Author Correction: FRQ-CK1 interaction determines the period of circadian rhythms in Neurospora.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

FRQ-CK1 interaction determines the period of circadian rhythms in Neurospora.

Circadian clock mechanisms have been extensively investigated but the main rate-limiting step that determines circadian period remains unclear. Formation of a stable complex between clock proteins and CK1 is a conserved feature in eukaryotic circadian mechanisms. Here we show that the FRQ-CK1 interaction, but not FRQ stability, correlates with circadian period in Neurospora circadian clock mutants. Mutations that specifically affect the FRQ-CK1 interaction lead to severe alterations in circadian period. The FRQ-CK1 interaction has two roles in the circadian negative feedback loop. First, it determines the FRQ phosphorylation profile, which regulates FRQ stability and also feeds back to either promote or reduce the interaction itself. Second, it determines the efficiency of circadian negative feedback process by mediating FRQ-dependent WC phosphorylation. Our conclusions are further supported by mathematical modeling and in silico experiments. Together, these results suggest that the FRQ-CK1 interaction is a major rate-limiting step in circadian period determination.

Robustness and period sensitivity analysis of minimal models for biochemical oscillators.

Biological systems exhibit numerous oscillatory behaviors from calcium oscillations to circadian rhythms that recur daily. These autonomous oscillators contain complex feedbacks with nonlinear dynamics that enable spontaneous oscillations. The detailed nonlinear dynamics of such systems remains largely unknown. In this paper, we investigate robustness and dynamical differences of five minimal systems that may underlie fundamental molecular processes in biological oscillatory systems. Bifurcation analyses of these five models demonstrate an increase of oscillatory domains with a positive feedback mechanism that incorporates a reversible reaction, and dramatic changes in dynamics with small modifications in the wiring. Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology. In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type. We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.

Role of active and inactive cytotoxic immune response in human immunodeficiency virus dynamics.

OBJECTIVES: Mathematical models can be helpful to understand the complex dynamics of human immunodeficiency virus infection within a host. Most of work has studied the interactions of host responses and virus in the presence of active cytotoxic immune cells, which decay to zero when there is no virus. However, recent research highlights that cytotoxic immune cells can be inactive but never be depleted. METHODS: We propose a mathematical model to investigate the human immunodeficiency virus dynamics in the presence of both active and inactive cytotoxic immune cells within a host. We explore the impact of the immune responses on the dynamics of human immunodeficiency virus infection under different disease stages. RESULTS: Standard mathematical and numerical analyses are presented for this new model. Specifically, the basic reproduction number is computed and local and global stability analyses are discussed. CONCLUSION: Our results can give helpful insights when designing more effective drug schedules in the presence of active and inactive immune responses.