Test System Repository

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One of the biggest problems in careful comparisons and validations of methods is the difficulty of trying to agree on a single number for the free energy. If one is not sure of the value of the free energy, fine comparisons of methods are very difficult. Additionally, different programs with different bookkeeping, or parameters that have been rounded in some way can have legitimate small differences in the free energies, obscuring differences in the methods.

Ideally test systems should have zero free energy, though this is not generally possible With a zero transformation, then it is necessary to partially specify the path, so that particularly clever methods do not manage to solve the problem in ways that would not be valid in general simulations. Because of this, the zero transformations here are defined with the endpoints and one midpoint along the transformation. This ensures that a large transformation is performed, but allows these systems to be used to improve free energy pathways as well.

Problem 1) Is the method at all valid for molecular systems?

• System: Simplest molecular free energy system = UA methane in TIP3P water.

• Notes: There are no bond, angle or torsions terms, or solute/solvent charge: this is the simplest system that can be truly defined as realistic.

Problem 2) Can the method handle water rearrangement around charges?

• System: Charged dipole on two LJ spheres tethered together. Currently testing +2/-2 charges, with 5 angstrom separation. The intermediate state is neutral.

• Notes: This setup allows avoidance of computing free energies of ions directly, which is still not handled completely correctly in many codes.

Problem 3) Can the free energy method handle multiple atomic sites efficiently?

• System: Anthracene solvation in water in TIP3P water

• Notes: No ligand degrees of freedom to complicate the analysis. Null transforms are possible, but these have ended up particularly difficult to implement in different simulation packages. We are deciding whether this could also perform the anthracene->benzene->anthracene transformation.

Future problems to tackle:

Problem 4) Can the method handle long time scale barriers along torsional degrees of freedom?

• Potential future system: 1-octanol -> ethane -> 1-octanol in TIP3P water.

• Notes: Topologically, the system would be set up as HO-(CH2)14-OH, with the middle two carbons remaining coupled to the environment for the entire transformation. The h-bonds between alcohols and water might hopefully slow down the torsional sampling).

Problem 5) Can the method handle complications caused by putting all together in complex systems?

• Potential Future System: Complicated substituted aromatic like Imatinib, with three substituted positions, with the transformation to cycle the substituents to different positions along the aromatic with benzene as the intermediate.

Estimators of the uncertainty should be validated against uncertainty generated directly from runs from independent configurations (100), and should include the computation of the correlation time of the observable used to calculate the uncorrelated samples used in the free energies (such as the potential energy differences or dH/dL).

1. Input topology and parameter files in a number of different formats:

• GROMACS

• AMBER

• DESMOND

We are interested in getting validated comparisons with the following systems

• GROMOS

• CHARMM

• NAMD

• DL_POLY

• TINKER

• LAMMPS

In each case, we have posted 100 starting configurations for each system, specifying initial box size and positions. We also list the exact energies of the starting configurations to make it easy to verify input files for additional programs.

4) Results from a number of different methods (TI, BAR, WHAM, Wang-Landau recursion).

• TI

• BAR, EXP, MBAR:

• Wang-Landau:

• Transition Matrix approaches

5) Optimization of variables

5a) Equilibrium methods

• For all: Spacing of states, pathway

• • TI: numerical integration methods

• • BAR: no others

• • MBAR:no others

• • DCMBAR: size of blocks, approximations in the dimension reduction of control variates.

5b) Equilibrium-at-limit methods

• For all : Spacing of states, pathway, MC or Gibbs sampling step type used

• • Wang-Landau: The degree of flatness for decrementing the weight step, the magnitude of the weight step

• • Transition state approaches: The transition kernel used