-Poisson-Nernst-Planck-Theory-Approach-to-the-calculation-of-ion-泊松能斯特-普朗克理論對離子課件

1、Poisson-Nernst-Planck Theory Approach to the calculation of ion transport through protein channelsGuozhen ZhangIon transport through protein channels“We human beings consist to about70% of salt water. This years Nobel Prize in Chemistry rewards two scientists whose discoveries have clarified how sal

2、ts (ions) and water are transported out of and into the cells of the body This is of great importance for our understanding of many diseases of e.g. the kidneys, heart, muscles and nervous system. “(Press release of the Nobel Prize in Chemistry 2019; Doyle, et al., 2019)Theoretical study of ion chan

3、nelsKinetic modelsElectrodiffusion modelsStochastic modelsMolecular DynamicsBrownian Dynamics(Kurnikova, et al., 2019; Coalson and Kurnikova, 2019)Poisson-Nernst-Planck theoryBasic ideaNumerical solutionValidity Application to Gramicidin A channelImprovementSummaryPreconditions of PNP theoryCoarse g

4、rained approximation mobile ions continuous charge distribution surroundings 3D grid with different dielectric constantHigh-friction assumption Brownian motion Smoluchowski equationSteady-state assumption the particle flux is time-independent(Kurnikova, et al., 2019)standard PNP theoryNernst-Planck

5、equation Poisson equationTotal Potential Energy (Kurnikova, et al., 2019)Solving 3D Poisson equation on a cubic grid1D case a. division of grid where the lattice cell extends from (j-1/2)h to (j-1/2)h b. discretization of Poisson equation on the grid 3D case where ij is the 3D generalization of the

6、matrix defined in the above equation, bi (D) are the effective source terms associated with the Dirichlet boundary condition. (Graf, et al., 2000)i,j+1,ki,j-1,ki-1,j,ki+1,j,ki,j,k+1i,j,k-1i, j, kSolving 3D NP Eq. by successive over-relaxationi. Flux ii. Steady-state flux conditioniii. Concentration

7、for central pointWhere , is the number of nearest-neighbor lattice pointsiv. SOR iteration equation;(Crdenas, et al., 2000;Kurnikova, et al., 2019)Calibration of the accuracy of the 3D code(Kurnikova, et al., 2019)Application to Gramicidin A channel(Kurnikova, et al., 2019)(Kurnikova, et al., 2019)(

8、Kurnikova, et al., 2019)Comparison with experiments(Kurnikova, et al., 2019)standard PNP theoryNernst-Planck equation Poisson equationTotal Potential Energy (Kurnikova, et al., 2019)Dielectric-Energy PNP theoryNernst-Planck equationPoisson equationThe free energy of ions of species i in solution (Gr

9、af, et al., 2019; Coalson and Kurnikova, 2019)Performance of DSEPNP(Coalson and Kurnikova, 2019)Potential of Mean Force PNP theoryThe protein structure used in both BD and DSEPNP simulations is taken to be rigid, while in reality the protein structure responds dynamically to an ions presence. Such a

10、 defect usually exhibits very small superlinear currents for voltages up to 200mV for narrow channels.This issue can in principle be solved by a full atomistic simulation which requires complete sampling of the system configuration space. But its formidable for current computing capability.Limited s

11、ampling of the environment configurational space has been introduced to deal with the problem. A combined MD/continuum electrostatics approach is then proposed to obtain GSIP at an average solvent effect level, which is then used in PNP formalism. Such a procedure is termed PMFPNP.(Coalson and Kurni

12、kova, 2019)Results of the PMFPNP calculationsThe overall structure of peptide doesnt change much over the course of MD trajectory, so the GDSE contribution to the overall GSIP doesnt vary much. Small local distortions of pore-lining parts of the peptide (especially carbonyl groups) significantly sta

13、bilize cations as they move through it.PMFPNP theory is able to account for effects that are beyond the reach of primitive PNP theory, namely, saturation of ion current through the channel as the concentration of bathing solutions increases to a sufficiently high value.(Coalson and Kurnikova, 2019)T

14、he saturation mechanism(Coalson and Kurnikova, 2019)Summary3D PNP theory is of conceptual simplicity. It relies on a caricature of the microscopic world in which background media are treated as dielectric slabs and the mobile ions of interest are “smeared out” into a continuous charge distribution.

15、The inherent restriction of the theory is mainly due to its simplicity. It may be unrealistic for treating certain properties of certain ion channels. Also, the mean-field continuum solvent/ion theory of this type is inadequate to accurately describe the underlying dynamics.Despite of these restrict

16、ions, PNP theory will continue to play a useful role in computing and understanding the kinetics of ion permeation through (wider) biological channels.(Coalson and Kurnikova, 2019)ReferencesCrdenas, A. E., R. D. Coalson, and M. G. Kurnikova. 2000. Three-Dimensional Poisson-Nernst-Planck Theory Studi

17、es: Influence of Membrane Electrostatics on Gramicidin A Channel Conductance. Biophys. J. 79 : 80-93.Coalson, R. D., and M. G. Kurnikova. 2019. PoissonNernstPlanck Theory Approach to the Calculation of Current Through Biological Ion Channels. IEEE T Nanobiosci. 4 : 81-93.Doyle, D.A., J. M. Cabral, R

18、. A. Pfuetzner, A. Kuo, J. M. Gulbis, S. L. Cohen, B.T. Chait, and R. MacKinnon. 2019. The structure of the potassium channel: Molecular basis of K+conduction and selectivity. Science. 280 : 69-77. Graf, P., A. Nitzan, M. G. Kurnikova, and R. D. Coalson. 2000. A dynamic lattice Monte Carlo model of ion