Somatic mutations in neurodegeneration: An update

Mosaicism, the presence of genomic differences between cells due to post-zygotic somatic mutations, is widespread in the human body, including within the brain. A role for this in neurodegenerative diseases has long been hypothesised, and technical developments are now allowing the question to be addressed in detail. The rapidly accumulating evidence is discussed in this review, with a focus on recent developments. Somatic mutations of numerous types may occur, including single nucleotide variants (SNVs), copy number variants (CNVs), and retrotransposon insertions. They could act as initiators or risk factors, especially if they arise in development, although they could also result from the disease process, potentially contributing to progression. In common sporadic neurodegenerative disorders, relevant mutations have been reported in synucleinopathies, comprising somatic gains of SNCA in Parkinson’s disease and multiple system atrophy, and in Alzheimer’s disease, where a novel recombination mechanism leading to somatic variants of APP, as well as an excess of somatic SNVs affecting tau phosphorylation, have been reported. In Mendelian repeat expansion disorders, mosaicism due to somatic instability, first detected 25 years ago, has come to the forefront. Brain somatic SNVs occur in DNA repair disorders, and there is evidence for a role of several ALS genes in DNA repair. While numerous challenges, and need for further validation, remain, this new, or perhaps rediscovered, area of research has the potential to transform our understanding of neurodegeneration

Spatial Correlation Functions of one-dimensional Bose gases at Equilibrium

The dependence of the three lowest order spatial correlation functions of a harmonically confined Bose gas on temperature and interaction strength is presented at equilibrium. Our analysis is based on a stochastic Langevin equation for the order parameter of a weakly-interacting gas. Comparison of the predicted first order correlation functions to those of appropriate mean field theories demonstrates the potentially crucial role of density fluctuations on the equilibrium coherence length. Furthermore,the change in both coherence length and shape of the correlation function, from gaussian to exponential, with increasing temperature is quantified. Moreover, the presented results for higher order correlation functions are shown to be in agreeement with existing predictions. Appropriate consideration of density-density correlations is shown to facilitate a precise determination of quasi-condensate density profiles, providing an alternative approach to the bimodal density fits typically used experimentally

Phase coherence in quasicondensate experiments: an ab initio analysis via the stochastic Gross-Pitaevskii equation

We perform an ab initio analysis of the temperature dependence of the phase coherence length of finite temperature, quasi-one-dimensional Bose gases measured in the experiments of Richard et al. (Phys. Rev. Lett. 91, 010405 (2003)) and Hugbart et al. (Eur. Phys. J. D 35, 155-163 (2005)), finding very good agreement across the entire observed temperature range ($0.8<T/T_{\phi}<28$). Our analysis is based on the one-dimensional stochastic Gross-Pitaevskii equation, modified to self-consistently account for transverse, quasi-one-dimensional effects, thus making it a valid model in the regime $\mu ~ few \hbar \omega_\perp$. We also numerically implement an alternative identification of $T_{\phi}$, based on direct analysis of the distribution of phases in a stochastic treatment.Comment: Amended manuscript with improved agreement to experiment, following some additional clarifications by Mathilde Hugbart and Fabrice Gerbier and useful comments by the reviewer; accepted for publication in Physical Review

Modeling and estimation of ambiguities in linear arrays

Published versio

A Dynamical Self-Consistent Finite Temperature Kinetic Theory: The ZNG Scheme

We review a self-consistent scheme for modelling trapped weakly-interacting quantum gases at temperatures where the condensate coexists with a significant thermal cloud. This method has been applied to atomic gases by Zaremba, Nikuni, and Griffin, and is often referred to as ZNG. It describes both mean-field-dominated and hydrodynamic regimes, except at very low temperatures or in the regime of large fluctuations. Condensate dynamics are described by a dissipative Gross-Pitaevskii equation (or the corresponding quantum hydrodynamic equation with a source term), while the non-condensate evolution is represented by a quantum Boltzmann equation, which additionally includes collisional processes which transfer atoms between these two subsystems. In the mean-field-dominated regime collisions are treated perturbatively and the full distribution function is needed to describe the thermal cloud, while in the hydrodynamic regime the system is parametrised in terms of a set of local variables. Applications to finite temperature induced damping of collective modes and vortices in the mean-field-dominated regime are presented.Comment: Unedited version of chapter to appear in Quantum Gases: Finite Temperature and Non-Equilibrium Dynamics (Vol. 1 Cold Atoms Series). N.P. Proukakis, S.A. Gardiner, M.J. Davis and M.H. Szymanska, eds. Imperial College Press, London (in press). See http://www.icpress.co.uk/physics/p817.htm