Special Functions and Pathways for Problems in Astrophysics: An Essay in Honor of A.M. Mathai

The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information and statistical distribution theory. The results presented in the essay cover a period of time in Mathai's research from 1982 to 2008 and are all related to the thematic area of the gravitationally stabilized solar fusion reactor and fractional reaction-diffusion, taking into account concepts of non-extensive statistical mechanics. The time period referred to above coincides also with Mathai's exceptional contributions to the establishment and operation of the Centre for Mathematical Sciences, India, as well as the holding of the United Nations (UN)/European Space Agency (ESA)/National Aeronautics and Space Administration (NASA) of the United States/ Japanese Aerospace Exploration Agency (JAXA) Workshops on basic space science and the International Heliophysical Year 2007, around the world. Professor Mathai's contributions to the latter, since 1991, are a testimony for his social con-science applied to international scientific activity.

Fractional Calculus of P-transforms

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99

Matrix-Variate Statistical Distributions and Fractional Calculus

MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthday

Inhibition of p38 pathway leads to OA-like changes in a rat animal model

Objectives The p38 mitogen-activated protein kinase (MAPK) signal transduction pathway is involved in a variety of inflammatory responses, including cytokine generation, cell differentiation proliferation and apoptosis. Here, we examined the effects of systemic p38 MAPK inhibition on cartilage cells and osteoarthritis (OA) disease progression by both in vitro and in vivo approaches. Methods p38 kinase activity was evaluated in normal and OA cartilage cells by measuring the amount of phosphorylated protein. To examine the function of p38 signaling pathway in vitro, normal chondrocytes were isolated and differentiated in the presence or absence of p38 inhibitor; SB203580 and analysed for chondrogenic phenotype. Effect of systemic p38 MAPK inhibition in normal and OA (induced by menisectomy) rats were analysed by treating animals with vehicle alone (DMS0) or p38 inhibitor (SB203580). Damage to the femur and tibial plateau was evaluated by modified Mankin score, histology and immunohistochemistry. Results Our in vitro studies have revealed that a down-regulation of chondrogenic and increase of hypertrophic gene expression occurs in the normal chondrocytes, when p38 is neutralized by a pharmacological inhibitor. We further observed that the basal levels of p38 phosphorylation were decreased in OA chondrocytes compared with normal chondrocytes. These findings together indicate the importance of this pathway in the regulation of cartilage physiology and its relevance to OA pathogenesis. At in vivo level, systematic administration of a specific p38 MAPK inhibitor, SB203580, continuously for over a month led to a significant loss of proteoglycan; aggrecan and cartilage thickness. On the other hand, SB203580 treated normal rats showed a significant increase in TUNEL positive cells, cartilage hypertrophy markers such as Type 10 collagen, Runt-related transcription factor and Matrix metalloproteinase-13 and substantially induced OA like phenotypic changes in the normal rats. In addition, menisectomy induced OA rat models that were treated with p38 inhibitor showed aggravation of cartilage damage. Conclusions In summary, this study has provided evidence that the component of the p38 MAPK pathway is important to maintain the cartilage health and its inhibition can lead to severe cartilage degenerative changes. The observations in this study highlight the possibility of using activators of the p38 pathway as an alternative approach in the treatment of OA.

Excessive bone formation in a mouse model of ankylosing spondylitis is associated with decreases in Wnt pathway inhibitors

Introduction: Ankylosing spondylitis (AS) is unique in its pathology where inflammation commences at the entheses before progressing to an osteoproliferative phenotype generating excessive bone formation that can result in joint fusion. The underlying mechanisms of this progression are poorly understood. Recent work has suggested that changes in Wnt signalling, a key bone regulatory pathway, may contribute to joint ankylosis in AS. Using the proteoglycan-induced spondylitis (PGISp) mouse model which displays spondylitis and eventual joint fusion following an initial inflammatory stimulus, we have characterised the structural and molecular changes that underlie disease progression. Methods: PGISp mice were characterised 12 weeks after initiation of inflammation using histology, immunohistochemistry (IHC) and expression profiling. Results: Inflammation initiated at the periphery of the intervertebral discs progressing to disc destruction followed by massively excessive cartilage and bone matrix formation, as demonstrated by toluidine blue staining and IHC for collagen type I and osteocalcin, leading to syndesmophyte formation. Expression levels of DKK1 and SOST, Wnt signalling inhibitors highly expressed in joints, were reduced by 49% and 63% respectively in the spine PGISp compared with control mice (P < 0.05) with SOST inhibition confirmed by IHC. Microarray profiling showed genes involved in inflammation and immune-regulation were altered. Further, a number of genes specifically involved in bone regulation including other members of the Wnt pathway were also dysregulated. Conclusions: This study implicates the Wnt pathway as a likely mediator of the mechanism by which inflammation induces bony ankylosis in spondyloarthritis, raising the potential that therapies targeting this pathway may be effective in preventing this process.

MPTP activates ASK1-p38 MAPK signaling pathway through TNF-dependent Trx1 oxidation in parkinsonism mouse model

Activation of apoptosis signal regulating kinase 1 (ASK1)-p38 MAPK death signaling cascade is irn plicated in the death of dopaminergic neurons in substantia nigra in Parkinson's disease (PD). We investigated upstream activators of ASK1 using an MPTP mouse model of parkinsonism and assessed the temporal cascade of death signaling in ventral midbrain (VMB) and striatum (ST). MPTP selectively activated ASK1 and downstream 1)38 MAPK in a time dependent manner in VMB alone. This occurred through selective protein thiol oxidation of the redox-sensitive thiol disulfide oxidoreductase, thiorcdoxin (Trxl), resulting in release of its inhibitory association with ASK1, while glutathione-S-transferase ji 1 (GSTM1) remained in reduced form in association with ASK1. Levels of tumor necrosis factor (TNF), a known activator of ASK1, increased early after MPTP in VMB. Protein ovariation netvvork analysis (PCNA) using protein states as nodes revealed TNF to be an important node regulating the ASK1 signaling cascade. In confirmation, blocking MPTP-mecliated TNF signaling through intrathecal administration of TNFneutralizing antibody prevented Trxl oxidation and downstream ASK1-p38 MAPK activation. Averting an early increase in TNF, which leads to protein thiol oxidation resulting in activation of ASK1-p38 signaling, may be critical for neuroprotection in PD. Importantly, network analysis can help in understanding the cause/effect relationship within protein networks in complex disease states. (C) 2015 Published by Elsevier Inc.

Cytokine pathway disruption in a mouse model of schizophrenia induced by Munc18-1a overexpression in the brain

Background: An accumulating body of evidence points to the significance of neuroinflammation and immunogenetics in schizophrenia, and an imbalance of cytokines in the central nervous system (CNS) has been suggested to be associated with the disorder. Munc18-overexpressing mice (Munc18-OE) have provided a model for the study of the alterations that may underlie the symptoms of subjects with schizophrenia. The aim of the present study was to elucidate the involvement of neuroinflammation and cytokine imbalance in this model. Methods: Cytokines were evaluated in the cortex and the striatum of Munc18-OE and wild-type (WT) mice by enzyme-linked immunosorbent assay (ELISA). Protein levels of specific microglia and macrophage, astrocytic and neuroinflammation markers were quantified by western blot in the cortex and the striatum of Munc18-OE and WT mice. Results: Each cytokine evaluated (Interferon-gamma (IFN-gamma), Tumor Necrosis Factor-alpha (TNF-alpha), Interleukin-2 (IL-2) and CCL2 chemokine) was present at higher levels in the striatum of Munc18-OE mice than WT. Cortical TNF-alpha and IL-2 levels were significantly lower in Munc18-OE mice than WT mice. The microglia and macrophage marker CD11b was lower in the cortexes of Munc18-OE mice than WT, but no differences were observed in the striatum. Glial Fibrillary Acidic Protein (GFAP) and Nuclear Factor-kappaB (NF-kappa B)p65 levels were not different between the groups. Interleukin-1beta (IL-1 beta) and IL-6 levels were beneath detection limits. Conclusions: The disrupted levels of cytokines detected in the brain of Munc18-OE mice was found to be similar to clinical reports and endorses study of this type for analysis of this aspect of the disorder. The lower CD11b expression in the cortex but not in the striatum of the Munc18-OE mice may reflect differences in physiological activity. The cytokine expression pattern observed in Munc18-OE mice is similar to a previously published model of schizophrenia caused by maternal immune activation. Together, these data suggest a possible role for an immune imbalance in this disorder.

Effect of Neonatal Asphyxia on the Impairment of the Auditory Pathway by Recording Auditory Brainstem Responses in Newborn Piglets: A New Experimentation Model to Study the Perinatal Hypoxic-Ischemic Damage on the Auditory Syste

Introduction Hypoxia-ischemia (HI) is a major perinatal problem that results in severe damage to the brain impairing the normal development of the auditory system. The purpose of the present study is to study the effect of perinatal asphyxia on the auditory pathway by recording auditory brain responses in a novel animal experimentation model in newborn piglets. Method Hypoxia-ischemia was induced to 1.3 day-old piglets by clamping 30 minutes both carotid arteries by vascular occluders and lowering the fraction of inspired oxygen. We compared the Auditory Brain Responses (ABRs) of newborn piglets exposed to acute hypoxia/ischemia (n = 6) and a control group with no such exposure (n = 10). ABRs were recorded for both ears before the start of the experiment (baseline), after 30 minutes of HI injury, and every 30 minutes during 6 h after the HI injury. Results Auditory brain responses were altered during the hypoxic-ischemic insult but recovered 30-60 minutes later. Hypoxia/ischemia seemed to induce auditory functional damage by increasing I-V latencies and decreasing wave I, III and V amplitudes, although differences were not significant. Conclusion The described experimental model of hypoxia-ischemia in newborn piglets may be useful for studying the effect of perinatal asphyxia on the impairment of the auditory pathway.

The role of lipid peroxidation products and oxidative stress in activation of the canonical wingless-type MMTV integration site (WNT) pathway in a rat model of diabetic retinopathy

Our recent studies suggest that activation of the wingless-type MMTV integration site (WNT) pathway plays pathogenic roles in diabetic retinopathy and age-related macular degeneration. Here we investigated the causative role of oxidative stress in retinal WNT pathway activation in an experimental model of diabetes.

Genome-wide gene pathway analysis of psychotic illness symptom dimensions based on a new schizophrenia-specific model of the OPCRIT

Empirically derived phenotypic measurements have the potential to enhance gene-finding efforts in schizophrenia. Previous research based on factor analyses of symptoms has typically included schizoaffective cases. Deriving factor loadings from analysis of only narrowly defined schizophrenia cases could yield more sensitive factor scores for gene pathway and gene ontology analyses. Using an Irish family sample, this study 1) factor analyzed clinician-rated Operational Criteria Checklist items in cases with schizophrenia only, 2) scored the full sample based on these factor loadings, and 3) implemented genome-wide association, gene-based, and gene-pathway analysis of these SCZ-based symptom factors (final N= 507). Three factors emerged from the analysis of the schizophrenia cases: a manic, a depressive, and a positive symptom factor. In gene-based analyses of these factors, multiple genes had q<. 0.01. Of particular interest are findings for PTPRG and WBP1L, both of which were previously implicated by the Psychiatric Genomics Consortium study of SCZ; results from this study suggest that variants in these genes might also act as modifiers of SCZ symptoms. Gene pathway analyses of the first factor indicated over-representation of glutamatergic transmission, GABA-A receptor, and cyclic GMP pathways. Results suggest that these pathways may have differential influence on affective symptom presentation in schizophrenia.

Abnormal alterations in the Ca2+/CaV1.2/calmodulin/caMKII signaling pathway in a tremor rat model and in cultured hippocampal neurons exposed to Mg2+-free solution

Voltage-dependent calcium channels (VDCCs) are key elements in epileptogenesis. There are several binding-sites linked to calmodulin (CaM) and several potential CaM-dependent protein kinase II (CaMKII)-mediated phosphorylation sites in CaV1.2. The tremor rat model (TRM) exhibits absence‑like seizures from 8 weeks of age. The present study was performed to detect changes in the Ca2+/CaV1.2/CaM/CaMKII pathway in TRMs and in cultured hippocampal neurons exposed to Mg2+‑free solution. The expression levels of CaV1.2, CaM and phosphorylated CaMKII (p‑CaMKII; Thr‑286) in these two models were examined using immunofluorescence and western blotting. Compared with Wistar rats, the expression levels of CaV1.2 and CaM were increased, and the expression of p‑CaMKII was decreased in the TRM hippocampus. However, the expression of the targeted proteins was reversed in the TRM temporal cortex. A significant increase in the expression of CaM and decrease in the expression of CaV1.2 were observed in the TRM cerebellum. In the cultured neuron model, p‑CaMKII and CaV1.2 were markedly decreased. In addition, neurons exhibiting co‑localized expression of CaV1.2 and CaM immunoreactivities were detected. Furthermore, intracellular calcium concentrations were increased in these two models. For the first time, o the best of our knowledge, the data of the present study suggested that abnormal alterations in the Ca2+/CaV1.2/CaM/CaMKII pathway may be involved in epileptogenesis and in the phenotypes of TRMs and cultured hippocampal neurons exposed to Mg2+‑free solution.

Fungi, bacteria and soil pH: the oxalate-carbonate pathway as a model for metabolic interaction

The oxalatecarbonate pathway involves the oxidation of calcium oxalate to low-magnesium calcite and represents a potential long-term terrestrial sink for atmospheric CO2. In this pathway, bacterial oxalate degradation is associated with a strong local alkalinization and subsequent carbonate precipitation. In order to test whether this process occurs in soil, the role of bacteria, fungi and calcium oxalate amendments was studied using microcosms. In a model system with sterile soil amended with laboratory cultures of oxalotrophic bacteria and fungi, the addition of calcium oxalate induced a distinct pH shift and led to the final precipitation of calcite. However, the simultaneous presence of bacteria and fungi was essential to drive this pH shift. Growth of both oxalotrophic bacteria and fungi was confirmed by qPCR on the frc (oxalotrophic bacteria) and 16S rRNA genes, and the quantification of ergosterol (active fungal biomass) respectively. The experiment was replicated in microcosms with non-sterilized soil. In this case, the bacterial and fungal contribution to oxalate degradation was evaluated by treatments with specific biocides (cycloheximide and bronopol). Results showed that the autochthonous microflora oxidized calcium oxalate and induced a significant soil alkalinization. Moreover, data confirmed the results from the model soil showing that bacteria are essentially responsible for the pH shift, but require the presence of fungi for their oxalotrophic activity. The combined results highlight that the interaction between bacteria and fungi is essential to drive metabolic processes in complex environments such as soil.

A mathematical model of the sterol regulatory element binding protein 2 cholesterol biosynthesis pathway

Cholesterol is one of the key constituents for maintaining the cellular membrane and thus the integrity of the cell itself. In contrast high levels of cholesterol in the blood are known to be a major risk factor in the development of cardiovascular disease. We formulate a deterministic nonlinear ordinary differential equation model of the sterol regulatory element binding protein 2 (SREBP-2) cholesterol genetic regulatory pathway in an hepatocyte. The mathematical model includes a description of genetic transcription by SREBP-2 which is subsequently translated to mRNA leading to the formation of 3-hydroxy-3-methylglutaryl coenzyme A reductase (HMGCR), a main precursor of cholesterol synthesis. Cholesterol synthesis subsequently leads to the regulation of SREBP-2 via a negative feedback formulation. Parameterised with data from the literature, the model is used to understand how SREBP-2 transcription and regulation affects cellular cholesterol concentration. Model stability analysis shows that the only positive steady-state of the system exhibits purely oscillatory, damped oscillatory or monotic behaviour under certain parameter conditions. In light of our findings we postulate how cholesterol homestasis is maintained within the cell and the advantages of our model formulation are discussed with respect to other models of genetic regulation within the literature.