Multiplicative Lévy noise-induced transitions in gene expression

Gene expression is intrinsically noisy. Experimental studies have shown that random fluctuations are large bursts and heavy-tailed distributions. Therefore, this study aims to consider transition dynamics in a gene transcriptional regulatory system via the mean first exit time (MFET) and first escape probability (FEP), when the degradation rate is under multiplicative non-Gaussian Lévy fluctuations in the sense of Itô and Marcus forms. We find that, in the Marcus form case, the FEP corresponding to different stability index and noise intensity has an intersection point, whereas in the Itô form case, the turning point only occurs at stability index. Increasing the initial CI concentration is helpful for improving the likelihood of transcription in both cases. Our results also imply that larger jumps of Lévy noise and smaller noise intensity can shorten the time of state transition to boost protein production.