Numerical solution of a partial differential equation system describing chemical kinetics and diffusion in a cell with the aid of compartmentalization

✍ Scribed by U. Salzner; P. Otto; J. Ladik

• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 767 KB
• Volume: 11
• Category: Article
• ISSN: 0192-8651
• DOI: 10.1002/jcc.540110205

✦ Synopsis

To build a kinetic model of a cell with diffusion one has to solve a coupled nonlinear partial differential equation system consisting of several hundred equations. (Several hundred chemical components undergoing several hundred reactions.) To solve this formidable mathematical problem the division of the model cell into compartments (most biochemical reactions take place in a certain part of the cell) was suggested.' Solving the differential equation system in one compartment, the results can be used as input at other compartments until mutually consistent solutions are achieved.

To test this suggestion 10 coupled chemical reactions with diffusion were investigated in a model that contains three compartments. The results in the case of pure diffusion are in excellent agreement with and without compartmentalization. After this the full problem was treated by compartmentalization using for the solution of the differential equation system a discretization of the concentrations as functions of space and time and the Newton-Raphson iterative procedure. The results obtained give reasonable space and time dependence for the concentrations of all 10 components.