Reaction Diffusion Models in One Dimension with Disorder

We study a large class of 1D reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g. of several species) undergo diffusion with random local bias (Sinai model) and react upon meeting. We obtain the large time decay of the density of each specie, their associated universal amplitudes, and the spatial distribution of particles. We also derive the spectrum of exponents which characterize the convergence towards the asymptotic states. For reactions with several asymptotic states, we analyze the dynamical phase diagram and obtain the critical exponents at the transitions. We also study persistence properties for single particles and for patterns. We compute the decay exponents for the probability of no crossing of a given point by, respectively, the single particle trajectories ($\theta$) or the thermally averaged packets ($\bar{\theta}$). The generalized persistence exponents associated to n crossings are also obtained. Specifying to the process $A+A \to \emptyset$ or A with probabilities $(r,1-r)$, we compute exactly the exponents $\delta(r)$ and $\psi(r)$ characterizing the survival up to time t of a domain without any merging or with mergings respectively, and $\delta_A(r)$ and $\psi_A(r)$ characterizing the survival up to time t of a particle A without any coalescence or with coalescences respectively. $\bar{\theta}, \psi, \delta$ obey hypergeometric equations and are numerically surprisingly close to pure system exponents (though associated to a completely different diffusion length). Additional disorder in the reaction rates, as well as some open questions, are also discussed.Comment: 54 pages, Late

Molecular basis of Orb2 amyloidogenesis and blockade of memory consolidation

Amyloids are ordered protein aggregates that are typically associated with neurodegenerative diseases and cognitive impairment. By contrast, the amyloid-like state of the neuronal RNA binding protein Orb2 in Drosophila was recently implicated in memory consolidation, but it remains unclear what features of this functional amyloid-like protein give rise to such diametrically opposed behaviour. Here, using an array of biophysical, cell biological and behavioural assays we have characterized the structural features of Orb2 from the monomer to the amyloid state. Surprisingly, we find that Orb2 shares many structural traits with pathological amyloids, including the intermediate toxic oligomeric species, which can be sequestered in vivo in hetero-oligomers by pathological amyloids. However, unlike pathological amyloids, Orb2 rapidly forms amyloids and its toxic intermediates are extremely transient, indicating that kinetic parameters differentiate this functional amyloid from pathological amyloids. We also observed that a well-known anti-amyloidogenic peptide interferes with long-term memory in Drosophila. These results provide structural insights into how the amyloid-like state of the Orb2 protein can stabilize memory and be nontoxic. They also provide insight into how amyloid-based diseases may affect memory processes.This research was supported by funds from SAF2013-49179-C2-1-R JPND_CD_FP-688- 059 (AC14/00037 ISCIII) to MCV, SIMR to KS, SAF2013-49179-C2-2-R JPND_CD_FP-688-059 (AC14/00037 ISCIII) to DVL, BFU2012-36825, S2011/BMD-2457 (Comunidad de Madrid)Peer Reviewe