Statistics
During our runs, we saw that not only the α of the protein is important. Actually it is limited by a series of factors, specially complex formation. Also the time of production is more coupled with the basal expression, that actually represents the strength of the promoter, than with the connection with the sender, represented by the α of the protein. So, for doing a good analysis of the system we should do an N-dimensional analysis of the system.
Also, considering that we are working with a scale with a lot of stochastic influence, the statistics of it are far more complicated then deterministic events. So, combining both ideas, we propose here an analysis for the system, which could elucidate more about the results of works with Quorum Sensing.
Our proposal is to use a simple computational method: During the ODE integration, we are going to do a stochastic perturbation and at each step, keep doing this. Using this simple approach we can run a Monte Carlo simulation to establish a confidence interval that we can compare to our data. This is a kind of stochastic deviation that is intrinsic to the processes, not simply of the measurement, therefore is way harder to be treated with.
This is a very known approach, specially in ecology, to compare simulations to the experimental data. But the catch is then to make a dimensional analysis of the models, where we can adjust the parameters and variables to find stable states of our system for each parameter of interest, basal expression or the relation between complex formation and separation, which limits the entire system. Then, use this approach with Monte Carlo simulation to create small perturbations around the values of these parameters and combine them with the variations in the systems itself, creating a combination in a N-dimensional space which can not only test our data, but also, by knowing some few chemical data, we could predict an entire set of systems.