Fluctuations and quality of control in biological cells: zero-order ultrasensitivity reinvestigated

Living cells differ from most other chemical systems in that they involve regulation pathways that depend very nonlinearly on chemical species that are present in low copy numbers per cell. This leads to a variety of intracellular kinetic phenomena that elude macroscopic modeling, which implicitly assumes that cells are infinitely large and fluctuations negligible. It is of particular importance to assess how fluctuations affect regulation in cases where precision and reliability are required. Here, taking finite cell size and stochastic aspects into account, we reinvestigate theoretically the mechanism of zero-order ultrasensitivity for covalent modification of target enzymes ( Proc. Natl. Acad. Sci. USA. 78:6840-6844). Macroscopically, this mechanism can produce a very sharp transition in target concentrations for very small changes in the activity of the converter enzymes. This study shows that the transition is much more gradual in a finite cell or a population of finite cells. It also demonstrates that the switch is exactly analogous to a thermodynamic phase transition and that ultrasensitivity is inevitably coupled to random ultravariation. As a consequence, the average response in a large population of cells will often be much more gradual than predicted from macroscopic descriptions.