MOLECULAR PHYSICS, 2002, VOL. 100, NO. 14, 2361±2368 Monte Carlo study of the selectivity of calcium channels: improved geometrical model Bless ’em all, bless ’em all! The long and the short and the tall! (From a popular WWII song) DEZSO È BODA 1 , DOUGLAS HENDERSON 2 * and DAVID D. BUSATH 3 1 Department of Physical Chemistry, University of Veszpre m, H-8201 Veszpre m, PO Box 158, Hungary 2 Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602, USA 3 Department of Zoology and Center for Neuroscience (Received 21 September 2001; revised version accepted 28 January 2002) An extended model of a calcium channel is described involving a channel with a ®nite length. With this new geometry the channel is still selective but less so than in an in®nite cylinder geometry (Boda, D., Busath, D. D., Henderson, D., and Sokolowski, S., 2000, J. phys. Chem. B, 104, 8903). The selectivity of the channel depends on the width and length of the channel ®lter but is not signi®cantly aected by changes in the size of the entry vestibules. Interestingly, changes in the size of the entry vestibules do aect the details of the concentration pro®les of some of the ions. 1. Introduction There have been several recent applications of statis- tical mechanics to channels, including those that are of physiological interest [1±20]. Most of these papers are concerned with the permeation of the ions. However, references [16±20] are concerned with the selectivity of the channel. This is the topic considered here. Channels are protein molecules that contain a hole that selectively allows the passage of an ion species and that control many physiological functions. For ex- ample calcium channels convey the signal that causes the heart to beat. If these calcium channels, which favour the absorption and permeation of Ca 2‡ ions, were to malfunction for several minutes, death would occur. Nonner et al. [16] published an important paper in which they accounted for the selectivity of a calcium channel by what might be called the charge space com- petition (CSC) mechanism. Divalent ions displace monovalent ions from the channel because of their ability to deliver twice the charge while occupying about the same excluded volume, and thus to neutralize the negatively charged side chains of the channel ®lter more eectively. Nonner et al. [16] used a simple model of a homogeneous electrolyte consisting of charged hard spheres (the so called primitive model or PM). More recently, they [17] have examined this CSC concept using a homogeneous electrolyte that consists of charged hard spheres in a solvent of hard spheres (sol- vent primitive model or SPM). The polar nature of the solvent was taken into account by a dielectric constant in both the PM and the SPM systems. The speci®c approximation that was employed for the homogeneous electrolyte was the mean spherical approximatio n (MSA). However, the most daring step was the assump- tion that the electrolyte in the channel ®lter could be treated as homogeneous. It is far from obvious that this approximation is even reasonable, let alone reliable. Boda et al. [18, 19] have made Monte Carlo (MC) simulations using the PM with the assumption that the channel ®lter is in®nitely long. Certainly, a channel and its ®lter have a ®nite length. However, we note that the use of an in®nite cylinder as an approximation for a channel is quite common [8±10, 12, 13, 18±20] and cer- tainly it is more reasonable than the assumption that is implicit in the work of Nonner et al. [16, 17], where the channel is in®nite in extent in every direction. The MC simulations of Boda et al. showed that the results of the Nonner et al. approach are quite accurate. It is of interest to note the recent work of Raj Ganesh et al . [21], where a calcium channel was simulated using Molecular Physics ISSN 0026±8976 print/ISSN 1362±3028 online # 2002 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/0026897021012530 4 * Author for correspondence. e-mail: doug@huey.byu.edu