Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemic...

A biochemical oscillator model, describing developmental stage of myxobacteria, is analyzed mathematically. Observations from numerical simulations show that in a certain range parameters, the corresponding system ordinary differential equations displays stable and robust oscillations. In this work, we use geometric singular perturbation theory blow-up method to prove existence strongly attract...

Biological networks have been recently found to exhibit many topological properties of the so-called complex networks. It has been reported that they are, in general, both highly skewed and directed. In this paper, we report on the dynamics of a Michaelis-Menten like model when the topological features of the underlying network resemble those of real biological networks. Specifically, instead o...

The rate of hydrochloric acid production by isolated, bullfrog gastric mucosae depends critically on the supply of chloride ion to the serosal surface. Secretion of acid is negligible if chloride is completely replaced by glucuronate and gluconate ion. The experimental evidence indicates that the rate of acid secretion may be regarded as a reaction velocity, depending on chloride concentration ...