The Miles theory of wave amplification by wind is extended to the case of finite depth h and a shear flow with (constant) vorticity {\Omega}. Vorticity is characterised through the non-dimensional parameter {\nu} = {\Omega} U_1 /g, where g the gravitational acceleration, U_1 a characteristic wind velocity and k the wavenumber. The notion of 'wave age' is generalised to account for the effect of vorticity. Several widely used growth rates are derived analytically from the dispersion relation of the wind/water interface, and their dependence on both water depth and vorticity is derived and discussed. Vorticity is seen to shift the maximum wave age, similar to what was previously known to be the effect of water depth. At the same time, a novel effect arises and the growth coefficients, at identical wave age and depth, are shown to experience a net increase or decrease according to the shear gradient in the water flow.

We extend the paradigmatic and versatile TASEP (Totally Asymmetric Simple Exclusion Process) for stochastic 1d transport to allow for two different particle species, each having specific entry and exit rates. We offer a complete mean-field analysis, including a phase diagram, by mapping this model onto an effective one-species TASEP. Stochastic simulations confirm the results, but indicate deviations when the particle species have very different exit rates. We illustrate that this is due to a phenomenon of intermittency, and formulate a refined 'intermittent' mean-field (iMF) theory for this regime. We discuss how non-stationary effects may further enrich the phenomenology.

The cytoskeleton in eukaryotic cells plays several crucial roles. In terms of intracellular transport, motor proteins use the cytoskeletal filaments as a backbone along which they can actively transport biological cargos such as vesicles carrying biochemical reactants. Crossings between such filaments constitute a key element, as they may serve to alter the destination of such payload. Although motor proteins are known to display a rich behaviour at such crossings, the latter have so far only been modelled as simple branching points. Here we explore a model for a crossing between two microtubules which retains the individual tracks consisting of protofilaments, and we construct a schematic representation of the transport paths. We study collective transport exemplified by the Totally Asymmetric Simple Exclusion Process (TASEP), and provide a full analysis of the transport features and the associated phase diagram, by a generic mean-field approach which we confirm through particle-based stochastic simulations. In particular we show that transport through such a compound crossing cannot be approximated from a coarse-grained structure with a simple branching point. Instead, it gives rise to entirely new and counterintuitive features: the fundamental current-density relation for traffic flow is no longer a single-valued function, and it furthermore differs according to whether it is observed upstream or downstream from the crossing. We argue that these novel features may be directly relevant for interpreting experimental measurements.

We raise the question whether a simple model for traffic, generic but based on microscopic rules, can provide an additional angle for interpreting flow through a road system. Using the totally simple exclusion process (TASEP) on a road segment with ramps, we show that measuring the flow directly at the road junctions may be a useful setup. We show that the presence of junctions affects the characterisation of traffic, suggesting that interpretations in terms of a 2-phase or a 3-phase description may be complementary, rather than contradictory. We furthermore argue that hysteresis-like features can appear in a system with junctions, which is intriguing as the TASEP dynamics as such do not lead to hysteresis. We discuss our findings in the light of boundary-driven phase transitions.

ABout our activities on physico-mathematical modelling of intracellularmolecular transport

Compte rendu des activités autour de la modélisation physico-mathématique du transport moléculaire intracellulaire

The well established phenomenon of ribosome drop-off plays crucial roles in translational accuracy and nutrient starvation responses during protein translation. When cells are under stress conditions, such as amino acid starvation or aminoacyl-tRNA depletion due to a high level of recombinant protein expression, ribosome drop-off can substantially affect the efficiency of protein expression. Here we introduce a mathematical model that describes the effects of ribosome drop-off on the ribosome density along the mRNA and on the concomitant protein synthesis rate. Our results show that ribosome premature termination may lead to non-intuitive ribosome density profiles, such as a ribosome density which increases from the 5' to the 3' end. Importantly, the model predicts that the effects of ribosome drop-off on the translation rate are mRNA-specific, and we quantify their resilience to drop-off, showing that the mRNAs which present ribosome queues are much less affected by ribosome drop-off than those which do not. Moreover, among those mRNAs that do not present ribosome queues, resilience to drop-off correlates positively with the elongation rate, so that sequences using fast codons are expected to be less affected by ribosome drop-off. This result is consistent with a genome-wide analysis of S. cerevisiae, which reveals that under favourable growth conditions mRNAs coding for proteins involved in the translation machinery, known to be highly codon biased and using preferentially fast codons, are highly resilient to ribosome drop-off. Moreover, in physiological conditions, the translation rate of mRNAs coding for regulatory, stress-related proteins, is less resilient to ribosome drop-off. This model therefore allows analysis of variations in the translational efficiency of individual mRNAs by accounting for the full range of known ribosome behaviours, as well as explaining mRNA-specific variations in ribosome density emerging from ribosome profiling studies.