User talk:Kehrli/b

Kendrick Analysis 101
Kendrick analysis is often used as a name for methods that find homologous molecules using their mass residual after an operation that is equivalent to a modulo operation. For example, straight chain Alkanes belong to a homologous series of organic compounds in which the members differ by a constant mass of 14 Da corresponding to the CH2 group.

There are three different methods to do a Kendrick analysis:

Trend line method
The simplest way is to produce a graph where each molecule M is arranged according to its mass m(M) and its mass excess/defect ∆m(M) = m(M) - integer[m(M)]. When expressing the mass m in daltons, (in metrology terms: [m] = Da) this aligns all homologous molecules on trend lines whose slope depends on the "building block" of the molecules. The disadvantage of this method is that the offsets from sloped trendlines are difficult to read. The advantage is that no new units have to be introduced and that it works for all "building block" molecules.

Kendrick method
Kendrick realized that by using a mass scale with units equal to the mass of the building blocks, the trend lines would become horizontal for all homologous series of this "building block". This simplifies somewhat the reading of the mass defect. However, it requires a new mass scale and thereby a new unit for each building block as well as a conversion of each molecule mass into this unit.

CH2 Modulo method
Math has a tool called modular arithmetic that can reveal the same homologous relation using the modulo operation.
 * A ~ B (mod CH2)

The above statement is read: "A is modulo CH2 equivalent to B." Or, when considering the mass of the molecules A and B:
 * m(A) ~ m(B) (mod m(CH2))

"A has the same modulo CH2 mass as B."

The remainder mass of a molecule M, Δm(M), would be expressed as the remainder r:
 * Δm(M) = r = m(M) mod m(CH2)

If the modulo operation nor the remainder operation are defined
 * Δm(M) = m(M) - m(CH2)·round(m(M)/m(CH2))

This method has all advantages of the previous methods: it works with any building blocks, does not require new units, and it produces horizontal lines in a Kendrick plot.


 * Hsu, C. S.; Qian, K. N.; Chen, Y. N. C. Anal. Chim. Acta 1992, 264, 79-89. http://dx.doi.org/10.1016/0003-2670(92)85299-L
 * Alain Reinhardt, Christian Emmenegger, Bertran Gerrits, Christian Panse, Josef Dommen, Urs Baltensperger, Renato Zenobi, and Markus Kalberer; Anal. Chem. 2007, 79, 4074-4082)

Kendrick modulo method
Closer inspection reveals that above modulo method is not equivalent to the previous two methods. The modulo method above uses m(CH2) as the modulus whereas the Kendrick method effectively uses m(CH2)/14 as the modulus. The Kendrick mass defect of a molecule M, Δm(M), would be expressed as:
 * Δm(M) = m(M) mod m(CH2)/14

Thereby the range of the reminders shrinks from 14 Da to a range of 1 Da, effectively wrapping the reminders into a constrained space. Some groups have found that this leads to overcrowding with complex samples and therefore "unfolded" the effect of the Kendrick modulus by creating 14 versions of Kendrick plots, thereby recreating the properties of m(CH2) modulo method.
 * Hsu, C. S.; Qian, K. N.; Chen, Y. N. C. Anal. Chim. Acta 1992, 264, 79-89. http://dx.doi.org/10.1016/0003-2670(92)85299-L

The modulo-modulo plot
(Note: this section may contain original content. I have not found sources on this plot yet, but I am still searching. This section is intended for explaining the bigger picture, not for inclusion on this article). It is not exactly clear why Kendrick choose a m(CH2)/14 modulus instead of a m(CH2) modulus. It may be for visualization reasons. For low masses the mass defects are quite small. Therefore all molecules would be very close to the integer mass lines when using the m(CH2) modulus in a Kendrick type plot. In this case it would be interesting to see a plot with the m(CH2)/14 reminder (= Kendrick mass defect) on one axis (y-axis) and the m(CH2) reminder on the x-axis. This plot could be more informative than the traditional Kendrick plot. Both plots would just be different views of the 3D data structure where each molecule would be plotted in a 3D space with mass, m(CH2) reminder and m(CH2)/14 reminder as the axis'.