SummaryInfluenza virus polymerase transcribes or replicates the segmented RNA genome (vRNA) into respectively viral mRNA or full-length copies and initiates RNA synthesis by binding the conserved 3′ and 5′ vRNA ends (the promoter). In recent structures of promoter-bound polymerase, the cap-binding and endonuclease domains are configured for cap snatching, which generates capped transcription primers. Here, we present a FluB polymerase structure with a bound complementary cRNA 5′ end that exhibits a major rearrangement of the subdomains within the C-terminal two-thirds of PB2 (PB2-C). Notably, the PB2 nuclear localization signal (NLS)-containing domain translocates ∼90 Å to bind to the endonuclease domain. FluA PB2-C alone and RNA-free FluC polymerase are similarly arranged. Biophysical and cap-dependent endonuclease assays show that in solution the polymerase explores different conformational distributions depending on which RNA is bound. The inherent flexibility of the polymerase allows it to adopt alternative conformations that are likely important during polymerase maturation into active progeny RNPs.

Network calculus offers powerful tools to analyze the performances in communication networks, in particular to obtain deterministic bounds. This theory is based on a strong mathematical ground, notably by the use of (min,+) algebra. However, the algorithmic aspects of this theory have not been much addressed yet. This paper is an attempt to provide some efficient algorithms implementing network calculus operations for some classical functions. Some functions which are often used are the piecewise affine functions which ultimately have a constant growth. As a first step towards algorithmic design, we present a class containing these functions and closed under the main network calculus operations (min, max, +, −, convolution, subadditive closure, deconvolution): the piecewise affine functions which are ultimately pseudo-periodic. They can be finitely described, which enables us to propose some algorithms for each of the network calculus operations. We finally analyze their computational complexity.