This note studies the number of positive steady states in biomolecular reactions consisting of activation/deactivation futile cycles, such as those arising from phosphorylations and dephosphorylations at each level of a MAPK cascade. It is shown that (1) for some parameter ranges, there are at least n + 1 (if n is even) or n (if n is odd) steady states; (2) There never are more than 2n steady s...

this paper investigates the importance of considering biomass growth and decay for predicting a field scale microbial degradation of btex plume in an unconfined aquifer system in the pump station area of tehran oil refinery (tor), iran. a two-dimensional finite volume model has been presented to predict multi-species reactive transport incorporating physical, chemical and biological processes i...