TABLE 1

Definitions of indices, variables, and calculated quantities used in modeling atom fraction excess 18O for each bacterial taxon

ParameterDescription
Indices
    iTaxon
    jReplicate (or tube) within a treatment
    kFraction (within a replicate)
    INo. of taxa
    JNo. of replicates (within a treatment)
    KNo. of fractions (within a replicate)
Variables
    fjkTotal no. of 16S rRNA gene copies per μl (all taxa combined) in fraction k of replicate j (copies μl−1)
    pijkProportion of the total no. of 16S rRNA gene copies per μl that are taxon i in fraction k of replicate j (unitless)
    xjkDensity of fraction k of replicate j (g cm−3)
Calculated quantities
    yijkNo. of 16S rRNA gene copies per μl of taxon i in fraction k of replicate j (copies μl−1)
    yijTotal no. of 16S rRNA gene copies per μl of taxon i in replicate j (copies μl−1)
    WijObserved weighted avg density for taxon i in replicate j (g cm−3)
    WLABiMean observed weighted avg density for taxon i in the labeled treatment (mean across all replicates of the treatment with the heavy isotope) (g cm−3)
    WLIGHTiMean observed weighted avg density for taxon i in the unlabeled (i.e., natural abundance) treatment (mean across all replicates in all treatments without heavy isotopes) (g cm−3)
    GiGuanine-plus-cytosine content of taxon i (unitless)
    HCARBONiAvg no. of carbon atoms per DNA nucleotide for taxon i
    MLIGHTiObserved mol wt of the DNA fragment containing the 16S RNA gene for taxon i in the unlabeled (i.e., natural abundance) treatment (g mol−1)
    MHEAVYMAXiTheoretical mol wt of the DNA fragment containing the 16S RNA gene for taxon i assuming maximum labeling by the heavy isotope (g mol−1)
    MLABiObserved mol wt of the DNA fragment containing the 16S RNA gene for taxon i in the labeled treatment (g mol−1)
    ZiDifference in observed weighted avg densities of taxon i for the labeled and unlabeled treatments (g cm−3)
    AOXYGENiAtom fraction excess of 18O in the labeled vs unlabeled treatment for taxon i (unitless)
    ACARBONiAtom fraction excess of 13C in the labeled vs unlabeled treatment for taxon i (unitless)