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PROTEIN CRYSTALLIZATION Second Edition
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| Contents Foreword . . . . . vii Preface . . . . . xix Contributors . . . . . xxiii Part I. METHODS . . . . . 1 1. Some Words of Advice from an Old Hand . . . . . 3 Alexander McPherson 2. Rational Selection of Crystallization Techniques . . . . . 11 Joseph R. Luft and George T. DeTitta 2.1. Introduction . . . . . 13 2.2. Some Initial Considerations . . . . . 14 2.2.1. Screening . . . . . 15 2.2.2. Optimization . . . . . 15 2.2.3. The Container . . . . . 15 2.2.4. Temperature . . . . . 6 2.3. Choice of Method . . . . . 17 2.3.1. The Phase Diagram . . . . . 18 2.4. Batch Crystallization Methods . . . . . 19 2.4.1. How to Set Up a Batch Experiment . . . . . 22 2.4.2. Batch Methods That Use Oil . . . . . 23 2.5. Vapor-Diffusion Crystallization Methods . . . . . 23 2.5.1. How to Set Up a Vapor-Diffusion Experiment . . . . . 24 2.5.2. Choice of Reservoir Solution . . . . . 25 2.5.3. PEG Solutions and the Vapor Pressure of Water . . . . . 25 2.5.4. Volatile Additives . . . . . 26 2.5.5. Condensation . . . . . 26 2.5.6. Methods to Prevent Crystal Adhesion . . . . . 27 2.5.7. Containers and Supports for Hanging-Drop Experiments . . . . . 27 2.5.8. Sealants . . . . . 28 2.5.9. Sitting-Drop Vapor-Diffusion Methods . . . . . 29 2.6. Important Variables That Affect Kinetics . . . . . 29 2.6.1. Drop Volume and Shape . . . . . 30 2.6.2. Chemical Concentrations . . . . . 30 2.6.3. Different Chemicals Have Different Rates of Equilibration . . . . . 30 2.6.4. Experiment Drop Volume Ratios . . . . . 31 2.6.5. Drop-to-Reservoir Volume Ratio . . . . . 31 2.6.6 Passive Methods to Regulate the Rate of Vapor-Phase Equilibration . . . . . 32 2.7. Liquid-Diffusion Crystallization Methods . . . . . 32 2.7.1. Dialysis Liquid Diffusion . . . . . 33 2.7.2. How to Set Up a Dialysis Experiment . . . . . 33 2.7.3. Free-Interface Diffusion . . . . . 35 2.7.4. Counterdiffusion . . . . . 35 2.8. Practical Considerations for Crystallization Experiments . . . . . 37 2.8.1. A Chronological Sequence for Hanging-Drop Setups . . . . . 37 2.8.2. Mixing Experiment Drops . . . . . 38 2.9. Some Final Thoughts . . . . . 39 2.10. Summary of Key Points . . . . . 39 Acknowledgments . . . . . 40 Supplies . . . . . 40 References . . . . . 40 3. Automation for Crystallization: Practical Considerations in Choosing a System . . . . . 47 Joseph R. Luft and George T. DeTitta 3.1. Introduction . . . . . 49 3.2. Benefits of Automation . . . . . 50 3.2.1. Reduced Requirements for Protein Sample . . . . . 50 3.2.2. Replication . . . . . 51 3.2.3. Unstable Proteins . . . . . 51 3.2.4. Improved Output . . . . . 51 3.3. Automation for Liquid Handling of the Stock Solutions . . . . . 51 3.3.1. Formulation and Delivery of Cocktail Solutions . . . . . 52 3.3.2. Wash Cycles . . . . . 54 3.4. Automation for Crystallization . . . . . 54 3.4.1. Crystallization Method . . . . . 55 3.4.2. Screening, Optimization, or Both? . . . . . 55 3.4.3. Retrieving Crystals . . . . . 56 3.4.4. Dead, Priming, and Experiment Volumes . . . . . 56 3.4.5. Contact or Noncontact Delivery . . . . . 57 3.4.6. User Interface . . . . . 57 3.4.7. Periodic Maintenance and Quality Control . . . . . 57 3.5. Automation for Imaging the Experimental Outcomes . . . . . 58 3.5.1. Image Quality . . . . . 58 3.6. Automation for Information Management . . . . . 59 3.7. Caveat Emptor (Buyer Beware) . . . . . 60 3.7.1. Excess Capacity . . . . . 60 3.7.2. Personnel Costs . . . . . 60 3.7.3. Market Inquiries . . . . . 61 3.8. Concluding Remarks . . . . . 61 3.9. Summary of Key Points . . . . . 62 Acknowledgments . . . . . 62 References . . . . . 63 4. Oils for Screening and Optimization . . . . . 65 Naomi E. Chayen 4.1. Introduction . . . . . 67 4.2. The Rationale for Crystallization under Oil . . . . . 68 4.2.1. The Microbatch Technique . . . . . 68 4.2.2. Setting up Crystallization Trials by Microbatch . . . . . 68 4.2.3. Crystallization of Membrane Proteins in Oil . . . . . 70 4.2.4. Additional Benefits of Oil . . . . . 70 4.2.5. Harvesting Microbatch Crystals . . . . . 71 4.3. The Effect of Different Oils on Microbatch . . . . . 72 4.3.1. The Use of Different Oils in Screening . . . . . 72 4.3.2. Limitations of Crystallizing under Oil . . . . . 73 4.4. Use of Oils in Optimization . . . . . 73 4.4.1. Control of Nucleation . . . . . 74 4.4.2. Elimination of Surface Contact Leading to Access Nucleation . . . . . 74 4.5. Oil for the Miniaturization and Automation of Crystallization in Gels . . . . . 76 4.6. The Use of Oil for Controlling the Rate of Vapor-Diffusion Trials . . . . . 76 4.7. Conversion between Vapor Diffusion and Batch/Microbatch . . . . . 77 4.8. Summary . . . . . 79 References . . . . . 80 5. Crystallization in Gels and Capillaries . . . . . 83 Juan M. García-Ruiz 5.1. Why Use Gels and Capillaries for Protein Crystallization? . . . . . 85 5.2. Is Mass Transport by Diffusion Slower than Mass Transport by Convection? . . . . . 86 5.3. Is a Diffusive Environment Better than a Convective One for Obtaining High-Quality Crystals? . . . . . 87 5.4. Is There Convection in Vapor-Diffusion Experiments? . . . . . 88 5.5. How Can Convection Be Reduced in Crystallization Experiments? . . . . . 88 5.6. Which Gels Should Be Used? . . . . . 89 5.7. Is It Better to Use Gels or Capillaries for Reducing Convection? . . . . . 89 5.8. Can Gels and Capillaries Be Used with Classical Crystallization Techniques? . . . . . 90 5.9. How Does the Counterdiffusion Technique Work? . . . . . 90 5.10. Isn’t a Test Tube Too Large for the Small Amount of Proteins Usually Available? . . . . . 91 5.11. Is It Difficult to Fill Such a Small Capillary? . . . . . 92 5.12. What Kind of Capillaries Should Be Used for Counterdiffusion? . . . . . 92 5.13. Is It Possible to Cryoprotect the Crystals in the Capillaries? . . . . . 93 References . . . . . 93 6. Seeding . . . . . 95 Aengus Mac Sweeney and Allan D’Arcy 6.1. Introduction . . . . . 97 6.2. Streak Seeding . . . . . 99 6.3. Solution Microseeding . . . . . 101 6.3.1. Preparing a Microseed Stock . . . . . 101 6.3.2. Determining the Best Conditions for Solution Microseeding . . . . . 103 6.4. Macroseeding . . . . . 104 6.4.1. Obtaining the Best Possible Seed Crystals . . . . . 105 6.4.2. Determining the Crystal Solubility . . . . . 105 6.4.3. Determining Appropriate Crystal-Growth Conditions . . . . . 106 6.4.4. Washing and Transferring Crystals . . . . . 106 6.4.5. Feeding . . . . . 107 6.5. Seeding When Using Additives . . . . . 107 6.6. Automation and Microseeding . . . . . 108 6.7. Heterogeneous Seeding . . . . . 108 6.8. Summary . . . . . 111 6.9. Summary of Key Points . . . . . 112 References . . . . . 113 7. Heavy-Atom Derivatization . . . . . 115 Zbigniew Dauter and Mirosława Dauter 7.1. Why Heavy Atoms? . . . . . 117 7.2. Precautions . . . . . 119 7.3. Types of Heavy Atoms . . . . . 120 7.3.1. Classic Heavy-Metal Compounds . . . . . 120 7.3.2. Mercurials . . . . . 122 7.3.3. Lanthanides . . . . . 123 7.3.4 Metal Clusters . . . . . 123 7.3.5. Noble Gases . . . . . 124 7.3.6. Halides . . . . . 124 7.3.7. Iodination of Aromatics . . . . . 125 7.3.8. Rapid Soaks . . . . . 126 7.4. Confirming Derivatization . . . . . 127 7.4.1. Quick, Low-Resolution Data Collection . . . . . 127 7.4.2. Mass Spectrometry . . . . . 127 7.4.3. microPIXE . . . . . 128 7.4.4. X-Ray Absorption Spectroscopy . . . . . 128 7.4.5. Native Gel Shift Assay . . . . . 129 7.5. Radiation Damage . . . . . 129 7.6. Final Remarks . . . . . 130 References . . . . . 130 8. Preparation and Crystallization of Selenomethionine Protein . . . . . 135 Anna M. Larsson 8.1. Why Use Selenomethionine (SeMet)? . . . . . 137 8.2. When to Choose SeMet . . . . . 138 8.2.1. Methionine Content . . . . . 138 8.2.2. Expression Hosts . . . . . 139 8.2.3. Incorporation Analysis . . . . . 139 8.3. Other Related Approaches . . . . . 141 8.3.1. Selenocysteine . . . . . 141 8.3.2. Sulfur-SAD Phasing . . . . . 141 8.4. Properties of SeMet . . . . . 142 8.4.1. How to Avoid Oxidation . . . . . 142 8.4.2. How to Induce Oxidation and Why . . . . . 142 8.4.3. Sensitivity to Radiation Damage . . . . . 143 8.4.4. Data Collection Strategies . . . . . 143 8.4.5. L- or D,L-Selenomethionine . . . . . 143 8.4.6. Warning . . . . . 143 8.5. How to Express SeMet Protein . . . . . 144 8.5.1. Expression of SeMet-Labeled Protein in Escherichia coli . . . . . 144 8.5.2. Autoinduced Expression of SeMet-Labeled Protein in Escherichia coli . . . . . 145 8.5.3. Expression of SeMet-Labeled Protein in Pichia pastoris . . . . . 145 8.6. How to Purify and Crystallize SeMet Protein . . . . . 146 8.6.1. Purification . . . . . 146 8.6.2. Crystallization . . . . . 146 8.7. Summary . . . . . 147 References . . . . . 148 Appendix 8.1. Reagents for the Media . . . . . 151 9. Crystal Handling for Cryogenic Data Collection . . . . . 155 Elspeth F. Garman 9.1. Introduction . . . . . 157 9.2. Protocol for Finding Crystallization Conditions for Cryocrystallography . . . . . 162 9.3. Practical Tips for Crystal Transfer and Handling . . . . . 168 9.4. Methods for Introducing the Crystal into the Cryosolution . . . . . 169 9.4.1. Soaking . . . . . 169 9.4.2. Exchanging Mother Liquors . . . . . 169 9.4.3. Osmolarity Matching . . . . . 170 9.5. Postcrystallization Treatments . . . . . 170 9.5.1. Dry Mounting . . . . . 170 9.5.2. Annealing . . . . . 170 9.6. Summary of Key Points . . . . . 171 References . . . . . 172 PART II. TOOLS and STRATEGIES . . . . . 175 10. Interpretation of the Crystallization Drop Results . . . . . 177 Johan Philip Zeelen 10.1. Introduction . . . . . 179 10.2. The Stereomicroscope . . . . . 180 10.2.1. Bright- and Dark-Field Illumination . . . . . 180 10.2.2. Polarizers and Birefringence . . . . . 181 10.3. Optical Methods for Distinguishing Crystals of Protein, Salt, and Detergent . . . . . 182 10.4. Examination of the Crystallization Experiments . . . . . 184 10.5. Scoring . . . . . 185 10.6. Interpretation of the Drop Phenomena . . . . . 187 References and Further Reading . . . . . 193 11. Mass Spectrometry Applications in Protein Crystallography . . . . . 195 Sharon X. Gao and Marie Zhang 11.1. Introduction . . . . . 197 11.2. Mass Spectrometry Instrumentation . . . . . 198 11.2.1. Molecular Mass . . . . . 198 11.2.2. MALDI-MS . . . . . 199 11.2.3. ESI-MS . . . . . 202 11.2.4. Matrix-Free Desorption or Ionization on Porous Silicon (DIOS) . . . . . 204 11.3. Applications of MS in Protein Structure Determination . . . . . 204 11.3.1. High-Throughput MS Methods for Monitoring Protein Purity . . . . . 205 11.3.2. Verification of Protein Primary Structure . . . . . 205 11.3.3. Characterization of Posttranslational Modifications . . . . . 207 11.3.4. Detection of Heavy Atoms for Phasing . . . . . 209 11.3.5. Limited Proteolysis MS for Domain Mapping . . . . . 210 11.3.6. Large-Scale Limited Proteolysis and Crystallization Studies . . . . . 211 11.3.7. Probing Higher-Order Protein Structure with MS . . . . . 211 11.3.8. Analysis of the Content of Protein Crystals by MS . . . . . 212 11.4. Concluding Remarks . . . . . 213 References . . . . . 214 12. Dynamic Light Scattering . . . . . 221 Ulf Nobbmann and Terese Bergfors 12.1. Introduction . . . . . 223 12.1.1. How Does DLS Work? . . . . . 226 12.1.2. Relationship between Hydrodynamic Radius and Mass . . . . . 229 12.1.3. How Is the Dispersity Profile Obtained? . . . . . 230 12.2. Practical How-To . . . . . 233 12.2.1. Comparison with the Native PAGE . . . . . 233 12.2.2. Sample Preparation: Volume and Concentration . . . . . 234 12.2.3. Filtration . . . . . 235 12.2.4. Temperature . . . . . 235 12.2.5. More Things to Try: Increase the Ionic Strength . . . . . 236 12.2.6. Change the pH . . . . . 237 12.2.7. Increase Protein Concentration . . . . . 37 12.2.8. Additives . . . . . 238 12.3. Thermal Stability Measurements with DLS . . . . . 240 12.4. Data Interpretation . . . . . 241 12.5. Some Recommendations for Handling Your Protein Based on Its DLS Profile . . . . . 242 12.5.1. Monodisperse Samples (approximately 20% or less) . . . . . 242 12.5.2. Monodisperse Samples (approximately 30% or less) . . . . . 242 12.5.3. Bimodal and Polydisperse Samples . . . . . 243 12.6. Summary of Key Points . . . . . 243 References . . . . . 244 13. Improving Protein Crystallizability by Modifications and Engineering . . . . . 247 Xiayang Qiu and Cheryl A. Janson 13.1. Introduction . . . . . 249 13.2. Ligand Additions and Complexes . . . . . 250 13.2.1. Cofactors, Substrates, Inhibitors, and Other Ligands . . . . . 250 13.2.2. Protein–Protein and Protein–Nucleic Acid Complexes . . . . . 251 13.2.3. Complexes with Antibody Fragments . . . . . 251 13.3. Chemical and Biochemical Modifications . . . . . 252 13.3.1. Chemical Modification . . . . . 252 13.3.2. Biochemical Modification . . . . . 253 13.4. DNA-Construct Modification . . . . . 254 13.4.1. Affinity Tags and Protease Removal Sites . . . . . 254 13.4.2. Defining Domains for Construct Design . . . . . 255 13.4.3. Surface Mutations to Improve Solution Properties . . . . . 257 13.4.4. Surface Mutations to Facilitate Crystal Packing . . . . . 258 13.4.5. Metal–Ion-Mediated Crystallization . . . . . 260 13.5. Concluding Remarks . . . . . 262 References . . . . . 262 14. Handling the Protein Sample . . . . . 267 Terese Bergfors 14.1. Characterization of the Protein . . . . . 270 14.2. Concentrating the Protein . . . . . 271 14.3. Storage of the Protein . . . . . 273 14.3.1. Freezing . . . . . 273 14.3.2. Lyophilization . . . . . 276 14.3.3. Ammonium Sulfate Precipitation . . . . . 277 14.3.4. Heat Shock . . . . . 277 14.4. Buffer Choice: Implications for Screening . . . . . 279 14.5. Other Components in the Start Buffer . . . . . 282 14.5.1. Water . . . . . 282 14.5.2. Sodium Azide . . . . . 283 14.5.3. Reducing Agents . . . . . 284 14.6. Buffer Choice: Implications for Screening . . . . . 287 14.7. Other Components in the Start Buffer . . . . . 289 Acknowledgments . . . . . 289 References . . . . . 290 15. Two Approaches for Initial Screening: Evolution and Intelligent Design . . . . . 293 Janet Newman 15.1. Introduction . . . . . 295 15.2. Why Design a New Screen? . . . . . 296 15.2.1. Learning from the Past: Evolution (JCSG+) . . . . . 297 15.2.2. Intelligent Design (PACT) . . . . . 298 15.2.3. Does Limited Screening Work? . . . . . 302 15.3. Screening to Ease Optimization . . . . . 303 15.4. Designing Your Own Screen . . . . . 306 15.5. Summary of Key Points . . . . . 307 Supplies . . . . . 307 References . . . . . 307 16. Strategies for Protein Crystallization Screening . . . . . 309 Bernhard Rupp 16.1. Introduction . . . . . 311 16.1.1. Protein Crystals . . . . . 312 16.1.2. Basics of Protein Crystallization . . . . . 313 16.1.3. Beating the Odds . . . . . 313 16.2. Designing Your Protein . . . . . 314 16.2.1. Constructs and Tags . . . . . 314 16.2.2. Batch Variation and Contaminants . . . . . 315 16.2.3. Protein Concentration . . . . . 315 16.2.4. Purity, Freshness, and Conformational State . . . . . 316 16.2.5. Buffers, Salts, and Additives . . . . . 316 16.2.6. Temperature . . . . . 316 16.3. Choice of Crystallization Technique . . . . . 317 16.4. Crystallization Screening . . . . . 318 16.4.1. Crystallization As a Multivariate Sampling Problem . . . . . 319 16.4.2. Factorial Designs . . . . . 320 16.4.3. Sparse-Matrix Sampling . . . . . 321 16.4.4. Random Sampling and Number of Experiments . . . . . 322 16.4.5. Screening toward Optimization . . . . . 322 16.4.6. Practical Two-Tiered Approaches . . . . . 323 16.5. Robotics in the Academic Laboratory . . . . . 324 16.5. Summary of Key Points . . . . . 326 References . . . . . 327 17. Additives and Microcalorimetric Approaches for Optimization of Crystallization . . . . . 331 Joanne I. Yeh 17.1. Introduction . . . . . 333 17.2. Classes of Additives . . . . . 334 17.2.1. Cosmotropes . . . . . 334 17.2.2. Cations . . . . . 335 17.2.3. Polyols and Sugars . . . . . 335 17.2.4. Amino Acids . . . . . 336 17.2.5. Linkers . . . . . 336 17.2.6. Cofactors, Ligands, Substrates (Effectors) . . . . . 337 17.2.7. Reducing Agents and Chelators . . . . . 337 17.2.8. Chaotropes . . . . . 339 17.2.9. Surfactants . . . . . 339 17.3. What Concentration of Additive to Use . . . . . 341 17.4. Calorimetry Studies on Additives . . . . . 342 17.4.1. Instrumentation . . . . . 344 17.4.2. ITC and DSC Results . . . . . 346 17.5. Summary . . . . . 347 References . . . . . 347 PART III. LABORATORY EXERCISES . . . . . 351 LE. Laboratory Exercises . . . . . 353 LE1. Setting Up Microbatch Trials . . . . . 355 Naomi E. Chayen LE2. Limiting the Amount of Nucleation and Enhancing the Reproducibility of Experiments by Filtration . . . . . 359 Naomi E. Chayen LE3. Containerless Crystallization . . . . . 363 Naomi E. Chayen LE4. Insertion of Oil Barriers to Slow Down Vapor-Diffusion Experiments . . . . . 367 Naomi E. Chayen LE5. Improving Crystal Quality by Separating Nucleation and Growth in Hanging Drops . . . . . 371 Naomi E. Chayen LE6. Seeding with Lysozyme . . . . . 375 Aengus Mac Sweeney LE7. Studying the Influence of Supersaturation and Supersaturation Rate with the Crystallization Mushroom . . . . . 387 Juan Manuel García-Ruiz and Luis A. González-Ramírez LE8. Capillary Counterdiffusion Experiments with Granada Crystallization Boxes . . . . . 395 Juan Manuel García-Ruiz and Luis A. González-Ramírez LE9. Evaluation of Cryoprotectant Solutions . . . . . 401 Elspeth F. Garman LE10. Optimization Experiment with Additives . . . . . 405 Terese Bergfors LE11. Comparing Salt and Protein Crystals by Two Methods . . . . . 409 Terese Bergfors PART IV. A–Z . . . . . 415 A–Z . . . . . 417 Index . . . . . 427 |
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| Foreword This second edition of Protein Crystallization includes all the important methods, tools, and strategies that are presently used for crystallizing proteins. The result is a most impressive book—almost completely new as compared to the first edition. As with the first edition, the emphasis is on the practical procedures for performing the work in the laboratory. It will be an invaluable guide at the laboratory bench both for beginners and more experienced crystallizers of biological macromolecules. I have known Terese Bergfors since she came to our department in 1984. She has become one of the leading experts in the field of protein crystallization and her contributions are invaluable for her colleagues at our institute as well as for many crystallographers in other departments. She is an enthusiastic teacher and frequently teaches courses in protein crystallization here in Sweden and abroad. Terese Bergfors has done an excellent job of persuading well-known fellow scientists in her field to share their knowledge and experience on specific crystallization topics as authors for the different chapters of this book. In my view, this book constitutes perfect evidence that protein crystallization should now be considered a science rather than an art. However, as is strongly emphasized in the chapter by Joe Luft and George DeTitta, this presupposes that all the factors that influence crystallization are well controlled, even on a detailed level. The fact that this book is now in its second edition shows how rapidly our knowledge about protein crystallization is growing. The field has changed tremendously since its early days. In the beginning of the l960s, soon after the structures of myoglobin and hemoglobin were solved in Cambridge, our group in Uppsala started the structural determination of the enzyme human carbonic anhydrase. We purified the protein in enormous volumes from liters and liters of blood. The blood came from the University hospital after it had become too old to be used for blood transfusions. The crystallizations were done in dialysis bags containing milliliters of protein solution, a huge difference to the nanoliter volumes used today. In his chapter, Alexander McPherson concludes his thoughtful words of advice with the remark that “further advances in the field of protein crystallization are essential to greater progress in structural and molecular biology.” He encourages us all to contribute with new ideas, novel approaches, etc. Ideally this book will be a springboard for a development in this direction, as well as a great stimulus and guide for all protein crystallographers. Professor Emeritus Bror Strandberg, Uppsala University Member of Sir John Kendrew’s research team when determining the first three-dimensional structure of a protein (myoglobin) almost fifty years ago. Preface to the Second Edition Obtaining
crystals is currently the bottleneck despite the amazing progress in
the field of structural determination by X-ray crystallography. The aim
of this book is to help you procure crystals of good quality. It is
intended for active practitioners, the foot soldiers at the lab bench.
The earliest incarnation of this book was a photocopied manuscript
based on students’ questions. I began to compile materials and
protocols by way of answering them. The fact that this book is now in
its second edition, completely revised and updated, is an evidence of
the rapid development and importance of crystallization. The authors generously took their time to contribute to this book. I am indebted to them for their efforts. It has been a privilege to work with them and I have learned many things from the numerous discussions we shared this past year. I thank my colleagues who read the chapters and exercises and gave me valuable input. Some of my test readers deserve special mention: Anna Jansson, Bror Strandberg, Lars Liljas, Wojciech Krajewski, Gerard Kleywegt (all from Uppsala University), Jonas Vasur (Swedish Agricultural University), Joe Ng (University of Alabama in Huntsville), and Inés Muñoz (CNIO, Madrid). Matti Nikkola (Karolinska Institutet, Stockholm) and Christina Skans extricated me from some murky linguistic cul-de-sacs with their impressive knowledge of English. Mark Harris (Uppsala University) gave me invaluable help with the figures and his patience in explaining PhotoShop to me over and over verges on the saintly. Professor Alwyn Jones (Uppsala University) generously allowed me to devote myself to the book without interruption. Dr. Igor Tsigelny (International University Line) is editor of the series in which this book is a part. I am grateful to him for the opportunity to turn my photocopied papers into a book that has now reached its second edition. I thank Stefan Odestedt for sorting out the mysteries of Microsoft Excel for me and his moral support in general. Finally, I extend my deepest appreciation to my daughter, Carmen, for her forbearance yet once again during my preoccupation with this book. Uppsala, Sweden March 2009 Terese Bergfors |
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