2,144 research outputs found
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 metal electrode with
the 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, of
non-linear conduction in the drain characteristics with gate voltage . We
find that varies with the zero-bias conductance for a gate
bias as a power-law: with an exponent .
The origin of this power-law relationship is tentatively suggested as a result
of power-law variation of effective barrier height with , 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
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