Critical slowing down and attractive manifold: A mechanism for dynamic robustness in the yeast cell-cycle process

Biphasic amplitude oscillator characterized by distinct dynamics of trough and crest

Biphasic amplitude dynamics (BAD) of oscillation have been observed in many biological systems. However, the specific topology structure and regulatory mechanisms underlying these biphasic amplitude dynamics remain elusive. Here, we searched all possible two-node circuit topologies and identified the core oscillator that enables robust oscillation. This core oscillator consists of a negative feedback loop between two nodes and a self-positive feedback loop of the input node, which result in the fast and slow dynamics of the two nodes, thereby achieving relaxation oscillation. Landscape theory was employed to study the stochastic dynamics and global stability of the system, allowing us to quantitatively describe the diverse positions and sizes of the Mexican hat. With increasing input strength, the size of the Mexican hat exhibits a gradual increase followed by a subsequent decrease. The self-activation of input node and the negative feedback on input node, which dominate the fast dynamics of the input node, were observed to regulate BAD in a bell-shaped manner. Both deterministic and statistical analysis results reveal that BAD is characterized by the linear and nonlinear dependence of the oscillation trough and crest on the input strength. In addition, combining with computational and theoretical analysis, we addressed that the linear response of trough to input is predominantly governed by the negative feedback, while the nonlinear response of crest is jointly regulated by the negative feedback loop and the self-positive feedback loop within the oscillator. Overall, this study provides a natural and physical basis for comprehending the occurrence of BAD in oscillatory systems, yielding guidance for the design of BAD in synthetic biology applications.

Cell death modes are specified by the crosstalk dynamics within pyroptotic and apoptotic signaling

The crosstalk between pyroptosis and apoptosis pathways plays crucial roles in homeostasis, cancer, and other pathologies. However, its molecular regulatory mechanisms for cell death decision-making remain to be elucidated. Based on the recent experimental studies, we developed a core regulatory network model of the crosstalk between pyroptosis and apoptosis pathways. Sensitivity analysis and bifurcation analysis were performed to assess the death mode switching of the network. Both the approaches determined that only the level of caspase-1 or gasdermin D (GSDMD) has the potential to individually change death modes. The decrease of caspase-1 or GSDMD switches cell death from pyroptosis to apoptosis. Seven biochemical reactions among the 21 reactions in total that are essential for determining cell death modes are identified by using sensitivity analysis. While with bifurcation analysis of state transitions, nine reactions are suggested to be able to efficiently switch death modes. Monostability, bistability, and tristability are observed under different conditions. We found that only the reaction that caspase-1 activation induced by stimuli can trigger tristability. Six and two of the nine reactions are identified to be able to induce bistability and monostability, respectively. Moreover, the concurrence of pyroptosis and apoptosis is observed not only within proper bistable ranges, but also within tristable ranges, implying two potentially distinct regulatory mechanisms. Taken together, this work sheds new light on the crosstalk between pyroptosis and apoptosis and uncovers the regulatory mechanisms of various stable state transitions, which play important roles for the development of potential control strategies for disease prevention and treatment.