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...

The proteasome is an ATP-dependent, 2.5-megadalton machine responsible for selective protein degradation in eukaryotic cells. Here we present cryo-EM structures of the substrate-engaged human proteasome in seven conformational states at 2.8-3.6 Å resolution, captured during breakdown of a polyubiquitylated protein. These structures visualize a continuum of dynamic substrate-proteasome interactions from ubiquitin recognition to substrate translocation, during which ATP hydrolysis sequentially navigates through all six ATPases. Three principal modes of coordinated hydrolysis are observed, featuring hydrolytic events in two oppositely positioned ATPases, in two adjacent ATPases, and in one ATPase at a time. These hydrolytic modes regulate deubiquitylation, translocation initiation and processive unfolding of substrates, respectively. ATP hydrolysis powers a hinge-like motion in each ATPase that regulates its substrate interaction. Synchronization of ATP binding, ADP release and ATP hydrolysis in three adjacent ATPases drives rigid-body rotations of substrate-bound ATPases that are propagated unidirectionally in the ATPase ring and unfold the substrate.

The proteasome is the major engine of protein degradation in all eukaryotic cells. At the heart of this machine is a heterohexameric ring of AAA (ATPases associated with diverse cellular activities) proteins that unfolds ubiquitylated target proteins that are concurrently translocated into a proteolytic chamber and degraded into peptides. Using cryoelectron microscopy, we determined a near–atomic-resolution structure of the 2.5-MDa human proteasome in its ground state, as well as subnanometer-resolution structures of the holoenzyme in three alternative conformational states. The substrate-unfolding AAA-ATPase channel is narrowed by 10 inward-facing pore loops arranged into two helices that run in parallel with each other, one hydrophobic in character and the other highly charged. The gate of the core particle was unexpectedly found closed in the ground state and open in only one of the alternative states. Coordinated, stepwise conformational changes of the regulatory particle couple ATP hydrolysis to substrate translocation and regulate gating of the core particle, leading to processive degradation.