The modified ILDM (Intrinsic Low-Dimensional Manifold) algorithm, developed by our group, is designed to distinguish between “slow” and “fast” metabolites, rather than “modes.” This approach allows the results of the analysis to be formulated directly—without requiring a linear transformation of the reaction system.
To select fast metabolites, COPASI employs the same numerical technique used in the original ILDM (Deuflhard) method: a local Schur decomposition of the Jacobian matrix.
The vector referred to as the “fast space” indicates the metabolites that contribute most significantly to the fast modes. This information is used to suggest the next candidate metabolite, whose designation as “fast” is then tested against an error tolerance criterion.
As a result, two matrices and two vectors are produced, describing the contribution of each metabolite to slow and fast spaces, respectively. This analysis is carried out using Schur transformation matrices. Importantly, the resulting sets of slow and fast components now correspond to the actual slow and fast metabolites, rather than simply to mathematical modes.
