Stoichiometric synthesis of metabolic pathways

A vector-matrix approach to the theoretical design of metabolic pathways converting chemical compounds, viz., preset substrates, into desirable products is described. It is a mathematical basis for computer-aided generation of alternative biochemical reaction sets executing the given substrate-product conversion. The pathways are retrieved from the used database of biochemical reacions and utilize the reaction stoichiometry and restrictions based on the irreversibility of a part of them. Particular attention is paid to the analysis of restriction interrelations. It is shown that the number of restrictions can be notably reduced due to the existence of families of parallel restricting planes in the space of reaction flows. Coinciding planes of contradirectional restrictions result in the existence of fixed reaction flow values. The problem of exclusion of so called futile cycles is also considered. Utilization of these factors allows essential lowering of the problem complexity and necessary computational resources. An example of alternative biochemical pathway computation for conversion of glucose and glycerol into succinic acid is given. It is found that for a preset “substrate-product”; pair many pathways have the same high-energy bond balance.