CHAPTER 12 Molecular Modeling and Simulation Studies of Ion Channel Structures, Dynamics and Mechanisms Kaihsu Tai, Philip Fowler, Younes Mokrab, Phillip Stansfeld, and Mark S.P. Sansom Department of Biochemistry University of Oxford Oxford, OX1 3QU, United Kingdom Abstract I. Introduction II. Homology-Based Structure Prediction of Transmembrane Proteins A. Homology Modeling: A Biological Approach to Protein Structure Prediction B. Process of Homology Modeling C. Accuracy of Homology Models D. Case Study of the Application of Homology Modeling III. PB Profiles for the Energetics of an Ion in a Channel A. Theory B. Calculations IV. MD Simulations A. Theory B. MD Software C. Setting up the System D. Analysis of the Simulations V. Free Energy Methods A. Alchemical Methods B. Potential of Mean Force Methods VI. Summary References METHODS IN CELL BIOLOGY, VOL. 90 0091-679X/08 $35.00 Copyright 2008, Elsevier Inc. All rights reserved. 233 DOI: 10.1016/S0091-679X(08)00812-1

Abstract Ion channels are integral membrane proteins that enable selected ions to flow passively across membranes. Channel proteins have been the focus of computa- tional approaches to relate their three-dimensional (3D) structure to their physio- logical function. We describe a number of computational tools to model ion channels. Homology modeling may be used to construct structural models of channels based on available X-ray structures. Electrostatics calculations enable an approximate evaluation of the energy profile of an ion passing through a channel. Molecular dynamics simulations and free-energy calculations provide information on the thermodynamics and kinetics of channel function. I. Introduction Ion channels are integral membrane proteins that allow ionic currents to flow across membranes. Channels allow selected ions to flow across membranes down their electrochemical gradients through nanoscopic pores through the centre of the channel protein molecule (Hille, 2001). Channels play key roles in the physiology of a wide range of cells, especially those with excitable membranes, and are important drug targets. They have also been the focus of a wide range of computational approaches in an attempt to relate their 3D structure to their physiological function. In this context, we review a range of computational tools which can be used to reveal the workings of ion channels. Firstly, we discuss homology modeling which may be used to construct models which complement available crystallographic structures. Secondly, electrostatics calculations based on the Poisson���Boltzmann (PB) equation provide a computationally inexpensive way to evaluate the energy profile of an ion going through the pore of a channel. Finally, molecular dynamics (MD) simulations, and especially free-energy calculations, can provide information on the thermody- namics and kinetics of channel function. Together, these tools can reveal the inner workings of ion channels and their interactions with the membrane environment. II. Homology-Based Structure Prediction of Transmembrane Proteins Transmembrane (TM) proteins comprise roughly 30% of all proteins (Wallin and von Heijne, 1998) and play key roles in many cellular processes. In addition, nearly two-thirds of all current drug targets are TM receptors and ion channels (Terstappen and Reggiani, 2001). Being diYcult to express and purify, to date, few distinct TM protein structures have been solved by high-resolution methods such as X-ray crys- tallography and nuclear magnetic resonance (NMR), accounting for less than 1% of the total number of structures deposited to the Protein Data Bank (PDB) (Berman 234 Kaihsu Tai et al.

et al., 2000). Direct structural determination, especially for many eukaryotic TM proteins, may remain diYcult for years to come. In an attempt to overcome this problem, approaches for modeling 3D structures computationally have been developed (Petrey and Honig, 2005), which have aided not only experimental studies but also theoretical calculations, such as MD and molecular docking. In this section, we discuss the basics of some methods used to model 3D structures of TM proteins and provide an illustrative case study of modeling an ion channel protein. A. Homology Modeling: A Biological Approach to Protein Structure Prediction Despite a qualitative understanding of the forces that shape the protein folding process, current knowledge is not suYcient to predict protein structure from first principles on a reasonable timescale. However, the accumulation of a large number of sequenced genomes and protein structures has led to the development of knowledge-based methods for predicting the 3D structure of a protein from its amino acid sequence. Over the years, three main approaches of structure prediction have developed: ab initio prediction, homology-based modeling, and threading (Petrey and Honig, 2005). These are distinguished by how much information from amino acid sequence and protein structural databases is used in building the model. In principle, ab initio prediction makes no use of information from databases the goal being to predict the structure based entirely on laws of physics and chemistry. In practice, the terms ������ab initio������ or ������de novo������ are often used to describe methods, which predict the structure for a protein with no similar structures, but still use information from predicted secondary structure or local sequence and structural relationships to short protein fragments (Bradley et al., 2005). Homology-based modeling (or simply, homology modeling), which currently gives the most accurate and reliable models, is based on the general observation that evolutionarily related (homologous) proteins are likely to have similar structures (Chothia and Lesk, 1986). Consequently, a structure model can be built for a protein of interest (target) based on the known structure of a close homologue (template). Threading refers to the case in which the structures of one or more distant homologues exist but can not be easily recognized because of the low sequence similarity. Here, the biggest challenge is to find and use such template(s) to build the model, which is often a diYcult task. Therefore, with the exception of pure physics-based approaches, most protein prediction methods make use of templates that range from relatively small frag- ments as in the ab initio methods to entire proteins as in homology modeling. For a given target, there are often several potential templates with various levels of similarity, including those which cover only certain regions of the protein. This led to the raising of questions about the nature of the evolutionary relationships between proteins and protein domains. Methods were developed for the superpo- sition of 3D structures (Kolodny et al., 2005), helping to recognize homology that was not evident from sequence. Subsequently, databases such as SCOP (Murzin et al., 1995) and CATH (Orengo et al., 1997) were constructed, in which protein 12. Molecular Modeling and Simulation Studies of Ion Channels 235

structures were divided into domains and organized hierarchically. The domains were grouped into families based on simple sequence relationships, into super- families based on structural and functional relationships and less obvious sequence relationships, and into folds based entirely on structure. However, protein classification can be diYcult especially at the fold level. There is a great deal of ambiguity in the definition of a fold, and some argue that fold space should be viewed as continuous, whereby available structures can be divided into substructures that may fall under a number of diVerent known folds (Berman et al., 2000). Therefore, a main challenge in structure prediction is to recognize sequence and structure relationships between proteins that might not be expected to be related, at least based on existing classification schemes. A significant improvement to homology recognition is expected to come from the ongoing structural genomics initiatives. These aim at solving 3D structures for the repre- sentatives of as many protein families as possible so that homology models can be built for, or at least overall topology can be assigned to, other family members (Brenner and Levitt, 2000). B. Process of Homology Modeling As illustrated in Fig. 1, a typical homology modeling exercise consists of six steps repeated iteratively until a satisfactory model is obtained: (1) finding one or more suitable template proteins related to the target (homology recognition), (2) align- ing the target and template sequences, (3) building a preliminary model for the target based on the 3D structure of the template, (4) ab initio modeling of side- chains and loops in the target that are diVerent from the template, (5) refining the model, which often involves changing its conformation slightly, and finally (6) evaluating the model. These steps are explained in details in the next subsections. 1. Template Identification A sequence alignment method is used to identify a statistically significant relationship between the target and one or more possible templates. Methods of increasing sophistication have been developed for this task, in which the target and template sequences are represented in various ways. The current state-of-the-art alignment methods represent templates and/or targets as position-specific substi- tution matrices (also known as profiles), such as PSI-BLAST (Altschul et al., 1997) or as hidden Markov models (HMMs) (Eddy, 1998). In a profile or HMM, each position represents not a single amino acid as in standard sequence alignments, but a group of features which are obtained form a multiple sequence alignment involving homologous proteins. In this way, profiles and HMMs take into account the variability at individual position in a protein sequence, leading to more sensi- tive homology detection (Marti-Renom et al., 2004). Recently, better profiles and HMMs methods were built by accounting for common features in protein struc- tures, leading to the identification of more remote homologues compared to 236 Kaihsu Tai et al.

180 135 90 45 0 Psi (deg) ���45 ���90 ���135 ���180���135 ���90 ���45 ���0 Phi (deg) Pdb 1m0m Altering alignment Template Template selection Structural database Homology search M N T �� l ��� y e i p p A A g 1 1 L a L V I I D I I I P Y F I T L G V A Target sequence Model building Structure-sequence alignment M N I I I I I T T T T I I P Y F F F F F Y Y Y Y P P P P I I I I I I I I I I L L G G G S I L L L V V A A A A A V V S S V V V V V I N N N N M M M D D F D D D M M M Select alternative model Validation Refinement Final model ���45 90 135 180 Fig. 1 The various steps in homology modeling. First, starting from a target sequence, suitable template(s) are obtained through a homology search. An alignment is then generated between the target and template, identifying regions that are structurally conserved and those which are variable such as insertions and missing N and C termini. A model is then built for the target Ca backbone and sidechains are modeled. The resulting model is refined and evaluated iteratively by altering the alignment and selecting alternative models (discontinuous lines). 12. Molecular Modeling and Simulation Studies of Ion Channels 237