Optimal bounds for the approximation of boolean functions and some applications

This paper presents an optimal bound on the Shannon function L(n,m,) that gives the worstcase circuit-size complexity to approximate, within an approximation degree at least , partial boolean functions having n inputs and domain size m. That is

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. Our bound applies to any partial boolean function and any approximation degree, and thus completes the study of boolean function approximation introduced by Pippenger (1977).

Our results give an upper bound for the hardness function h(ƒ), introduced by Nisan and Wigderson (1994), which denotes the minimum value l for which there exists a circuit of size at most l that approximates a boolean function ƒ with degree at least 1/l. Indeed, if H(n) denotes the maximum hardness value achieved by boolean functions with n inputs, we prove that for almost every nH(n)n/3 + n² + O(1). The exponent n/3 in the above inequality implies that no family of boolean functions exists which has ‘full’ hardness. This fact establishes connections with Allender and Strauss' (1994) work that explores the structure of BPP.

Finally, we show that for almost every n and for almost every boolean function ƒ of n inputs we have h(ƒ)2^{n/3−2 log n}. The contribution in the proof of the upper bound for L(n, m, ) can be viewed as a set of technical results that globally show how boolean linear operators are ‘well’ distributed on the class of 4-regular domains. This property is then applied to approximate partial boolean functions on general domains using a suitable composition of boolean linear operators.     

Identification of a Maturation Plasma Cell Index through a Highly Sensitive Droplet Digital PCR Assay Gene Expression Signature Validation in Newly Diagnosed Multiple Myeloma Patients

DNA microarrays and RNA-based sequencing approaches are considered important discovery tools in clinical medicine. However, cross-platform reproducibility studies undertaken so far have highlighted that microarrays are not able to accurately measure gene expression, particularly when they are expressed at low levels. Here, we consider the employment of a digital PCR assay (ddPCR) to validate a gene signature previously identified by gene expression profile. This signature included ten Hedgehog (HH) pathways’ genes able to stratify multiple myeloma (MM) patients according to their self-renewal status. Results show that the designed assay is able to validate gene expression data, both in a retrospective as well as in a prospective cohort. In addition, the plasma cells’ differentiation status determined by ddPCR was further confirmed by other techniques, such as flow cytometry, allowing the identification of patients with immature plasma cells’ phenotype (i.e., expressing CD19+/CD81+ markers) upregulating HH genes, as compared to others, whose plasma cells lose the expression of these markers and were more differentiated. To our knowledge, this is the first technical report of gene expression data validation by ddPCR instead of classical qPCR. This approach permitted the identification of a Maturation Index through the integration of molecular and phenotypic data, able to possibly define upfront the differentiation status of MM patients that would be clinically relevant in the future.     

The Interplay of Lung Cancer,COVID-19, and Vaccines

Patients with cancer are more susceptible to a higher risk of coronavirus infection and its severe complications than the general population. In addition, these patients were not included in the pivotal clinical trials for COVID-19 vaccines. Therefore, considerable uncertainty remains regarding the management of cancer patients during the COVID-19 pandemic and the safety of COVID-19 vaccinations in cancer patients. In this review, we summarize the current knowledge generated from the beginning of the COVID-19 pandemic on the vulnerability of cancer patients to the coronavirus disease, as well as the effectiveness of COVID-19 vaccines in this population. We also discuss the available data on the effects of anticancer treatment with immune checkpoint inhibitors on the immune responses to SARS-CoV-2 in cancer patients. Special attention in this review will be given to patients with lung cancer, as such patients are at an increased risk for severe effects from COVID-19.     

Malignant Transformation of Giant Cell Tumour of Bone: A Review of Literature and the Experience of a Referral Centre

Giant cell tumour of bone (GCTB) is a benign, locally aggressive primary bone neoplasm that represents 5% of all bone tumours. The principal treatment approach is surgery. Although generally GCTB is considered only a locally aggressive disease, it can metastasise, and lung metastases occur in 1–9% of patients. To date, only the use of denosumab has been approved as medical treatment for GCTB. Even more rarely, GCTB undergoes sarcomatous transformation into a malignant tumour (4% of all GCTB), but history of this malignant transformation is unclear and unpredictable. Considering the rarity of the event, the data in the literature are few. In this review, we summarise published data of GCTB malignant transformation and we analyse three cases of malignant transformation of GCTB, evaluating histopathology, genetics, and radiological aspects. Despite the rarity of this event, we conclude that a strict follow up is recommended to detect early malignant transformation.     

The Deubiquitinating Enzyme USP48 Interacts with the Retinal Degeneration-Associated Proteins UNC119a and ARL3

Proteins related to the ubiquitin-proteasome system play an important role during the differentiation and ciliogenesis of photoreceptor cells. Mutations in several genes involved in ubiquitination and proteostasis have been identified as causative of inherited retinal dystrophies (IRDs) and ciliopathies. USP48 is a deubiquitinating enzyme whose role in the retina is still unexplored although previous studies indicate its relevance for neurosensory organs. In this work, we describe that a pool of endogenous USP48 localises to the basal body in retinal cells and provide data that supports the function of USP48 in the photoreceptor cilium. We also demonstrate that USP48 interacts with the IRD-associated proteins ARL3 and UNC119a, and stabilise their protein levels using different mechanisms. Our results suggest that USP48 may act in the regulation/stabilisation of key ciliary proteins for photoreceptor function, in the modulation of intracellular protein transport, and in ciliary trafficking to the photoreceptor outer segment.     

The PINK1 p.Asn521Thr Variant Is Associated with Earlier Disease Onset in GRN/C9orf72 Frontotemporal Lobar Degeneration

Genetic frontotemporal lobar degeneration (FTLD) is characterized by heterogeneous phenotypic expression, with a disease onset highly variable even in patients carrying the same mutation. Herein we investigated if variants in lysosomal genes modulate the age of onset both in FTLD due to GRN null mutations and C9orf72 expansion. In a total of 127 subjects (n = 74 GRN mutations and n = 53 C9orf72 expansion carriers), we performed targeted sequencing of the top 98 genes belonging to the lysosomal pathway, selected based on their high expression in multiple brain regions. We described an earlier disease onset in GRN/C9orf72 pedigrees in subjects carrying the p.Asn521Thr variant (rs1043424) in PTEN-induced kinase 1 (PINK1), a gene that is already known to be involved in neurodegenerative diseases. We found that: (i) the PINK1 rs1043424 C allele is significantly associated with the age of onset; (ii) every risk C allele increases hazard by 2.11%; (iii) the estimated median age of onset in homozygous risk allele carriers is 10–12 years earlier than heterozygous/wild type homozygous subjects. A replication study in GRN/C9orf72 negative FTLD patients confirmed that the rs1043424 C allele was associated with earlier disease onset (−5.5 years in CC versus A carriers). Understanding the potential mechanisms behind the observed modulating effect of the PINK1 gene in FTLD might prove critical for identifying biomarkers and/or designing drugs to modify the age of onset, especially in GRN/C9orf72-driven disease.     

Modeling RTT Syndrome by iPSC-Derived Neurons from Male and Female Patients with Heterogeneously Severe Hot-Spot MECP2 Variants

Rett syndrome caused by MECP2 variants is characterized by a heterogenous clinical spectrum accounted for in 60% of cases by hot-spot variants. Focusing on the most frequent variants, we generated in vitro iPSC-neurons from the blood of RTT girls with p.Arg133Cys and p.Arg255*, associated to mild and severe phenotype, respectively, and of an RTT male harboring the close to p.Arg255*, p.Gly252Argfs*7 variant. Truncated MeCP2 proteins were revealed by Western blot and immunofluorescence analysis. We compared the mutant versus control neurons at 42 days for morphological parameters and at 120 days for electrophysiology recordings, including girls’ isogenic clones. A precocious reduced morphological complexity was evident in neurons with truncating variants, while in p.Arg133Cys neurons any significant differences were observed in comparison with the isogenic wild-type clones. Reduced nuclear size and branch number show up as the most robust biomarkers. Patch clamp recordings on mature neurons allowed the assessment of cell biophysical properties, V-gated currents, and spiking pattern in the mutant and control cells. Immature spiking, altered cell capacitance, and membrane resistance of RTT neurons, were particularly pronounced in the Arg255* and Gly252Argfs*7 mutants. The overall results indicate that the specific markers of in vitro cellular phenotype mirror the clinical severity and may be amenable to drug testing for translational purposes.     

Tomato Sterol 22-desaturase Gene CYP710A11: Its Roles in Meloidogyne incognita Infection and Plant Stigmasterol Alteration

Sterols are isoprenoid-derived lipids that play essential structural and functional roles in eukaryotic cells. Plants produce a complex mixture of sterols, and changes in plant sterol profiles have been linked to plant–pathogen interactions. β-Sitosterol and stigmasterol, in particular, have been associated with plant defense. As nematodes have lost the ability to synthesize sterols de novo, they require sterols from the host. Tomato (Solanum lycopersicum) plants infected by the plant parasitic nematode Meloidogyne incognita show a reduced level of stigmasterol and a repression of the gene CYP710A11, encoding the sterol C-22 desaturase that is responsible for the conversion of β-sitosterol to stigmasterol. In this study, we investigated the role of the tomato sterol C-22 desaturase gene CYP710A11 in the response to infection by M. incognita. We explored the plant–nematode interaction over time by analyzing the plant sterol composition and CYP710A11 gene regulation in S. lycopersicum after M. incognita infection. The temporal gene expression analysis showed that 3 days after inoculation with M. incognita, the CYP710A11 expression was significantly suppressed in the tomato roots, while a significant decrease in the stigmasterol content was observed after 14 days. A cyp710a11 knockout mutant tomato line lacking stigmasterol was analyzed to better understand the role of CYP710A11 in nematode development. M. incognita grown in the mutant line showed reduced egg mass counts, presumably due to the impaired growth of the mutant. However, the nematodes developed as well as they did in the wild-type line. Thus, while the suppression of CYP710A11 expression during nematode development may be a defense response of the plant against the nematode, the lack of stigmasterol did not seem to affect the nematode. This study contributes to the understanding of the role of stigmasterol in the interaction between M. incognita and tomato plants and shows that the sterol C-22 desaturase is not essential for the success of M. incognita.     

CRISPR/Cas9-Based Knock-Out of the PMR4 Gene Reduces Susceptibility to Late Blight in Two Tomato Cultivars

Phytophthora infestans, the causal agent of late blight (LB) in tomato (Solanum lycopersicum L.), is a devastating disease and a serious concern for plant productivity. The presence of susceptibility (S) genes in plants facilitates pathogen proliferation; thus, disabling these genes may help provide a broad-spectrum and durable type of tolerance/resistance. Previous studies on Arabidopsis and tomato have highlighted that knock-out mutants of the PMR4 susceptibility gene are tolerant to powdery mildew. Moreover, PMR4 knock-down in potato has been shown to confer tolerance to LB. To verify the same effect in tomato in the present study, a CRISPR–Cas9 vector containing four single guide RNAs (sgRNAs: sgRNA1, sgRNA6, sgRNA7, and sgRNA8), targeting as many SlPMR4 regions, was introduced via Agrobacterium-tumefaciens-mediated transformation into two widely grown Italian tomato cultivars: ‘San Marzano’ (SM) and ‘Oxheart’ (OX). Thirty-five plants (twenty-six SM and nine OX) were selected and screened to identify the CRISPR/Cas9-induced mutations. The different sgRNAs caused mutation frequencies ranging from 22.1 to 100% and alternatively precise insertions (sgRNA6) or deletions (sgRNA7, sgRNA1, and sgRNA8). Notably, sgRNA7 induced in seven SM genotypes a −7 bp deletion in the homozygous status, whereas sgRNA8 led to the production of fifteen SM genotypes with a biallelic mutation (−7 bp and −2 bp). Selected edited lines were inoculated with P. infestans, and four of them, fully knocked out at the PMR4 locus, showed reduced disease symptoms (reduction in susceptibility from 55 to 80%) compared to control plants. The four SM lines were sequenced using Illumina whole-genome sequencing for deeper characterization without exhibiting any evidence of mutations in the candidate off-target regions. Our results showed, for the first time, a reduced susceptibility to Phytophtora infestans in pmr4 tomato mutants confirming the role of KO PMR4 in providing broad-spectrum protection against pathogens.