The Fuchsian differential equation of the square lattice Ising model χ(3)\chi(3) susceptibility

Using an expansion method in the variables $x_i$ that appear in the $(n-1)$-dimensional integrals representing the $n$-particle contribution to the Ising square lattice model susceptibility $\chi$, we generate a long series of coefficients for the 3-particle contribution $\chi^{(3)}$, using a $N^4$ polynomial time algorithm. We give the Fuchsian differential equation of order seven for $\chi^{(3)}$ that reproduces all the terms of our long series. An analysis of the properties of this Fuchsian differential equation is performed.Comment: 15 pages, no figures, submitted to J. Phys.

Contribution of Cerebellar Sensorimotor Adaptation to Hippocampal Spatial Memory

Complementing its primary role in motor control, cerebellar learning has also a bottom-up influence on cognitive functions, where high-level representations build up from elementary sensorimotor memories. In this paper we examine the cerebellar contribution to both procedural and declarative components of spatial cognition. To do so, we model a functional interplay between the cerebellum and the hippocampal formation during goal-oriented navigation. We reinterpret and complete existing genetic behavioural observations by means of quantitative accounts that cross-link synaptic plasticity mechanisms, single cell and population coding properties, and behavioural responses. In contrast to earlier hypotheses positing only a purely procedural impact of cerebellar adaptation deficits, our results suggest a cerebellar involvement in high-level aspects of behaviour. In particular, we propose that cerebellar learning mechanisms may influence hippocampal place fields, by contributing to the path integration process. Our simulations predict differences in place-cell discharge properties between normal mice and L7-PKCI mutant mice lacking long-term depression at cerebellar parallel fibre-Purkinje cell synapses. On the behavioural level, these results suggest that, by influencing the accuracy of hippocampal spatial codes, cerebellar deficits may impact the exploration-exploitation balance during spatial navigation

Transport and dispersion across wiggling nanopores

The transport of fluids at the nanoscale has achieved major breakthroughs over recent years 1-4 ; however, artificial channels still cannot match the efficiency of biological porins in terms of fluxes or selectivity. Pore shape agitation-due to thermal fluctuations or in response to external stimuli-is believed to facilitate transport in biochannels 5-9 , but its impact on transport in artificial pores remains largely unex-plored. Here we introduce a general theory for transport through thermally or actively fluctuating channels, which quantifies the impact of pore fluctuations on confined diffusion in terms of the spectral statistics of the channel fluctuations. Our findings demonstrate a complex interplay between transport and surface wiggling: agitation enhances diffusion via the induced fluid flow, but spatial variations in pore geometry can induce a slowing down via entropic trapping , in full agreement with molecular dynamics simulations and existing observations from the literature. Our results elucidate the impact of pore agitation in a broad range of artificial and biological porins, but also, at larger scales, in vascular motion in fungi, intestinal contractions and micro-fluidic surface waves. These results open up the possibility that transport across membranes can be actively tuned by external stimuli, with potential applications to nanoscale pumping, osmosis and dynamical ultrafiltration.Interactions induites par des fluctuations entre interfaces molles dans les systèmes complexesTransport hors equilibre de fluides aux échelles nanométriquesEquipement d'excellence de calcul intensif de Mesocentres coordonnés - Tremplin vers le calcul petaflopique et l'exascal

End-Point Targeted Molecular Dynamics: Large-Scale Conformational Changes in Potassium Channels

Large-scale conformational changes in proteins that happen often on biological time scales may be relatively rare events on the molecular dynamics time scale. We have implemented an approach to targeted molecular dynamics called end-point targeted molecular dynamics that transforms proteins between two specified conformational states through the use of nonharmonic “soft” restraints. A key feature of the method is that the protein is free to discover its own conformational pathway through the plethora of possible intermediate states. The method is applied to the Shaker Kv1.2 potassium channel in implicit solvent. The rate of cycling between the open and closed states was varied to explore how slow the cycling rate needed to be to ensure that microscopic reversibility along the transition pathways was well approximated. Results specific to the K+ channel include: 1), a variation in backbone torsion angles of residues near the Pro-Val-Pro motif in the inner helix during both opening and closing; 2), the identification of possible occlusion sites in the closed channel located among Pro-Val-Pro residues and downstream; 3), a difference in the opening and closing pathways of the channel; and 4), evidence of a transient intermediate structural substate. The results also show that likely intermediate conformations during the opening-closing process can be generated in computationally tractable simulation times