Energy barriers along transition paths

[martinsipka]

Dear Development Team,

I was reviewing Table 2 in your paper and had a few questions regarding the reported energy values:

1. What unit of energy is used? I assume it is kJ/mol, but could you confirm?

2. Why is only the MinMax energy reported? Since energy is always defined up to a constant, a more informative metric would be the difference between the maximum energy and the values at the endpoints. This would provide insight into the predicted energy barriers, making comparisons with literature values more meaningful.

3. Why is a lower minimum energy considered better? In any realistic system, there is a physically meaningful barrier that cannot be arbitrarily lowered, as it determines the reaction rate. Typically, the free energy barrier is reported, while the energy barrier can be slightly higher—typically in the range of 20–100 kJ/mol for alanine dipeptide, depending on the force field. For a fixed force field, reliable methods should yield comparable results. It is important to verify this, as some methods might artificially lower barriers by tunneling through high-energy regions.

Could you clarify the rationale behind this metric and, if possible, provide the energy values at the start and endpoint?

Additionally, I have concerns regarding the reported Chignolin transition path. The 3000 kJ/mol energy barrier seems unusually high—far beyond values reported in the literature. Typically, the free energy barrier is around 25–50 kJ/mol, and while the energy barrier can be slightly higher (due to the absence of stabilizing entropic effects), it should still be in a comparable range. A 3000 kJ/mol barrier suggests a potential issue with the method, possibly indicating that the simulation is passing through an unphysically high-energy region.

Could this be a unit conversion issue? One way to verify this is by comparing the method with an established technique like metadynamics. Several studies have used metadynamics for Chignolin, such as this paper.

For reference, in my own work (paper), I investigated alanine dipeptide and conducted a detailed comparison with eABF, a commonly used method for estimating barriers. Using TorchMD with the AMBER force field (setup similar to yours), I consistently found free energy barriers around 50 kJ/mol.

I’d appreciate your thoughts on these points and any insights you could share regarding the methodology.

[plainerman]

Dear Development Team,

I was reviewing Table 2 in your paper and had a few questions regarding the reported energy values:

Dear Martin, we appreciate your detailed questions and try our best to address them.

1. What unit of energy is used? I assume it is kJ/mol, but could you confirm?

Yes, your assumption is correct. The unit of the reported energies is kJ/mol.

2. Why is only the MinMax energy reported? Since energy is always defined up to a constant, a more informative metric would be the difference between the maximum energy and the values at the endpoints. This would provide insight into the predicted energy barriers, making comparisons with literature values more meaningful.

Our goal in this work was to develop a method that can generate transition paths comparable in quality to those produced by MCMC-based techniques (such as shooting). Since all methods are evaluated on the same underlying potential energy surface, comparing MinMax energies provides a consistent basis for comparison.

We agree that reporting endpoint energies and differences to the transition state would provide additional insight into the barrier heights. For Chignolin, we included such a visualization (see Fig. 4). A similar analysis for alanine dipeptide (ALDP) would indeed be informative and is something we plan to include in follow-up work. We are currently extending our benchmarks to a broader set of systems and metrics, and will keep your suggestion in mind for more comprehensive reporting. (We included concrete values for the energy down below)

3. Why is a lower minimum energy considered better? In any realistic system, there is a physically meaningful barrier that cannot be arbitrarily lowered, as it determines the reaction rate. Typically, the free energy barrier is reported, while the energy barrier can be slightly higher—typically in the range of 20–100 kJ/mol for alanine dipeptide, depending on the force field. For a fixed force field, reliable methods should yield comparable results. It is important to verify this, as some methods might artificially lower barriers by tunneling through high-energy regions.
   Could you clarify the rationale behind this metric

Our rationale for using the MinMax energy was to provide a single scalar summary over the entire ensemble of sampled paths. While we agree that this metric does not fully capture the shape of the energy profile-particularly potential tunneling through high-energy regions-it still offers a coarse indicator of path quality when used consistently across methods.

In the context of transition path sampling, trajectories are ideally distributed according to their likelihood under the path distribution induced by the force field. A method that consistently identifies lower barriers is more likely to have converged to the correct distribution. Nevertheless, we recognize the limitations of MinMax energy as a sole metric. As you suggest, metrics that explicitly consider endpoint energy differences and barrier heights provide more detailed physical insights.

In our ongoing work, we will be including trajectory log-likelihoods, to more accurately evaluate path ensembles while still being able to compute it relatively easy also for larger systems. We appreciate the suggestion and will incorporate it into future benchmarking efforts.

[Could you ...] provide the energy values at the start and endpoint?

Yes, certainly.
For alanine dipeptide, the startpoint has an energy of $-81.47$ kJ/mol and the endpoint $-60.26$ kJ/mol.
For Chignolin, the startpoint has an energy of $-411.38$ kJ/mol and the endpoint $-398.27$ kJ/mol.

Additionally, I have concerns regarding the reported Chignolin transition path. The 3000 kJ/mol energy barrier seems unusually high—far beyond values reported in the literature. Typically, the free energy barrier is around 25–50 kJ/mol, and while the energy barrier can be slightly higher (due to the absence of stabilizing entropic effects), it should still be in a comparable range. A 3000 kJ/mol barrier suggests a potential issue with the method, possibly indicating that the simulation is passing through an unphysically high-energy region.
Could this be a unit conversion issue? One way to verify this is by comparing the method with an established technique like metadynamics. Several studies have used metadynamics for Chignolin, such as this paper.
For reference, in my own work (paper), I investigated alanine dipeptide and conducted a detailed comparison with eABF, a commonly used method for estimating barriers. Using TorchMD with the AMBER force field (setup similar to yours), I consistently found free energy barriers around 50 kJ/mol.

Thank you for raising this concern. We agree that the $3000$ kJ/mol barrier appears unusually high compared to the literature. Our current results are based on transition paths sampled with a fixed transition time $T$, which can force the system to take short trajectories with steep energies. We believe, that this could be one reason for this issue. This means that it is possible that our fixed $T$ is too small relative to the natural timescale of Chignolin’s folding transition, leading to artifacts such as an excessively high barrier. Also, we have opted for a potential without solvent (i.e., vacuum) which could potentially also lead to different results.

However, we do not rule out the possibility of a unit conversion or scaling error. We will re-examine the conversion factors and numerical implementation carefully.

In our ongoing work, we have observed lower energy barriers, suggesting that our current configuration may be converging to a suboptimal solution with our present architecture (it is just a simple MLP). In addition, we used Cartesian coordinates for Chignolin, but we have opted to switch to internal coordinates, which are rotation-invariant. As this has further improved the results for Alanine Dipeptide.

If you have suggestions regarding appropriate values for T based on your experience, we would certainly welcome the feedback.

Again, we would like to thank you for your detailed response. We believe that this will improve our presentation in the future and give us some more literature to look into.