Grand canonical Monte Carlo simulations of bulk electrolytes and calcium channels

Transcription

1 Grand canoncal Monte Carlo smulatons of bulk electrolytes and calcum channels Thess of Ph.D. dssertaton Prepared by: Attla Malascs M.Sc. n Chemstry Supervsor: Dr. Dezső Boda Unversty of Pannona Insttute of Chemstry Department of Phscal Chemstry 2010

2 Introducton The man goal of the thess s the study of nhomogeneous systems of electrolytes usng grand canoncal Monte Carlo smulatons (GCMC). Specfcally, we studed the selectvty propertes of a reduced model of the L-type calcum channel. The on channel, the membrane n whch t s embedded, and the bulk phases surroundng these (the electrolytes nsde and outsde the cell) form an nhomogeneous electrolyte system. In equlbrum, any property of the system apart from the temperature, the pressure, and the chemcal potental can be poston dependent. The propertes of the nhomogeneous part of the system - the structure of ths regon - depends on the composton of the homogeneous phase. In the case of the selectvty studes of on channels, the followng questons are mposed. Whch caton s conducted preferentally by the channel from an electrolyte wth gven composton? What s the mechansm of ths selectvty? The grand canoncal ensemble s especally approprate to study ths problem, because there s an equlbrum not only between the on channel and the bulk phase nsde the smulaton cell, but these two phases are also n equlbrum wth an external bath of fxed composton. Ths equlbrum s ensured by the equalty of the chemcal potentals n the smulaton cell and the external bath. Because, n practce, we usually study systems wth prescrbed composton, we need the chemcal potentals that correspond to ths composton. In the canoncal ensemble, the Wdom test partcle method can be used for ths purpose, but n the concentraton range relevant n our calcum channel studes ts feasblty s lmted. In the grand canoncal ensemble, the densty fluctuatons are treated more effcently. Therefore, we decded to develop a method whch can determne the chemcal potentals correspondng to prescrbed concentratons based on GCMC smulatons. Because the chemcal potental s the nput parameter n the grand canoncal ensemble, ths procedure s necessarly teratve. The soul of the procedure s the algorthm whch computes the chemcal potentals for the next teraton on the bass of the results of the prevous teraton. The frst part of the thess presents the ntroducton and testng of these algorthms and dscusses how can we make them more effcent. The second part of the thess deals wth certan aspects of the selectvty propertes of the L-type calcum channel. The accurate three-dmensonal structure of the L-type calcum channel s unknown. Therefore, we use a smple model for ths channel based on the mnmal structural nformaton that the selectvty flter of the channel contans four negatvely charged glutamc acds. The carboxyl groups at the ends of the sde chans are modeled by structural ons that are confned to the flter but free to move nsde (eght oxygen ons wth -1/2e charge each). The ons are charged hard spheres, whle the solvent

3 s consdered as a delectrc background. The model, despte ts smplcty, successfully reproduced a seres of electrophysologcal expermental results. In these experments, the currents flowng through the channels are measured at varous concentratons n the bulk phases. The success of the model ndcates that t properly grabs the essence of the most mportant physcal forces competng n the channel: the electrostatc nteractons and volume excluson due to the fnte sze of the ons. Accordng to ths pcture, the basc reason of the strong calcum vs. sodum selectvty of the L-type calcum channel s that calcum ons provde twce the charge to balance the negatve charge of the flter whle occupyng about the same space ( Charge Space Competton mechansm). Theses (1) In the frst half of the dssertaton we suggest teraton algorthms based on GCMC smulatons that determne the chemcal potentals correspondng to prescrbed concentratons. (1.1) One of these algorthms s s based on the frst order seres expanson of the concentraton as a functon of the chemcal potentals. The thermodynamc dervatves correspondng to the expanson coeffcents are determned from GCMC smulatons as fluctuaton formulae. The method works approprately f the ntal state of the teraton s close to the fnal state. The method s qute senstve to ntal condtons. (1.2) The other algorthm s defned by the equaton: μ n+ 1 = μ n + ktlog c c targ n K ze Q n, 32πε εl where the chemcal potental n the next teraton, μ n+1, s determned by the relaton of the concentraton obtaned n the prevous teraton as an ensemble average, c n, to 0

4 targ the targeted concentraton, c. We have shown that the algorthm s robust, converges fast, and s not senstve to ntal condtons. (1.3) If we use the algorthm to determne the chemcal potentals of ndvdual ons, we need the correcton energy term n the above equaton. Ths s because the set of chemcal potentals n a gven teraton does not necessarly produce a charge neutral system. The correcton term estmates the nteraton of on z e wth ths excess charge Q n. We have shown that usng ths term accelerates the convergence of the teraton consderably. (1.4) We have shown that our algorthm s more effcent and shows faster convergence than the algorthm of the Inverse GCMC method proposed by Lampersk. The other proposal of Lampersk to compute the fnal result as the average of the chemcal potentals n the teratons mproved the effcency of our algorthm further. (2) In the second half of the dssertaton we analyzed the selectvty propertes of the L-type calcum channel. We presented our results by showng densty profles, occupances of the flter by varous ons, and conductances of the channel for varous ons. The conductance was estmated from the ntegrated Nernst-Planck equaton. (2.1) We have shown that the calcum vs. sodum selectvty of the model channel can be tuned to some degree by changng the flter's shape (the rato of the length and the radus of the flter). The selectvty of the channel changes more f the volume of the flter s also changed durng changng the shape. If we change the flter's shape keepng ts volume fxed, the selectvty propertes change less. Our results show that the frst order determnant of the calcum vs. sodum selectvty s the volume of the flter (keepng the charge of the flter fxed). (2.2) We have shown that confnng the oxygen ons to the flter by soft walls nstead of hard walls does not change selectvty despte the fact that the densty profles of the oxygen ons are profoundly dfferent n ths case. (2.3) We have shown that addng Gd 3+ ons to mxtures of dvalent (10 mm Ca 2+, Sr 2+, vagy Ba 2+ ) and monovalent (150 mm Na + ) ons, the trvalent on completely blocks the current of the other two ons at very low Gd 3+ concentratons n accordance wth experments. We have reproduced the expermental result that ths block appears at lower Gd 3+ concentratons f the dvalent on s smaller. (2.4) We have made varous predctons for the case when Ca 2+ s added to mxtrures of Gd 3+ and Na + ons, because the competton of the three ons wth dfferent valences makes a rch selectvty behavor possble. Furthermore, our smulatons ndcate that the smaller Gd 3+ on blocks more effcently than the larger La 3+ on.

5 Our results obtaned for the L-type calcum channel further support the hypothess that the on selectvty of calcum channels s determned by the balance of a handful of very basc physcal nteractons and the role of the mnor detals of the proten structure s secondary. Publcatons on whch the dssertaton s based [1] A. Malascs, D. Gllespe, and D. Boda: Smulatng prescrbed partcle denstes n the grand canoncal ensemble usng teratve algorthms. J. Chem. Phys., 128(12):124102, IF: 3.149, #Refs = 5 [2] A. Malascs, D. Gllespe, W. Nonner, D. Henderson, B. Esenberg, and D. Boda: Proten structure and onc selectvty n calcum channels: Selectvty flter sze, not shape, matters. Bochm. et Bophys. Acta - Bomembranes, 1788(12): , IF: [3] A. Malascs and D. Boda: An eff-cent teratve grand canoncal Monte Carlo algorthm to determne ndvdual onc chemcal potentals n electrolytes. J. Chem. Phys., 132(24): , IF: [4] A. Malascs, D. Boda, M. Valskó, D. Henderson, and D. Gllespe: Smulatons of calcum channel block by trvalent ons: Gd 3+ competes wth permeant ons for the selectvty flter. Bochm. et Bophys. Acta - Bomembranes, 1798(11): , IF: Publcaton not connected to the dssertaton [5] A. Malascs, D. Boda, and M. Valskó: Monte Carlo smulaton and renormalzed perturbaton theory study of the delectrc propertes of mxtures of polarzable hard spheres and polarzable dpolar hard spheres. Mol. Phys., 104(22-24): , IF: Conference posters [6] A. Malascs, D. Gllespe, D. Boda: Iteratve grand canoncal Monte Carlo algorthms to compute chemcal potentals for prescrbed denstes, 59 th Annual Meetng of the Internatonal Socety of Electrochemstry, Sevlla, Span, Sep 7-12, [7] A. Malascs, D. Gllespe, D. Boda: Iteratve grand canoncal Monte Carlo algorthms to compute chemcal potentals for prescrbed denstes, 7 th Lqud Matter Conference, Lund, Sweden, June 27- July 1, [8] A. Malascs and D. Boda: The Adaptve Grand Canoncal Monte Carlo algorthm to determne ndvdual onc chemcal potentals n electrolytes, 8 th Lblce Conference on the Statstcal Mechancs of Lquds, Brno, Check Republc, June 13-18, 2010.