The extent of protein hydration dictates the preference for heterogeneous or homogeneous nucleation generating either parallel or antiparallel β-sheet α-synuclein aggregates

α-Synuclein amyloid self-assembly is the hallmark of a number of neurodegenerative disorders, including Parkinson''s disease, although there is still very limited understanding about the factors and mechanisms that trigger this process. Primary nucleation has been observed to be initiated in vitro at hydrophobic/hydrophilic interfaces by heterogeneous nucleation generating parallel β-sheet aggregates, although no such interfaces have yet been identified in vivo. In this work, we have discovered that α-synuclein can self-assemble into amyloid aggregates by homogeneous nucleation, without the need of an active surface, and with a preference for an antiparallel β-sheet arrangement. This particular structure has been previously proposed to be distinctive of stable toxic oligomers and we here demonstrate that it indeed represents the most stable structure of the preferred amyloid pathway triggered by homogeneous nucleation under limited hydration conditions, including those encountered inside α-synuclein droplets generated by liquid–liquid phase separation. In addition, our results highlight the key role that water plays not only in modulating the transition free energy of amyloid nucleation, and thus governing the initiation of the process, but also in dictating the type of preferred primary nucleation and the type of amyloid polymorph generated depending on the extent of protein hydration. These findings are particularly relevant in the context of in vivo α-synuclein aggregation where the protein can encounter a variety of hydration conditions in different cellular microenvironments, including the vicinity of lipid membranes or the interior of membraneless compartments, which could lead to the formation of remarkably different amyloid polymorphs by either heterogeneous or homogeneous nucleation.     

The single-mode rate equations for semiconductor lasers with thermal effects

A mathematical model describing the coupling of electrical,optical and thermal effects in semiconductor lasers is introduced.Numerical and asymptotic solutions are derived, including expressionsfor key physical quantities such as the initial time delay,the frequency of spike oscillation and the temperature rise,together with its influence on the photon density, the electronconcentration and the threshold current. The consequences ofthermal effects in reducing efficiency are thus quantified.