One-third rule

Ion traps are favored for proteomics studies because of their ability to perform multistage mass analysis (MSn), thereby increasing the structural information obtained from molecules. Ion traps, however, do not provide information for ions that have lower mass-to-charge values (the one-third rule). Additionally, the sensitivity of ion traps can also be limiting because only about 50% of the ions within a trap are ejected to the detector. Ion traps are also subject to a space charging phenomenon that may occur when the concentration of ions in the trap is high and produces ion repulsion within the trap. Nevertheless, the versatility and robustness of ion trap MS underlies its popularity for several proteomics-related applications. 

Numerical integration of a variable / measured at a set of equally spaced values of the independent variable x. The integral 7(1,7) = [ydx is approximated with both the trapezoidal rule (a) and Simpson s one-third rule b). In each case, the value of Y is given by the area under the heavy lines. The light lines in b) represent extensions of the three parabolic sections that are used to construct this approximation. 

Simpson s Rules. There are better procedures for approximating the integral of a function that make use of quadratic and cubic forms rather than linear segments. The simplest of these is Simpson s one-third rule ... 

In cases where n is divisible neither by 2 nor by 3, the range of integration may be split into two parts, one for Simpson s one-third rule, the other for Simpson s three-eighths rule. Alternatively, if the curve is approximately linear in one or two intervals, the trapezoidal rule may be used in these intervals. 

The errors resulting from the use of Simpson s one-third rule are much smaller than those associated with the use of the trapezoidal rule. This is illustrated by the example given in Fig. 1. The points shown in this figure were generated from the function j = 10 - + 0.03/ and are given below ... 

Retrospective analysis of CT scans has suggested that early signs of extensive infarction on CT, corresponding to a very poor ASPECTS score of < 2 (Weir et al. 2006) are associated with 85% mortality without thrombolysis and poor outcome, including hemorrhagic transformation, after thrombolysis (von Kummer et al. 1994, 1997 Hacke et al. 1998 Dzialowski et al. 2006). These observations have led to the introduction of the one-third rule, that is, patients with signs of infarction of greater than one-third of the middle cerebral artery... 

Simpson s one-third rule (three-point) (Figure A-3). A more accurate evaluation of the integral can be found with the application of Simpson s rule ... 

Simpson s three-eighths rule (four-point) (Figure A-4). An improved version of Simpson s one-third rule can be made by applying Simpson s second rule ... 

This version of Simpson s rule is sometimes called Simpson s one-third rule because of the 3 in the denominator. There is another version, called Simpson s five-eighths rule, which corresponds to fitting third-degree polynomials to four points at a time. 

If h represents the common distance of the ordinates apart, we ba e the familiar result known as Simpson s one-third rule, thus,... 

Examples.—(1) Compare Simpson s one-third rule and the three-eighths rule when h = 1, with the result of the integration of... 

Bt = Cp(Tg,p — 7 )/(A/tv), where FFg.p is the fuel vapor mass fraction interpolated to the droplet location. For 7 > Jb, By is set equal to Bj. The Clausius-Qapeyron equilibrium vapor-pressure relationship is used to compute the fuel mass fraction at the droplet surface. In addition, convective correction actors (based on Ranz and Marshall correlations) are applied to obtain spray evaporation rates at high Reynolds numbers. Liquid properties are evaluated using the one third rule for reference mass fractions [28]. Advanced models for droplet evaporation accounting for nonequilibrium effects can also be incorporated in the above framework by altering the timescales associated with the droplet lifetime and the convective heating. 

QITs are remarkable instruments because spectra can be obtained, ions stored, and sophisticated MS/MS experiments conducted, all in a cost-effective way (with a small footprint). One limitation, applicable to all ion traps, is the so-called one-third rule, which states that in CID MS/MS it is not possible to detect product ions that are less than about one-third of the value of the precursor ion e.g., for a precursor ion of mJz 900 the detection limit for product ions is miz -300. This limit can be frustrating e.g., it is not possible to detect the immonium ions formed from amino acids during CID of a peptide, nor can QIT be used with CID for certain techniques, such as iTRAQ (Section 3.5.19.3). Similarly to quadmpoles, from which they are derived, QITs have limited resolution. Alternative fragmentation induced by rf pulsing provides a type of scan in which the one-third rule does not apply and low mass ions can be observed. 

For both chemical and physical reasons, product ions of low mass can be problematic for MRM detection. The practical interpretation of low mass in this context varies with circumstances. Thus, the chemical disadvantage is mainly concerned with the observation (Aebi 1996) that chemical noise (background) from API sources is considerably more intense at lower m/z values. While this observation directly affects SIM rather than MRM detection, it can also apply to MRM to some extent. The physical problem with low mass product ions for MRM concerns the low mass cut off that exists for all RF-quadrupolar field devices (Section 6.4.2). This problem is extremely important for 3D ion traps, as expressed in the so-called one third rule whereby the low mass (really low m/z) cut off for product ions in MS/MS is 30%... 

The corrective coefficient/takes into account the contemporary occurrence of heat and mass transfer. The Nusselt number is determined according to Eq. (17.73). By combining Eqs. (17.68) and (17.79), it is possible to determine the temperature of the droplet. In this process iterative procedures are usually adopted to determine unknown quantities, moreover the properties of the saturated vapor around the droplet are evaluated resorting to the one-third rule (Eq. 17.26). 

Once again, the oo subscript indicates the gas condition at far field from the liquid film, whereas the condition s refers to quantities evaluated at the film surface using the one-third rule. The specific heat capacity Cp is evaluated with the one-third rule, whereas Le indicates the Lewis number defined as the ratio between the thermal diffusivity and the molecular diflfusivity. This number can be also expressed as the ratio between Prandtl and Schmidt numbers ... 

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