How many negative feedbacks are needed in a genetic cascade? — A numerical study

In a typical genetic cascade, the positive feedbacks from one gene to another are necessary for the amplification of signals. However, continuous positive regulations would enlarge the noise such that the system will no longer stable. In this article, we have numerically studied the minimal number of negative feedbacks in a genetic cascade with 51 genes, and studied the effect of the distribution of the positions of negative regulations on the noise level. Our results showed that at least 1/4 regulations should be negative feedbacks, and no continuous 6 positive feedback could appear to avoid the uncontrollable random noise if the current noise is at the average level. Our conclusions may shed light on the design of a reasonable genetic cascade.