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RNP: Root-non-produced; RNC: Root-non-consumed; DNP: Downstream-non-produced; UNC: Upstream-non-consume; UM: Unconnected module; FBA: Flux balance analysis; CBM: Constraint based modeling; GSM: Genome scale model; RS: Reactions subset; LP: Linear programming; MILP: Mixed integer linear programming; GPR: Gene-protein-reaction; EC: Enzyme commission number; TC: Transport commission number.
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Suppose there are n r reactions in cluster r and n s reactions in cluster s.
Assume we have a metabolic network that comprises R reactions and C metabolites.
In each iteration, a random subnetwork containing r reactions was selected.
Suppose that a given biochemical mechanism has N species and R reactions.
A model with n species, r reactions and p parameters is designated by M n, r, p).
The analyses concluded by comparing R reactions between 3d and 8d (Fig. 3E; Supplementary Table Nine) and S reactions between 3d and 8d (Fig. 3F; Supplementary Table Ten).
The r × 1 rate vector, v, contains the rate equations of the r reactions in the network, which are typically expressed in terms of enzyme kinetics.
Let x = (x1,..., xr) be a vector of metabolite concentrations and S ∈ ℤ m × r the stoichiometry matrix of a dynamical system with m metabolites and r reactions.
The bilateral upregulation of tachykinin immunoreactivity and increase in tachykinin concentration may be linked to the bilateral up-regulation in the NK-1 R reactions [ 18].
To this end, we fit to it a hierarchical random graph [ 27], once represented as a bipartite network with M metabolites and R reactions (see Figure 1).
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