| Great writeup. Here's a full-text review that contains all the math needed to build a model of this process (2013): "Quantitative modeling of bacterial chemotaxis: Signal amplification and accurate adaptation, Yuhai Tu" https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3737589/ The main points are: * Both receptor cooperativity and accurate adaptation can be described quantitatively by simple mathematical models. * An integrated model (the “standard model”), which contains both signal amplification and adaptation, is developed to predict responses of it E. coli cells to any time-dependent stimuli quantitatively. * Exponential ramps induce activity shifts, which depend on the ramp rate through the methylation rate function F(a). * Responses to oscillatory signals reveal that E. coli computes time-derivative in the low-frequency regime. * E. coli memorizes the logarithm of the ligand concentration and the Weber-Fetcher law holds in E. coli chemotaxis. It also goes into cooperative phase transitions in the receptor complexes as a means of signal amplification, using the same model as in Ising ferromagnetic spin-spin interactions in physics. |