###### Time-of-Flight Mass Spectrometry Resolution and Mass Measurement Accuracy

Resolution and mass measurement accuracy are two fundamental concepts in TOF mass spectrometry that must be understood to fully utilize the experiment. Resolution is the experimental observable of the resolving power of the instrument. Resolving power is the ability to separate components that are similar within the separating medium. In TOF mass spectrometry, the resolving power of the instrument is the ability to separate ions of similar flight times into separate signals.

The resolution observed in TOF mass spectrometry is calculated from the signals observed and is derived from the relationship between m/z and flight time. The m/z is related to flight time by Equation 1, where m is mass, D is distance, and t is time.

**m = (2eV / d2) * t2 [Eq. 1]**

The derivative of Equation 1 yields:

**dm = (2eV / d2) * 2t dt [Eq. 2]**

The relationship of m / dm yields:

**m / dm = t / 2dt [Eq. 3]**

Alternatively, Equation 3 can be written as follows:

**m / Δm = t / 2Δt [Eq. 4]**

where Dt is equal to the full width at half maximum (FWHM) of the peak measured.

Equation 4 is the definition of resolution for TOF mass spectrometry and is calculate from the FWHM of a peak along with the respective centroid in time or m/z.

The resolution obtained affects the ability to accurately determine the m/z of the analyte. Below are two plots of relative intensity versus m/z for a protonated ion of the peptide bradykinin (Mr = 1061.22). The plots in Figures 1a and 1b are for bradykinin acquired when the maximum resolution observed is 1000 and 5000 m/Δm, respectively. The peak profile in Figure 1a is the sum of the various 13C isotopic contributions from the molecular formula; whereas, in Figure 1b the isotopic contributions of 13C are separated into discrete signals. The heavier isotopes of nitrogen and oxygen also contribute to the multiplet, but carbon is the most abundant element by percent in organic molecules like peptides and 13C is the major contributor to the multiplet. For a more detailed explanation, see **Effect of Mass on Isotopic Peak Profiles**.

An accurate determination of the m/z ratio of a signal depends on how well one knows the standard used for calibration and how well one can measure the center of mass of the unknown signal. The average mass of a molecule is obtained from the sum of the average weight of each element. Due to the variability in percent composition of the isotopes, the certainty of the number is good to five or six significant figures. Therefore, at m/z 1062.2 of bradykinin, the accuracy is only certain to the first decimal place or 0.1% (1000 ppm). The uncertainty is in the second decimal position or error >0.01% (>100ppm). The monoisotopic mass (the mass derived from the most abundant isotope of each element) is certain to eight or nine significant figures. Thus, at m/z 1060.5692 (monoisotopic mass of the protonated bradykinin ion) the certainty is to the fourth decimal place, or 0.1 ppm. Therefore, the mass measurement accuracy of a data set acquired with sufficient resolving power to observe the monoisotopic profile of ions will be greater than a data set acquired where only average mass profiles are observed.

Isotopic peaks are approximately 1 mass unit apart. Therefore, to continue to observe the isotopic profile of an ion as m/z increases (Δm remains constant), resolution must increase. Figures 1, 2, 3, and 4 contain an overlay of the isotopic and average profiles for bradykinin, melittin, insulin (bovine), and cytochrome c (equus), respectively. The resolution used to observe the isotopic profiles of bradykinin, melittin, insulin, and cytochrome c are 1000, 5000, 15000, and 25000 respectively. Typically, the resolution needed to resolve the isotopes of a singly charged ion is twice the m/z. That is, for an ion of 1000 m/z, the resolution required to distinguish the isotopes is 2000 m/Δm.

There is a practical limit to resolution. Currently, the maximum resolving power of the state-of-the-art TOF mass spectrometer is approximately 20,000 m/Δm. There is also limit to the utility of isotopic resolution. As the monoisotopic peak decreases in relative intensity (e.g., bovine insulin and greater mass) it becomes difficult to obtain a signal from which an accurate center of mass can be determined. When such a problem occurs it is often better to use the average mass of the peak.