On correlated reaction sets and coupled reaction sets in metabolic networks

Two reactions are in the same "correlated reaction set" (or "Co-Set") if their fluxes are linearly correlated. On the other hand, two reactions are "coupled" if nonzero flux through one reaction implies nonzero flux through the other reaction. Flux correlation analysis has been previously used in the analysis of enzyme dysregulation and enzymopathy, while flux coupling analysis has been used to predict co-expression of genes and to model network evolution. The goal of this paper is to emphasize, through a few examples, that these two concepts are inherently different. In other words, except for the case of full coupling, which implies perfect correlation between two fluxes (R2 = 1), there are no constraints on Pearson correlation coefficients (CC) in case of any other type of (un)coupling relations. In other words, Pearson CC can take any value between 0 and 1 in other cases. Furthermore, by analyzing genome-scale metabolic networks, we confirm that there are some examples in real networks of bacteria, yeast and human, which approve that flux coupling and flux correlation cannot be used interchangeably.

A Two-Dimensional Solution of the Advection–Diffusion Equation with Dry Deposition to the Ground

A mathematical scheme is developed to simulate the vertical turbulent dispersion of air pollution that is absorbed or deposited to the ground. The scheme is an exact analytical solution of the atmospheric diffusion equation, without any restriction to the vertical profile of wind speed and eddy diffusivities, and taking into account the dry deposition by a boundary condition of a nonzero flux to the ground. The performances of the solution, with a proper parameterization of the vertical profiles of the wind and eddy diffusivities, were evaluated against the dataset from the Hanford (Washington) diffusion experiment, in which two tracers (one depositing and one nondepositing) were released simultaneously. In addition, the solution derived in this work is compared with four different models, with deposition at the ground, found in the literature.