The number of globular proteins for which high resolution structures are available is rapidly increasing. In each case the particular sequence of the polypeptide appears to yield only a single, compact, biologically active structure. However, peptides with no obvious sequence similarity may form remarkably similar structures.

Short runs of adenines are a ubiquitous DNA element in regulatory regions of many organisms. When runs of 4–6 adenine base pairs (‘A-tracts’) are repeated with the helical periodicity, they give rise to global curvature of the DNA double helix, which can be macroscopically characterized by anomalously slow migration on polyacrylamide gels. The molecular structure of these DNA tracts is unusual and distinct from that of canonical B-DNA. We review here our current knowledge about the molecular details of A-tract structure and its interaction with sequences flanking them of either side and with the environment. Various molecular models were proposed to describe A-tract structure and how it causes global deflection of the DNA helical axis. We review old and recent findings that enable us to amalgamate the various findings to one model that conforms to the experimental data. Sequences containing phased repeats of A-tracts have from the very beginning been synonymous with global intrinsic DNA bending. In this review, we show that very often it is the unique structure of A-tracts that is at the basis of their widespread occurrence in regulatory regions of many organisms. Thus, the biological importance of A-tracts may often be residing in their distinct structure rather than in the global curvature that they induce on sequences containing them.

The proton has been the nucleus of choice for NMR studies of macromolecules because it is ubiquitous; it provides the highest sensitivity; its resonances can be identified with types of amino and nucleic acids by means of experiments utilizing proton spin-spin interaction and chemical shift; and, most important, proton NMR yields distance information via the nuclear Overhauser effect (NOE). Many of these advantages are lost for larger biopolymers (molecular weight more than 15 kDa) for which the line width is considerably greater than the proton-proton spin-spin interaction. The spin-spin interaction is then useless or difficult to use for assignment; and furthermore the proton line width and the number of proton resonances both increase in proportion to the molecular weight, thereby increasing the problem of resonance overlap to an intolerable degree.

Magnetization transfer techniques are specialized NMR experiments which can measure the rate of chemical reactions while concentrations of products and reactants are maintained constant. These techniques are being used to measure the rates of enzyme catalysed reactions in a variety of living systems and in vitro. The magnetization transfer measurements in vivo of the ATP synthetase and the creatine kinase reactions have been particularly useful in describing rates of major energy transducing reactions involving ATP and phosphocreatine. As a result, a wide range of biomedicai scientists are becoming aware of the potentials of these techniques. The purpose of this review is thus threefold: first, to present a concise, conceptual review of the underlying principles for these non-specialists; secondly, to review the important biochemical applications of the method which have appeared, and thirdly, to discuss potential applications and limitations of the method.

1. Introduction 2

2. Heterotrimeric G-protein structure 3

2.1. G-protein α subunit 3

2.2. G-protein βγ dimer 8

2.3. Unique role of Gβ5 in complexes with RGS proteins 9

2.4. Heterotrimer structure 10

2.5. Lipid modifications direct membrane association 11

3. Receptor–G protein complex 11

3.1. Low affinity interactions between inactive receptors (R) and G proteins 11

3.2. Receptor activation exposes the high-affinity G-protein binding site 12

3.3. Receptor–G protein interface 14

3.4. Structural determinants of receptor–G protein specificity 15

3.5. Models of the receptor–G protein complex 17

3.6. Sequential interactions may form the receptor–G protein complex 19

4. Molecular basis for G-protein activation 19

4.1. Potential mechanisms of receptor-catalyzed GDP release 20

4.2. GTP-mediated alteration of the receptor–G protein complex 23

5. Activation of downstream effector proteins 24

5.1. Gα interactions with effectors 24

5.2. Gβγ interactions with effectors and regulatory proteins 26

6. G-protein inactivation 28

6.1. Intrinsic GTPase-activity of Gα 28

6.2. GTPase-activating proteins 30

7. Novel regulation of G-protein signaling 31

8. New approaches to study G-protein dynamics 32

8.1. Nuclear magnetic resonance spectroscopy 32

8.2. Site-directed labeling techniques 33

8.3. Mapping allosteric connectivity with computational approaches 34

8.4. Studies of G-protein function in living cells 36

9. Conclusions 37

10. References 38

Heterotrimeric guanine-nucleotide-binding proteins (G proteins) act as molecular switches in signaling pathways by coupling the activation of heptahelical receptors at the cell surface to intracellular responses. In the resting state, the G-protein α subunit (Gα) binds GDP and Gβγ. Receptors activate G proteins by catalyzing GTP for GDP exchange on Gα, leading to a structural change in the Gα(GTP) and Gβγ subunits that allows the activation of a variety of downstream effector proteins. The G protein returns to the resting conformation following GTP hydrolysis and subunit re-association. As the G-protein cycle progresses, the Gα subunit traverses through a series of conformational changes. Crystallographic studies of G proteins in many of these conformations have provided substantial insight into the structures of these proteins, the GTP-induced structural changes in Gα, how these changes may lead to subunit dissociation and allow Gα and Gβγ to activate effector proteins, as well as the mechanism of GTP hydrolysis. However, relatively little is known about the receptor–G protein complex and how this interaction leads to GDP release from Gα. This article reviews the structural determinants of the function of heterotrimeric G proteins in mammalian systems at each point in the G-protein cycle with special emphasis on the mechanism of receptor-mediated G-protein activation. The receptor–G protein complex has proven to be a difficult target for crystallography, and several biophysical and computational approaches are discussed that complement the currently available structural information to improve models of this interaction. Additionally, these approaches enable the study of G-protein dynamics in solution, which is becoming an increasingly appreciated component of all aspects of G-protein signaling.

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.

Parkinson's disease (PD) is characterized by proteinaceous aggregates named Lewy Bodies and Lewy Neurites containing α-synuclein fibrils. The underlying aggregation mechanism of this protein is dominated by a secondary process at mildly acidic pH, as in endosomes and other organelles. This effect manifests as a strong acceleration of the aggregation in the presence of seeds and a weak dependence of the aggregation rate on monomer concentration. The molecular mechanism underlying this process could be nucleation of monomers on fibril surfaces or fibril fragmentation. Here, we aim to distinguish between these mechanisms. The nature of the secondary processes was investigated using differential sedimentation analysis, trap and seed experiments, quartz crystal microbalance experiments and super-resolution microscopy. The results identify secondary nucleation of monomers on the fibril surface as the dominant secondary process leading to rapid generation of new aggregates, while no significant contribution from fragmentation was found. The newly generated oligomeric species quickly elongate to further serve as templates for secondary nucleation and this may have important implications in the spreading of PD.

Understanding protein–inorganic surface interactions is central to the rational design of new tools in biomaterial sciences, nanobiotechnology and nanomedicine. Although a significant amount of experimental research on protein adsorption onto solid substrates has been reported, many aspects of the recognition and interaction mechanisms of biomolecules and inorganic surfaces are still unclear. Theoretical modeling and simulations provide complementary approaches for experimental studies, and they have been applied for exploring protein–surface binding mechanisms, the determinants of binding specificity towards different surfaces, as well as the thermodynamics and kinetics of adsorption. Although the general computational approaches employed to study the dynamics of proteins and materials are similar, the models and force-fields (FFs) used for describing the physical properties and interactions of material surfaces and biological molecules differ. In particular, FF and water models designed for use in biomolecular simulations are often not directly transferable to surface simulations and vice versa. The adsorption events span a wide range of time- and length-scales that vary from nanoseconds to days, and from nanometers to micrometers, respectively, rendering the use of multi-scale approaches unavoidable. Further, changes in the atomic structure of material surfaces that can lead to surface reconstruction, and in the structure of proteins that can result in complete denaturation of the adsorbed molecules, can create many intermediate structural and energetic states that complicate sampling. In this review, we address the challenges posed to theoretical and computational methods in achieving accurate descriptions of the physical, chemical and mechanical properties of protein-surface systems. In this context, we discuss the applicability of different modeling and simulation techniques ranging from quantum mechanics through all-atom molecular mechanics to coarse-grained approaches. We examine uses of different sampling methods, as well as free energy calculations. Furthermore, we review computational studies of protein–surface interactions and discuss the successes and limitations of current approaches.

1. Introduction 222

2. What is an RNA motif? 222

2.1 Sequence vs. structural motifs 222

2.2 RNA structural motifs 223

2.3 RNA structural elements vs. motifs 223

2.4 Specific recognition motifs 224

2.5 Tools for identifying and classifying elements and motifs 226

3. Types of RNA structural motifs 228

3.1 Helices 228

3.2 Hairpin loops 228

3.3 Internal loops 230

3.4 Junction loops/multiloops 230

3.5 Binding motifs 232

3.5.1 Metal binding 232

3.5.2 Natural and selected aptamers 234

3.6 Tertiary interactions 234

4. Future directions 236

5. Acknowledgments 239

6. References 239

RNAs are modular biomolecules, composed largely of conserved structural subunits, or motifs. These structural motifs comprise the secondary structure of RNA and are knit together via tertiary interactions into a compact, functional, three-dimensional structure and are to be distinguished from motifs defined by sequence or function. A relatively small number of structural motifs are found repeatedly in RNA hairpin and internal loops, and are observed to be composed of a limited number of common ‘structural elements’. In addition to secondary and tertiary structure motifs, there are functional motifs specific for certain biological roles and binding motifs that serve to complex metals or other ligands. Research is continuing into the identification and classification of RNA structural motifs and is being initiated to predict motifs from sequence, to trace their phylogenetic relationships and to use them as building blocks in RNA engineering.

1. Introduction 92

2. Methods and models 93

2.1 Density Functional Theory 93

2.2 Chemical models 98

3. Examples of mechanisms studied 104

3.1 Photosystem II 105

3.2 Cytochrome c oxidase 108

3.3 Manganese catalase 112

3.4 Ribonucleotide reductase 114

3.5 Methane mono-oxygenase 119

3.6 Methyl coenzyme M reductase 122

3.7 Intra- and extradiol dioxygenases 124

3.8 Tyrosinase and catechol oxidase 126

3.9 Amino-acid hydroxylases 130

3.10 Isopenicillin N synthase 132

3.11 Cytochrome c peroxidase 134

3.12 Copper-dependent amine oxidase 136

3.13 Galactose oxidase 138

4. Summary and conclusions 138

5. Acknowledgements 140

6. References 140

The study of metalloenzymes using quantum chemical methods of high accuracy is a relatively new field. During the past five years a quite good understanding has been reached concerning the methods and models to be used for these systems. For systems containing transition metals hybrid density functional methods have proven both accurate and computationally efficient. A background on these methods and the accuracy achieved in benchmark tests are given first in this review. The rest of the review describes examples of studies on different metalloenzymes. Most of these examples describe mechanisms where dioxygen is either formed, as in photosystem II, or cleaved as in many other enzymes life cytochrome c oxidase, ribonucleotide reductase, methane mono-oxygenase and tyrosinase. In the descriptions below high emphasis is put on the actual determination of the transition states, which are the key points determining the mechanisms.

Protein chains are usually folded into one or several discrete globular units called domains (Schulz & Schirmer, 1979). Levitt & Chothia (1976) have shown that the structures of such domains frequently fall into one of the following three classes; α-proteins which are mainly α-helical, β-proteins which contain antiparallel β-strands and α/β proteins which have a central core consisting of a sheet of strands, most of which are parallel. The connexions between the parallel strands in αβ-proteins frequently contain helices which are packed on both sides of the sheet in a regular way (Chothia, Levitt & Richardson, 1977).

As recently as 10 years ago, the prospect of solving the structure of any membrane protein by X-ray crystallography seemed remote. Since then, the threedimensional (3-D) structures of two membrane protein complexes, the bacterial photosynthetic reaction centres of Rhodopseudomonas viridis (Deisenhofer et al. 1984, 1985) and of Rhodobacter sphaeroides (Allen et al. 1986, 1987 a, 6; Chang et al. 1986) have been determined at high resolution. This astonishing progress would not have been possible without the pioneering work of Michel and Garavito who first succeeded in growing 3-D crystals of the membrane proteins bacteriorhodopsin (Michel & Oesterhelt, 1980) and matrix porin (Garavito & Rosenbusch, 1980). X-ray crystallography is still the only routine method for determining the 3-D structures of biological macromolecules at high resolution and well-ordered 3-D crystals of sufficient size are the essential prerequisite.

The membrane-spanning portions of many integral membrane proteins consist of one or a number of transmembrane α-helices, which are expected to be independently stable on thermodynamic grounds. Side-by-side interactions between these transmembrane α-helices are important in the folding and assembly of such integral membrane proteins and their complexes. In considering the contribution of these helix–helix interactions to membrane protein folding and oligomerization, a distinction between the energetics and specificity should be recognized. A number of contributions to the energetics of transmembrane helix association within the lipid bilayer will be relatively non-specific, including those resulting from charge–charge interactions and lipid–packing effects. Specificity (and part of the energy) in transmembrane α-helix association, however, appears to rely mainly upon a detailed stereochemical fit between sets of dynamically accessible states of particular helices. In some cases, these interactions are mediated in part by prosthetic groups.

The present study is best understood as an extension and critique of two schools of thought. The first is that of Malloe and his students, among whom we number ourselves. It is to Maaloe that we are indebted for the idea that logarithmically growing bacteria assemble and use tibosomes in amounts that are optimally adjusted to yield the maximal growth rates supported by different media. Her, we begin our analysis by applying this optimization priciple to all the components of a logarithmically growing system. Our objective is to use the growth optimization constraint as a tool to explore the physiological limits on the accuracy of gene expression. This brings us to our second source of inspiration, which is Orgel's (1963) conception of a problem that Ninio (1982) has referred to as the ‘great error loop’.

(A) Evolutionary similarities of protein structures Two decades have passed from the time that the three dimensional structure of the first globular protein, sperm whale myoglobin, was decoded (Kendrew et al. 1960). Its structure, which now looks so simple and habitual, then seemed to be unusually complicated. The decoding of the subsequent proteins, lysozyme (Blake et al. 1965), ribonuclease (Kartha, Bello & Harker, 1967), chymotrypsin (Matthews et al. 1967), carboxypeptidase (Lipscomb et al. 1969) redoubled the feeling of amazement and even of some confusion before the extremely complicated, intricate and, above all, absolutely unlike protein structures. Some consolation against this background was the evident and far-reaching similarity between the three-dimensional structures of myoglobin and hemoglobin subunits (Perutz, Kendrew & Watson, 1965) and an analogous similarity between the structures of chymotrypsin and other serine proteases, elastase (Shotton & Watson, 1970) and trypsin (Stroud, Kay & Dickerson, 1972). However this similarity was easily explained by the far-reaching homology between the primary structures of myoglobin and hemoglobin and between the primary structures of serine proteases.

1. Introduction 111

2. Levinthal's paradox and energy landscapes 115

2.1 Including randomness in the energy function 121

2.2 Some effects of energetic correlations between structurally similar states 126

3. Resolution of problems by funnel theory 128

3.1 Physical origin of free-energy barriers 133

4. Generic mechanisms in folding 138

4.1 Collapse, generic and specific 139

4.2 Helix formation 139

4.3 Nematic ordering 141

4.4 Microphase separation 142

5. Signatures of a funneled energy landscape 145

6. Statistical Hamiltonians and self-averaging 152

7. Conclusions and future prospects 156

8. Acknowledgments 157

9. Appendix: Glossary of terms 157

10. References 158

The current explosion of research in molecular biology was made possible by the profound discovery that hereditary information is stored and passed on in the simple, one-dimensional (1D) sequence of DNA base pairs (Watson & Crick, 1953). The connection between heredity and biological function is made through the transmission of this 1D information, through RNA, to the protein sequence of amino acids. The information contained in this sequence is now known to be sufficient to completely determine a protein's geometrical 3D structure, at least for simpler proteins which are observed to reliably refold when denatured in vitro, i.e. without the aid of any cellular machinery such as chaperones or steric (geometrical) constraints due to the presence of a ribosomal surface (for example Anfinsen, 1973) (see Fig. 1). Folding to a specific structure is typically a prerequisite for a protein to function, and structural and functional probes are both often used in the laboratory to test for the in vitro yield of folded proteins in an experiment.

Due to the development of two-dimensional Fourier transformation techniques (for reviews see Bax, 1982; Ernst et al. 1987), NMR spectroscopy has become a powerful tool for determining the 3D structures of small proteins (MW ≤ 10 kDa); for reviews see Wüthrich, 1986; Clore & Gronenborn, 1987. For larger molecules, however, the amount of detailed structural information that can be obtained using homonuclear 2D NMR techniques is limited because of the vast number of overlapping signals. In order to extend the capabilities of NMR to the study of larger systems, new approaches are required.

The magnetic state of iron in haem proteins has long been recognized as a convenient indicator of chemical coordination as well as more subtle biochemical properties. In the trivalent case in particular, there are three magnetically distinct configurations of the five 3d electrons, yielding spin states of S = 1/2, 3/2 and 5/2. The first and third are extremely familiar, and often lie close enough in energy so that a thermal mixture of low-spin S = 1/2 and high-spin S = 5/2 states exists in an ensemble of molecules. Selection rules for common perturbations (ΔS = ∘, ± 1 for the spin-orbit interaction and ΔS = ∘ for the electronic Zeeman interaction) ensure that quantum mixtures, in which the wave function is a true combination of S = 1/2 and S = 5/2 components, are not observed. The mid-spin, S = 3/2, state, and allowed 5/2–3/2 and 1/2–3/2 quantum mixtures including it, are much less well known. These have only rarely been invoked in recent years as an explanation for experimental haem protein magnetic data.

1. INTRODUCTION 2

2. OVERALL STRUCTURE AND SUBSTRUCTURES 5

2.1 Overall structure and components 5

2.2 Bidirectional rotary motor 5

2.3 Drive shaft 8

2.4 Bushing 8

2.5 Universal joint 9

2.6 Helical propeller 9

2.7 Axial junction 10

2.8 Capping structure 11

3. ASSEMBLY PROCESS OF THE FLAGELLUM 11

3.1 Step by step assembly 11

3.2 Flagellum-specific export apparatus and the channel 12

4. UNIQUE CHARACTERISTICS OF THE FLAGELLAR MOTOR DYNAMICS 13

5. STRUCTURAL DESIGN OF FLAGELLIN FOR ASSEMBLY REGULATION AND POLYMORPHISM 14

5.1 Domain organization and terminal disorder of flagellin 15

5.2 The role of terminal disorder in filament formation and polymorphism 17

5.3 Common structural motif for regulation of self-assembly 21

6. STRUCTURAL DESIGN OF FLAGELLAR FILAMENTS FOR POLYMORPHISM 22

6.1 Polymorphic mechanism 23

6.2 Structures of the filaments deduced by electron microscopy 25

6.2.1 Overview of the electron microscopic studies 25

6.2.2 Helical image reconstruction procedure 27

6.2.3 Structural details of the filament 28

6.3 X-ray fibre diffraction studies 32

6.3.1 Overview of the X-ray studies 32

6.3.2 Orientation of liquid crystalline sols and diffraction patterns 33

6.3.3 Equatorial analysis 35

6.3.4 A preliminary map refined at 11 resolution 37

6.4 Overall chain folding of the subunit in the filament 38

6.4.1 Mapping out the terminal and central regions 38

6.4.2 The chain folding and role of each domain 42

6.5 Polymorphic nature of flagellar filament 43

6.5.1 Comparison of the L- and R-type 43

6.5.2 New helical symmetry Lt-type 46

6.5.3 Direct comparison of the Lt-type lattice to the other two 48

6.5.4 Plausible conformational changes involved in polymorphism 51

7. PERSPECTIVE 55

8. ACKNOWLEDGEMENTS 55

9. REFERENCES 55