A simplified approach for modeling diffusion into cells

Regulation of the intracellular concentration of substrates is essential fo r the maintenance of a stable cellular environment. Diffusion and reaction processes supply and consume substrates within cells and determine their st eady-state concentrations. To realistically represent these processes by co mputer simulation they must be modeled in three dimensions. Yet three-dimen sional models are inherently computing intensive. This study describes a me thod, which substantially simplifies the modeling of diffusion into a polyh edral body (a cube), that was used as a model representation of a cell. The method is applied to a case study of oxygen diffusion into nitrogen-fixing , rhizobia-infected cells in legume nodules. The method involved generating a one-dimensional representation of the three-dimensional problem to provi de a "surface area profile" of three-dimensional diffusion. The one-dimensi onal models were significantly easier to program, several orders of magnitu de faster to solve and in this study were validated by assessing their resu lts against those of comparable three-dimensional models of diffusion into the same body. The results show the one-dimensional method to be a close ap proximation of a three-dimensional source-sink problem with systematic diff erences below 10% for fractional oxygenation of leghemoglobin, cell respira tion and nitrogenase activity. Larger differences between models (up to 45% ) in the predicted average and innermost O-2 concentrations had no effects on the physiological conclusions of the study, but were attributed to the p oorer resolution of the three- than the one-dimensional model, and to an in herent simplification in the derivation of the one-dimensional surface area profiles. The one-dimensional modeling approach was found to be a simple, yet powerful tool for the study of diffusion and reaction in biological sys tems. (C) 2000 Academic Press.