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演講者: 洪子倫 教授(Department of Applied Mathematics, Feng Chia University)

講題:3D Poisson-Boltzmann computation of KcsA potassium channel

時間:1/16(二)上午 11:20


摘要:Ion channels are pore-forming trans-membrane proteins that allow ions to enter/leave cell. There are many important cell functions involving ion channel, e.g., establishing and regulating action potential in neurons and myocytes. The average time for an ion passing through ion channel is in the order of ms, which is infeasible for molecular dynamics simulation so far. Continuum model like Poisson-Boltzmann equation (PB) and Poisson-Nernst-Planck (PNP) equations are popular to describe ion channel in equilibrium and non-equilibrium situations. KcsA potassium channel is chosen to be studied here, since it is one of few ion channels having X-ray crystallographic structure. 3D PB and PNP simulations of KcsA channel have been a challenging task, since (1) geometry is complicated especially the narrow filter part requiring high resolution when generating meshes; (2) mathematical models are complicated since there are various versions of modified PB/PNP to choose; (3) physics is complicated such as distributions of dielectric constant and diffusion coefficient, necessity to employ steric effect or not and solvation energy should be included or not. Here, a PDB 3F7Y KcsA structure with filter part replaced by that of PDB 1K4C is used as the structure for simulation. Unlike all other KcsA PDB structures, this synthetic structure guarantees that the channel is open. PB and modified PB equations are first extended to be pseudo-time-dependent with the steady-state solution being our only interest. The numerical framework adopted here to solve these time-dependent equations for electric potential is method of lines (MOL). Governing equation is first semi-discretized in space by 2nd order finite volume method under Cartesian grids with the edge value to cope with interface condition. This semi-discretized system forms a system of ordinary differential algebraic equations (ODAE) that can be further integrated by popular ODAE solvers. Mathematical models simulated here are (I) Classical PB, (II) modified PB with steric effect described by Bikerman model, and (III) modified PB as (II) with solvation energy included in addition. From simulation results, we found potassium ion is unrealistically crowded in the filter for model (I). For model (II), though potassium ion is no more unrealistically crowded in filter due to the inclusion of steric effect, there is no room for water to be in the filter. Finally, model (III) delivers the most reasonable physical result among all three models by obtaining reasonable potassium concentration under steric effect and allowing water residence in the filter at the same time.



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