Period doubling induced by thermal noise amplification in genetic circuits

Abstract

Rhythms of life are dictated by oscillations, which take place in a wide rage of biological scales. In bacteria, for example, oscillations have been proven to control many fundamental processes, ranging from gene expression to cell divisions. In genetic circuits, oscillations originate from elemental block such as autorepressors and toggle switches, which produce robust and noise-free cycles with well defined frequency. In some circumstances, the oscillation period of biological functions may double, thus generating bistable behaviors whose ultimate origin is at the basis of intense investigations. Motivated by brain studies, we here study an “elemental” genetic circuit, where a simple nonlinear process interacts with a noisy environment. In the proposed system, nonlinearity naturally arises from the mechanism of cooperative stability, which regulates the concentration of a protein produced during a transcription process. In this elemental model, bistability results from the coherent amplification of environmental fluctuations due to a stochastic resonance of nonlinear origin. This suggests that the period doubling observed in many biological functions might result from the intrinsic interplay between nonlinearity and thermal noise.

ADC border effect and suppression of quantization error in the digital dynamic measurement

“…In applications, the error of measuring results in the biggest impact, therefore, we need to calibrate all quantitative borders in ADC to make sure of the high precision of the measurement results. [50] In experiments, inevitably noise of the circuit itself and additive noise [51] will be added to the measured results, which leads to a small jitter in the actual conversion border and it has higher instability than the actual stability. So the quantitative random deviation of the border value should be taken into account in data processing and by selecting subsequent values at the borders, we can get rid of the interference of random noise [47][48][49] to make it closer to the border of its true position.…”

Quantitative imaging with Fucci and mathematics to uncover temporal dynamics of cell cycle progression

“…; Hellen et al . ; Ruocco & Fratalocchi ). Whether the period of the segmentation clock really affects the timing of the posterior shift of the G1/S transition window in zebrafish notochord remains to be elucidated.…”

“…Since oscillating gene expression patterns have not been reported in notochordal cells and the stochastic window of the G1/S transition is always located posteriorly to the newly formed somites, there is a possibility that the G1/S transition is triggered by the periodic signals of the segmentation clock (Oates et al 2012;Benazeraf & Pourquie 2013). Several mathematical models have been successfully used to explain the period-doubling phenomena using nonlinear oscillatory systems (Mandelblat et al 2001;Jia et al 2012;Hellen et al 2013;Ruocco & Fratalocchi 2014). Whether the period of the segmentation clock really affects the timing of the posterior shift of the G1/ S transition window in zebrafish notochord remains to be elucidated.…”