The functionals of double phase type $$\begin{array}{} \displaystyle {\cal H} (u):= \int \left(|Du|^{p} + a(x)|Du|^{q} \right) dx, ~~ ~~~(q \gt p \gt 1,~~a(x)\geq 0) \end{array}$$ are introduced in the epoch-making paper by Colombo-Mingione [1] for constants p and q, and investigated by them and Baroni. They obtained sharp regularity results for minimizers of such functionals. In this paper we treat the case that the exponents are functions of x and partly generalize their regularity results.

The RNA that is packaged into exosomes is termed as exosomal-shuttle RNA (esRNA); however, the players, which take this subset of RNA (esRNA) into exosomes, remain largely unknown. We hypothesized that RNA binding proteins (RBPs) could serve as key players in this mechanism, by making complexes with RNAs and transporting them into exosomes during the biosynthesis of exosomes. Here, we demonstrate the presence of 30 RBPs in exosomes that were shown to form RNA–RBP complexes with both cellular RNA and exosomal-RNA species. To assess the involvement of these RBPs in RNA-transfer into exosomes, the gene transcripts encoding six of the proteins identified in exosomes (HSP90AB1, XPO5, hnRNPH1, hnRNPM, hnRNPA2B1, and MVP) were silenced by siRNA and subsequent effect on esRNA was assessed. A significant reduction of total esRNA was observed by post-transcriptional silencing of MVP, compared to other RBPs. Furthermore, to confirm the binding of MVP with esRNA, a biotinylated-MVP was transiently expressed in HEK293F cells. Higher levels of esRNA were recovered from MVP that was eluted from exosomes of transfected cells, as compared to those of non-transfected cells. Our data indicate that these RBPs could end up in exosomes together with RNA molecules in the form of RNA–ribonucleoprotein complexes, which could be important for the transport of RNAs into exosomes and the maintenance of RNAs inside exosomes. This type of maintenance may favor the shuttling of RNAs from exosomes to recipient cells in the form of stable complexes.

Long non-coding RNAs (lncRNAs) and circular RNAs (circRNAs) contribute to the onset of many neoplasias through RNA-RNA competitive interactions; in addition, they could be secreted by cancer cells into biological fluids, suggesting their potential diagnostic application. By analyzing the expression of 17 lncRNAs and 31 circRNAs in biopsies and serum exosomes from colorectal cancer (CRC) patients through qRT-PCR, we detected CCAT1, CCAT2, HOTAIR, and UCA1 upregulation and CDR1AS, MALAT1, and TUG1 downregulation in biopsies. In serum exosomes, UCA1 was downregulated, while circHIPK3 and TUG1 were upregulated. Combined receiver operating characteristic (ROC) curves of TUG1:UCA1 and circHIPK3:UCA1 showed high values of sensitivity and specificity. Through in vitro (i.e., RNA silencing and mitogen-activated protein kinase [MAPK] inhibition) and in silico analyses (i.e., expression correlation and RNA-RNA-binding prediction), we found that UCA1 could (1) be controlled by MAPKs through CEBPB; (2) sequester miR-135a, miR-143, miR-214, and miR-1271, protecting ANLN, BIRC5, IPO7, KIF2A, and KIF23 from microRNA (miRNA)-induced degradation; and (3) interact with mRNA 3'-UTRs, preventing miRNA binding. UCA1 and its co-regulated antisense LINC01764 could interact and reciprocally mask their own miRNA-binding sites. Functional enrichment analysis of the RNA-RNA network controlled by UCA1 suggested its potential involvement in cellular migration. The UCA1 regulatory axis would represent a promising target to develop innovative RNA-based therapeutics against CRC.

Uveal melanoma (UM) represents approximately 5-6% of all melanoma diagnoses and up to 50% of patients succumb to their disease. Although several methods are available, accurate diagnosis is not always easily feasible because of potential accidents (e.g., intraocular hemorrhage). Based on the assumption that the profile of circulating miRNAs is often altered in human cancers, we verified whether UM patients showed different vitreous humor (VH) or serum miRNA profiles with respect to healthy controls. By using TaqMan Low Density Arrays, we analyzed 754 miRNAs from VH, vitreal exosomes, and serum of 6 UM patients and 6 healthy donors: our data demonstrated that the UM VH profile was unique and only partially overlapping with that from serum of the same patients. Whereas, 90% of miRNAs were shared between VH and vitreal exosomes, and their alterations in UM were statistically overlapped with those of VH and vitreal exosomes, suggesting that VH alterations could result from exosomal dysregulation. We report 32 miRNAs differentially expressed in UM patients in at least 2 different types of samples analyzed. We validated these data on an independent cohort of 12 UM patients. Most alterations were common to VH and vitreal exosomes (e.g., upregulation of miR-21,-34 a,-146a). Interestingly, miR-146a was upregulated in the serum of UM patients, as well as in serum exosomes. Upregulation of miR-21 and miR-146a was also detected in formalin-fixed, paraffin-embedded UM, suggesting that VH or serum alterations in UM could be the consequence of disregulation arising from tumoral cells. Our findings suggest the possibility to detect in VH and serum of UM patients "diagnostic" miRNAs released by the affected eye: based on this, miR-146a could be considered a potential circulating marker of UM.