Table 1.
[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 . (m0) is not included in the Σm. The ratios (m1)/(Σm) and (m2)/(Σm) are not affected by the product dilution.
(Σmn) stands for 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.