Communications in Information and Systems

Volume 22 (2022)

Number 2

Computing electrostatic binding energy with the TABI Poisson–Boltzmann solver

Pages: 247 – 273



Leighton Wilson (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)

Jingzhen Hu (Department of Mathematics, Duke University, Durham, North Carolina, U.S.A.)

Jiahui Chen (Department of Mathematics, Michigan State University, East Lansing, Mich., U.S.A.)

Robert Krasny (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)

Weihua Geng (Department of Mathematics, Southern Methodist University, Dallas, Texas, U.S.A.)


Computations of the electrostatic binding energy $\Delta \Delta G_{\operatorname{elec}}$ are presented for 51 solvated biomolecular complexes using the treecode-accelerated boundary integral (TABI) Poisson–Boltzmann solver. TABI computes the electric potential on the triangulated molecular surface of a complex and its monomers, and further processing yields the solvation free energy $\Delta G_{\operatorname{solv}}$ needed to compute $\Delta \Delta G_{\operatorname{elec}}$. The accuracy of the TABI results was verified using the high-order finite-difference Matched Interface and Boundary (MIB) method as the reference. Among two codes used here for surface triangulation, MSMS and NanoShaper, the latter is found to be more accurate, efficient, and robust. It is shown that the accuracy of the computed $\Delta \Delta G_{\operatorname{elec}}$ using TABI can be efficiently improved by extrapolating low triangulation density results to the high density limit. The calculations needed to compute $\Delta \Delta G_{\operatorname{elec}}$ are susceptible to loss of precision due to cancellation of digits and this emphasizes the need for relatively higher accuracy in computing $\Delta G_{\operatorname{solv}}$.

Leighton Wilson was supported by a National Defense Science and Engineering Graduate Fellowship.

Jingzhen Hu was partially supported by the SMU Hamilton Scholarship.

This work was supported in part by National Science Foundation grants DMS-1418957, DMS-1418966, DMS-1819094, DMS-1819193. Computing services were provided by the Center for Scientific Computation at Southern Methodist University and Advanced Research Computing at the University of Michigan.

Received 17 September 2021

Published 19 May 2022