Detection of cellular rhythms and global stability within interlocked feedback systems

Model-based robustness and bistability analysis for methylation-based, epigenetic memory systems

In recent years, epigenetic memory systems have been developed based on DNA methylation and positive feedback systems. Achieving a robust design for these systems is generally a challenging and multifactorial task. We developed and validated a novel mathematical model to describe methylation-based epigenetic memory systems that capture switching dynamics of methylation levels and methyltransferase amounts induced by different inputs. A bifurcation analysis shows that the system operates in the bistable range, but in its current setup is not robust to changes in parameters. An expansion of the model captures heterogeneity of cell populations by accounting for distributed cell division rates. Simulations predict that the system is highly sensitive to variations in temperature, which affects cell division and the efficiency of the zinc finger repressor. A moderate decrease in temperature leads to a highly heterogeneous response to input signals and bistability on a single-cell level. The predictions of our model were confirmed by flow cytometry experiments conducted in this study. Overall, the results of our study give insights into the functional mechanisms of methylation-based memory systems and demonstrate that the switching dynamics can be highly sensitive to experimental conditions.

Analyzing fixed points of intracellular regulation networks with interrelated feedback topology

Background

Modeling the dynamics of intracellular regulation networks by systems of ordinary differential equations has become a standard method in systems biology, and it has been shown that the behavior of these networks is often tightly connected to the network topology. We have recently introduced the circuit-breaking algorithm, a method that uses the network topology to construct a one-dimensional circuit-characteristic of the system. It was shown that this characteristic can be used for an efficient calculation of the system’s fixed points.

Results

Here we extend previous work and show several connections between the circuit-characteristic and the stability of fixed points. In particular, we derive a sufficient condition on the characteristic for a fixed point to be unstable for certain graph structures and demonstrate that the characteristic does not contain the information to decide whether a fixed point is asymptotically stable. All statements are illustrated on biological network models.

Conclusions

Single feedback circuits and their role for complex dynamic behavior of biological networks have extensively been investigated, but a transfer of most of these concepts to more complex topologies is difficult. In this context, our algorithm is a powerful new approach for the analysis of regulation networks that goes beyond single isolated feedback circuits.

MicroRNA-mediated regulation in the mammalian circadian rhythm

Mammalian circadian rhythms have been extensively studied for many years and many computational models have been presented. Most of the circadian rhythms are based on interlocked positive and negative feedback loops involving coding regions of some 'clock' genes. Recent works have implicated that microRNAs (miRNAs) may play crucial roles in modulating the circadian clock. Here we develop a computational model involving four genes, Per, Cry, Bmal1, and Clock, and two miRNAs, miRNA-219 and miRNA-132, to show their post-transcriptional roles in the modulation of the circadian rhythm. The model is based on experimental observations, by which the miRNAs are incorporated into a classic model including only coding genes. In agreement with experimental observations, the model predicts that miRNA-mediated regulation plays critical roles in modulating the circadian clock. In addition, parameter sensitivity analysis indicates that the period of circadian rhythm with miRNA-mediated regulation is more insensitive to perturbations, showing that the miRNA-mediated regulation can enhance the robustness of the circadian rhythms. This study may help us understand the microRNA-mediated regulation in the mammalian circadian rhythm more clearly.

Architecture-dependent robustness and bistability in a class of genetic circuits

Understanding the relationship between genotype and phenotype is a challenge in systems biology. An interesting yet related issue is why a particular circuit topology is present in a cell when the same function can supposedly be obtained from an alternative architecture. Here we analyzed two topologically equivalent genetic circuits of coupled positive and negative feedback loops, named NAT and ALT circuits, respectively. The computational search for the oscillation volume of the entire biologically reasonable parameter region through large-scale random samplings shows that the NAT circuit exhibits a distinctly larger fraction of the oscillatory region than the ALT circuit. Such a global robustness difference between two circuits is supplemented by analyzing local robustness, including robustness to parameter perturbations and to molecular noise. In addition, detailed dynamical analysis shows that the molecular noise of both circuits can induce transient switching of the different mechanism between a stable steady state and a stable limit cycle. Our investigation on robustness and dynamics through examples provides insights into the relationship between network architecture and its function.

Dynamics of microRNA-mediated motifs

In the past, most research on gene regulation has focused on transcriptional regulation and post-translational regulation. Recently, the post-transcriptional regulation by small non-coding RNAs has drawn much attention. This mode of regulation was found in both prokaryotes and eukaryotes. In this study, the authors integrate transcriptional and post-transcriptional regulation into four different kinds of microRNA-mediated motifs and investigate the mechanism of microRNAs regulation from the viewpoints of dynamics. Theoretical analysis and numerical simulations show that all the four motifs exhibit strong robustness to external and stochastic perturbations.