta\tau}]. Where s = -1 for forward shooting and s = 1 for backward shooting, \kappa is the given spring constant and \Delta\tau = \tau^{\prime} - \tau is the number of shifted frames of the new shooting point \tau^{\prime} compared to the previous accepted shooting point \tau. The choice of \tau^{\prime} is limited to the interval [-\Delta\tau_{max}, \Delta\tau_{max}]. The shooting move is rejected if a \tau^{\prime} is selected that is outside of the current path and is accepted if the trajectory satisfies the path ensemble.

The main difference of this module compared to the paper is that instead of using a rejection algorithm to sample from the correct distribution, the correct distribution is sampled directly.

The implementation introduces the following new classes:

  • SpringShootingSelector inherits from ShootingPointSelector and implements the shooting point selection, using a bias of the shape \min[1, e^{s\kappa\Delta\tau}]. At initialization it also takes an initial_guess as the initial reference point. This will default to floor(len(trajectory)/2). To correctly keep track of the history the selector has to be the same instance for the forward and backward mover. The pick function has to be called with a direction in order to be able to use the correct value for s. The selector then draws a random number in the range [0,1), multiplies it with the sum of the biases. It the sums the biases from -\Delta\tau_{max} to \Delta\tau_{max} and returns the index when this sum is bigger than the random number. The restart_from_step function makes it possible to restart the selector at a specific step. It takes an MCStep and reconstructs the correct history from the MoveDetails.
  • SpringMover inherits from EngineMover and is the parent class for the ForwardSpringMover and BackwardSpringMover classes. It calls the selector.pick function with self.direction to get the correct shooting point. It also build adds the needed MoveDetails in order to be able to restart the selector. If an invalid snapshot has been chosen it will not run dynamics but will build a Sample with an acceptance probability of 0.0.
  • SpringShootingMover inherits from RandomChoiceMover and behaves similar, except it takes the extra arguments: delta_max, k_spring and initial_guess. These are then used to make the SpringShootingSelector and this selector is given to both the forward and backward mover.
  • SpringShootingStrategy inherits from SingleEnsembleMoveStrategy and will make the SpringShootingMover for every ensemble, with the given values of delta_max, k_spring and initial_guess.
  • SpringShootingMoveScheme inherits from MoveScheme and it will use the SpringShootingStrategy to build all the necessary movers for the given network, with the given values of delta_max, k_spring and initial_guess. Also the functions to_dict and from_dict have been adapted to save and load with all the data

Background Information

This module builds on OpenPathSampling, a Python package for path sampling simulations. To learn more about OpenPathSampling, you might be interested in reading:

Testing

Tests in OpenPathSampling use the nose package.

The tests for this module can be run by downloading its source code (see the Source Code section below), installing its requirements and installing it by running python setup.py install from the root directory of the package. Test this module by running the command nosetests from the root directory of the repository.

Examples

Source Code

The source code for this module can be found in: https://gitlab.e-cam2020.eu/sroet/spring_shooting/tree/master.