Modern biology provides many networks describing regulations between many species of molecules. It is widely believed that the dynamics of molecular activities based on such regulatory networks are the origin of biological functions. However, we currently have a limited understanding of the relationship between the structure of a regulatory network and its dynamics. In this study we develop a new theory to provide an important aspect of dynamics from information of regulatory linkages alone. We show that the "feedback vertex set" (FVS) of a regulatory network is a set of "determining nodes" of the dynamics. The theory is powerful to study real biological systems in practice. It assures that (i) any long-term dynamical behavior of the whole system, such as steady states, periodic oscillations or quasi-periodic oscillations, can be identified by measurements of a subset of molecules in the network, and that (ii) the subset is determined from the regulatory linkage alone. For example, dynamical attractors possibly generated by a signal transduction network with 113 molecules can be identified by measurement of the activity of only 5 molecules, if the information on the network structure is correct. Our theory therefore provides a rational criterion to select key molecules to control a system. We also demonstrate that controlling the dynamics of the FVS is sufficient to switch the dynamics of the whole system from one attractor to others, distinct from the original.
SignificanceThe most abundant modification in mRNA is the N6-methylation of internal adenosines (m6A), but m6A’s physiological function is unknown for most mRNAs. Here we show that Casein Kinase 1 Delta mRNA (Ck1δ), coding for a critical kinase in the control of circadian rhythms, is regulated by m6A. When m6A is inhibited, the expression of two CK1δ isoforms, uncharacterized until now, increases due to enhanced translation. This increase in CK1δs leads to a slower clock because of increased phosphorylation of the clock protein PER2 at a key residue, leading to the stabilization of PER2 protein.
An intriguing property of the cyanobacterial circadian clock is that endogenous rhythm persists when protein abundances are kept constant either in the presence of translation and transcription inhibitors or in the constant dark condition. Here we propose a regulatory mechanism of KaiC phosphorylation for the generation of circadian oscillations in cyanobacteria. In the model, clock proteins KaiA and KaiB are assumed to have multiple states, regulating the KaiC phosphorylation process. The model can explain 1), the sustained oscillation of gene expression and protein abundance when the expression of the kaiBC gene is regulated by KaiC protein, and 2), the sustained oscillation of phosphorylated KaiC when transcription and translation processes are inhibited and total protein abundance is fixed. Results of this work suggest that KaiA and KaiB strengthen the nonlinearity of KaiC phosphorylation, thereby promoting the circadian rhythm in cyanobacteria.
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