Biomolecular electrostatics with continuum models: a boundary integral implementation and applications to biosensors

The implicit-solvent model uses continuum electrostatic theory to represent the salt solution around dissolved biomolecules, leading to a coupled system of the Poisson-Boltzmann and Poisson equations. This thesis uses the implicit-solvent model to study solvation, binding and adsorption of proteins. We developed an implicit-solvent model solver that uses the boundary element method (BEM), called PyGBe. BEM numerically solves integral equations along the biomolecule-solvent interface only, therefore, it does not need to discretize the entire domain. PyGBe accelerates the BEM with a treecode algorithm and runs on graphic processing units. We performed extensive verification and validation of the code, comparing it with experimental observations, analytical solutions, and other numerical tools. Our results suggest that a BEM approach is more appropriate than volumetric based methods, like finite-difference or finite-element, for high accuracy calculations. We also discussed the effect of features like solvent-filled cavities and Stern layers in the implicit-solvent model, and realized that they become relevant in binding energy calculations. The application that drove this work was nano-scale biosensors-- devices designed to detect biomolecules. Biosensors are built with a functionalized layer of ligand molecules, to which the target molecule binds when it is detected. With our code, we performed a study of the orientation of proteins near charged surfaces, and investigated the ideal conditions for ligand molecule adsorption. Using immunoglobulin G as a test case, we found out that low salt concentration in the solvent and high positive surface charge density leads to favorable orientations of the ligand molecule for biosensing applications. We also studied the plasmonic response of localized surface plasmon resonance (LSPR) biosensors. LSPR biosensors monitor the plasmon resonance frequency of metallic nanoparticles, which shifts when a target molecule binds to a ligand molecule. Electrostatics is a valid approximation to the LSPR biosensor optical phenomenon in the long-wavelength limit, and BEM was able to reproduce the shift in the plasmon resonance frequency as proteins approach the nanoparticle

High-productivity, high-performance workflow for virus-scale electrostatic simulations with Bempp-Exafmm

Biomolecular electrostatics is key in protein function and the chemical processes affecting it.Implicit-solvent models expressed by the Poisson-Boltzmann (PB) equation can provide insights with less computational power than full atomistic models, making large-system studies -- at the scale of viruses, for example -- accessible to more researchers. This paper presents a high-productivity and high-performance computational workflow combining Exafmm, a fast multipole method (FMM) library, and Bempp, a Galerkin boundary element method (BEM) package. It integrates an easy-to-use Python interface with well-optimized computational kernels that are written in compiled languages. Researchers can run PB simulations interactively via Jupyter notebooks, enabling faster prototyping and analyzing. We provide results that showcase the capability of the software, confirm correctness, and evaluate its performance with problem sizes between 8,000 and 2 million boundary elements. A study comparing two variants of the boundary integral formulation in regards to algebraic conditioning showcases the power of this interactive computing platform to give useful answers with just a few lines of code. As a form of solution verification, mesh refinement studies with a spherical geometry as well as with a real biological structure (5PTI) confirm convergence at the expected $1/N$ rate, for $N$ boundary elements. Performance results include timings, breakdowns, and computational complexity. Exafmm offers evaluation speeds of just a few seconds for tens of millions of points, and $\mathcal{O}(N)$ scaling. This allowed computing the solvation free energy of a Zika virus, represented by 1.6 million atoms and 10 million boundary elements, at 80-min runtime on a single compute node (dual 20-core Intel Xeon Gold 6148). All results in the paper are presented with utmost care for reproducibility.Comment: 14 pages, 6 figure

Grid convergence of PyGBe with protein G B1 D4'

<p>Reproducibility package containing data, running script, plotting script and final plot of a grid-convergence study on protein G B1 D4' near a charged surface. </p><p>The running script invokes the (open-source) bioelectrostatics solver PyGBe with the given input data, computes the extrapolated value of solvation plus surface energy (with Richardson extrapolation), and plots the final result of convergence.</p> <p>This result is part of the following publication:</p> <p>—<strong>"Poisson–Boltzmann model for protein-surface electrostatic interactions and grid-convergence study using the PyGBe code,"</strong> Christopher D. Cooper and Lorena A. Barba, Comput. Phys. Comm. (2016) doi:10.1016/j.cpc.2015.12.019</p> <p>PyGBe solves biomolecular electrostatics problems using an implicit-solvent model (Poisson-Boltzmann) and it uses GPU hardware for fast execution. It is written in Python, PyCUDA and CUDA.</p> <p>More information about the PyGBe code in:</p> <p><em>—"Validation of the PyGBe code for Poisson-Boltzmann equation with boundary element methods,"</em> Christopher Cooper, Lorena A. Barba. figshare.<br>http://dx.doi.org/10.6084/m9.figshare.154331</p> <p>—"A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers," Christopher D. Cooper, Jaydeep P. Bardhan, L. A. Barba. <em>Comput. Phys. Comm.</em>,<strong> 185</strong>(3):720–729 (March 2014). 10.1016/j.cpc.2013.10.028 // Preprint arXiv:1309.4018</p> <p><strong>Acknowledgement:</strong><br>This research is made possible by support from the Office of Naval Research, Applied Computational Analysis Program, N00014-11-1-0356. LAB also acknowledges support from NSF CAREER award OCI-1149784.</p> <p> </p