The interactions between proteins, DNA, and RNA in living cells constitute molecular networks that govern various cellular functions. To investigate the global dynamical properties and stabilities of such networks, we studied the cell-cycle regulatory network of the budding yeast. With the use of a simple dynamical model, it was demonstrated that the cell-cycle network is extremely stable and robust for its function. The biological stationary state, the G1 state, is a global attractor of the dynamics. The biological pathway, the cell-cycle sequence of protein states, is a globally attracting trajectory of the dynamics. These properties are largely preserved with respect to small perturbations to the network. These results suggest that cellular regulatory networks are robustly designed for their functions. Despite the complex environment in and outside of the cell, various cellular functions are carried out reliably by the underlying biomolecular networks. How is the stability of a cell state achieved? How can a biological pathway take the cell from one state to another reliably? Evolution must have played a crucial role in the selection of the architectures of these networks for them to have such a remarkable property. Much attention has recently been focused on the ''topological'' properties of largescale networks (1-5). It was argued that a power-law distribution of connectivity, which is apparent for some bionetworks (2, 4), is more tolerable against random failure (1). Here we address this question from a dynamic systems point of view. We study the network regulating the cell cycle of the budding yeast, investigating its global dynamical property and stability. We find that the stationary states of the cell, or states at the checkpoints in general, correspond to global attractors of the dynamics: almost all initial protein states flow to these biological stationary states. Furthermore, the biological pathway of the cell-cycle sequence, which is a particular trajectory in the state space, is a globally stable and attracting trajectory of the dynamics. These dynamic properties, arising from the underlying network connection, are also robust against small perturbations to the network. They are directly responsible for the robustness of the cellular process. The Yeast Cell-Cycle NetworkThe cell-cycle process, by which one cell grows and divides into two daughter cells, is a vital biological process the regulation of which is highly conserved among the eukaryotes (6). The process consists of four phases: G 1 (in which the cell grows and, under appropriate conditions, commits to division), S (in which the DNA is synthesized and chromosomes replicated), G 2 (a ''gap'' between S and M), and M (in which chromosomes are separated and the cell is divided into two). After the M phase, the cell enters the G 1 phase, hence completing a ''cycle.'' The process has been studied in great detail in the budding yeast Saccharomyces cerevisiae, a single-cell model eukaryotic organism (see supporting information, which is publishe...

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The NLR family apoptosis inhibitory proteins (NAIPs) bind conserved bacterial ligands, such as the bacterial rod protein PrgJ, and recruit NLR family CARD-containing protein 4 (NLRC4) as the inflammasome adapter to activate innate immunity. We found that the PrgJ-NAIP2-NLRC4 inflammasome is assembled into multisubunit disk-like structures through a unidirectional adenosine triphosphatase polymerization, primed with a single PrgJ-activated NAIP2 per disk. Cryo–electron microscopy (cryo-EM) reconstruction at subnanometer resolution revealed a ~90° hinge rotation accompanying NLRC4 activation. Unlike in the related heptameric Apaf-1 apoptosome, in which each subunit needs to be conformationally activated by its ligand before assembly, a single PrgJ-activated NAIP2 initiates NLRC4 polymerization in a domino-like reaction to promote the disk assembly. These insights reveal the mechanism of signal amplification in NAIP-NLRC4 inflammasomes.