From dynamical scaling to local scale-invariance: a tutorial

Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced. Schr\"odinger-invariance, the most simple example of local scale-invariance, will be introduced as a dynamical symmetry in the Edwards-Wilkinson universality class of interface growth. The Lie algebra construction, its representations and the Bargman superselection rules will be combined with non-equilibrium Janssen-de Dominicis field-theory to produce explicit predictions for responses and correlators, which can be compared to the results of explicit model studies. At the next level, the study of non-stationary states requires to go over, from Schr\"odinger-invariance, to ageing-invariance. The ageing algebra admits new representations, which acts as dynamical symmetries on more general equations, and imply that each non-equilibrium scaling operator is characterised by two distinct, independent scaling dimensions. Tests of ageing-invariance are described, in the Glauber-Ising and spherical models of a phase-ordering ferromagnet and the Arcetri model of interface growth.Comment: 1+ 23 pages, 2 figures, final for

Ageing, dynamical scaling and its extensions in many-particle systems without detailed balance

Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving branching-annihilating random walk, two exactly solvable particle-reaction models and kinetic growth models. While the generic scaling descriptions known from magnetic system can be taken over, some of the scaling relations between the ageing exponents are no longer valid. In particular, there is no obvious generalization of the universal limit fluctuation-dissipation ratio. The form of the scaling function of the two-time response function is compared with the prediction of the theory of local scale-invariance.Comment: Latex2e with IOP macros, 32 pages; extended discussion on contact process and new section on kinetic growth processe

Architecture of polyglutamine-containing fibrils from time-resolved fluorescence decay

The disease risk and age of onset of Huntington disease (HD) and nine other repeat disorders strongly depend on the expansion of CAG repeats encoding consecutive polyglutamines (polyQ) in the corresponding disease protein. PolyQ length-dependent misfolding and aggregation are the hallmarks of CAG pathologies. Despite intense effort, the overall structure of these aggregates remains poorly understood. Here, we used sensitive time-dependent fluorescent decay measurements to assess the architecture of mature fibrils of huntingtin (Htt) exon 1 implicated in HD pathology. Varying the position of the fluorescent labels in the Htt monomer with expanded 51Q (Htt51Q) and using structural models of putative fibril structures, we generated distance distributions between donors and acceptors covering all possible distances between the monomers or monomer dimensions within the polyQ amyloid fibril. Using Monte Carlo simulations, we systematically scanned all possible monomer conformations that fit the experimentally measured decay times. Monomers with four-stranded 51Q stretches organized into five-layered β-sheets with alternating N termini of the monomers perpendicular to the fibril axis gave the best fit to our data. Alternatively, the core structure of the polyQ fibrils might also be a zipper layer with antiparallel four-stranded stretches as this structure showed the next best fit. All other remaining arrangements are clearly excluded by the data. Furthermore, the assessed dimensions of the polyQ stretch of each monomer provide structural evidence for the observed polyQ length threshold in HD pathology. Our approach can be used to validate the effect of pharmacological substances that inhibit or alter amyloid growth and structure