Modeling the interactions of sense and antisense Period transcripts in the mammalian circadian clock network

Impacts of the feedback loop between sense-antisense RNAs in regulating circadian rhythms

Antisense transcripts are a unique group of non-coding RNAs and play regulatory roles in a variety of biological processes, including circadian rhythms. Per2AS is an antisense transcript to the sense core clock gene Period2 (Per2) in mouse and its expression is rhythmic and antiphasic to Per2. To understand the impact of Per2AS-Per2 interaction, we developed a new mathematical model that mechanistically described the mutually repressive relationship between Per2 and Per2AS. This mutual repression can regulate both amplitude and period of circadian oscillation by affecting a negative feedback regulation of Per2. Simulations from this model also fit with experimental observations that could not be fully explained by our previous model. Our revised model can not only serve as a foundation to build more detailed models to better understand the impact of Per2AS-Per2 interaction in the future, but also be used to analyze other sense-antisense RNA pairs that mutually repress each other.

Impacts of the feedback loop between sense-antisense RNAs in regulating circadian rhythms

Antisense transcripts are a unique group of non-coding RNAs that are transcribed from the opposite strand of a sense coding gene in an antisense orientation. Even though they do not encode a protein, these transcripts play a regulatory role in a variety of biological processes, including circadian rhythms. We and others found an antisense transcript, Per2AS , that is transcribed from the strand opposite the sense transcript Period2 ( Per2 ) and exhibits a rhythmic and antiphasic expression pattern compared to Per2 in mouse. By assuming that Per2AS and Per2 mutually repress each other, our previous mathematical model predicted that Per2AS regulates the robustness and the amplitude of circadian rhythms. In this study, we revised our previous model and developed a new mathematical model that mechanistically described the mutually repressive relationship between Per2 and Per2AS via transcriptional interference. We found that the simulation results are largely consistent with experimental observations including the counterintuitive ones that could not be fully explained by our previous model. These results indicate that our revised model serves as a foundation to build more detailed models in the future to better understand the impact of Per2AS-Per2 interaction in the mammalian circadian clock. Our mechanistic description of Per2AS-Per2 interaction can also be extended to other mathematical models that involve sense-antisense RNA pairs that mutually repress each other.

Root locus-based stability analysis for biological systems

Background: The first objective for realizing and handling biological systems is to choose a suitable model prototype and then perform structure and parameter identification. Afterwards, a theoretical analysis is needed to understand the characteristics, abilities, and limitations of the underlying systems. Generalized Michaelis-Menten kinetics (MM) and S-systems are two well-known biochemical system theory-based models. Research on steady-state estimation of generalized MM systems is difficult because of their complex structure. Further, theoretical analysis of S-systems is still difficult because of the power-law structure, and even the estimation of steady states can be easily achieved via algebraic equations. Aim: We focus on how to flexibly use control technologies to perform deeper biological system analysis. Methods: For generalized MM systems, the root locus method (proposed by Walter R. Evans) is used to predict the direction and rate (flux) limitations of the reaction and to estimate the steady states and stability margins (relative stability). Mode analysis is additionally introduced to discuss the transient behavior and the setting time. For S-systems, the concept of root locus, mode analysis, and the converse theorem are used to predict the dynamic behavior, to estimate the setting time and to analyze the relative stability of systems. Theoretical results were examined via simulation in a Simulink/MATLAB environment. Results: Four kinds of small functional modules (a system with reversible MM kinetics, a system with a singular or nearly singular system matrix and systems with cascade or branch pathways) are used to describe the proposed strategies clearly. For the reversible MM kinetics system, we successfully predict the direction and the rate (flux) limitations of reactions and obtain the values of steady state and net flux. We observe that theoretically derived results are consistent with simulation results. Good prediction is observed ([Formula: see text]% accuracy). For the system with a (nearly) singular matrix, we demonstrate that the system is neither globally exponentially stable nor globally asymptotically stable but globally semistable. The system possesses an infinite gain margin (GM denoting how much the gain can increase before the system becomes unstable) regardless of how large or how small the values of independent variables are, but the setting time decreases and then increases or always decreases as the values of independent variables increase. For S-systems, we first demonstrate that the stability of S-systems can be determined by linearized systems via root loci, mode analysis, and block diagram-based simulation. The relevant S-systems possess infinite GM for the values of independent variables varying from zero to infinity, and the setting time increases as the values of independent variables increase. Furthermore, the branch pathway maintains oscillation until a steady state is reached, but the oscillation phenomenon does not exist in the cascade pathway because in this system, all of the root loci are located on real lines. The theoretical predictions of dynamic behavior for these two systems are consistent with the simulation results. This study provides a guideline describing how to choose suitable independent variables such that systems possess satisfactory performance for stability margins, setting time and dynamic behavior. Conclusion: The proposed root locus-based analysis can be applied to any kind of differential equation-based biological system. This research initiates a method to examine system dynamic behavior and to discuss operating principles.

Timing without coding: How do long non-coding RNAs regulate circadian rhythms?

Long non-coding RNAs (lncRNAs) are a new class of regulatory RNAs that play important roles in disease development and a variety of biological processes. Recent studies have underscored the importance of lncRNAs in the circadian clock system and demonstrated that lncRNAs regulate core clock genes and the core clock machinery in mammals. In this review, we provide an overview of our current understanding of how lncRNAs regulate the circadian clock without coding a protein. We also offer additional insights into the challenges in understanding the functions of lncRNAs and other unresolved questions in the field. We do not cover other regulatory ncRNAs even though they also play important roles; readers are highly encouraged to refer to other excellent reviews on this topic.

Natural antisense transcript of Period2, Per2AS, regulates the amplitude of the mouse circadian clock

In mammals, a set of core clock genes form transcription-translation feedback loops to generate circadian oscillations. We and others recently identified a novel transcript at the Period2 (Per2) locus that is transcribed from the antisense strand of Per2 This transcript, Per2AS, is expressed rhythmically and antiphasic to Per2 mRNA, leading to our hypothesis that Per2AS and Per2 mutually inhibit each other's expression and form a double negative feedback loop. By perturbing the expression of Per2AS, we found that Per2AS transcription, but not transcript, represses Per2 However, Per2 does not repress Per2AS, as Per2 knockdown led to a decrease in the Per2AS level, indicating that Per2AS forms a single negative feedback loop with Per2 and maintains the level of Per2 within the oscillatory range. Per2AS also regulates the amplitude of the circadian clock, and this function cannot be solely explained through its interaction with Per2, as Per2 knockdown does not recapitulate the phenotypes of Per2AS perturbation. Overall, our data indicate that Per2AS is an important regulatory molecule in the mammalian circadian clock machinery. Our work also supports the idea that antisense transcripts of core clock genes constitute a common feature of circadian clocks, as they are found in other organisms.

Genome-wide correlation analysis to identify amplitude regulators of circadian transcriptome output

Cell-autonomous circadian system, consisting of core clock genes, generates near 24-h rhythms and regulates the downstream rhythmic gene expression. While it has become clear that the percentage of rhythmic genes varies among mouse tissues, it remains unclear how this variation can be generated, particularly when the clock machinery is nearly identical in all tissues. In this study, we sought to characterize circadian transcriptome datasets that are publicly available and identify the critical component(s) involved in creating this variation. We found that the relative amplitude of 13 genes and the average level of 197 genes correlated with the percentage of cycling genes. Of those, the correlation of Rorc in both relative amplitude and the average level was one of the strongest. In addition, the level of Per2AS, a novel non-coding transcript that is expressed at the Period 2 locus, was also linearly correlated, although with a much lesser degree compared to Rorc. Overall, our study provides insight into how the variation in the percentage of clock-controlled genes can be generated in mouse tissues and suggests that Rorc and potentially Per2AS are involved in regulating the amplitude of circadian transcriptome output.

Deciphering the Dynamics of Interlocked Feedback Loops in a Model of the Mammalian Circadian Clock

Mathematical models of fundamental biological processes play an important role in consolidating theory and experiments, especially if they are systematically developed, thoroughly characterized, and well tested by experimental data. In this work, we report a detailed bifurcation analysis of a mathematical model of the mammalian circadian clock network developed by Relógio et al., noteworthy for its consistency with available data. Using one- and two-parameter bifurcation diagrams, we explore how oscillations in the model depend on the expression levels of its constituent genes and the activities of their encoded proteins. These bifurcation diagrams allow us to decipher the dynamics of interlocked feedback loops by parametric variation of genes and proteins in the model. Among other results, we find that REV-ERB, a member of a subfamily of orphan nuclear receptors, plays a critical role in the intertwined dynamics of Relógio's model. The bifurcation diagrams reported here can be used for predicting how the core clock network responds-in terms of period, amplitude and phases of oscillations-to different perturbations.