NESSie.jl

Nonlocal Electrostatics in Structured Solvents

Motivation

Electrostatic interactions are a major contributor to protein-protein and protein-ligand interactions. In contrast to other molecular interaction components, they can be significant over medium to long distances and are thus crucial for molecular visibility. One major challenge in this context is the treatment of the solvent the molecules are immersed in, e.g., water in a biological context. Strong simplifications of the structure of such polarizable and highly structured solvents are commonplace to achieve the required computational efficiency, but invariably lead to inaccuracies.

Usage example

The following Julia code shows how to compute and print the nonlocal reaction field energy of a single Na+ ion (modeled as a spherically-symmetric, vacuum-filled system) in water:

using NESSieusing NESSie.BEMusing NESSie.Format: readoff, readpqr# I. Create modelmodel           = readoff("data/born/na.off")model.charges   = readpqr("data/born/na.pqr")model.params.εΩ = 1   # dielectric constant for vacuum modelmodel.params.εΣ = 78  # dielectric constant for water# II. Apply nonlocal solverbem = solve(NonlocalES, model)# III. Apply postprocessorval = rfenergy(bem)println("Reaction field energy: $val kJ/mol")

More examples are available in the docs/examples/ directory.

Citing

If you use NESSie.jl in your research, please cite the following publications:

Kemmer, T, Rjasanow, S., Hildebrandt, A (2018). NESSie. jl - Efficient and Intuitive Finite Element and Boundary Element Methods for Nonlocal Protein Electrostatics in the Julia Language. Journal of Computational Science 28, 193-203. DOI: 10.1016/j.jocs.2018.08.008

Kemmer, T (2021). Space-efficient and exact system representations for the nonlocal protein electrostatics problem. Ph. D. thesis, Johannes Gutenberg University Mainz. Mainz, Germany. DOI: 10.25358/openscience-5689

With BibTeX, you can use the following entries:

@article{nessie-2018,
    author = {Kemmer, Thomas and Rjasanow, Sergej and Hildebrandt, Andreas},
    title = {{NESSie.jl -- Efficient and Intuitive Finite Element and Boundary Element Methods for Nonlocal Protein Electrostatics in the Julia Language}},
    year = {2018},
    journal = {Journal of Computational Science},
    volume = {28},
    pages = {193-203},
    doi = {10.1016/j.jocs.2018.08.008}
}
@phdthesis{cunessie-2021,
    author = {Kemmer, Thomas},
    title = {{Space-efficient and exact system representations for the nonlocal protein electrostatics problem}},
    year = {2021},
    school = {Johannes Gutenberg University Mainz},
    address = {Mainz, Germany},
    doi = {10.25358/openscience-5689}
}

References

• [Åqv90] J. Åqvist, Ion-water interaction potentials derived from free energy pertubation simulations. J. Phys. Chem. 94: 8021, 1990. DOI: 10.1021/j100384a009

• [Hil05] A. Hildebrandt, Biomolecules in a structured solvent: A novel formulation of nonlocal electrostatics and its numerical solution. PhD thesis. Saarbrücken, Germany. Saarland University, 2005. DOI: 10.22028/D291-25912

• [Kea86] P. Keast, Moderate degree tetrahedral quadrature formulas. CMAME 55: 339-348, 1986. DOI: 10.1016/0045-7825(86)90059-9

• [Rad48] J. Radon, Zur mechanischen Kubatur (in German). Monatsh. für Math. 52(4): 286-300, 1948. DOI: 10.1007/BF01525334

• [Rja90] S. Rjasanow, Vorkonditionierte iterative Auflösung von Randelementgleichungen für die Dirichlet-Aufgabe (in German). Wissenschaftliche Schriftreihe der Technischen Universität Karl-Marx-Stadt, 7/1990.

• [Ste03] O. Steinbach, Numerische Näherungsverfahren für elliptische Randwertprobleme - Finite Elemente und Randelemente (in German). Advances in Numerical Matheamtics. Teubner Verlag/GWV Fachverlage GmbH, Wiesbaden, 2003. DOI: 10.1007/978-3-322-80054-1

• [Xie16] D. Xie, H. W. Volkmer, and J. Ying, Analytical solutions of nonlocal Poisson dielectric models with multiple point charges inside a dielectric sphere. Physical Review E 93(4): 043304, 2016. DOI: 10.1103/PhysRevE.93.043304