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From the new infrared (IR) reflectivity and time-domain terahertz spectra combined with available highfrequencydielectric data above the megahertz range in a broad temperature range of 10 to 900 K, a fullpicture of the soft- and central-mode behavior in the classical relaxor ferroelectric Pb(Mg1/3Nb2/3)O3 (PMN) issuggested. A detailed comparison is made with the recent hyper-Raman spectroscopy data [Hehlen et al., Phys.Rev. Lett. 117, 155501 (2016)] and also with other available experiments based on inelastic light and neutronscattering. It is revealed that each type of experiment provides slightly different data. The closest agreementis with the hyper-Raman data: both techniques yield the same number of soft-mode components and the samehigh-temperature softening towards the temperature T∗ ≈ 400 K. In addition to evaluation of the IR-terahertz datausing fitting with the standard factorized form of the dielectric function, we performed a successful fitting of thesame data using the effective medium approach (EMA), originally based on the assumption that the mesoscopicstructure of PMNconsists of randomly oriented uniaxially anisotropic polar nanodomains (PNDs) with somewhatharder transverse optical polar modes in the direction along the local PND dipole [Hlinka et al., Phys. Rev. Lett.96, 027601 (2006)]. Evaluation using Bruggeman EMA modeling has been successfully applied in the entireinvestigated temperature range. These results suggest that the response perpendicular to the local dipole moment,at high temperatures induced by random fields rather than PNDs, undergoes a classical softening from hightemperatures with permittivity obeying the Curie-Weiss law, ε⊥ = C/(T − TC), where C = 1.7 × 105K andTC = 380 K, whereas the response parallel to it shows no softening. Below the Burns temperature, ∼620 K, agigahertz relaxation ascribed to flipping of the PNDs emerges from the soft-mode response, slows down, andbroadens, remaining quite strong towards the cryogenic temperatures, where it can be assigned to fluctuations ofthe PND boundaries.

Existing evidence such as codon usage bias suggests that protein translation of fast-growing organisms has been optimised for accuracy and better yield. One possibility for optimisation stems from the fact that different codons are translated at different rates. Common measures for optimal codon choice, which ignore the dynamics of this process, have so far had mixed success in predicting protein levels. Recent advances in experimental techniques such as ribosome profiling allow us to study dynamical details of this intricate process and theoretical modelling is required to interpret the new data. In this work we study a kinetic model for translation that takes into account stochastic movement of individual ribosomes along the mRNA molecule. Unlike previous studies of this and similar models that were limited to numerical simulations, we develop a novel mathematical method to find the steady state solution when the translation initiation is a rate-limiting step. This allows us, for the first time, to find an analytic prediction for the translation rate and ribosome density. We use these predictions to address some of the long-standing controversies surrounding the determinants of translation efficiency.

rotein synthesis rates are determined, at the translational level, by properties of the transcript’s sequence. The e ciency of an mRNA can be tuned by varying the ribosome binding sites controlling the recruitment of the ribosomes, or the codon usage establishing the speed of protein elongation. In this work we propose transcript length as a further key determinant of translation e ciency. Based on a physical model that considers the kinetics of ribosomes advancing on the mRNA and di using in its surrounding, as well as mRNA circularisation and ribosome drop-o , we explain how the transcript length may play a central role in establishing ribosome recruitment and the overall translation rate of an mRNA. According to our results, the proximity of the 3′ end to the ribosomal recruitment site of the mRNA could induce a feedback in the translation process that would favour the recycling of ribosomes. We also demonstrate how this process may be involved in shaping the experimental ribosome density-gene length dependence. Finally, we argue that cells could exploit this mechanism to adjust and balance the usage of its ribosomal resources.

Protein synthesis rates are determined, at the translational level, by properties of the transcript’s sequence. The efficiency of an mRNA can be tuned by varying the ribosome binding sites controlling the recruitment of the ribosomes, or the codon usage establishing the speed of protein elongation. In this work we promote transcript length as a further key determinant of translation efficiency. Based on a physical model that considers the kinetics ofribosomes advancing on the mRNA and diffusing in its surrounding, we explain how the transcript length might play a central role in establishing ribosome recruitment and the overall translation rate of an mRNA. We also demonstrate how this process might be involved in shaping the experimental ribosome density-gene length dependence. Finally, we argue that cells could exploit this mechanism to adjust and balance the usage of its ribosomal resources.