labarba
commented
2 years ago The authors appear to deflect an essential problem for their software: It does not converge as the state-of-art
This reviewer's claim is not backed up by any justification, and contradicts the results presented. Our results show clearly that our solver converges as expected for a boundary element method. Let us quote Reviewer #6:
- "Mesh-refinement studies confirm convergence as 1/N, for N boundary elements…"
As explained in the paper, a convergence rate of 1/N is the same O(h^2) for a mesh spacing of h (second-order convergence). According to Chen et al. 2011, MIBPB converges as h^2.
The reviewer claims that a Fenley and Amaro article (https://doi.org/10.1007/978-3-319-12211-3_3) points to a convergence problem with the APBS solver. That is incorrect. Let us cite from Fenley and Amaro:
- "Results calculated using APBS display a clear convergence behavior with the grid spacing, making it easier to judge what an appropriate grid spacing is for the biological system being studied. DelPhi and PBSA even at large grid spacing provide a reasonable estimate of Epolar(bind) and display only minor fluctuations as a function of the grid spacing.”
What their paper does say is that APBS is not great with large grid spacings, compared to other codes (DelPhi and PBSA). But as the mesh is refined, they all converge to a similar answer (Fig 3.2 of the Fenley and Amaro reference). In this same article, they recommend using a mesh spacing of 0.5 Å or less. Our simulations with APBS use meshes that are finer that this.
Geng and Krasny (https://www.sciencedirect.com/science/article/pii/S0021999113002404) do not point out any convergence issues. Fig 8 of their paper shows the solvation energy obtained with APBS decreasing linearly with mesh spacing, and Table 4 shows the error in this quantity converging linearly.
The fact that Amber parameterizes their GB model with MIBPB rather than APBS is just a choice. MIBPB does claim to be more accurate than APBS for the same mesh size (Chen et al. 2011), and the choice of using MIBPB might be related to that.
Reviewer
#3(Remarks to the Author):In Table 6, why are the computational domains chosen as cubics for all proteins for APBS? It is unfair for APBS in terms of efficiency.
In Table 7, solvation free energy comparison shows very large differences (i.e., up to 1.9%) between MIBPB and the proposed method for some molecules. This is a series problem. The convergence of MIBPB is known in the literature (see for example: Nguyen et al. "Accurate, robust, and reliable calculations of Poisson–Boltzmann binding energies." Journal of computational chemistry 38.13 (2017): 941-948.). As shown in Figure 3 of this reference, the averaged relative absolute error of the electrostatic solvation free energies for all the 153 molecules with mesh size refinements from 1.1 to 0.2 ̊A is under 0.3%. I suggest the authors to carry out the same calculations at Nguyen et al. to find out the averaged relative absolute errors of the present method and plot them against those of MIBPB. Please report the numbers of elements at all resolutions.
As noticed by Fenley and coworkers (Influence of Grid Spacing in Poisson-Boltzmann Equation Binding Energy Estimation, J Chem Theory Comput. 2013 August 13; 9(8): 3677–3685), the calculations of Poisson–Boltzmann binding energies is a challenging task. The authors need to produce reliable Poisson–Boltzmann binding energies as shown by Nguyen et al. (see Figure 6 of the above-mentioned JCC reference) for the challenging task proposed Fenley and coworkers. This test will reveal the level of performance of the present method.
Reviewer
#3(Remarks to the Author After Authors' Reply):[x] The authors appear to deflect an essential problem for their software: It does not converge as the state-of-art schemes do. There is indeed no exact solution for electrostatic solvation free energies for biomolecules. However, pointed out by Fenley and coworkers, grid independence is essential. Fenley and Amaro (https://doi.org/10.1007/978-3-319-12211-3_3) pointed out many years ago that APBS has a convergence problem. The same problem was pointed out by Geng and Krasny. Although APBS is one of the most popular PB solvers in the user community, it is well known in the community of PB and GB developers that APBS is not the most trusted solver. For example, the generalized Born (GB) solver in Amber is calibrated with MIBPB, rather than APBS (see the work of Onufriev). It is a bad idea to compare convergence patterns with APBS.
[x] While APBS has not resolved this problem, researchers have put much effort to improve the convergence of DelPhi, PBFD used in Amber, and MIBPB in the past decade. It is clear for me that judged by Table 2, Bempp has the same convergence problem as APBS does, which has been criticized by Amaro, Fenley and coworkers, and many others in the literature. If the authors do want to admit this problem, they should compare the convergence of Bempp with that of MIBPB for the molecules reported by Nguyen et al. I am quite sure that Bempp is not convergent as DelPhi, PBFD used in Amber, and MIBPB. It is inappropriate for the authors to make unverified statements as PB method developers.
[x] Three tables (i.e., Table 2, Table 6, and Table 7) appear to be designed to mislead. They should be merged into one table in which APBS, DelPhi, PBFD, MIBPB, and Bempp are compared at mesh sizes 0.25, 0.5, and 1.0 to analyse their convergence rates.
[x] It is well known that MIBPB is not as fast as DelPhi and APBS at a given mesh for a given protein. However, it might outperform all other methods in terms of efficiency in the sense that at a given convergence level, it requests the smallest amount of time. It is unfair to compare the execution time of MIBPB in the paper. But the authors should compare efficiency after they have established the convergence characteristics of their method.
[x] Thank the authors for bringing my attention to the work of Geng et al in 2007. Can the authors use the designed solutions in that paper to validate their method?
[x] It is not valid to use different boundary settings and different formulations to skip necessary comparisons as suggested in my earlier comments. All methods should give essentially the same solvation free energy for a given protein with a given interface definition.
[x] The Galerkin formulation is not automatically immune Bempp from the problem of geometric singularity. The geometric singularity from protein solvent excluded surfaces is much worse than Lipschitz as shown by Geng and Krasny in their work. Krasney and Geng have been working on this issue for more than ten years. The authors need to define and construct high-order elements to achieve desirable convergence. I cannot find much-related information about this aspect in this manuscript.
[x] It might be misleading to use the Zika virus (PDB ID 6C08) as an example. This protein complex is highly symmetric. It would be silly to not make use of its symmetry in computations. It would be deceiving if symmetry is used. I would suggest the authors use the HIV viral capsid (1E6J), which is far less symmetric than the Zika viral capsid. Frankly, with the help of GPU and parallel architectures, it is quite easy for any of the above mentioned PB solvers to produce electrostatic analysis of these viruses.