Work/Precision Tradeoffs in Continuum Models of Biomolecular Electrostatics

The structure and function of biological molecules are strongly influenced by the water and dissolved ions that surround them. This aqueous solution (solvent) exerts significant electrostatic forces in response to the biomolecule's ubiquitous atomic charges and polar chemical groups. In this work, we investigate a simple approach to numerical calculation of this model using boundary-integral equation (BIE) methods and boundary-element methods (BEM). Traditional BEM discretizes the protein--solvent boundary into a set of boundary elements, or panels, and the approximate solution is defined as a weighted combination of basis functions with compact support. The resulting BEM matrix then requires integrating singular or near singular functions, which can be slow and challenging to compute. Here we investigate the accuracy and convergence of a simpler representation, namely modeling the unknown surface charge distribution as a set of discrete point charges on the surface. We find that at low resolution, point-based BEM is more accurate than panel-based methods, due to the fact that the protein surface is sampled directly, and can be of significant value for numerous important calculations that require only moderate accuracy, such as the preliminary stages of rational drug design and protein engineering.Comment: 10 pages, 8 figures, in Proceedings of ASME 2015 International Mechanical Engineering Congress & Exposition, 201

Modeling Charge-Sign Asymmetric Solvation Free Energies With Nonlinear Boundary Conditions

We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory but replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [J. Phys. Chem. B, v. 112:2408, 2008]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.Comment: 7 pages, 2 figures, accepted to Journal of Chemical Physic

Multiscale models and approximation algorithms for protein electrostatics

Electrostatic forces play many important roles in molecular biology, but are hard to model due to the complicated interactions between biomolecules and the surrounding solvent, a fluid composed of water and dissolved ions. Continuum model have been surprisingly successful for simple biological questions, but fail for important problems such as understanding the effects of protein mutations. In this paper we highlight the advantages of boundary-integral methods for these problems, and our use of boundary integrals to design and test more accurate theories. Examples include a multiscale model based on nonlocal continuum theory, and a nonlinear boundary condition that captures atomic-scale effects at biomolecular surfaces.Comment: 12 pages, 6 figure

Effects of Phase Fluctuations on Phase Sensitivity and Visibility of Path-Entangled Photon Fock States

We study effects of phase fluctuations on phase sensitivity and visibility of a class of robust path-entangled photon Fock states (known as mm' states) as compared to the maximally path-entangled N00N states in presence of realistic phase fluctuations such as turbulence noise. Our results demonstrate that the mm' states, which are more robust than the N00N state against photon loss, perform equally well when subject to such fluctuations. We show that the phase sensitivity with parity detection for both of the above states saturates the quantum Cramer-Rao bound in presence of such noise, suggesting that the parity detection presents an optimal detection strategy.Comment: 7 pages, 5 figure

A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers

The continuum theory applied to bimolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known APBS finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2%, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the APBS solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe code is in the order of 1-2% error, when running on one GPU card (NVIDIA Tesla C2075), compared with APBS running on six Intel Xeon CPU cores. PyGBe achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using GPUs via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license.Comment: 12 pages, 11 figure

Generalizing The Mean Spherical Approximation as a Multiscale, Nonlinear Boundary Condition at the Solute--Solvent Interface

In this paper we extend the familiar continuum electrostatic model with a perturbation to the usual macroscopic boundary condition. The perturbation is based on the mean spherical approximation (MSA), to derive a multiscale hydration-shell boundary condition (HSBC). We show that the HSBC/MSA model reproduces MSA predictions for Born ions in a variety of polar solvents, including both protic and aprotic solvents. Importantly, the HSBC/MSA model predicts not only solvation free energies accurately but also solvation entropies, which standard continuum electrostatic models fail to predict. The HSBC/MSA model depends only on the normal electric field at the dielectric boundary, similar to our recent development of an HSBC model for charge-sign hydration asymmetry, and the reformulation of the MSA as a boundary condition enables its straightforward application to complex molecules such as proteins.Comment: 14 pages, 2 figure

Analytical Nonlocal Electrostatics Using Eigenfunction Expansions of Boundary-Integral Operators

In this paper, we present an analytical solution to nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for analytical calculations in separable geometries, we rederive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion layer and then a dilute electrolyte (modeled with the linearized Poisson--Boltzmann equation). Our main result, however, is an analytical method for calculating the reaction potential in a protein embedded in a nonlocal-dielectric solvent, the Lorentz model studied by Dogonadze and Kornyshev. The analytical method enables biophysicists to study the new nonlocal theory in a simple, computationally fast way; an open-source MATLAB implementation is included as supplemental information.Comment: 19 pages, 7 figure

Efficient Evaluation of Ellipsoidal Harmonics for Potential Modeling

Ellipsoidal harmonics are a useful generalization of spherical harmonics but present additional numerical challenges. One such challenge is in computing ellipsoidal normalization constants which require approximating a singular integral. In this paper, we present results for approximating normalization constants using a well-known decomposition and applying tanh-sinh quadrature to the resulting integrals. Tanh-sinh has been shown to be an effective quadrature scheme for a certain subset of singular integrands. To support our numerical results, we prove that the decomposed integrands lie in the space of functions where tanh-sinh is optimal and compare our results to a variety of similar change-of-variable quadratures

Dynamical decoupling with tailored waveplates for long distance communication using polarization qubits

We address the issue of dephasing effects in flying polarization qubits propagating through optical fiber by using the method of dynamical decoupling. The control pulses are implemented with half waveplates suitably placed along the realistic lengths of the single mode optical fiber. The effects of the finite widths of the waveplates on the polarization rotation are modeled using tailored refractive index profiles inside the waveplates. We show that dynamical decoupling is effective in preserving the input qubit state with the fidelity close to one when the polarization qubit is subject to the random birefringent noise in the fiber, as well the rotational imperfections (flip-angle errors) due to the finite width of the waveplates.Comment: 8 pages, 5 figure

Gap states controlled transmission through 1D Metal-Nanotube junction

Understanding the nature of metal/1D-semiconductor contacts such as metal/carbon nanotubes is a fundamental scientific and technological challenge for realizing high performance transistors\cite{Francois,Franklin}. A Schottky Barrier(SB) is usually formed at the interface of the $2D$ metal electrode with the $1D$ semiconducting carbon nanotube. As yet, experimental\cite{Appenzeller,Chen, Heinze, Derycke} and numerical \cite{Leonard, Jimenez} studies have generally failed\cite{Svensson} to come up with any functional relationship among the relevant variables affecting carrier transport across the SB owing to their unique geometries and complicated electrostatics. Here, we show that localized states called the metal induced gap states (MIGS)\cite{Tersoff,Leonard} already present in the barrier determines the transistor drain characteristics. These states seem to have little or no influence near the ON-state of the transistor but starts to affect the drain characteristics strongly as the OFF-state is approached. The role of MIGS is characterized by tracking the dynamics of the onset bias, $V_o$ of non-linear conduction in the drain characteristics with gate voltage $V_g$. We find that $V_o$ varies with the zero-bias conductance $G_o(V_g)$ for a gate bias $V_g$ as a power-law: $V_o$ $\sim$ ${G_o(V_g)}^x$ with an exponent $x$. The origin of this power-law relationship is tentatively suggested as a result of power-law variation of effective barrier height with $V_g$, corroborated by previous theoretical and experimental results\cite{Appenzeller}. The influence of MIGS states on transport is further verified independently by temperature dependent measurements. The unexpected scaling behavior seem to be very generic for metal/CNT contact providing an experimental forecast for designing state of the art CNT devices