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Electrophoresis in Practice: A Guide to Methods and Applications of DNA and Protein Separations, 5th Edition

Electrophoresis in Practice: A Guide to Methods and Applications of DNA and Protein Separations, 5th Edition

Reiner Westermeier

ISBN: 978-3-527-33880-1

May 2016

458 pages

Description

This fifth edition of the successful, long-selling classic has been completely revised and expanded, omitting some topics on obsolete DNA electrophoresis, but now with a completely new section on electrophoretic micro-methods and on-the-chip electrophoresis.
The text is geared towards advanced students and professionals and contains extended background sections, protocols and a trouble-shooting section. It is now also backed by a supplementary website providing all the figures for teaching purposes, as well as a selection of animated figures tested in many workshops to explain the underlying principles of the different electrophoretic methods.
Foreword XIX

Abbreviations, Symbols, Units XXI

Preface XXV

Part I Fundamentals 1

Introduction 1

Principle 1

Areas of Applications 3

The Sample 3

The Buffer 4

Electroendosmosis 5

References 6

1 Electrophoresis 7

1.1 General 7

1.1.1 Electrophoresis in Free Solution 7

1.1.2 Electrophoresis in Supporting Media 12

1.1.3 Gel Electrophoresis 13

1.1.3.1 Gel Types 13

1.1.3.2 Instrumentation for Gel Electrophoresis 17

1.1.3.3 Current and Voltage Conditions 17

1.1.4 Power Supply 19

1.1.5 Separation Chambers 20

1.1.5.1 Vertical Systems 20

1.1.5.2 Horizontal Systems 21

1.2 Electrophoresis in Nonrestrictive Gels 25

1.2.1 Agarose Gel Electrophoresis 25

1.2.1.1 Zone Electrophoresis 25

1.2.1.2 Immunoelectrophoresis 26

1.2.1.3 Affinity Electrophoresis 27

1.2.2 Polyacrylamide Gel Electrophoresis of Low MolecularWeight Substances 28

1.3 Electrophoresis in Restrictive Gels 28

1.3.1 The Ferguson Plot 28

1.3.2 Agarose Gel Electrophoresis 29

1.3.2.1 Proteins 29

1.3.2.2 Nucleic Acids 29

1.3.3 Pulsed-Field Gel Electrophoresis 30

1.3.4 Polyacrylamide Gel Electrophoresis of Nucleic Acids 32

1.3.4.1 DNA Sequencing 32

1.3.4.2 DNA Typing 34

1.3.4.3 Mutation Detection Methods 35

1.3.4.4 Denaturing PAGE of Microsatellites 37

1.3.4.5 Two-dimensional DNA Electrophoresis 37

1.3.5 Polyacrylamide Gel Electrophoresis of Proteins 37

1.3.5.1 Disc Electrophoresis 37

1.3.5.2 Gradient Gel Electrophoresis 39

1.3.5.3 SDS Electrophoresis 40

1.3.5.4 Cationic Detergent Electrophoresis 47

1.3.5.5 Blue Native Electrophoresis 47

1.3.5.6 Rehydrated Polyacrylamide Gels 48

1.3.5.7 Two-Dimensional Electrophoresis Techniques 49

1.3.5.8 GeLC-MS 50

References 51

2 Isotachophoresis 57

2.1 Migration with the Same Speed 57

2.2 ""Ion Train"" Separation 59

2.3 Zone Sharpening Effect 59

2.4 Concentration Regulation Effect 59

2.5 Quantitative Analysis 60

References 61

3 Isoelectric Focusing 63

3.1 Principles 63

3.2 Gels for IEF 65

3.2.1 Polyacrylamide Gels 65

3.2.2 Agarose Gels 67

3.3 Temperature 68

3.4 Controlling the pH Gradient 68

3.5 Kinds of pH Gradients 69

3.5.1 Free Carrier Ampholytes 69

3.5.1.1 Electrode Solutions 70

3.5.1.2 Denaturing IEF: Urea IEF 71

3.5.1.3 Separator IEF 72

3.5.1.4 Plateau Phenomenon 73

3.5.1.5 TheWorkflow of a Carrier Ampholyte IEF Run 73

3.5.2 Immobilized pH Gradients (IPG) 73

3.5.2.1 Preparation of Immobilized pH Gradients 75

3.5.2.2 Applications of Immobilized pH Gradients 76

3.6 Protein Detection in IEF Gels 77

3.7 Preparative Isoelectric Focusing 77

3.7.1 Carrier Ampholyte IEF in Gel 77

3.7.2 Carrier Ampholyte IEF in Free Solution 78

3.7.3 Immobilized pH Gradients 78

3.7.3.1 Isoelectric Membranes 78

3.7.3.2 Off-Gel IEF 79

3.8 Titration Curve Analysis 80

References 82

4 High-Resolution Two-Dimensional Electrophoresis 85

4.1 IEF in Immobilized pH Gradient Strips 85

4.1.1 Strip Lengths 86

4.1.2 pH Gradient Types 86

4.1.3 The Influence of Salts and Buffer Ions on the Separation 87

4.1.4 Basic IPG Gradients 88

4.1.5 Advantages of Immobilized pH Gradient Strips in 2D Electrophoresis 89

4.1.6 Rehydration of IPG Strips 90

4.1.6.1 Basic pH Gradients 90

4.1.6.2 Reswelling Tray 91

4.1.6.3 Cover Fluid 91

4.1.6.4 Rehydration Time 92

4.1.7 Sample Application on IPG Strips 92

4.1.8 IEF Conditions 95

4.1.8.1 Electrode Pads 95

4.1.8.2 Temperature 95

4.1.8.3 Electric Conditions 95

4.1.8.4 Time 96

4.1.9 Instrumentation 96

4.1.9.1 The Strip Tray Accessory 97

4.1.9.2 Dedicated Instruments for IPG Strips 97

4.1.9.3 Running IEF in IPG Strips 97

4.2 SDS-PAGE 98

4.2.1 Equilibration of the IPG Strips 98

4.2.2 Technical Concepts for the Second Dimension (SDS-PAGE) 99

4.2.2.1 Vertical Set-ups 99

4.2.2.2 Horizontal Set-ups 99

4.2.3 Gel Types 101

4.2.3.1 Gel Sizes 101

4.2.3.2 Vertical Gels 101

4.2.3.3 Horizontal Gels 102

4.2.4 Gel Casting 102

4.2.4.1 Gels for Multiple Vertical Systems 102

4.2.4.2 Gels for Horizontal Systems 104

4.2.5 Running the SDS Gels 105

4.2.5.1 Vertical Systems 105

4.2.5.2 Horizontal Systems 106

4.3 Proteomics 106

References 108

5 Protein Sample Preparation 111

5.1 Protein Quantification Methods 111

5.2 Preparation of Native Samples 112

5.3 Samples for SDS Electrophoresis 113

5.3.1 SDS Treatment 113

5.3.1.1 Nonreducing SDS Treatment 114

5.3.1.2 Reducing SDS Treatment 115

5.3.1.3 Reducing SDS Treatment with Subsequent Alkylation 116

5.3.2 Clean-up and Protein Enrichment 117

5.3.2.1 Precipitation 117

5.3.2.2 Protein Enrichment by Affinity Beads 118

5.4 Samples for High-Resolution 2D PAGE 118

5.4.1 CellWashing 119

5.4.2 Cell Disruption 119

5.4.3 Sample Acquisition and Storage 119

5.4.4 Protease Inactivation 122

5.4.5 Phosphatase Inactivation 122

5.4.6 Alkaline Conditions 123

5.4.7 Removal of Contaminants 123

5.4.7.1 Precipitation Methods 123

5.4.7.2 Affinity Beads 125

5.4.8 Prefractionation 125

5.4.8.1 Depletion of Highly Abundant Proteins 125

5.4.8.2 Equalizer Technology 125

5.4.8.3 Preseparation of Cell Organelles 126

5.4.8.4 Prefractionation according to Isoelectric Points 126

5.4.9 Special Case: Plant Proteins 127

References 127

6 Protein Detection 131

6.1 Fixation 131

6.1.1 IEF Gels 132

6.1.2 Agarose Gels 132

6.1.3 SDS Polyacrylamide Gels 132

6.2 Poststaining Methods 133

6.2.1 Organic Dyes 133

6.2.1.1 Monodisperse Coomassie Brilliant Blue Staining 133

6.2.1.2 Colloidal Coomassie Brilliant Blue Staining 133

6.2.1.3 Acid Violet 17 Staining for IEF Gels 134

6.2.2 Silver Staining 134

6.2.2.1 Colloidal Silver Staining 134

6.2.2.2 Silver Nitrate Staining 134

6.2.2.3 Ammoniacal Silver Staining 135

6.2.3 Negative Staining 136

6.2.3.1 Copper Staining 136

6.2.3.2 Imidazole Zinc Staining 136

6.2.4 Fluorescent Staining 136

6.2.5 Specific Detection 138

6.2.5.1 Proteins with Posttranslational Modifications 138

6.2.5.2 Isoenzymes 139

6.2.6 Stain-Free Technology 140

6.3 Prelabeling 140

6.3.1 Prelabeling with Fluorescent Tags 140

6.3.2 Radioactive Labeling of Living Cells 141

6.3.3 Labeling with Stable Isotopes 141

6.4 Difference Gel Electrophoresis (DIGE) 143

6.4.1 Minimum Lysine Labeling 143

6.4.2 SaturationCysteine Labeling 144

6.4.3 The Internal Standard 146

6.4.4 Experimental Design 147

6.4.5 Major Benefits of 2D DIGE 147

6.4.6 Specific Labeling of Cell-Surface Proteins 148

6.4.7 Comparative Fluorescence Gel Electrophoresis 148

6.5 Imaging, Image Analysis, Spot Picking 149

6.5.1 Quantitative Evaluation 149

6.5.1.1 Quantification Prerequisites 149

6.5.1.2 Critical Issues in Quantification 150

6.5.2 Imaging Systems 151

6.5.2.1 Optical Density 152

6.5.2.2 Densitometry 152

6.5.2.3 CCD Cameras 153

6.5.3 Image Analysis 154

6.5.3.1 One-Dimensional Gel Software 155

6.5.3.2 Two-Dimensional Gel Software 156

6.5.4 Protein Identification and Characterization 158

6.5.4.1 Spot-Picking 159

References 160

7 Blotting 165

7.1 Transfer Methods 165

7.1.1 Diffusion Blotting 165

7.1.2 Capillary Blotting 165

7.1.3 Pressure Blotting 166

7.1.4 Vacuum Blotting 167

7.1.5 Electrophoretic Blotting 168

7.1.5.1 Tank Blotting 168

7.1.5.2 Semidry Blotting 169

7.1.5.3 Electrophoretic Blotting of Film-Backed Gels 171

7.2 Blotting Membranes 171

7.3 Buffers for Electrophoretic Transfers 172

7.3.1 Proteins 172

7.3.1.1 Tank Blotting 172

7.3.1.2 Semidry Blotting 173

7.3.2 Nucleic Acids 174

7.3.2.1 Tank Blotting 174

7.3.2.2 Semidry Blotting 174

7.4 General Staining 174

7.5 Blocking 175

7.6 Specific Detection 175

7.6.1 Hybridization 175

7.6.2 Enzyme Blotting 176

7.6.3 Immunoblotting 176

7.6.4 Lectin Blotting 179

7.6.5 Stripping, Reprobing 179

7.6.6 Double Blotting 180

7.7 Protein Sequencing 180

7.8 Transfer Issues 180

7.9 Electro-Elution of Proteins from Gels 181

References 183

Part II Equipment and Methods 187

Equipment 187

Methods 187

Small Molecules 187

Proteins 187

DNA 188

Instrumentation 188

Accessories 189

Consumables 190

8 Special Laboratory Equipment 191

9 Consumables 193

10 Chemicals 195

10.1 Reagents 195

Method 1 PAGE of Dyes 197

M1.1 Sample Preparation 197

M1.2 Stock Solutions 197

M1.3 Preparing the Casting Cassette 198

M1.3.1 Gasket 198

M1.3.2 Slot-Former 198

M1.3.3 Assembling the Gel Cassette 199

M1.4 Casting Ultra-Thin-Layer Gels 200

M1.5 Electrophoretic Separation 201

M1.5.1 Removing the Gel from the Cassette 201

Method 2 Agarose and Immunoelectrophoresis 205

M2.1 Sample Preparation 205

M2.2 Stock Solutions 206

M2.3 Preparing the Gels 206

M2.3.1 Agarose Gel Electrophoresis 206

M2.3.1.1 Preparing the Slot-Former 207

M2.3.1.2 Assembling the Gel Cassette 207

M2.3.2 Immunoelectrophoresis Gels 209

M2.3.2.1 Punching Out the SampleWells and Troughs 210

M2.4 Electrophoresis 211

M2.4.1 Grabar–Williams Technique 212

M2.4.2 Laurell Technique 212

M2.5 Protein Detection 214

M2.5.1 Coomassie Staining (Agarose Electrophoresis) 214

M2.5.2 Immunofixing of Agarose Electrophoresis 214

M2.5.3 Coomassie Staining (Immunoelectrophoresis) 215

M2.5.4 Silver Staining 215

References 216

Method 3 Titration Curve Analysis 217

M3.1 Sample Preparation 217

M3.2 Stock Solutions 217

M3.3 Preparing the Blank Gels 218

M3.3.1 Preparing the Casting Cassette 218

M3.3.2 Assembling the Gel Cassette 219

M3.3.3 Filling the Gel Cassette 220

M3.3.4 Removing the Gel from the Cassette 221

M3.3.5 Washing the Gel 221

M3.4 Titration Curve Analysis 222

M3.4.1 Reswelling the Rehydratable Gel 222

M3.4.2 Formation of the pH Gradient 222

M3.4.3 Native Electrophoresis in the pH Spectrum 223

M3.5 Coomassie and Silver Staining 224

M3.5.1 Colloidal Coomassie Staining 224

M3.5.2 Acid Violet 17 Staining 224

M3.5.3 Five-Minute Silver Staining of Dried Gels 225

M3.6 Interpreting the Curves 225

References 227

Method 4 Native PAGE in Amphoteric-Buffers 229

M4.1 Sample Preparation 230

M4.2 Stock Solutions 230

M4.3 Preparing the Empty Gels 231

M4.3.1 Slot-Former 231

M4.3.2 Assembling the Casting Cassette 232

M4.3.3 Polymerization Solutions 233

M4.3.4 Filling the Cooled Gel Cassette 234

M4.3.5 Removing the Gel from the Casting Cassette 234

M4.3.6 Washing the Gel 234

M4.4 Electrophoresis 235

M4.4.1 Rehydration in Amphoteric Buffers 235

M4.5 Coomassie and Silver Staining 240

M4.5.1 Colloidal Coomassie Staining 240

M4.5.2 Acid Violet 17 Staining 240

M4.5.3 Five-Minute Silver Staining of Dried Gels 241

References 242

Method 5 Agarose IEF 243

M5.1 Sample Preparation 243

M5.2 Preparing the Agarose Gel 244

M5.2.1 Making the Spacer Plate Hydrophobic 244

M5.2.2 Assembling the Casting Cassette 244

M5.2.3 Preparation of Electrode Solutions 246

M5.3 Isoelectric Focusing 247

M5.4 Protein Detection 249

M5.4.1 Coomassie Blue Staining 249

M5.4.2 Immunofixation 249

M5.4.3 Silver Staining 250

References 251

Method 6 PAGIEF in Rehydrated Gels 253

M6.1 Sample Preparation 253

M6.2 Stock Solutions 254

M6.3 Preparing the Blank Gels 254

M6.3.1 Making the Spacer Plate Hydrophobic 254

M6.3.2 Assembling the Casting Cassette 255

M6.3.3 Filling the Gel Cassette 256

M6.3.4 Removing the Gel from the Casting Cassette 257

M6.3.5 Washing the Gel 257

M6.4 Isoelectric Focusing 257

M6.4.1 Rehydration Solution with Carrier Ampholytes (SERVALYT™, Pharmalyte™) 257

M6.4.2 Reswelling the Gel 257

M6.4.3 Separation of Proteins 259

M6.4.4 Sample Application 259

M6.5 Coomassie and Silver Staining 260

M6.5.1 Colloidal Coomassie Staining 260

M6.5.2 Acid Violet 17 Staining 261

M6.5.3 Five-Minute Silver Staining of Dried Gels 261

M6.5.4 The Most Sensitive Silver Staining Procedure for IEF 262

M6.6 Perspectives 264

References 266

Method 7 Horizontal SDS-PAGE 267

M7.1 Sample Preparation 267

M7.1.1 Nonreducing SDS Treatment 267

M7.1.2 Reducing SDS Treatment 268

M7.1.3 Reducing SDS Treatment with Alkylation 268

M7.2 Prelabeling with Fluorescent Dye 269

M7.2.1 Labeling 269

M7.2.2 Detection 269

M7.3 Stock Solutions for Gel Preparation 270

M7.4 Preparing the Casting Cassette 271

M7.4.1 Preparing the Slot-Former 271

M7.4.2 Assembling the Casting Cassette 272

M7.5 Gradient Gel 273

M7.5.1 Pouring the Gradient 273

M7.6 Electrophoresis 277

M7.6.1 Preparing the Separation Chamber 277

M7.6.2 Placing the Gel on the Cooling Plate 277

M7.6.3 Electrophoresis 278

M7.7 Protein Detection 279

M7.7.1 Hot Coomassie Staining 279

M7.7.2 Colloidal Staining 280

M7.7.2.1 Stock Solutions 280

M7.7.2.2 Fixation Solution 280

M7.7.2.3 Staining Solution 280

M7.7.2.4 Staining Procedure 281

M7.7.3 Reversible Imidazole–Zinc Negative Staining 281

M7.7.4 Silver Staining 281

M7.7.4.1 Blue Toning 282

M7.7.5 Fluorescent Staining with SERVA Purple 283

M7.7.5.1 Stock Solutions 283

M7.7.5.2 Staining Protocol 283

M7.7.5.3 Detection 284

M7.8 Blotting 284

M7.9 Perspectives 285

M7.9.1 Gel Characteristics 285

M7.9.2 SDS Electrophoresis inWashed and Rehydrated Gels 285

M7.9.3 SDS Disc Electrophoresis in a Rehydrated and Selectively Equilibrated Gel 285

M7.9.4 Peptide Separation 286

References 287

Method 8 Vertical PAGE 289

M8.1 Sample Preparation and Prelabeling 290

M8.2 Stock Solutions for SDS- PAGE 290

M8.3 Single Gel Casting 291

M8.3.1 Discontinuous SDS-Polyacrylamide Gels 292

M8.3.2 Porosity Gradient Gels 293

M8.4 Multiple Gel Casting 295

M8.4.1 Multiple Discontinuous SDS Polyacrylamide Gels 296

M8.4.2 Multiple SDS Polyacrylamide Gradient Gels 298

M8.5 Electrophoresis 299

M8.5.1 Running Conditions 300

M8.6 SDS Electrophoresis of Small Peptides 301

M8.7 Blue Native PAGE 303

M8.8 Two-Dimensional Electrophoresis 306

M8.9 DNA Electrophoresis 307

M8.10 Long-Shelf-Life Gels 308

M8.11 Protein Detection 308

M8.12 Preparing Glass Plates with Bind-Silane 308

M8.12.1 Coating a Glass Plate with Bind-Silane 309

M8.12.2 Removal of Gel and Bind-Silane from a Glass Plate 309

References 310

Method 9 Semidry Blotting of Proteins 311

M9.1 Transfer Buffers 313

M9.2 Technical Procedure 314

M9.2.1 GelsWithout Support Film 315

M9.2.2 Gels on Film Backing 315

M9.2.2.1 Using a Nitrocellulose (NC) Blotting Membrane 316

M9.2.2.2 Using a PVDF Blotting Membrane 316

M9.2.2.3 Transfer from Cut-Off Gels 317

M9.3 Staining of Blotting Membranes 318

References 320

Method 10 IEF in Immobilized pH Gradients 321

M10.1 Sample Preparation 322

M10.2 Stock Solutions 322

M10.3 Immobiline Recipes 323

M10.3.1 Custom-Made pH Gradients 323

M10.4 Preparing the Casting Cassette 327

M10.4.1 Making the Spacer Plate Hydrophobic 327

M10.4.2 Assembling the Casting Cassette 327

M10.5 Preparing the pH Gradient Gels 328

M10.5.1 Pouring the Gradient 328

M10.5.1.1 Setting Up the Casting Apparatus 328

M10.5.1.2 Filling the Cassette 329

M10.5.1.3 Washing the Gel 331

M10.5.1.4 Storage 332

M10.5.1.5 Rehydration 332

M10.6 Isoelectric Focusing 332

M10.6.1 Placing the Gel on the Cooling Plate 332

M10.6.2 Sample Application 335

M10.6.3 Electrode Solutions 335

M10.6.4 Focusing Conditions 335

M10.6.5 Measuring the pH Gradient 336

M10.7 Staining 336

M10.7.1 Colloidal Coomassie Staining 336

M10.7.2 Acid Violet 17 Staining 337

M10.7.3 Staining Procedure 337

M10.7.4 Silver Staining 337

M10.7.5 Practical Tip 337

M10.8 Strategies for IPG Focusing 337

References 339

Method 11 High-Resolution 2D Electrophoresis 341

M11.1 Sample Preparation 342

M11.1.1 Sample Clean-Up 343

M11.2 Prelabeling of Proteins with Fluorescent Dyes 346

M11.2.1 Labeling of One Sample 346

M11.2.2 DIGE Labeling 347

M11.2.2.1 Experimental Design 347

M11.2.2.2 Sample Preparation 347

M11.2.2.3 Reconstitution of the CyDyes 348

M11.2.2.4 Minimal Labeling of the Lysines 349

M11.2.2.5 Saturation Labeling of the Cysteines 350

M11.2.2.6 Preparation for Loading the Samples onto the IPG Strips 351

M11.2.2.7 Detection of DIGE Spots 352

M11.3 Stock Solutions for Gel Preparation 352

M11.4 Preparing the Gels 354

M11.4.1 IPG Strips 354

M11.4.2 SDS Polyacrylamide Gels 358

M11.5 Separation Conditions 359

M11.5.1 First Dimension (IPG-IEF) 359

M11.5.1.1 IPG-IEF with Conventional Equipment 360

M11.5.1.2 IPG-IEF with IPG Strip Kit (Figure ) 360

M11.5.1.3 IPG-IEF in Individual Ceramic Trays 362

M11.5.1.4 Equipment and Trays for Cup Loading 363

M11.5.2 Equilibration 366

M11.5.3 Second Dimension (SDS Electrophoresis) 366

M11.5.3.1 Vertical Gels 366

M11.5.3.2 Horizontal Gels 367

M11.6 Staining Procedures 370

M11.6.1 Staining of Multiple Gels 371

M11.6.2 Colloidal Coomassie Staining 371

M11.6.2.1 Stock Solutions 371

M11.6.2.2 Fixation Solution 372

M11.6.2.3 Staining Solution 372

M11.6.2.4 Staining Procedure: 372

M11.6.3 Reversible Imidazole–Zinc Negative Staining 372

M11.6.4 Silver Staining 373

M11.6.4.1 Mass Spectrometry Analysis of Silver-Stained Spots 374

M11.6.4.2 Blue Toning 374

M11.6.5 Fluorescent Staining with SERVA Purple 374

M11.6.5.1 Stock Solutions 374

M11.6.5.2 Staining Protocol 375

M11.6.5.3 Detection 376

References 377

Method 12 PAGE of DNA Fragments 379

M12.1 Stock Solutions 380

M12.2 Preparing the Gels 381

M12.3 Sample Preparation 385

M12.4 Electrophoresis 386

M12.5 Silver Staining 391

Appendix Troubleshooting 393

A1.1 Frequent Mistakes 393

A1.1.1 Miscalculation of the Cross-Linking Factor of a Polyacrylamide Gel 393

A1.1.2 Polymerization Temperature and Time for a Polyacrylamide Gel 393

A1.1.3 Creating Aggregates in SDS Samples 394

A1.1.4 Titration of the Running Buffer in SDS Electrophoresis 394

A1.1.5 Incomplete Removal of PBS from Cells 395

A1.1.6 Over-focusing of IPG Strips in 2D PAGE 395

A1.1.6.1 Protein Degradation in Basic pH Gradients 395

A1.1.6.2 The ""Thiourea Effect"" 395

A1.2 Isoelectric Focusing 396

A1.2.1 PAGIEF with Carrier Ampholytes 396

A1.2.2 Agarose IEF with Carrier Ampholytes 402

A1.2.3 Immobilized pH Gradients 405

A1.3 SDS Electrophoresis 410

A1.3.1 Horizontal SDS-PAGE 410

A1.3.2 Vertical PAGE 418

A1.4 Two-Dimensional Electrophoresis 419

A1.5 Semi-Dry Blotting 426

A1.6 DNA Electrophoresis 431

Index 435