Redundant Mechanisms Prevent Mitotic Entry Following Replication Arrest in the Absence of Cdc25 Hyper-Phosphorylation in Fission Yeast

Following replication arrest the Cdc25 phosphatase is phosphorylated and inhibited by Cds1. It has previously been reported that expressing Cdc25 where 9 putative amino-terminal Cds1 phosphorylation sites have been substituted to alanine results in bypass of the DNA replication checkpoint. However, these results were acquired by expression of the phosphorylation mutant using a multicopy expression vector in a genetic background where the DNA replication checkpoint is intact. In order to clarify these results we constructed a Cdc25(9A)-GFP native promoter integrant and examined its effect on the replication checkpoint at endogenous expression levels. In this strain the replication checkpoint operates normally, conditional on the presence of the Mik1 kinase. In response to replication arrest the Cdc25(9A)-GFP protein is degraded, suggesting the presence of a backup mechanism to eliminate the phosphatase when it cannot be inhibited through phosphorylation

Consensus over Random Graph Processes: Network Borel-Cantelli Lemmas for Almost Sure Convergence

Distributed consensus computation over random graph processes is considered. The random graph process is defined as a sequence of random variables which take values from the set of all possible digraphs over the node set. At each time step, every node updates its state based on a Bernoulli trial, independent in time and among different nodes: either averaging among the neighbor set generated by the random graph, or sticking with its current state. Connectivity-independence and arc-independence are introduced to capture the fundamental influence of the random graphs on the consensus convergence. Necessary and/or sufficient conditions are presented on the success probabilities of the Bernoulli trials for the network to reach a global almost sure consensus, with some sharp threshold established revealing a consensus zero-one law. Convergence rates are established by lower and upper bounds of the $\epsilon$-computation time. We also generalize the concepts of connectivity/arc independence to their analogues from the $*$-mixing point of view, so that our results apply to a very wide class of graphical models, including the majority of random graph models in the literature, e.g., Erd\H{o}s-R\'{e}nyi, gossiping, and Markovian random graphs. We show that under $*$-mixing, our convergence analysis continues to hold and the corresponding almost sure consensus conditions are established. Finally, we further investigate almost sure finite-time convergence of random gossiping algorithms, and prove that the Bernoulli trials play a key role in ensuring finite-time convergence. These results add to the understanding of the interplay between random graphs, random computations, and convergence probability for distributed information processing.Comment: IEEE Transactions on Information Theory, In Pres