ABSTRACT

Narrow hydrophobic regions are a common feature of biological channels, with possible roles in ion-channel gating. We study the principles that govern ion transport through narrow hydrophobic membrane pores by molecular dynamics simulation of model membranes formed of hexagonally packed carbon nanotubes. We focus on the factors that determine the energetics of ion translocation through such nonpolar nanopores and compare the resulting free-energy barriers for pores with different diameters corresponding to the gating regions in closed and open forms of potassium channels. Our model system also allows us to compare the results from molecular dynamics simulations directly to continuum electrostatics calculations. Both simulations and continuum calculations show that subnanometer wide pores pose a huge free-energy barrier for ions, but a small increase in the pore diameter to ~1 nm nearly eliminates that barrier. We also find that in those wider channels the ion mobility is comparable to that in the bulk phase. By calculating local electrostatic potentials, we show that the long range Coulomb interactions of ions are strongly screened in the wide water-filled channels. Whereas continuum calculations capture the overall energetics reasonably well, the local water structure, which is not accounted for in this model, leads to interesting effects such as the preference of hydrated ions to move along the pore wall rather than through the center of the pore.

INTRODUCTION

Ion transport across membranes, mediated by ion-channel proteins, is central to many biological processes (1,2), such as neural signal transmission and electrical excitability of muscle. Recent progress in the expression, purification, and crystallization of membrane proteins has led to a rapidly growing number of high-resolution structures (3,4), including those of several ion channels (5-8). Channel structures, together with detailed biochemical and biophysical characterizations using, e.g., amino-acid mutation studies and single-channel conductance measurements, provide key insights into the energetics, selectivity, and gating of ion channels. The availability of atomic structures has also enabled increasingly detailed computational studies that relate ion-channel structure and dynamics to functional mechanisms (9-21).

Understanding ion selectivity has been a major focus of both structural and computational studies, and enormous progress has been made in particular for potassium channels, which are highly permeable for K+ ions but not Na+ ions. Structural studies of potassium channels have also provided new insight into ion-channel gating, relating ion permeability and impermeability to differences in the channel structures between the "open" and "closed" states, respectively. The first high-resolution x-ray structures showed the potassium channel in a closed state, but recently the structure of the MthK potassium channel in the open state was reported (22). Remarkably, the open pore of the MthK channel is lined predominantly by nonpolar amino acids. One of the questions we address in this article is a functional role of the nonpolar pore region of potassium channels.

Narrow and relatively hydrophobic pore regions are a repeatedly observed feature of biological channels facilitating the transport of polar species such as water, protons, and ions. They are present in the potassium channels, e.g., KcsA, MthK, or the Kir family (7,22,23). The mechanosensitive channels (e.g., MscS (24)), and the nicotinic acetylcholine receptor nAChr (25) have similar hydrophobic regions, which may function as gating regions that control the ion permeability (26,27). Narrow, mostly hydrophobic cavities are also involved in the regulation of water or proton transport in several biological systems, such as aquaporins (28,29), cytochrome c oxidase (30), and bacteriorhodopsin (31).

The presence of nonpolar pores as conduits for ions seems at first sight rather surprising for electrostatic reasons. From a simple dielectric model of ion permeation through a hydrophobic pore, one might expect a substantial barrier for displacing a charged particle from the high dielectric solution into a channel surrounded by a low dielectric medium, uncompensated by strong interactions with polar residues lining the channel wall (32). The high conductivity of potassium channels in the open state thus raises the question whether hydrophobic channels are more permeable for ions than one may think based on this simple dielectric argument. To address this question, we will use a combination of computer simulations and continuum electrostatics calculations.

Biomolecular systems as large and complex as membrane channels are becoming accessible to computer simulations thanks to advances both in the raw computational power and in the simulation methodology (9-18,33). However, one problem in theoretical ion-channel research is the complexity of the resulting systems of membrane-embedded proteins, making it difficult to identify the principles underlying the functional mechanisms in the wealth of detailed information provided by molecular simulations. The irregularly shaped pores are lined by both hydrophilic and hydrophobic regions of various widths, and single amino-acid residues can play a crucial role at specific sites. Separating the overall free energies for ion transport into individual contributions to quantify the roles of, e.g., "electrostatics", "hydrogen bonds", "desolvation", or "conformational fluctuations" thus proves difficult, with results that can depend on the separation procedure.

Therefore, to answer the general question about a functional relevance of hydrophobic pores for gating we pursue a different strategy. We avoid the complexity of the biological systems by studying simpler model systems designed to capture specific properties. In addition to being more easily interpretable, such systems are also computationally less expensive than the more realistic membrane-protein systems. For ion translocation through channels, this is of particular relevance, because long-range electrostatics plays an important role in the energetics. To avoid surface effects, molecular dynamics simulations of molecular systems are usually performed either with periodic boundary conditions or for solvent droplets, possibly "embedded" in a dielectric continuum. In either case, electrostatic artifacts seem possible because of the long range of the Coulomb interaction, the strong dielectric discontinuity at the membrane, and the weakly screened interactions within the low-dielectric membrane region. By using a comparatively simple system, we can explicitly explore the energetic contributions coming from the simulation boundary conditions. Moreover, using a simple channel system enables us also to perform direct and fully quantitative comparisons of explicit molecular dynamics simulations to continuum electrostatics calculations. Normally, the motions of protein and membrane, and the inhomogeneous dielectric environment permit only qualitative comparisons. Here, we will study a system with a relatively rigid pore and a well-defined dielectric constant of the entire membrane region.

We focus on the basic principles that govern ion transport through narrow hydrophobic pores by simulation of model membranes formed of hcxagonally packed carbon nanotubes (CNTs), as displayed in Fig. 1. Central questions of our study are: Which factors determine the energetics of ion translocation through such nonpolar nanopores? How large is the free-energy barrier for ion translocation through a hydrophobic pore with a diameter similar to that of the KcsA channel in the closed-state structure (7)? How much does that barrier drop if the pore is widened to a diameter corresponding to that of the open-state structure of the MthK potassium channel (22), and how mobile are ions in wide channels?

Our model system also allows us to explore methodological issues in computational studies of ion translocation (34). By comparing continuum electrostatics calculations to results from molecular dynamics simulations, we will address the question which level of theory/simulation is required to understand various aspects of the translocation process.

The article is organized as follows. We first present different computational approaches to investigate ion transport through membrane channels and describe the simulation methods used in this study. Then, we present our results on the translocation of a Na+ ion through model membranes formed by carbon nanotubes. Finally, based on our simulation results, we discuss the role of hydrophobia cavities and the water phase inside them in the process of charge transport through biological membranes.

METHODS

Overview