Reliability of Transcriptional Cycles and the Yeast Cell-Cycle Oscillator

Abstract

A recently published transcriptional oscillator associated with the yeast cell cycle provides clues and raises questions about the mechanisms underlying autonomous cyclic processes in cells. Unlike other biological and synthetic oscillatory networks in the literature, this one does not seem to rely on a constitutive signal or positive auto-regulation, but rather to operate through stable transmission of a pulse on a slow positive feedback loop that determines its period. We construct a continuous-time Boolean model of this network, which permits the modeling of noise through small fluctuations in the timing of events, and show that it can sustain stable oscillations. Analysis of simpler network models shows how a few building blocks can be arranged to provide stability against fluctuations. Our findings suggest that the transcriptional oscillator in yeast belongs to a new class of biological oscillators.

Autonomous Boolean modelling of developmental gene regulatory networks

“…Autonomous Boolean modelling has been applied to yeast cell cycle [13] and electronic circuits [14,15]. Here we show how to implement the approach for developmental GRNs, which requires the introduction of processor nodes for more faithful representation of processes involving multiple regulators, and the representation of cell -cell signalling in multicellular systems undergoing cell division.…”

Causal structure of oscillations in gene regulatory networks: Boolean analysis of ordinary differential equation attractors

“…The class contains networks of the type suggested for modeling the transcriptional oscillator associated with the yeast cell cycle 1 as well as the typical negative feedback oscillator, such as the repressilator. 2 As we will see below, the negative feedback loop is necessary either as the primary source of oscillations or as a stabilizing factor when the oscillations are generated by the positive loop.…”

“…If a signal arrives at time t that causes A to switch back from 1 to 0 (or 0 to 1) and t À s < r A;1 (or r A;2 ), then Aðt 0 Þ is set to 0 (or 1) for the entire interval s < t 0 < t and we say that the short pulse (or dip) is rejected. 1,7,8 Note that the restrictions s AY;1 ! r A;1 and s AY;2 !…”

“…Stochastic fluctuations may be modeled by adding a random increment to each event time as it is added to the queue. 1,5 For present purposes, we neglect the dependence of the time delay on the recent history of the source and target; i.e., we do not attempt to model the fact that a node that has just recently turned off may turn on more quickly than one that has been off for a long time. In some physical systems, such as unclocked digital electronic circuits, history dependent effects can be important and the dynamics of the network may be chaotic.…”

“…In this case, the ABN analysis clearly distinguishes between two types of oscillators, frustration oscillators that rely on negative feedback to generate the oscillations and transmission oscillators in which a negative feedback loop serves only to regulate the duration of a pulse of activity that travels around a positive feedback loop. 1 …”