fractional dynamics of globally slow transcription and its impact on deterministic genetic oscillation部分全球动力学缓慢转录基因振荡及其对确定性的影响.pdfVIP

Fractional Dynamics of Globally Slow Transcription and Its Impact on Deterministic Genetic Oscillation 1,2 1 1 1 Kun Wei *, Shilong Gao , Suchuan Zhong , Hong Ma * 1 College of Mathematics, Sichuan University, Chengdu, Sichuan Province, People’s Republic of China, 2 College of Life Sciences, Sichuan University, Chengdu, Sichuan Province, People’s Republic of China Abstract In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE). Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE) to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models – the Goodwin ¨ oscillator and the Rossler oscillator. By constructing a ‘‘dual memory’’ oscillator – the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback,