Development and Application of Numerical Methods in Biomolecular Solvation

This work addresses the development of fast summation methods for long range particle interactions and their application to problems in biomolecular solvation, which describes the interaction of proteins or other biomolecules with their solvent environment. At the core of this work are treecodes, tree-based fast summation methods which, for N particles, reduce the cost of computing particle interactions from O(N^2) to O(N log N). Background on fast summation methods and treecodes in particular, as well as several treecode improvements developed in the early stages of this work, are presented. Building on treecodes, dual tree traversal (DTT) methods are another class of tree-based fast summation methods which reduce the cost of computing particle interactions for N particles to O(N). The primary result of this work is the development of an O(N) dual tree traversal fast summation method based on barycentric Lagrange polynomial interpolation (BLDTT). This method is implemented to run across multiple GPU compute nodes in the software package BaryTree. Across different problem sizes, particle distributions, geometries, and interaction kernels, the BLDTT shows consistently better performance than the previously developed barycentric Lagrange treecode (BLTC). The first major biomolecular solvation application of fast summation methods presented is to the Poisson–Boltzmann implicit solvent model, and in particular, the treecode-accelerated boundary integral Poisson–Boltzmann solver (TABI-PB). The work on TABI-PB consists of three primary projects and an application. The first project investigates the impact of various biomolecular surface meshing codes on TABI-PB, and integrated the NanoShaper software into the package, resulting in significantly better performance. Second, a node patch method for discretizing the system of integral equations is introduced to replace the previous centroid collocation scheme, resulting in faster convergence of solvation energies. Third, a new version of TABI-PB with GPU acceleration based on the BLDTT is developed, resulting in even more scalability. An application investigating the binding of biomolecular complexes is undertaken using the previous Taylor treecode-based version of TABI-PB. In addition to these projects, work performed over the course of this thesis integrated TABI-PB into the popular Adaptive Poisson–Boltzmann Solver (APBS) developed at Pacific Northwest National Laboratory. The second major application of fast summation methods is to the 3D reference interaction site model (3D-RISM), a statistical-mechanics based continuum solvation model. This work applies cluster-particle Taylor expansion treecodes to treat long-range asymptotic Coulomb-like potentials in 3D-RISM, and results in significant speedups and improved scalability to the 3D-RISM package implemented in AmberTools. Additionally, preliminary work on specialized GPU-accelerated treecodes based on BaryTree for 3D-RISM long-range asymptotic functions is presented.PHDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168120/1/lwwilson_1.pd

Feeding beets and potatoes for butter

The farmers of Iowa are growing sugar beets to learn the adaptation of the soils and climates of the state to sugar production. The feeding value of the beet entire without the sugar extracted, is a matter of interest to them. The crop of potatoes in 1891 was large, and where they were unsalable owing to remoteness from markets, or for other causes, it became interesting to ascertain feeding values for dairy products. In conformity with inquiries concerning these subjects, this station fed four cows during three months, beginning December 1st, 1891, and ending February 29, 1892

Improvements to the APBS biomolecular solvation software suite

The Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve the equations of continuum electrostatics for large biomolecular assemblages that has provided impact in the study of a broad range of chemical, biological, and biomedical applications. APBS addresses three key technology challenges for understanding solvation and electrostatics in biomedical applications: accurate and efficient models for biomolecular solvation and electrostatics, robust and scalable software for applying those theories to biomolecular systems, and mechanisms for sharing and analyzing biomolecular electrostatics data in the scientific community. To address new research applications and advancing computational capabilities, we have continually updated APBS and its suite of accompanying software since its release in 2001. In this manuscript, we discuss the models and capabilities that have recently been implemented within the APBS software package including: a Poisson-Boltzmann analytical and a semi-analytical solver, an optimized boundary element solver, a geometry-based geometric flow solvation model, a graph theory based algorithm for determining p$K_a$ values, and an improved web-based visualization tool for viewing electrostatics

About the p-mode frequency shifts in HD 49933

We study the frequency dependence of the frequency shifts of the low-degree p modes measured in the F5V star HD 49933, by analyzing the second run of observations collected by the CoRoT satellite. The 137-day light curve is divided into two subseries corresponding to periods of low and high stellar activity. The activity-frequency relationship is obtained independently from the analysis of the mode frequencies extracted by both a local and a global peak-fitting analyses, and from a cross-correlation technique in the frequency range between 1450 microHz and 2500 microHz. The three methods return consistent results. We show that the frequency shifts measured in HD 49933 present a frequency dependence with a clear increase with frequency, reaching a maximal shift of about 2 microHz around 2100 microHz. Similar variations are obtained between the l=0 and l=1 modes. At higher frequencies, the frequency shifts show indications of a downturn followed by an upturn, consistent between the l=0 and 1 modes. We show that the frequency variation of the p-mode frequency shifts of the solar-like oscillating star HD 49933 has a comparable shape to the one observed in the Sun, which is understood to arise from changes in the outer layers due to its magnetic activity.Comment: 5 pages, 3 figures, 1 table, Accepted for publication in A\&

Does the Babcock--Leighton Mechanism Operate on the Sun?

The contribution of the Babcock-Leighton mechanism to the generation of the Sun's poloidal magnetic field is estimated from sunspot data for three solar cycles. Comparison of the derived quantities with the A-index of the large-scale magnetic field suggests a positive answer to the question posed in the title of this paper.Comment: 5 pages, 2 figures, to apper in Astronomy Letter

Exploring the challenges of accessing medication for patients with cystic fibrosis

Reducing treatment burden in cystic fibrosis (CF) is the top research priority for patients and clinicians. Difficulty accessing medication is one aspect of treatment burden. We investigated this with an online survey available globally for patients with CF and healthcare professionals. Almost three quarters of patients with CF in our survey report difficulty getting repeat prescriptions on time, and most community pharmacists experience interrupted supplies of CF-specific medications. These barriers affect emotional and physical health of people with CF. Two-thirds of people with CF would like to get all their CF medication from one place, their CF centre

Mediation in the Law Curriculum

Cited by Lord Neuberger in ‘Educating Future Mediators’ at the 4th Civil Mediation Council National Conference, May 201