Numerical Analysis of Nonlinear Boundary Integral Equations Arising in Molecular Biology

Simple item page
dc.contributor.advisorRivière, Béatrice M.en_US
dc.contributor.committeeMemberKnepley, Matthew G.en_US
dc.creatorKlotz, Thomas Sen_US
dc.date.accessioned2019-05-16T16:31:59Zen_US
dc.date.available2019-11-01T05:01:15Zen_US
dc.date.created2019-05en_US
dc.date.issued2019-04-18en_US
dc.date.submittedMay 2019en_US
dc.date.updated2019-05-16T16:32:00Zen_US
dc.description.abstractThe molecular electrostatics problem, which asks for the potential generated by a charged solute suspended in a dielectric solvent, is of great importance in computational biology. Poisson models, which treat the solvent as a dielectric continuum, have inherent inaccuracies which can ruin energy predictions. These inaccuracies are primarily due to the inability of continuum models to capture the structure of solvent molecules in close proximity to the solute. A common approach to overcome these inaccuracies is to adjust the dielectric boundary by changing atomic radii. This adjustment procedure can accurately reproduce the expected solvation free energy, but fails to predict thermodynamic behavior. The Solvation Layer Interface Method (SLIC) replaces the standard dielectric boundary condition in Poisson models with a nonlinear boundary condition which accounts for the small-scale arrangement of solvent molecules close to the dielectric interface. Remarkably, SLIC retains the accuracy of Poisson models and furthermore predicts solvation entropies and heat capacities, while removing the need to adjust atomic radii. In this thesis, we perform foundational numerical analysis for the SLIC model. The first major result is a proof that a solution exists for the nonlinear boundary integral equation arising in the SLIC model. We are able to do this by proving existence for an auxiliary equation whose solutions correspond to the SLIC model's equation. Next, we prove that solutions to the SLIC model are unique for spherical geometries, which are common in biological solutes. Finally, we have experimented with nonlinear solvers for the nonlinear BIE, such as Anderson Acceleration, as well as two discretization techniques, in order to provide scalable numerical methods which can be applied to a variety of problems in drug design and delivery.en_US
dc.embargo.terms2019-11-01en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationKlotz, Thomas S. "Numerical Analysis of Nonlinear Boundary Integral Equations Arising in Molecular Biology." (2019) Diss., Rice University. <a href="https://hdl.handle.net/1911/105338">https://hdl.handle.net/1911/105338</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/105338en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectpotential theoryen_US
dc.subjectnumerical analysisen_US
dc.subjectcomputational biologyen_US
dc.subjectimplicit solvationen_US
dc.subjectboundary integral equationsen_US
dc.titleNumerical Analysis of Nonlinear Boundary Integral Equations Arising in Molecular Biologyen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
KLOTZ-DOCUMENT-2019.pdf
Size:
4.04 MB
Format:
Adobe Portable Document Format
Download
License bundle
Now showing 1 - 2 of 2
No Thumbnail Available
Name:
PROQUEST_LICENSE.txt
Size:
5.84 KB
Format:
Plain Text
Description:
Download
No Thumbnail Available
Name:
LICENSE.txt
Size:
2.61 KB
Format:
Plain Text
Description:
Download
Collections
Rice University Theses and Dissertations