最新文档-Poisson-Nernst-Planck-Theory-Approach-to-the-

Poisson-Nernst-PlanckTheoryApproachtothecalculationofiontransportthroughproteinchannelsGuozhenZhangIontransportthroughproteinchannels“Wehumanbeingsconsisttoabout70%ofsaltwater.Thisyear'sNobelPrizeinChemistryrewardstwoscientistswhosediscoverieshaveclarifiedhowsalts(ions)andwateraretransportedoutofandintothecellsofthebody…Thisisofgreatimportanceforourunderstandingofmanydiseasesofe.g.thekidneys,heart,musclesandnervoussystem.“(PressreleaseoftheNobelPrizeinChemistry2019;Doyle,etal.,2019)Theoreticalstudyofionchannels•Kineticmodels•Electrodiffusionmodels•Stochasticmodels•MolecularDynamics•BrownianDynamics(Kurnikova,etal.,2019;CoalsonandKurnikova,2019)Poisson-Nernst-Plancktheory•Basicidea•Numericalsolution•Validity•ApplicationtoGramicidinAchannel•Improvement•SummaryPreconditionsofPNPtheory•Coarsegrainedapproximationmobileions—continuouschargedistributionsurroundings—3Dgridwithdifferentdielectricconstant•High-frictionassumptionBrownianmotion—Smoluchowskiequation•Steady-stateassumptiontheparticlefluxistime-independent(Kurnikova,etal.,2019)standardPNPtheory•Nernst-Planckequation•Poissonequation•TotalPotentialEnergyiii0[()()()];1,...,cRcRVRiNfii1(()())4[()()]NiRRRqcRii()()()VRURqR(Kurnikova,etal.,2019)Solving3DPoissonequationonacubicgrid•1Dcasea.divisionofgridwherethelatticecellextendsfrom(j-1/2)×hto(j-1/2)×hb.discretizationofPoissonequationonthegrid•3Dcasewhere∠ijisthe3Dgeneralizationofthematrixdefinedintheaboveequation,bi(D)aretheeffectivesourcetermsassociatedwiththeDirichletboundarycondition.(Graf,etal.,2000)i,j+1,ki,j-1,ki-1,j,ki+1,j,ki,j,k+1i,j,k-1i,j,kx1ijx1ijy1jjy1jjz1kjz1kjSolving3DNPEq.bysuccessiveover-relaxation]2/))(([]2/)[(,,1,,1,,1,,1x1jijijijijijijijiiccVVccaDDji.Fluxx1ijii.Steady-statefluxcondition001111x1x1zkzkyjyjiijjjjjjjiii.ConcentrationforcentralpointeffNiiifeNiiiiDVVDcVVcf10100)])(2/(1[)])(2/(1[Where,isthenumberofnearest-neighborlatticepoints2/)(0DDDiieffNiv.SORiterationequation0)1(wccwcoldii1w;(Cárdenas,etal.,2000;Kurnikova,etal.,2019)Calibrationoftheaccuracyofthe3Dcode(Kurnikova,etal.,2019)ApplicationtoGramicidinAchannel(Kurnikova,etal.,2019)(Kurnikova,etal.,2019)(Kurnikova,etal.,2019)Comparisonwithexperiments(Kurnikova,etal.,2019)standardPNPtheory•Nernst-Planckequation•Poissonequation•TotalPotentialEnergyiii0[()()()];1,...,cRcRVRiNfii1(()())4[()()]NiRRRqcRii()()()VRURqR(Kurnikova,etal.,2019)Dielectric-EnergyPNPtheory)]}()()()[({0iiiirrcrcrD)()()(iSIPmobileiirGrqriiimobile)(4))()((rcqrr)()()(iDSEproteiniiSIPrGrqrGNernst-PlanckequationPoissonequationThefreeenergyofionsofspeciesiinsolution)]()([4))()((fiiirrcqrr)()()(iDSEiirGrqri21DSEi2()(,)Grqgrr(Graf,etal.,2019;CoalsonandKurnikova,2019)PerformanceofDSEPNP(CoalsonandKurnikova,2019)PotentialofMeanForcePNPtheory•TheproteinstructureusedinbothBDandDSEPNPsimulationsistakentoberigid,whileinrealitytheproteinstructurerespondsdynamicallytoanion’spresence.Suchadefectusuallyexhibitsverysmallsuperlinearcurrentsforvoltagesupto200mVfornarrowchannels.•Thisissuecaninprinciplebesolvedbyafullatomisticsimulationwhichrequirescompletesamplingofthesystemconfigurationspace.Butit’sformidableforcurrentcomputingcapability.•Limitedsamplingoftheenvironmentconfigurationalspacehasbeenintroducedtodealwiththeproblem.AcombinedMD/continuumelectrostaticsapproachisthenproposedtoobtainΔGSIPatanaveragesolventeffectlevel,whichisthenusedinPNPformalism.SuchaprocedureistermedPMFPNP.(CoalsonandKurnikova,2019)ResultsofthePMFPNPcalculations•Theoverallstructureofpeptidedoesn’tchangemuchoverthecourseofMDtrajectory,sotheΔGDSEcontributiontotheoverallΔGSIPdoesn’tvarymuch.•Smalllocaldistortionsofpore-liningpartsofthepeptide(especiallycarbonylgroups)significantlystabilizecationsastheymovethroughit.•PMFPNPtheoryisabletoaccountforeffectsthatarebeyondthereachofprimitivePNPtheory,namely,saturationofioncurrentthroughthechannelastheconcentrationofbathingsolutionsincreasestoasufficientlyhighvalue.(CoalsonandKurnikova,2019)Thesaturationmechanism(CoalsonandKurnikova,2019)Summary•3DPNPtheoryisofconceptualsimplicity.Itreliesonacaricatureofthemicroscopicworldinwhichbackgroundmediaaretreatedasdielectricslabsandthemobileionsofinterestare“smearedout”intoacontinuouschargedistribution.•Theinherentrestrictionofthetheoryismainlyduetoitssimplicity.Itmaybeunrealisticfortreatingcertainpropertiesofcertainionchannels.Also,themean-fieldcontinuumsolvent/iontheoryofthistypeisinadequatetoaccuratelydescribetheunderlyingdynamics.•Despiteoftheserestrictions,PNPtheorywillcontinuetoplayausefulroleincomputingandunderstandingthekineticsofionpermeationthrough(wider)biologicalchannels.(CoalsonandKurnikova,2019)References•Cárdenas,A.E.,R.D.Coalson,andM.G.Kurnikova.2000.Three-DimensionalPoisson-Nernst-PlanckTheoryStudies:InfluenceofMembraneElectrostaticsonGramicidinAChannelConductance.Biophys.J.79:80-93.•Coalson,R.D.,andM.G.Kurnikova.2019.Poisson–