Isotope Dilution Mass Spectrometry J. Ignacio Garcia Alonso and Pablo Rodriguez-Gonzalez Faculty of Chemistry, University of Oviedo, Oviedo, Spain E-mail: jiga@uniovi.es, rodriguezpablo@uniovi.es RSC Publishing
Contents Chapter 1 Introduction to Isotope Dilution Mass Spectrometry (IDMS) 1.1 The Isotopic Nature of the Elements 1 1.1.1 Radioactive and Stable Isotopes: Decay Series 4 1.1.2 Historical Perspective: Early Mass Spectrometry Experiments 5 1.1.3 The Isotopic Composition of the Elements 6 1.1.4 The Atomic Weight of the Elements 8 1.2 Isotope Fractionation and Isotope Enrichment 8 1.2.1 The Mass-Dependent Fractionation Law 10 1.2.2 Artificial Procedures for Isotope Enrichment: Manufacture of Enriched Stable Isotopes 11 1.3 The Concept of Isotope Dilution 12 1.3.1 Catch and Release Experiments in Biology 14 1.3.2 Isotope Dilution with Radioactive Isotopes 15 1.3.3 Isotope Dilution with Stable Isotopes 17 1.4 Measurement of Isotope Ratios and Isotope Abundances by Mass Spectrometry 20 1.4.1 Source Considerations 20 1.4.2 Analyser Considerations 25 1.4.3 Modes of Sample Introduction 26 1.5 Historical Development of IDMS 28 1.6 Isotope Dilution Mass Spectrometry as a Primary Analytical Method 33 1.7 Source and Selection of Isotopically Labelled Standards 35 1.8 Applications of IDMS 37 1.9 Conclusions 38 References 39 Isotope Dilution Mass Spectrometry J. Ignacio Garcia Alonso and Pablo Rodriguez-Gonzalez J. I. Garcia Alonso and P. Rodriguez-Gonzalez 2013 Published by the Royal Society of Chemistry, www.rsc.org xi
xii Contents Chapter 2 IDMS Procedures and Calculation Methods 2.1 Introduction 41 2.2 Development of the Elemental IDMS Equation Using Isotope Ratios 42 2.2.1 General Analytical Procedures for Elemental Analysis 45 2.3 Calibration Strategies in Organic Analysis 48 2.3.1 The Organic IDMS Equation Used as a Calibration Graph 50 2.3.2 Mass Overlap: Nonlinear Equations 53 2.3.3 The Selection of the Labelled Internal Standard: Labelling Element, Labelling Position and Number of Isotopes: Isotopic Effects 55 2.3.4 General Analytical Procedure in Organic Analysis 58 2.4 A General IDMS Procedure Using Isotope Abundances 62 2.4.1 Application of Isotope Pattern Deconvolution in Organic IDMS 66 2.4.2 Requirements for Isotope Labelling in Organic IDMS Using Multiple Linear Regression 68 2.4.3 Confirmation Capabilities 69 2.4.4 Internal Correction of Systematic Errors 71 2.5 Critical Comparison of IDMS Calculation Methodologies 72 2.5.1 Requirements for a Certified Spike Solution 72 2.5.2 Tolerance to Isotopic Effects 73 2.5.3 Tolerance to Mass Overlap 74 2.5.4 Implementation in Routine IDMS Measurements 74 2.6 Conclusions 76 References 76 Chapter 3 Online Isotope Dilution Mass Spectrometry 3.1 The Concept of Online IDMS 77 3.2 Modes of Isotope Equilibration 77 3.3 Advantages and Disadvantages over Batch Procedures 80 3.4 Equations for Online IDMS 80 3.4.1 Online IDMS Equations Using Molar Fractions 82 3.4.2 The Molar-Flow Chromatogram 83 3.5 Flow Configurations Suitable for Online IDMS 85
Contents xiii 3.6 Calibration of the Spike Flow 89 3.7 Application of Online IDMS for Routine Multielemental Analysis Using ICP-MS 90 3.8 Application of Postcolumn IDMS for Trace-Element Speciation 93 3.8.1 Advantages and Limitations for Trace-Element Speciation 94 3.8.2 Examples of Application 95 3.9 Application of Postcolumn IDMS for Quantitative Proteomics 97 3.9.1 Direct Determination of Proteins Using Sulfur 98 3.9.2 Protein Labelling with Metals 99 3.10 Application of Postcolumn IDMS for Carbon-Containing Compounds 99 3.10.1 GC-Combustion-MS Configurations 100 3.10.2 LC-Oxidation-MS Configurations 103 3.11 Capabilities and Limitations of Online IDMS 106 3.12 Conclusions 107 References 108 Chapter 4 The Use of Multiple Enriched Isotopes for IDMS 4.1 Introduction 110 4.2 Multiple Spiking in Trace-Element Speciation 113 4.2.1 Historical Development 113 4.2.2 Analytical Consideration 114 4.3 Mathematical Approaches for Multiple-Spiking IDMS 116 4.3.1 Method 1: Calculation of Stable Isotope Concentrations 119 4.3.2 Method 2: "Speciated Isotope Dilution Mass Spectrometry" 122 4.3.3 Method 3: Multiple Species-Specific Isotope Dilution Analysis 124 4.3.4 Method 4: Isotope Pattern Deconvolution 126 4.4 Analytical Advantages and Applications of the Different Methods 130 4.4.1 Mathematical Complexity 130 4.4.2 Qualitative Information on any Spiked or Nonspiked Species Present in the Sample 131 4.4.3 Applications in Other Fields: Metabolic and Environmental Studies 133 4.4.4 Internal Correction of Mass Bias 135 4.4.5 Correction of Spectral Interferences 136 4.4.6 Applications with Molecular-Ion Sources 137
xiv Contents 4.4.7 Limitations of the Different Calculation Methods 137 4.5 General Procedure for Multiple Spiking Using Isotope Pattern Deconvolution 138 4.5.1 General Equations for IPD in Multiple-Spiking IDMS 139 4.5.2 General Equations for IPD and Interconverting Analytes 141 4.6 Applications in Mineral Metabolism: Combination of Metabolic and Quantification Tracers 145 4.7 Online IDMS with Multiple 4.8 Applications for the Tagging of Products and Living Tracers 151 Organisms 154 4.9 Conclusions 156 References 156 Chapter 5 The Isotope Composition of Natural-Abundance Elements and Molecules 5.1 The Isotope Composition of the Elements 159 5.1.1 Natural Variability: Isotopic Fractionation of the Elements 163 5.1.2 Correlation of Isotope Abundances: Isotope Ratio Uncertainties 167 5.1.3 The Uncertainties of the Atomic Weights 170 5.2 The Isotopic Composition of Natural-Abundance Molecules 171 5.2.1 Probabilities: the Binomial and Polynomial Distributions 172 5.2.2 The Calculation of Polynomial Distributions 176 5.2.3 The Matrix Multiplication Algorithm: Its Implementation Microsoft Excel 179 as a Visual Basic Macro for 5.2.4 Examples of Isotope Distribution Calculations 181 5.3 Uncertainties in the Isotope Composition of Molecules due to Natural Variability 185 5.3.1 Calculation of the Uncertainties Based on the Kragten Spreadsheet Procedure 186 5.4 The Calculation of Molecular Weights and Their Uncertainties 190 5.5 Conclusions 191 References 191
Contents xv Chapter 6 Selection of Isotopically Enriched Elements and Isotopically Labelled Molecules 6.1 Introduction 193 6.2 A General Mathematical Procedure for the Selection of Enriched Isotopes and the Isotope Labelling of Molecules 194 6.2.1 Development of the Error-Propagation Equations 195 6.2.2 Selection of the Enriched Tracer in Elemental Analysis 201 6.2.3 Selection of the Labelling of a Molecule in Organic IDMS 202 6.3 Additional Criteria for Isotope Selection in Elemental IDMS 205 6.3.1 Isobaric Overlaps 205 6.3.2 Polyatomic Interferences 207 6.4 Additional Criteria for Isotope Labelling in Organic IDMS 209 6.4.1 Selection of the Labelling Element 210 6.4.2 Selection of the Number of Labelling Isotopes 213 6.4.3 Selection of the Labelling Position 215 6.5 Calculation of the Isotope Composition of Labelled Molecules 216 6.5.1 The Isotope Distribution of Halogenated Compounds 217 6.5.2 The Isotope Distribution of Labelled Peptides 218 6.5.3 The Isotope Distribution of Labelled Steroids and Steroid Hormones 220 6.6 Calculation of the Isotope Composition of Mixtures of Natural-Abundance and Labelled Molecules 222 6.7 Conclusions 225 References 225 Chapter 7 The Measurement of the Isotope Composition of the Elements 7.1 Introduction 226 7.2 Ion Sources Employed for Elemental IDMS 227 7.2.1 The Thermal Ionisation Source 227 7.2.2 The Inductively Coupled Plasma Source 230 7.3 Mass Spectrometers Employed in Elemental IDMS 240 7.3.1 Quadrupoles 242 7.3.2 Double-Focusing Instruments 245 7.3.3 Multiple-Collector Instruments 248 7.4 Measurement of Isotope Compositions by ICP-MS 249
xvi Contents 7.4.1 Factors Affecting the Accuracy of the Measurements 249 7.4.2 Factors Affecting the Precision of the Measurements 270 7.5 The Measurement of Isotope Compositions on Transient Signals by ICP-MS 274 7.5.1 Factor Affecting the Accuracy of the Measurement 276 7.5.2 Factors Affecting the Precision of the Measurements 278 7.5.3 Multiple Linear Regression for Isotope-Ratio Measurement on Transient Signals 279 7.6 Applications of IDMS for Elemental Analysis 283 7.6.1 Total Elemental Determinations 283 7.6.2 Speciation Analysis 285 7.6.3 Mineral Metabolism Studies 286 7.6.4 Certification of Reference Materials 288 7.7 Conclusions 289 References 289 Chapter 8 The Measurement of the Isotope Composition of Molecules by Mass Spectrometry 8.1 Introduction 294 8.2 Ion Sources 295 8.2.1 The Electron Ionisation Source 295 8.2.2 The Electrospray Ion Source 300 8.3 Analysers and Detectors 302 8.3.1 Single-Quadrupole Analysers 304 8.3.2 Time-of-Flight (TOF) Analysers 309 8.3.3 Tandem Instruments 312 8.3.4 Detector Effects 314 8.4 Measuring Isotope Compositions in Transient Signals: Coupling Chromatography to Mass Spectrometry 317 8.4.1 Selection of the Measurement Conditions 317 8.4.2 Chromatographic Isotope Effects 319 8.4.3 Spectral Interferences and Matrix Effects 320 8.5 Non-IDMS Applications of the Measurement of Molecular Isotope Compositions 321 8.5.1 Identification or Confirmation of Molecules Based on its Isotope Composition 322 8.5.2 Determination of the Isotope Enrichment of Labelled Molecules 328 8.6 Applications of Enriched Isotopes in Proteomics 337 8.6.1 Relative Protein Quantification 338
Contents xvii 8.6.2 Absolute Quantification of Proteins 342 8.7 Conclusions 346 References 346 Chapter 9 Traceability in Isotope Dilution Mass Spectrometry 9.1 Introduction 351 9.2 IDMS as a Primary Method of Measurement 353 9.2.1 Certification of the Mass Fraction of the Tracers 354 9.2.2 Certification of Natural-Abundance Standards 355 9.2.3 Calibration of Instrumentation for the Measurement of Isotope Compositions 356 9.3 IDMS for the Certification of Reference Materials 357 9.3.1 Intercomparison Exercises Organised by the CCQM: Pilot Studies and Key Comparisons 360 9.3.2 IDMS in the Frame of National Metrology Institutes 362 9.4 IDMS for the Provision of Assigned Values to Proficiency Testing Exercises 363 9.4.1 Example of Proficiency Testing Exercise: Determination of Trace Elements in Waters 364 9.5 IDMS for Traceability in Clinical Chemistry 369 9.5.1 IDMS for the Determination of Total Cholesterol 371 9.5.2 IDMS for the Determination of Creatinine 372 9.5.3 IDMS for the Determination of Testosterone 373 9.6 Conclusions 376 References 376 Chapter 10 Uncertainty Evaluation in IDMS 10.1 Introduction 379 10.2 Basic Concepts 379 10.3 Combination of Uncertainty Sources: Uncertainty Propagation 382 10.3.1 Optimisation of Measurement Conditions in IDMS 384 10.3.2 The Case for Correlated Variables 386 10.3.3 Complex Measurement Functions 389 10.4 Kragten Spreadsheet Procedure for Uncertainty Propagation 390 10.4.1 Accuracy of the Partial Derivatives 392 10.4.2 Correlation between Variables 393
xviii Contents 10.5 Sources of Uncertainty and Their Propagation in Elemental IDMS 395 10.5.1 Single IDMS 395 10.5.2 Double IDMS 411 10.5.3 Exact-Matching IDMS 415 10.6 Sources of Uncertainty on Molecular IDMS Using a Calibration Graph 417 10.6.1 Selection of the Calibration Model 418 10.6.2 The Weighed Polynomial Regression 420 10.6.3 Uncertainty Propagation 10.7 Sources of Uncertainty in Isotope Pattern in Molecular IDMS 423 Deconvolution 425 10.7.1 Uncertainty from the Multiple Linear Regression 426 10.7.2 Uncertainties from the Theoretical and Experimental Isotope Compositions 428 10.7.3 Total Combined Uncertainty 431 10.8 Comparison of Uncertainties Using Different IDMS Calculation Methodologies 431 10.9 Conclusions 431 References 432 Appendix: Definition and Explanation of Symbols Used 434 Subject Index 439