Assumption:
We assume that the cellular state is in a steady phase, disregarding influences such as division or death, and that there is ample nutrition, preventing any bacteria from experiencing nutritional deficiencies. We also assume that Titin, once expressed, will not degrade, and that the expression of the T7 gene is not inhibited by any exogenous substances.
Derivation:
Since our objective is to evaluate the impact of IPTG concentration on protein expression levels, we can directly employ the Hill equation for this purpose. The equation is as follows: [equation should be inserted here if it was provided in the original text].
Under the previously established assumptions, we can hypothesize that a = 1, with a corresponding leakiness value of 0.01, and Xm equal to 10. Consequently, we can formulate the following expression: [the specific formula should be inserted here if it was provided in the original text].
Since the Hill equation is empirical, we must assume specific values for 'm' to approximate the most plausible curve. We hypothesize cases where m=5, 10, and 20, anticipating the derivation of a well-fitted graph.
In the future, we will endeavor to address the modeling issues related to the post-expression assembly of titin protein, integrating it into the current equation.
