Gluing together proof environments: Canonical extensions of LF type theories featuring locks

© F. Honsell, L. Liquori, P. Maksimovic, I. Scagnetto This work is licensed under the Creative Commons Attribution License.We present two extensions of the LF Constructive Type Theory featuring monadic locks. A lock is a monadic type construct that captures the effect of an external call to an oracle. Such calls are the basic tool for gluing together diverse Type Theories and proof development environments. The oracle can be invoked either to check that a constraint holds or to provide a suitable witness. The systems are presented in the canonical style developed by the CMU School. The first system, CLLF/p,is the canonical version of the system LLF p, presented earlier by the authors. The second system, CLLF p?, features the possibility of invoking the oracle to obtain a witness satisfying a given constraint. We discuss encodings of Fitch-Prawitz Set theory, call-by-value λ-calculi, and systems of Light Linear Logic. Finally, we show how to use Fitch-Prawitz Set Theory to define a type system that types precisely the strongly normalizing terms

An Open Logical Framework

The LFP Framework is an extension of the Harper-Honsell-Plotkin's Edinburgh Logical Framework LF with external predicates, hence the name Open Logical Framework. This is accomplished by defining lock type constructors, which are a sort of \u25a1-modality constructors, releasing their argument under the condition that a possibly external predicate is satisfied on an appropriate typed judgement. Lock types are defined using the standard pattern of constructive type theory, i.e. via introduction, elimination and equality rules. Using LFP, one can factor out the complexity of encoding specific features of logical systems, which would otherwise be awkwardly encoded in LF, e.g. side-conditions in the application of rules in Modal Logics, and sub-structural rules, as in non-commutative Linear Logic. The idea of LFP is that these conditions need only to be specified, while their verification can be delegated to an external proof engine, in the style of the Poincar Principle or Deduction Modulo. Indeed such paradigms can be adequately formalized in LFP. We investigate and characterize the meta-theoretical properties of the calculus underpinning LFP: strong normalization, confluence and subject reduction. This latter property holds under the assumption that the predicates are well-behaved, i.e. closed under weakening, permutation, substitution and reduction in the arguments. Moreover, we provide a canonical presentation of LFP, based on a suitable extension of the notion of \u3b2\u3b7-long normal form, allowing for smooth formulations of adequacy statements. \ua9 The Author, 2013

Dystrophinopathy Phenotypes and Modifying Factors in Exon 45-55 Deletion

Duchenne muscular dystrophy (DMD) exon 45-55 deletion (del45-55) has been postulated as a model that could treat up to 60% of DMD patients, but the associated clinical variability and complications require clarification. We aimed to understand the phenotypes and potential modifying factors of this dystrophinopathy subset. This cross-sectional, multicenter cohort study applied clinical and functional evaluation. Next generation sequencing was employed to identify intronic breakpoints and their impact on the Dp140 promotor, intronic long noncoding RNA, and regulatory splicing sequences. DMD modifiers (SPP1, LTBP4, ACTN3) and concomitant mutations were also assessed. Haplotypes were built using DMD single nucleotide polymorphisms. Dystrophin expression was evaluated via immunostaining, Western blotting, reverse transcription polymerase chain reaction (PCR), and droplet digital PCR in 9 muscle biopsies. The series comprised 57 subjects (23 index) expressing Becker phenotype (28%), isolated cardiopathy (19%), and asymptomatic features (53%). Cognitive impairment occurred in 90% of children. Patients were classified according to 10 distinct index-case breakpoints; 4 of them were recurrent due to founder events. A specific breakpoint (D5) was associated with severity, but no significant effect was appreciated due to the changes in intronic sequences. All biopsies showed dystrophin expression of >67% and traces of alternative del45-57 transcript that were not deemed pathogenically relevant. Only the LTBP4 haplotype appeared associated the presence of cardiopathy among the explored extragenic factors. We confirmed that del45-55 segregates a high proportion of benign phenotypes, severe cases, and isolated cardiac and cognitive presentations. Although some influence of the intronic breakpoint position and the LTBP4 modifier may exist, the pathomechanisms responsible for the phenotypic variability remain largely unresolved. ANN NEUROL 2022;92:793-80

The graph rewriting calculus: confluence and expressiveness

Introduced at the end of the nineties, the Rewriting Calculus (rho-calculus, for short) is a simple calculus that uniformly integrates term-rewriting and lambda-calculus. The Rhog has been recently introduced as an extension of the rho-calculus, handling structures with cycles and sharing. The calculus over terms is naturally generalized by using unification constraints in addition to the standard rho-calculus matching constraints. This leads to a term-graph representation in an equational style where terms consist of unordered lists of equations. In this paper we show that the (linear) Rhog is confluent. The proof of this result is quite elaborated, due to the non-termination of the system and to the fact that we work on equivalence classes of terms. We also show that the Rhog can be seen as a generalization of first-order term-graph rewriting, in the sense that for any term-graph rewrite step a corresponding sequence of rewritings can be found in the Rhog

Micro-CT imaging reveals<i> Mekk3 </i>heterozygosity prevents cerebral cavernous malformations in <i>Ccm2</i>-deficient mice

Mutations in CCM1 (aka KRIT1), CCM2, or CCM3 (aka PDCD10) gene cause cerebral cavernous malformation in humans. Mouse models of CCM disease have been established by deleting Ccm genes in postnatal animals. These mouse models provide invaluable tools to investigate molecular mechanism and therapeutic approaches for CCM disease. However, the full value of these animal models is limited by the lack of an accurate and quantitative method to assess lesion burden and progression. In the present study we have established a refined and detailed contrast enhanced X-ray micro-CT method to measure CCM lesion burden in mouse brains. As this study utilized a voxel dimension of 9.5μm (leading to a minimum feature size of approximately 25μm), it is therefore sufficient to measure CCM lesion volume and number globally and accurately, and provide high-resolution 3-D mapping of CCM lesions in mouse brains. Using this method, we found loss of Ccm1 or Ccm2 in neonatal endothelium confers CCM lesions in the mouse hindbrain with similar total volume and number. This quantitative approach also demonstrated a rescue of CCM lesions with simultaneous deletion of one allele of Mekk3. This method would enhance the value of the established mouse models to study the molecular basis and potential therapies for CCM and other cerebrovascular diseases

RNA Gain-of-Function in Spinocerebellar Ataxia Type 8

Microsatellite expansions cause a number of dominantly-inherited neurological diseases. Expansions in coding-regions cause protein gain-of-function effects, while non-coding expansions produce toxic RNAs that alter RNA splicing activities of MBNL and CELF proteins. Bi-directional expression of the spinocerebellar ataxia type 8 (SCA8) CTG CAG expansion produces CUG expansion RNAs (CUGexp) from the ATXN8OS gene and a nearly pure polyglutamine expansion protein encoded by ATXN8 CAGexp transcripts expressed in the opposite direction. Here, we present three lines of evidence that RNA gain-of-function plays a significant role in SCA8: 1) CUGexp transcripts accumulate as ribonuclear inclusions that co-localize with MBNL1 in selected neurons in the brain; 2) loss of Mbnl1 enhances motor deficits in SCA8 mice; 3) SCA8 CUGexp transcripts trigger splicing changes and increased expression of the CUGBP1-MBNL1 regulated CNS target, GABA-A transporter 4 (GAT4/Gabt4). In vivo optical imaging studies in SCA8 mice confirm that Gabt4 upregulation is associated with the predicted loss of GABAergic inhibition within the granular cell layer. These data demonstrate that CUGexp transcripts dysregulate MBNL/CELF regulated pathways in the brain and provide mechanistic insight into the CNS effects of other CUGexp disorders. Moreover, our demonstration that relatively short CUGexp transcripts cause RNA gain-of-function effects and the growing number of antisense transcripts recently reported in mammalian genomes suggest unrecognized toxic RNAs contribute to the pathophysiology of polyglutamine CAG CTG disorders

Long Tract of Untranslated CAG Repeats Is Deleterious in Transgenic Mice

The most frequent trinucleotide repeat found in human disorders is the CAG sequence. Expansion of CAG repeats is mostly found in coding regions and is thought to cause diseases through a protein mechanism. Recently, expanded CAG repeats were shown to induce toxicity at the RNA level in Drosophila and C. elegans. These findings raise the possibility that CAG repeats may trigger RNA-mediated pathogenesis in mammals. Here, we demonstrate that transgenic mice expressing EGFP transcripts with long CAG repeats in the 3′ untranslated region develop pathogenic features. Expression of the transgene was directed to the muscle in order to compare the resulting phenotype to that caused by the CUG expansion, as occurs in myotonic dystrophy. Transgenic mice expressing 200, but not those expressing 0 or 23 CAG repeats, showed alterations in muscle morphology, histochemistry and electrophysiology, as well as abnormal behavioral phenotypes. Expression of the expanded CAG repeats in testes resulted in reduced fertility due to defective sperm motility. The production of EGFP protein was significantly reduced by the 200 CAG repeats, and no polyglutamine-containing product was detected, which argues against a protein mechanism. Moreover, nuclear RNA foci were detected for the long CAG repeats. These data support the notion that expanded CAG repeat RNA can cause deleterious effects in mammals. They also suggest the possible involvement of an RNA mechanism in human diseases with long CAG repeats

Defining the Functional Domain of Programmed Cell Death 10 through Its Interactions with Phosphatidylinositol-3,4,5-Trisphosphate

Cerebral cavernous malformations (CCM) are vascular abnormalities of the central nervous system predisposing blood vessels to leakage, leading to hemorrhagic stroke. Three genes, Krit1 (CCM1), OSM (CCM2), and PDCD10 (CCM3) are involved in CCM development. PDCD10 binds specifically to PtdIns(3,4,5)P3 and OSM. Using threading analysis and multi-template modeling, we constructed a three-dimensional model of PDCD10. PDCD10 appears to be a six-helical-bundle protein formed by two heptad-repeat-hairpin structures (α1–3 and α4–6) sharing the closest 3D homology with the bacterial phosphate transporter, PhoU. We identified a stretch of five lysines forming an amphipathic helix, a potential PtdIns(3,4,5)P3 binding site, in the α5 helix. We generated a recombinant wild-type (WT) and three PDCD10 mutants that have two (Δ2KA), three (Δ3KA), and five (Δ5KA) K to A mutations. Δ2KA and Δ3KA mutants hypothetically lack binding residues to PtdIns(3,4,5)P3 at the beginning and the end of predicted helix, while Δ5KA completely lacks all predicted binding residues. The WT, Δ2KA, and Δ3KA mutants maintain their binding to PtdIns(3,4,5)P3. Only the Δ5KA abolishes binding to PtdIns(3,4,5)P3. Both Δ5KA and WT show similar secondary and tertiary structures; however, Δ5KA does not bind to OSM. When WT and Δ5KA are co-expressed with membrane-bound constitutively-active PI3 kinase (p110-CAAX), the majority of the WT is co-localized with p110-CAAX at the plasma membrane where PtdIns(3,4,5)P3 is presumably abundant. In contrast, the Δ5KA remains in the cytoplasm and is not present in the plasma membrane. Combining computational modeling and biological data, we propose that the CCM protein complex functions in the PI3K signaling pathway through the interaction between PDCD10 and PtdIns(3,4,5)P3