  Comprehension of metabolic pathways is considerably enhanced by metabolic
flux analysis (MFA-ILE) in isotope labeling experiments. The balance equations
are given by hundreds of algebraic (stationary MFA) or ordinary differential
equations (nonstationary MFA), and reducing the number of operations is
therefore a crucial part of reducing the computation cost. The main bottleneck
for deterministic algorithms is the computation of derivatives, particularly
for nonstationary MFA. In this article we explain how the overall
identification process may be speeded up by using the adjoint approach to
compute the gradient of the residual sum of squares. The proposed approach
shows significant improvements in terms of complexity and computation time when
it is compared with the usual (direct) approach. Numerical results are obtained
for the central metabolic pathways of Escherichia coli and are validated
against reference software in the stationary case. The methods and algorithms
described in this paper are included in the sysmetab software package
distributed under an Open Source license at
http://forge.scilab.org/index.php/p/sysmetab/.
