Infinets: The parallel syntax for non-wellfounded proof-theory

Logics based on the µ-calculus are used to model induc-tive and coinductive reasoning and to verify reactive systems. A well-structured proof-theory is needed in order to apply such logics to the study of programming languages with (co)inductive data types and automated (co)inductive theorem proving. While traditional proof system suffers some defects, non-wellfounded (or infinitary) and circular proofs have been recognized as a valuable alternative, and significant progress have been made in this direction in recent years. Such proofs are non-wellfounded sequent derivations together with a global validity condition expressed in terms of progressing threads. The present paper investigates a discrepancy found in such proof systems , between the sequential nature of sequent proofs and the parallel structure of threads: various proof attempts may have the exact threading structure while differing in the order of inference rules applications. The paper introduces infinets, that are proof-nets for non-wellfounded proofs in the setting of multiplicative linear logic with least and greatest fixed-points (µMLL ∞) and study their correctness and sequentialization. Inductive and coinductive reasoning is pervasive in computer science to specify and reason about infinite data as well as reactive properties. Developing appropriate proof systems amenable to automated reasoning over (co)inductive statements is therefore important for designing programs as well as for analyzing computational systems. Various logical settings have been introduced to reason about such inductive and coinductive statements, both at the level of the logical languages modelling (co)induction (such as Martin Löf's inductive predicates or fixed-point logics, also known as µ-calculi) and at the level of the proof-theoretical framework considered (finite proofs with explicit (co)induction rulesà la Park [23] or infinite, non-wellfounded proofs with fixed-point unfold-ings) [6-8, 4, 1, 2]. Moreover, such proof systems have been considered over classical logic [6, 8], intuitionistic logic [9], linear-time or branching-time temporal logic [19, 18, 25, 26, 13-15] or linear logic [24, 16, 4, 3, 14]

Observed communication semantics for classical processes

Classical Linear Logic (CLL) has long inspired readings of its proofs as communicating processes. Wadler's CP calculus is one of these readings. Wadler gave CP an operational semantics by selecting a subset of the cut-elimination rules of CLL to use as reduction rules. This semantics has an appealing close connection to the logic, but does not resolve the status of the other cut-elimination rules, and does not admit an obvious notion of observational equivalence. We propose a new operational semantics for CP based on the idea of observing communication, and use this semantics to define an intuitively reasonable notion of observational equivalence. To reason about observational equivalence, we use the standard relational denotational semantics of CLL. We show that this denotational semantics is adequate for our operational semantics. This allows us to deduce that, for instance, all the cut-elimination rules of CLL are observational equivalences

(Mathematical) Logic for Systems Biology (Invited Paper)

International audienceWe advocates here the use of (mathematical) logic for systems biology, as a unified framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these properties. The potential candidate logics should have a traditional proof theoretic pedigree (including a sequent calculus presentation enjoying cut-elimination and focusing), and should come with (certified) proof tools. Beyond providing a reliable framework, this allows the adequate encodings of our biological systems. We present two candidate logics (two modal extensions of linear logic, called HyLL and SELL), along with biological examples. The examples we have considered so far are very simple ones-coming with completely formal (interactive) proofs in Coq. Future works includes using automatic provers, which would extend existing automatic provers for linear logic. This should enable us to specify and study more realistic examples in systems biology, biomedicine (diagnosis and prognosis), and eventually neuroscience

Dysregulated Nephrin in Diabetic Nephropathy of Type 2 Diabetes: A Cross Sectional Study

Podocyte specific proteins are dysregulated in diabetic nephropathy, though the extent of their expression loss is not identical and may be subject to different regulatory factors. Quantifying the degree of loss may help identify the most useful protein to use as an early biomarker of diabetic nephropathy.Protein expression of synaptopodin, podocin and nephrin were quantified in 15 Type 2 diabetic renal biopsies and 12 control patients. We found statistically significant downregulation of synaptopodin (P<0.0001), podocin (P = 0.0002), and nephrin (P<0.0001) in kidney biopsies of diabetic nephropathy as compared with controls. Urinary nephrin levels (nephrinuria) were then measured in 66 patients with Type 2 diabetes and 10 healthy controls by an enzyme-linked immunosorbent assay (Exocell, Philadelphia, PA). When divided into groups according to normo-, micro-, and macroalbuminuria, nephrinuria was found to be present in 100% of diabetic patients with micro- and macroalbuminuria, as well as 54% of patients with normoalbuminuria. Nephrinuria also correlated significantly with albuminuria (rho = 0.89, p<0.001), systolic blood pressure (rho = 0.32, p = 0.007), and correlated negatively with serum albumin (rho = -0.48, p<0.0001) and eGFR (rho = -0.33, p = 0.005).These data suggest that key podocyte-specific protein expressions are significantly and differentially downregulated in diabetic nephropathy. The finding that nephrinuria is observed in a majority of these normoalbuminuric patients demonstrates that it may precede microalbuminuria. If further research confirms nephrinuria to be a biomarker of pre-clinical diabetic nephropathy, it would shed light on podocyte metabolism in disease, and raise the possibility of new and earlier therapeutic targets

Alterations of renal phenotype and gene expression profiles due to protein overload in NOD-related mouse strains

BACKGROUND: Despite multiple causes, Chronic Kidney Disease is commonly associated with proteinuria. A previous study on Non Obese Diabetic mice (NOD), which spontaneously develop type 1 diabetes, described histological and gene expression changes incurred by diabetes in the kidney. Because proteinuria is coincident to diabetes, the effects of proteinuria are difficult to distinguish from those of other factors such as hyperglycemia. Proteinuria can nevertheless be induced in mice by peritoneal injection of Bovine Serum Albumin (BSA). To gain more information on the specific effects of proteinuria, this study addresses renal changes in diabetes resistant NOD-related mouse strains (NON and NOD.B10) that were made to develop proteinuria by BSA overload. METHODS: Proteinuria was induced by protein overload on NON and NOD.B10 mouse strains and histology and microarray technology were used to follow the kidney response. The effects of proteinuria were assessed and subsequently compared to changes that were observed in a prior study on NOD diabetic nephropathy. RESULTS: Overload treatment significantly modified the renal phenotype and out of 5760 clones screened, 21 and 7 kidney transcripts were respectively altered in the NON and NOD.B10. Upregulated transcripts encoded signal transduction genes, as well as markers for inflammation (Calmodulin kinase beta). Down-regulated transcripts included FKBP52 which was also down-regulated in diabetic NOD kidney. Comparison of transcripts altered by proteinuria to those altered by diabetes identified mannosidase 2 alpha 1 as being more specifically induced by proteinuria. CONCLUSION: By simulating a component of diabetes, and looking at the global response on mice resistant to the disease, by virtue of a small genetic difference, we were able to identify key factors in disease progression. This suggests the power of this approach in unraveling multifactorial disease processes

A screening-based approach identifies cell cycle regulators AURKA, CHK1 and PLK1 as targetable regulators of chondrosarcoma cell survival

Chondrosarcomas are malignant cartilage tumors that are relatively resistant towards conventional therapeuticapproaches. Kinase inhibitors have been investigated and shown successful for several different cancer types. Inthis study we aimed at identifying kinase inhibitors that inhibit the survival of chondrosarcoma cells and therebyserve as new potential therapeutic strategies to treat chondrosarcoma patients.An siRNA screen targeting 779 different kinases was conducted in JJ012 chondrosarcoma cells in parallelwith a compound screen consisting of 273 kinase inhibitors in JJ012, SW1353 and CH2879 chondrosarcoma celllines. AURKA, CHK1 and PLK1 were identified as most promising targets and validated further in a morecomprehensive panel of chondrosarcoma cell lines. Dose response curves were performed using tyrosine kinaseinhibitors: MK-5108 (AURKA), LY2603618 (CHK1) and Volasertib (PLK1) using viability assays and cell cycleanalysis. Apoptosis was measured at 24 h after treatment using a caspase 3/7 assay. Finally, chondrosarcomapatient samples (N = =34) were used to examine the correlation between AURKA, CHK1 and PLK1 RNAexpression and documented patient survival.Dose dependent decreases in viability were observed in chondrosarcoma cell lines after treatment with MK-5108, LY2603618 and volasertib, with cell lines showing highest sensitivity to PLK1 inhibition. In additionincreased sensitivity to conventional chemotherapy was observed after CHK1 inhibition in a subset of the celllines. Interestingly, whereas AURKA and CHK1 were both expressed in chondrosarcoma patient samples, PLK1expression was found to be low compared to normal cartilage. Analysis of patient samples revealed that highCHK1 RNA expression correlated with a worse overall survival.AURKA, CHK1 and PLK1 are identified as important survival genes in chondrosarcoma cell lines. Althoughfurther research is needed to validate these findings, inhibiting CHK1 seems to be the most promising potentialtherapeutic target for patients with chondrosarcoma.Toxicolog

Alteration of Forkhead Box O (Foxo4) Acetylation Mediates Apoptosis of Podocytes in Diabetes Mellitus

The number of kidney podocytes is reduced in diabetic nephropathy. Advanced glycation end products (AGEs) accumulate in patients with diabetes and promote the apoptosis of podocyte by activating the forkhead box O4 (Foxo4) transcription factor to increase the expression of a pro-apoptosis gene, Bcl2l11. Using chromatin immunoprecipitation we demonstrate that AGE-modified bovine serum albumin (AGE-BSA) enhances Foxo4 binding to a forkhead binding element in the promoter of Bcl2lll. AGE-BSA also increases the acetylation of Foxo4. Lysine acetylation of Foxo4 is required for Foxo4 binding and transcription of Bcl2l11 in podocytes treated with AGE-BSA. The expression of a protein deacetylase that targets Foxo4 for deacetylation, sirtuin (Sirt1), is down regulated in cultured podocytes by AGE-BSA treatment and in glomeruli of diabetic patients. SIRT1 over expression in cultured murine podocytes prevents AGE-induced apoptosis. Glomeruli isolated from diabetic db/db mice have increased acetylation of Foxo4, suppressed expression of Sirt1, and increased expression of Bcl2l11 compared to non-diabetic littermates. Together, our data provide evidence that alteration of Foxo4 acetylation and down regulation of Sirt1 expression in diabetes promote podocyte apoptosis. Strategies to preserve Sirt1 expression or reduce Foxo4 acetylation could be used to prevent podocyte loss in diabetes

Angiogenesis and chronic kidney disease

The number of patients requiring renal replacement therapy due to end-stage renal disease (ESRD) is increasing worldwide. The prevalence of chronic kidney disease (CKD), and the importance of CKD as a risk factor in development of ESRD and in complicating cardiovascular disease (CVD) have been confirmed. In recent years, the involvement of angiogenesis-related factors in the progression of CKD has been studied, and the potential therapeutic effects on CKD of modulating these factors have been identified. Vascular endothelial growth factor (VEGF)-A, a potent pro-angiogenic factor, is involved in the development of the kidney, in maintenance of the glomerular capillary structure and filtration barrier, and in the renal repair process after injury. VEGF-A is also involved in the development of early diabetic nephropathy, demonstrated by the therapeutic effects of anti-VEGF-A antibody. Angiopoietin (Ang)-1 induces the maturation of newly formed blood vessels, and the therapeutic effects of Ang-1 in diabetic nephropathy have been described. In experimental models of diabetic nephropathy, the therapeutic effects of angiogenesis inhibitors, including angiostatin, endostatin and tumstatin peptides, the isocoumarin NM-3, and vasohibin-1, have been reported