Understanding of the Effects of Ionic Strength on the Bimolecular Rate Constant between Structurally Identified Redox Enzymes and Charged Substrates Using Numerical Simulations on the Basis of the Poisson–Boltzmann Equation

2016 ◽  
Vol 120 (12) ◽  
pp. 3122-3128 ◽  
Author(s):  
Yu Sugimoto ◽  
Yuki Kitazumi ◽  
Osamu Shirai ◽  
Masahiro Yamamoto ◽  
Kenji Kano
Keyword(s):  
Boltzmann Equation ◽  
Ionic Strength ◽  
Numerical Simulations ◽  
Rate Constant ◽  
Redox Enzymes ◽  
Bimolecular Rate Constant ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

scholarly journals Fast solution of the linearized Poisson–Boltzmann equation with nonaffine parametrized boundary conditions using the reduced basis method

2020 ◽  
Vol 23 (1-4) ◽  
Author(s):  
Cleophas Kweyu ◽  
Lihong Feng ◽  
Matthias Stein ◽  
Peter Benner
Keyword(s):  
Boltzmann Equation ◽  
Ionic Strength ◽  
Boundary Conditions ◽  
Reduced Basis Method ◽  
Special Focus ◽  
Reduced Basis ◽  
Order Model ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Basis Method

AbstractThe Poisson–Boltzmann equation (PBE) is a nonlinear elliptic parametrized partial differential equation that arises in biomolecular modeling and is a fundamental tool for structural biology. It is used to calculate electrostatic potentials around an ensemble of fixed charges immersed in an ionic solution. Efficient numerical computation of the PBE yields a high number of degrees of freedom in the resultant algebraic system of equations, ranging from several hundred thousand to millions. Coupled with the fact that in most cases the PBE requires to be solved multiple times for a large number of system configurations, for example, in Brownian dynamics simulations or in the computation of similarity indices for protein interaction analysis, this poses great computational challenges to conventional numerical techniques. To accelerate such onerous computations, we suggest to apply the reduced basis method (RBM) and the (discrete) empirical interpolation method ((D)EIM) to the PBE with a special focus on simulations of complex biomolecular systems, which greatly reduces this computational complexity by constructing a reduced order model (ROM) of typically low dimension. In this study, we employ a simple version of the PBE for proof of concept and discretize the linearized PBE (LPBE) with a centered finite difference scheme. The resultant linear system is solved by the aggregation-based algebraic multigrid (AGMG) method at different samples of ionic strength on a three-dimensional Cartesian grid. The discretized LPBE, which we call the high-fidelity full order model (FOM), yields solution as accurate as other LPBE solvers. We then apply the RBM to the FOM. DEIM is applied to the Dirichlet boundary conditions which are nonaffine in the parameter (ionic strength), to reduce the complexity of the ROM. From the numerical results, we notice that the RBM reduces the model order from $${\mathcal {N}} = 2\times 10^{6}$$ N = 2 × 10 6 to $$N = 6$$ N = 6 at an accuracy of $${\mathcal {O}}(10^{-9})$$ O ( 10 - 9 ) and reduces the runtime by a factor of approximately 7600. DEIM, on the other hand, is also used in the offline-online phase of solving the ROM for different values of parameters which provides a speed-up of 20 for a single iteration of the greedy algorithm.

scholarly journals Monte Carlo methods for linear and non-linear Poisson-Boltzmann equation

2015 ◽  
Vol 48 ◽  
pp. 420-446 ◽  
Author(s):  
Mireille Bossy ◽  
Nicolas Champagnat ◽  
Hélène Leman ◽  
Sylvain Maire ◽  
Laurent Violeau ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Monte Carlo Methods ◽  
Non Linear ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation
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