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Salt Contribution to RNA Tertiary Structure Folding Stability
"... to R po nsiv an re f om em uctu siv dimensional (3D) structure (1,2,4). An RNA sequence the free energy for specific tertiary contacts. These different tures, the ion effect can be particularly complex (28–38). of ions (8,34,35,62) in the vicinity of RNAs, i.e., the potena tethered DNA duplex syste ..."
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Cited by 5 (2 self)
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to R po nsiv an re f om em uctu siv dimensional (3D) structure (1,2,4). An RNA sequence the free energy for specific tertiary contacts. These different tures, the ion effect can be particularly complex (28–38). of ions (8,34,35,62) in the vicinity of RNAs, i.e., the potena tethered DNA duplex system (62), it was found that the*Correspondence:
Mathematical and Numerical Aspects of the Adaptive Fast Multipole PoissonBoltzmann Solver
"... Abstract. This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole PoissonBoltzmann (AFMPB) solver. We introduce and discuss the following components in order: the PoissonBoltzmann model, boundary integral equation reformulation, surfa ..."
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Abstract. This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole PoissonBoltzmann (AFMPB) solver. We introduce and discuss the following components in order: the PoissonBoltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to largescale longtime molecular dynamics simulations. The potential of the solver is demonstrated with preliminary numerical results.
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, 2015
"... ava i lable at www.sciencedirect.com journal homepage: www.europeanurology.com Article info Article history: ..."
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ava i lable at www.sciencedirect.com journal homepage: www.europeanurology.com Article info Article history:
An Iterative Discontinuous Galerkin Method for Solving the Nonlinear Poisson Boltzmann Equation
, 2014
"... Abstract. An iterative discontinuous Galerkin (DG) method is proposed to solve the nonlinear Poisson Boltzmann (PB) equation. We first identify a function space in which the solution of the nonlinear PB equation is iteratively approximated through a series of linear PB equations, while an appropriat ..."
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Abstract. An iterative discontinuous Galerkin (DG) method is proposed to solve the nonlinear Poisson Boltzmann (PB) equation. We first identify a function space in which the solution of the nonlinear PB equation is iteratively approximated through a series of linear PB equations, while an appropriate initial guess and a suitable iterative parameter are selected so that the solutions of linear PB equations are monotone within the identified solution space. For the spatial discretization we apply the direct discontinuous Galerkin method to those linear PB equations. More precisely, we use one initial guess when the Debye parameter λ=O(1), and a special initial guess for λ≪1 to ensure convergence. The iterative parameter is carefully chosen to guarantee the existence, uniqueness, and convergence of the iteration. In particular, iteration steps can be reduced for a variable iterative parameter. Both one and twodimensional numerical results are carried out to demonstrate both accuracy and capacity of the iterative DG method for both cases of λ=O(1) and λ ≪ 1. The (m+1)th order of accuracy for L2 and mth order of accuracy for H1 for Pm elements are numerically obtained.
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"... tiga an me com (22–33). For tertiary structure folding, however, our underDNA helices suggested the existence of a helixhelix attrac(59) and the PB theory (60–65)—have been used successsurface. The PB theory ignores such potentially important (TBI) model (66,67) (see the Supporting Materialfor a ..."
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tiga an me com (22–33). For tertiary structure folding, however, our underDNA helices suggested the existence of a helixhelix attrac(59) and the PB theory (60–65)—have been used successsurface. The PB theory ignores such potentially important (TBI) model (66,67) (see the Supporting Materialfor a