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| The Mass Defect |
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The mass defect (mdefect) is related to the nuclear binding energy released upon formation and stabilization of the nucleus of a given isotope.[1] The mass equivalent of the nuclear binding energy can be calculated as the difference between the actual mass of the isotope (mactual) and the mass of the protons (1.00728 amu) and neutrons (1.00867 amu) that went into the creation of the nucleus of the elemental isotope:
(1)
By this definition the mass of every atom is slightly less than that of its constituent protons and neutrons. This difference is liberated as energy (E = mc2) upon formation of the specific elemental isotope.
In the days of Avogadro, however, the exact masses of protons and neutrons weren’t known and Einstein had yet to formulate his theory of relativity. Therefore, by convention, the mass defect of 12C is defined as zero atomic mass units (amu), and the mass defect of any other stable elemental isotope is calculated as the difference between the actual mass of the isotope (relative to the exact defined mass of 12C as 12.00000 amu) and the isotope’s nominal mass (i.e., the integer sum of the numbers of protons and neutrons).[2]
(2)
The difference between these two calculation averages 0.007975 amu per nucleon. The periodic table shown above uses the 12C zero mass defect convention. This convention keeps everything consistent with Avogadro’s number (6.022 x 1023 particles/g-atom).
The mass defects of other elements commonly found in biomolecules differ negligibly from that of carbon: 14N is 0.0031 amu, 16O is -0.0051 amu, and 1H is 0.0078 amu. Sulfur and phosphorus, which are generally at lower abundance in biomolecules, exhibit slightly larger mass defects of -0.0279 amu and -0.0262 amu, respectively, for the most abundant isotopes 32S and 31P. An analysis of the mass defects for the most abundant stable nuclei [2] of all of the elements shows a maximal mass defect value of approximately -0.1 amu for elements with atomic numbers between 35 (Br) and 63 (Eu).
For high resolution mass spectrometers, the ability to distinguish ions is dominated by the mass accuracy of the instrument at the low end of the mass-to-charge scale. For example, a mass accuracy of 30 ppm can resolve a 0.1 amu mass difference to a total mass of 3300 amu for a single charge state, assuming instrumental resolution is not limiting. Greater mass defect discrimination is possible if multiple mass defect elements are incorporated into a single tag. Bromine and iodine are particularly good mass defect elements in that they are easily incorporated into organic tags. Bromine is particularly advantageous since it has a lower mass than iodine and has a nearly equivalent natural abundance of its two stable isotopes 79Br and 81Br.
In high resolution mass spectrometers, the space between the single and higher charge states of biomolecules (i.e., negligible mass defect species) leave a window of nearly 0.4 amu unoccupied in nearly every amu of the mass spectrum. Therefore, it is possible to incorporate up to 4 mass defect atoms into an IDBEST™ reagent before substantial overlaps with other biomolecules are encountered. Since each mass defect element shifts the peak of the tagged species by an additional -0.1 amu, a 1 mass defect IDBEST™ tag can be resolved from a 2 mass defect IDBEST™ tag and so on.
1. Bueche, Principles of Physics, 3rd ed. (McGraw-Hill, NY, 1977).
2. Weast, R.C., CRC Handbook of Chemistry and Physics, 60th Ed. (CRC Press, Boca Raton, FL, 1974).
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