Experimental evidence confirms that signaling pathways may cause unique dynamics of transcription factor (TF) stimulation, but the way an input signal is encoded by this type of lively, noisy TF and farther deciphered by downstream genes remains largely unclear signal decoding. Here, utilizing a method of stochastic transcription with sign regulation, we now show that (1) maintaining the degree of the signal sound invariant but controlling the sign length can both improve the mutual information (MI) and lower the energetic cost (EC); (2) when the signal length is adjusted, the bigger MI requires the bigger EC, but when the signal interval is fixed, there’s an optimum time that the sign spends at a lower branch, for example that MI reaches the max; (3) if the interval and the length will be concurrently fixed, raising the input sound can always improve MI in the event of transcription regulation instead of in the event of degradation regulation. Additionally, we discover that the input sound can cause stochastic focusing on a method. These results show not just the mechanism of signal but also the purpose of sound in gene expression levels that are controlling.

Introduction
Cells are vulnerable to environments and will need to respond to signs for survival that was superior. There are two chief mechanisms to procedure (actually encode) signs in cellular signaling pathways1,2,3,4,5,6: amplitude modulation (AM) where the complete concentration of an inner signaling molecule encodes the input , and frequency modulation (FM) where the interval between successive bursts signifies the stimulating signal. Even though both of these signal-encoding mechanics are found in signaling pathways, of a signal is deciphered to the data, the question remains evasive.

There’s experimental evidence to confirm that FM or AM or both may happen in gene regulation. Here we record several examples that are relevant. To begin with, p53, a tumor transcription factor (TF), can answer the UV radiation at an AM or a FM manner1,2,3. Secondly, at the yeast Saccharomyces cerevisiae, the concentration of this TF Msn2 is proportional to the concentration that is H2O2 below stress, indicating an AM mechanism7. After inputting the nucleus in bursts8, third modulates a hundred target genes. Stimulus’ degree impacts the burst frequency but not the burst amplitude and the length, indicating an mechanism.