The COD balances closed within 3 8 % of the initial, thus confirming the reliability of the data.
The carbon balances closed between 96 113% in all the cultures (41.6 C-mmol/g DW [ 19]).
However, this estimation will generally be inaccurate, often lying outside feasible biological boundaries, even for a consistent, overdetermined system with carbon and nitrogen balances closed within experimental error.
On average, nitrogen and carbon balances closed to 70%and88%8%, respectively, and experimental data were consistent with the assumed biochemistry and the pseudo-steady state hypothesis (see Methods).
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As shown in the last row of the table, the carbon balance closes for all four sets of cultivations.
The set [ a, b ] = { x ∈ Y : a ⪯ x ⪯ b } is called a closed interval in Y. Obviously, every closed interval [ − b, b ] in an ordered vector space with convergence Y is a convex, balanced, closed and bounded set.
The carbon balance closed for 92 and 90 % for propionaldehyde and valeraldehyde, respectively.
However, for the actual hydrolysate the carbon mass balance closes at 1.06, which means that there is 6% more carbon being formed than the carbon consumed.
Taking the conversion of PAA to ortho-hydroxyphenyl acetic acid (o-OH-PAA) into account, which in our cultures accounted for approximately 10% of the total PAA consumption, the PAA balance closed between 90 - 110%, indicating the absence of PAA catabolism, which is in agreement with earlier observations [ 23].
