Recent advances in real geometric reasoning

In the 1930s Tarski showed that real quantifier elimination was possible, and in 1975 Collins gave a remotely practicable method, albeit with doubly-exponential complexity, which was later shown to be inherent. We discuss some of the recent major advances in Collins method: such as an alternative approach based on passing via the complexes, and advances which come closer to "solving the question asked" rather than "solving all problems to do with these polynomials"

Bistability, Probability Transition Rate and First-Passage Time in an Autoactivating Positive-Feedback Loop

A hallmark of positive-feedback regulation is bistability, which gives rise to distinct cellular states with high and low expression levels, and that stochasticity in gene expression can cause random transitions between two states, yielding bimodal population distribution (Kaern et al., 2005, Nat Rev Genet 6: 451-464). In this paper, the probability transition rate and first-passage time in an autoactivating positive-feedback loop with bistability are investigated, where the gene expression is assumed to be disturbed by both additive and multiplicative external noises, the bimodality in the stochastic gene expression is due to the bistability, and the bistability determines that the potential of the Fokker-Planck equation has two potential wells. Our main goal is to illustrate how the probability transition rate and first-passage time are affected by the maximum transcriptional rate, the intensities of additive and multiplicative noises, and the correlation of additive and multiplicative noises. Our main results show that (i) the increase of the maximum transcription rate will be useful for maintaining a high gene expression level; (ii) the probability transition rate from one potential well to the other one will increase with the increase of the intensity of additive noise; (iii) the increase of multiplicative noise strength will increase the amount of probability in the left potential well; and (iv) positive (or negative) cross-correlation between additive and multiplicative noises will increase the amount of probability in the left (or right) potential well

Citalopram reduces aggregation of ATXN3 in a YAC transgenic mouse model of Machado-Joseph disease

Machado-Joseph disease, also known as spinocerebellar ataxia type 3, is a fatal polyglutamine disease with no disease-modifying treatment. The selective serotonin reuptake inhibitor citalopram was shown in nematode and mouse models to be a compelling repurposing candidate for Machado-Joseph disease therapeutics. We sought to confirm the efficacy of citalopram to decrease ATXN3 aggregation in an unrelated mouse model of Machado-Joseph disease. Four-week-old YACMJD84.2 mice and non-transgenic littermates were given citalopram 8 mg/kg in drinking water or water for 10 weeks. At the end of treatment, brains were collected for biochemical and pathological analyses. Brains of citalopram-treated YACMJD84.2 mice showed an approximate 50% decrease in the percentage of cells containing ATXN3-positive inclusions in the substantia nigra and three examined brainstem nuclei compared to controls. No differences in ATXN3 inclusion load were observed in deep cerebellar nuclei of mice. Citalopram effect on ATXN3 aggregate burden was corroborated by immunoblotting analysis. While lysates from the brainstem and cervical spinal cord of citalopram-treated mice showed a decrease in all soluble forms of ATXN3 and a trend toward reduction of insoluble ATXN3, no differences in ATXN3 levels were found between cerebella of citalopram-treated and vehicle-treated mice. Citalopram treatment altered levels of select components of the cellular protein homeostatic machinery that may be expected to enhance the capacity to refold and/or degrade mutant ATXN3. The results here obtained in a second independent mouse model of Machado-Joseph disease further support citalopram as a potential drug to be repurposed for this fatal disorder.This work was funded by Becky Babcox Research Fund/pilot research award G015617, University of Michigan to M.C.C. and NINDS/NIH R01NS038712 to H.L.P. The work performed at the University of Minho was funded by the European Regional Development Funds (FEDER), through the Competitiveness Factors Operational Programme (COMPETE), and by National funds, through the Foundation for Science and Technology (FCT), under the scope of the project POCI-01-0145-FEDER-007038. This article was developed under the scope of the project NORTE-01-0145-FEDER-000013, supported by the Northern Portugal Regional Operational Program (NORTE 2020), under the Portugal 2020 Partnership Agreement, through the FEDER. This work was also supported by FCT and COMPETE through the projects [PTDC/SAU-GMG/112617/2009] (to P.M.) and [EXPL/BIM-MEC/ 0239/2012] (to A.T.C.); by FCT through the project [POCI-01-0145- FEDER-016818 (PTDC/NEU-NMC/3648/2014)] (to P.M.); by National Ataxia Foundation (to P.M. and to A.T.C.); and by Ataxia UK (to P.M.). S.D.S. and A.T.C. were supported by fellowships from FCT, SFRH/BD/ 78388/2011 and SFRH/BPD/102317/2014, respectively. FCT fellowships are co-financed by POPH, QREN, Governo da República Portuguesa and EU/FSE

p16 Mutation Spectrum in the Premalignant Condition Barrett's Esophagus

Background: Mutation, promoter hypermethylation and loss of heterozygosity involving the tumor suppressor gene p16 (CDKN2a/INK4a) have been detected in a wide variety of human cancers, but much less is known concerning the frequency and spectrum of p16 mutations in premalignant conditions. Methods and Findings: We have determined the p16 mutation spectrum for a cohort of 304 patients with Barrett’s esophagus, a premalignant condition that predisposes to the development of esophageal adenocarcinoma. Forty seven mutations were detected by sequencing of p16 exon 2 in 44 BE patients (14.5%) with a mutation spectrum consistent with that caused by oxidative damage and chronic inflammation. The percentage of patients with p16 mutations increased with increasing histologic grade. In addition, samples from 3 out of 19 patients (15.8%) who underwent esophagectomy were found to have mutations. Conclusions: The results of this study suggest the environment of the esophagus in BE patients can both generate an

Proteasome Activator Enhances Survival of Huntington's Disease Neuronal Model Cells

In patients with Huntington's disease (HD), the proteolytic activity of the ubiquitin proteasome system (UPS) is reduced in the brain and other tissues. The pathological hallmark of HD is the intraneuronal nuclear protein aggregates of mutant huntingtin. We determined how to enhance UPS function and influence catalytic protein degradation and cell survival in HD. Proteasome activators involved in either the ubiquitinated or the non-ubiquitinated proteolysis were overexpressed in HD patients' skin fibroblasts or mutant huntingtin-expressing striatal neurons. Following compromise of the UPS, overexpression of the proteasome activator subunit PA28γ, but not subunit S5a, recovered proteasome function in the HD cells. PA28γ also improved cell viability in mutant huntingtin-expressing striatal neurons exposed to pathological stressors, such as the excitotoxin quinolinic acid and the reversible proteasome inhibitor MG132. These results demonstrate the specific functional enhancements of the UPS that can provide neuroprotection in HD cells

Assimilating Seizure Dynamics

Observability of a dynamical system requires an understanding of its state—the collective values of its variables. However, existing techniques are too limited to measure all but a small fraction of the physical variables and parameters of neuronal networks. We constructed models of the biophysical properties of neuronal membrane, synaptic, and microenvironment dynamics, and incorporated them into a model-based predictor-controller framework from modern control theory. We demonstrate that it is now possible to meaningfully estimate the dynamics of small neuronal networks using as few as a single measured variable. Specifically, we assimilate noisy membrane potential measurements from individual hippocampal neurons to reconstruct the dynamics of networks of these cells, their extracellular microenvironment, and the activities of different neuronal types during seizures. We use reconstruction to account for unmeasured parts of the neuronal system, relating micro-domain metabolic processes to cellular excitability, and validate the reconstruction of cellular dynamical interactions against actual measurements. Data assimilation, the fusing of measurement with computational models, has significant potential to improve the way we observe and understand brain dynamics

Assessment of Blood Hemodynamics by USPIO-Induced R1 Changes in MRI of Murine Colon Carcinoma

The objective of this study is to assess whether ultrasmall superparamagnetic iron oxide (USPIO)-induced changes of the water proton longitudinal relaxation rate (R1) provide a means to assess blood hemodynamics of tumors. Two types of murine colon tumors (C26a and C38) were investigated prior to and following administration of USPIO blood-pool contrast agent with fast R1 measurements. In a subpopulation of mice, R1 was measured following administration of hydralazine, a well-known blood hemodynamic modifier. USPIO-induced R1 increase in C38 tumors (ΔR1 = 0.072 ± 0.0081 s−1) was significantly larger than in C26a tumors (ΔR1 = 0.032 ± 0.0018 s−1, N = 9, t test, P < 0.001). This was in agreement with the immunohistochemical data that showed higher values of relative vascular area (RVA) in C38 tumors than in C26a tumors (RVA = 0.059 ± 0.015 vs. 0.020 ± 0.011; P < 0.05). Following administration of hydralazine, a decrease in R1 value was observed. This was consistent with the vasoconstriction induced by the steal effect mechanism. In conclusion, R1 changes induced by USPIO are sensitive to tumor vascular morphology and to blood hemodynamics. Thus, R1 measurements following USPIO administration can give novel insight into the effects of blood hemodynamic modifiers, non-invasively and with a high temporal resolution