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Progranulin (PGRN) is a key regulator of lysosomes, and its deficiency has been linked to various lysosomal storage diseases (LSDs), including Gaucher disease (GD), one of the most common LSD. Here, we report that PGRN plays a previously unrecognized role in autophagy within the context of GD. PGRN deficiency is associated with the accumulation of LC3-II and p62 in autophagosomes of GD animal model and patient fibroblasts, resulting from the impaired fusion of autophagosomes and lysosomes. PGRN physically interacted with Rab2, a critical molecule in autophagosome-lysosome fusion. Additionally, a fragment of PGRN containing the Grn E domain was required and sufficient for binding to Rab2. Furthermore, this fragment significantly ameliorated PGRN deficiency-associated impairment of autophagosome-lysosome fusion and autophagic flux. These findings not only demonstrate that PGRN is a crucial mediator of autophagosome-lysosome fusion but also provide new evidence indicating PGRN's candidacy as a molecular target for modulating autophagy in GD and other LSDs in general. KEY MESSAGES : PGRN acts as a crucial factor involved in autophagosome-lysosome fusion in GD. PGRN physically interacts with Rab2, a molecule in autophagosome-lysosome fusion. A 15-kDa C-terminal fragment of PGRN is required and sufficient for binding to Rab2. This PGRN derivative ameliorates PGRN deficiency-associated impairment of autophagy. This study provides new insights into autophagy and may develop novel therapy for GD.

We derived analytical formula for the cross-spectral density of a radially polarized partially coherent twist (RPPCT) beam propagating in a uniaxial crystal orthogonal to the optical axis with the help of the extended Huygens-Fresnel integral formula and unified theory of coherence and polarization. Furthermore, we explore the evolution properties of a RPPCT beam propagating in a uniaxial crystal. It is found that the RPPCT beam becomes an anisotropic RPPCT beam and the beam spot is rotating with beam propagation in uniaxial crystal. Its evolution properties change with twist factor and the ratio of extraordinary index to ordinary refractive index. The twist factor affects their rotation orientation angles, and the ratio of extraordinary index to ordinary refractive index has an effect on their twisted levels.

This article presents the investigation of the propagation properties of a Multi-Gaussian Schell-Model (MGSM) beam in a uniaxial crystal, orthogonal to the optical axis. The analytic expressions for the elements of the cross-spectral density matrix of an MGSM beam in such a crystal are derived. Using the derived expressions for numerical analysis, the distributions of the normalized intensity and degree of polarization for MGSM beams are studied. The results show that not only does the normalized distribution intensity of the beam form a flat shape, but also the distribution of degree of polarization reaches a plateau in the central area when propagating in a uniaxial crystals orthogonal to the optical axis. The parameters of the source and refractive indices are major factors that affect the distributions. With a suitable choice of parameters, the intensity distribution changes to a rounded rectangular plateau and the degree of polarization distribution changes to an elliptic plateau. The results also indicate that a uniaxial crystal can modulate these MGSM beam distributions, which is beneficial for the optical manipulation of microscopic particles and nonlinear optics, involving a specific profile and polarization.

Based on the vectorial Rayleigh-Sommerfeld formulas, the concept of vectorial non-paraxial multi-Gaussian Schell-model beams is introduced. The explicit expressions for the intensity distribution and degree of polarization of the vectorial non-paraxial multi-Gaussian Schell-model beams in free space were derived. The paraxial approximation is treated as a special case of our general expressions. The effect of the beam parameters on the intensity distribution and polarization property are investigated analytically and numerically when the longitudinal components is considered.