Table 1.

An Illustration of the Use of Enrichment (Σmn), Molar Fraction (m), and Isotopomer Ratio (m/Σm)

[2-13C]-glycerol enrichment	Glycerol (m0)	Glycerol (m1)	Glucose (m0)*	Glucose (m1)	Glucose (m2)	(m2)/(m1)	(m1)/(Σm)&	(m2)/(Σm)	(Σmn)#
0%	1.0	0	1.0	0	0		na	na	0
10%	0.9	0.1	0.81	0.18	0.01	1/18	0.01/0.19	0.18/0.19	0.20
20%	0.8	0.2	0.64	0.32	0.04	1/8	0.04/0.36 (1/9)	0.32/0.36 (8/9)	0.40
20% with dilution by 50% unlabeled glucose			0.82	0.16	0.02	1/8	0.02/0.18 (1/9)	0.16/0.18 (8/9)	0.20

^*m0 stands for the fraction of molecule having no ¹³C; m1 fraction of molecule with one ¹³C and m2, two ¹³C substitution. The sum of m0+m1+m2 = 1. The molar fractions for m0, m1 and m2 are the coefficients of a binomial distribution (p+q)^2 where q is the enrichment of [2-¹³C]-glycerol and p=1-q.

^&(m1)/(Σm) and (m2)/(Σm) are m1 and m2 expressed as a fraction of molecules having ¹³C substitution. Σm is the abbreviation for $\sum _{i=1}^n{m}_i$ . (m0) is not included in the Σm. The ratios (m1)/(Σm) and (m2)/(Σm) are not affected by the product dilution.

^#(Σmn) stands for $\sum _{i=0}^n{m}_i\times i$ and is the sum of the products of the mass isotopomer fraction multiplied by the number of ¹³C substitutions - m0*0+m1*1+m2*2. It reflects the number of ¹³C per molecule in glucose. Thus dilution by unlabeled glucose also dilutes the corresponding Σmn.