title: Transitions in a genetic transcriptional regulatory system under Lévy motion.
abstract: Based on a stochastic differential equation model for a single genetic regulatory system, we examine the dynamical effects of noisy fluctuations, arising in the synthesis reaction, on the evolution of the transcription factor activator in terms of its concentration. The fluctuations are modeled by Brownian motion and α-stable Lévy motion. Two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), are used to analyse the transitions from the low to high concentration states. A shorter MFET or higher FEP in the low concentration region facilitates such a transition. We have observed that higher noise intensities and larger jumps of the Lévy motion shortens the MFET and thus benefits transitions. The Lévy motion activates a transition from the low concentration region to the non-adjacent high concentration region, while Brownian motion can not induce this phenomenon. There are optimal proportions of Gaussian and non-Gaussian noises, which maximise the quantities MFET and FEP for each concentration, when the total sum of noise intensities are kept constant. Because a weaker stability indicates a higher transition probability, a new geometric concept is introduced to quantify the basin stability of the low concentration region, characterised by the escaping behaviour.
authors.affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.|Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China.
authors.forename: Yayun
authors.initials: Y
authors.lastname: Zheng
authors.affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.|Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China.|Department of Science and Technology, University of Cape Verde, Praia 7600, Cape Verde.
authors.forename: Larissa
authors.initials: L
authors.lastname: Serdukova
authors.affiliation: Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China.|Department of Applied Mathematics, Illinois Institute of Technology,312-567-5335, Chicago 60616, USA.
authors.forename: Jinqiao
authors.initials: J
authors.lastname: Duan
authors.affiliation: Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China.|Research Domain on Transdisciplinary Concepts and Methods, Potsdam Institute for Climate Impact Research, PO Box 60 12 03, 14412 Potsdam, Germany.|Department of Physics, Humboldt University of Berlin, Newtonstrate 15, 12489 Berlin, Germany.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths
mesh_terms: D005246:Feedback; D005786:Gene Expression Regulation; D008957:Models, Genetic; D009038:Motion; D009622:Noise; D011336:Probability; D013269:Stochastic Processes; D013997:Time Factors; D014158:Transcription, Genetic