Existence, Uniqueness, and a Comparison of Nonintrusive Methods for the Stochastic Nonlinear Poisson--Boltzmann Equation

Heitzinger, Clemens; Leumuller, M.; Pammer, Gudmund; Rigger, Stefan

doi:10.1137/17m1127375

Cited by 3 publications

(2 citation statements)

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“…The most important feature that is covered by these approaches is the fact that the surface hybridization rate decreases with increasing receptor density at the surface. With this knowledge, topics of recent interest on the whole sensing process include the reduction of the noise levels [11][12][13][14][15][16], which enables lower detection limits, or the determination of waiting times until the biomolecules have been detected. Mathematical models for the average sensor response and their simulation including studies of the effect of device parameters have previously been reported in [17][18][19][20][21][22] for biomolecule detection and also for gas detection [23].…”

Section: Introductionmentioning

confidence: 99%

Brownian-motion based simulation of stochastic reaction–diffusion systems for affinity based sensors

Tulzer¹,

Heitzinger²

2016

Nanotechnology

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In this work, we develop a 2D algorithm for stochastic reaction-diffusion systems describing the binding and unbinding of target molecules at the surfaces of affinity-based sensors. In particular, we simulate the detection of DNA oligomers using silicon-nanowire field-effect biosensors. Since these devices are uniform along the nanowire, two dimensions are sufficient to capture the kinetic effects features. The model combines a stochastic ordinary differential equation for the binding and unbinding of target molecules as well as a diffusion equation for their transport in the liquid. A Brownian-motion based algorithm simulates the diffusion process, which is linked to a stochastic-simulation algorithm for association at and dissociation from the surface. The simulation data show that the shape of the cross section of the sensor yields areas with significantly different target-molecule coverage. Different initial conditions are investigated as well in order to aid rational sensor design. A comparison of the association/hybridization behavior for different receptor densities allows optimization of the functionalization setup depending on the target-molecule density.

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Section: Introductionmentioning

confidence: 99%

Brownian-motion based simulation of stochastic reaction–diffusion systems for affinity based sensors

Tulzer¹,

Heitzinger²

2016

Nanotechnology

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“…This strong motivation drives us to tackle these complex equations [23][24][25]. Here, we consider the model that is described in [26].…”

Section: Introductionmentioning

confidence: 99%

Solving Stochastic Nonlinear Poisson-Boltzmann Equations Using a Collocation Method Based on RBFs

et al. 2023

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In this paper, we present a numerical scheme based on a collocation method to solve stochastic non-linear Poisson–Boltzmann equations (PBE). This equation is a generalized version of the non-linear Poisson–Boltzmann equations arising from a form of biomolecular modeling to the stochastic case. Applying the collocation method based on radial basis functions (RBFs) allows us to deal with the difficulties arising from the complexity of the domain. To indicate the accuracy of the RBF method, we present numerical results for two-dimensional models, we also study the stability of this method numerically. We examine our results with the RBF-reference value and the Chebyshev Spectral Collocation (CSC) method. Furthermore, we discuss finding the appropriate shape parameter to obtain an accurate numerical solution besides greatest stability. We have exerted the Newton–Raphson approach for solving the system of non-linear equations resulting from discretization by the RBF technique.

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An Introduction to Uncertainty Quantification for Kinetic Equations and Related Problems

Pareschi

2021

Trails in Kinetic Theory

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Existence, Uniqueness, and a Comparison of Nonintrusive Methods for the Stochastic Nonlinear Poisson--Boltzmann Equation

Cited by 3 publications

References 25 publications

Brownian-motion based simulation of stochastic reaction–diffusion systems for affinity based sensors

Brownian-motion based simulation of stochastic reaction–diffusion systems for affinity based sensors

Solving Stochastic Nonlinear Poisson-Boltzmann Equations Using a Collocation Method Based on RBFs

An Introduction to Uncertainty Quantification for Kinetic Equations and Related Problems

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