1. Introduction 475

1.1 Ion channels 475

1.1.1 Gramicidin 476

1.1.2 Helix bundle channels 477

1.1.3 K channels 480

1.1.4 Porins 483

1.1.5 Nicotinic acetylcholine receptor 483

1.1.6 Physiological properties 483

1.2 Simulations 484

1.2.1 Atomistic versus mean-field simulations 484

2. Atomistic simulations 485

2.1 Modelling of ion-interaction parameters 485

2.1.1 Interatomic distances and the problem of ionic radii 486

2.1.2 Solvation energy 487

2.1.3 Hydration shells and coordination numbers 489

2.1.4 Parameters in common use and transferability 491

2.1.5 Summary 491

2.2 Water in pores versus bulk 491

2.2.1 Simple pore models 494

2.2.2 gA 495

2.2.3 Alm 496

2.2.4 LS36 (and LS24) 496

2.2.5 Nicotinic receptor M2δ5 497

2.2.6 Influenza A M2 497

2.2.7 K channels 497

2.2.8 nAChR 498

2.2.9 Porins 498

2.2.10 Relevance 499

2.2.11 Problems with simulations 501

2.3 Dynamics of ions in pores 503

2.3.1 Simple pore models 503

2.3.2 Helix bundles 504

2.3.3 gA and KcsA 505

2.4 Energetics of permeation and ion selectivity 509

2.4.1 Potential and free energy profiles 509

2.4.2 gA 510

2.4.3 α-Helix bundles 511

2.4.4 KcsA 512

2.4.5 Ion selectivity 514

2.4.6 Problems of estimating energetic profiles 515

2.5 Conformational changes 516

2.5.1 gA 516

2.5.2 Alm and LS3 516

2.5.3 KcsA 517

2.6 Protonation states 523

3. Coarse-grained simulations 524

3.1 Introduction 524

3.1.1 Predicting conductance magnitudes 525

3.2 Electro-diffusion: the Nernst–Planck approach 526

3.2.1 Calculating the potential profile from Poisson and PB theory 528

3.2.2 Calculating the potential profile from BD simulations 530

3.2.3 Combining Nernst–Planck and Poisson: PNP 530

3.3 Beyond PNP 532

3.4 BD simulations 532

3.4.1 Basic theory in ion channels 532

3.4.2 Incorporating the environment 533

3.5 Applications 535

3.5.1 Model systems 535

3.5.1.1 Solving the Poisson and PB equation for channel-like geometries 535

3.5.1.2 Comparing PB, PNP and BD 536

3.5.2 Applications to known structures 537

3.5.2.1 gA 537

3.5.2.2 Porin 539

3.5.2.3 LS3 540

3.5.2.4 Alm 542

3.5.2.5 nAChR 542

3.5.2.6 KcsA 543

3.6 pKa calculations 543

3.7 Selectivity 544

3.7.1 Anion/cation selectivity 545

3.7.2 Monovalent/divalent ion selectivity 545

4. Problems 546

4.1 Atomistic simulations 546

4.1.1 Problems 546

4.1.2 Parameters 548

4.2 BD 549

4.3 Mean-field simulations 549

5. Conclusions 550

5.1 Progress 550

5.2 The future 550

6. Acknowledgements 551

7. References 551

Ion channels are proteins that form ‘holes’ in membranes through which selected ions move passively down their electrochemical gradients. The ions move quickly, at (nearly) diffusion limited rates (ca. 107 ions s−1 per channel). Ion channels are central to many properties of cell membranes. Traditionally they have been the concern of neuroscientists, as they control the electrical properties of the membranes of excitable cells (neurones, muscle; Hille, 1992). However, it is evident that ion channels are present in many types of cell, not all of which are electrically excitable, from diverse organisms, including plants, bacteria and viruses (where they are involved in functions such as cell homeostasis) in addition to animals. Thus ion channels are of general cell biological importance. They are also of biomedical interest, as several dizeases (‘channelopathies’) have been described which are caused by changes in properties of a specific ion channel (Ashcroft, 2000). Moreover, passive diffusion channels for substances other than ions are common (porins, aquaporins), as are active membrane transport processes coupled to ion gradients or ATP hydrolysis. An understanding of ion channels may also provide a gateway to understanding these processes.