Abstractα-Synuclein (αS) is a presynaptic disordered protein whose aberrant aggregation is associated with Parkinson’s disease. The functional role of αS is still debated, although it has been involved in the regulation of neurotransmitter release via the interaction with synaptic vesicles (SVs). We report here a detailed characterisation of the conformational properties of αS bound to the inner and outer leaflets of the presynaptic plasma membrane (PM), using small unilamellar vesicles. Our results suggest that αS preferentially binds the inner PM leaflet. On the basis of these studies we characterise in vitro a mechanism by which αS stabilises, in a concentration-dependent manner, the docking of SVs on the PM by establishing a dynamic link between the two membranes. The study then provides evidence that changes in the lipid composition of the PM, typically associated with neurodegenerative diseases, alter the modes of binding of αS, specifically in a segment of the sequence overlapping with the non-amyloid component region. Taken together, these results reveal how lipid composition modulates the interaction of αS with the PM and underlie its functional and pathological behaviours in vitro.

Preferential flow through weathered bedrock leads to rapid rise of the water table after the first rainstorms and significant water storage (also known as ''rock moisture'') in the fractures. We present a new parameterization of hydraulic conductivity that captures the preferential flow and is easy to implement in global climate models. To mimic the naturally varying heterogeneity with depth in the subsurface, the model represents the hydraulic conductivity as a product of the effective saturation and a background hydraulic conductivity K bkg , drawn from a lognormal distribution. The mean of the background K bkg decreases monotonically with depth, while its variance reduces with the effective saturation. Model parameters are derived by assimilating into Richards' equation 6 years of 30 min observations of precipitation (mm) and water table depths (m), from seven wells along a steep hillslope in the Eel River watershed in Northern California. The results show that the observed rapid penetration of precipitation and the fast rise of the water table from the well locations, after the first winter rains, are well captured with the new stochastic approach in contrast to the standard van Genuchten model of hydraulic conductivity, which requires significantly higher levels of saturated soils to produce the same results. ''Rock moisture,'' the moisture between the soil mantle and the water table, comprises 30% of the moisture because of the great depth of the weathered bedrock layer and could be a potential source of moisture to sustain trees through extended dry periods. Furthermore, storage of moisture in the soil mantle is smaller, implying less surface runoff and less evaporation, with the proposed new model.

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

8 This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived and present that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, which its exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz '96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show we are able to estimate parameters in both the drift (deterministic) and diffusion (stochastic) part of the model evolution equations using our new methods.