A time-fractional Borel-Pompeiu formula and a related hypercomplex operator calculus

In this paper we develop a time-fractional operator calculus in fractional Clifford analysis. Initially we study the $L_p$-integrability of the fundamental solutions of the multi-dimensional time-fractional diffusion operator and the associated time-fractional parabolic Dirac operator. Then we introduce the time-fractional analogues of the Teodorescu and Cauchy-Bitsadze operators in a cylindrical domain, and we investigate their main mapping properties. As a main result, we prove a time-fractional version of the Borel-Pompeiu formula based on a time-fractional Stokes' formula. This tool in hand allows us to present a Hodge-type decomposition for the forward time-fractional parabolic Dirac operator with left Caputo fractional derivative in the time coordinate. The obtained results exhibit an interesting duality relation between forward and backward parabolic Dirac operators and Caputo and Riemann-Liouville time-fractional derivatives. We round off this paper by giving a direct application of the obtained results for solving time-fractional boundary value problems.The work of M. Ferreira, M.M. Rodrigues and N. Vieira was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT–Fundação para a Ciência e a Tecnologia, within project UID/MAT/04106/2019. The work of the authors was supported by the project New Function Theoretical Methods in Computational Electrodynamics / Neue funktionentheoretische Methoden für instationäre PDE, funded by Programme for Cooperation in Science between Portugal and Germany (“Programa de Ações Integradas Luso-Alemãs 2017” - DAAD-CRUP - Acção No. A-15/17 / DAAD-PPP Deutschland-Portugal, Ref: 57340281). N. Vieira was also supported by FCT via the FCT Researcher Program 2014 (Ref: IF/00271/2014).publishe

Importance of Glycosylation on Function of a Potassium Channel in Neuroblastoma Cells

The Kv3.1 glycoprotein, a voltage-gated potassium channel, is expressed throughout the central nervous system. The role of N-glycans attached to the Kv3.1 glycoprotein on conducting and non-conducting functions of the Kv3.1 channel are quite limiting. Glycosylated (wild type), partially glycosylated (N220Q and N229Q), and unglycosylated (N220Q/N229Q) Kv3.1 proteins were expressed and characterized in a cultured neuronal-derived cell model, B35 neuroblastoma cells. Western blots, whole cell current recordings, and wound healing assays were employed to provide evidence that the conducting and non-conducting properties of the Kv3.1 channel were modified by N-glycans of the Kv3.1 glycoprotein. Electrophoretic migration of the various Kv3.1 proteins treated with PNGase F and neuraminidase verified that the glycosylation sites were occupied and that the N-glycans could be sialylated, respectively. The unglycosylated channel favored a different whole cell current pattern than the glycoform. Further the outward ionic currents of the unglycosylated channel had slower activation and deactivation rates than those of the glycosylated Kv3.1 channel. These kinetic parameters of the partially glycosylated Kv3.1 channels were also slowed. B35 cells expressing glycosylated Kv3.1 protein migrated faster than those expressing partially glycosylated and much faster than those expressing the unglycosylated Kv3.1 protein. These results have demonstrated that N-glycans of the Kv3.1 glycoprotein enhance outward ionic current kinetics, and neuronal migration. It is speculated that physiological changes which lead to a reduction in N-glycan attachment to proteins will alter the functions of the Kv3.1 channel

MicroRNAs in cell proliferation, cell death, and tumorigenesis

MicroRNAs (miRNAs) are a recently discovered class of ∼18–24 nucleotide RNA molecules that negatively regulate target mRNAs. All studied multicellular eukaryotes utilise miRNAs to regulate basic cellular functions including proliferation, differentiation, and death. It is now apparent that abnormal miRNA expression is a common feature of human malignancies. In this review, we will discuss how miRNAs influence tumorigenesis by acting as oncogenes and tumour suppressors

Absolute quantitative total-body small-animal SPECT with focusing pinholes

Purpose: In pinhole SPECT, attenuation of the photon flux on trajectories between source and pinholes affects quantitative accuracy of reconstructed images. Previously we introduced iterative methods that compensate for image degrading effects of detector and pinhole blurring, pinhole sensitivity and scatter for multi-pinhole SPECT. The aim of this paper is (1) to investigate the accuracy of the Chang algorithm in rodents and (2) to present a practical Changbased method using body outline contours obtained with optical cameras. Methods: Here we develop and experimentally validate a practical method for attenuation correction based on a Chang first-order method. This approach has the advantage that it is employed after, and therefore independently from, iterative reconstruction. Therefore, no new system matrix has to be calculated for each specific animal. Experiments with phantoms and animals were performed with a highresolution focusing multi-pinhole SPECT system (USPECT-II, MILabs, The Netherlands). This SPECT system provides three additional optical camera images of the animal for each SPECT scan from which the animal contour can be estimated. Results: Phantom experiments demonstrated that an average quantification error of –18.7% was reduced to –1.7% when both window-based scatter correction and Chang correction based on the body outline from optical images were applied. Without scatter and attenuation correction, quantification errors in a sacrificed rat containing sources with known activity ranged from –23.6 to –9.3%. These errors were reduced to values between –6.3 and +4.3% (with an average magnitude of 2.1%) after applying scatter and Chang attenuation correction. Conclusion: We conclude that the modified Chang correction based on body contour combined with window-based scatter correction is a practical method for obtaining small-animal SPECT images with high quantitative accuracy.Radiation, Radionuclides and ReactorsApplied Science

Hippocampal - diencephalic - cingulate networks for memory and emotion: An anatomical guide

This review brings together current knowledge from tract tracing studies to update and reconsider those limbic connections initially highlighted by Papez for their presumed role in emotion. These connections link hippocampal and parahippocampal regions with the mammillary bodies, the anterior thalamic nuclei, and the cingulate gyrus, all structures now strongly implicated in memory functions. An additional goal of this review is to describe the routes taken by the various connections within this network. The original descriptions of these limbic connections saw their interconnecting pathways forming a serial circuit that began and finished in the hippocampal formation. It is now clear that with the exception of the mammillary bodies, these various sites are multiply interconnected with each other, including many reciprocal connections. In addition, these same connections are topographically organised, creating further subsystems. This complex pattern of connectivity helps explain the difficulty of interpreting the functional outcome of damage to any individual site within the network. For these same reasons, Papez’s initial concept of a loop beginning and ending in the hippocampal formation needs to be seen as a much more complex system of hippocampal–diencephalic–cingulate connections. The functions of these multiple interactions might be better viewed as principally providing efferent information from the posterior medial temporal lobe. Both a subcortical diencephalic route (via the fornix) and a cortical cingulate route (via retrosplenial cortex) can be distinguished. These routes provide indirect pathways for hippocampal interactions with prefrontal cortex, with the preponderance of both sets of connections arising from the more posterior hippocampal regions. These multi-stage connections complement the direct hippocampal projections to prefrontal cortex, which principally arise from the anterior hippocampus, thereby creating longitudinal functional differences along the anterior–posterior plane of the hippocampus

Plasticity and rectangularity in survival curves

Living systems inevitably undergo a progressive deterioration of physiological function with age and an increase of vulnerability to disease and death. To maintain health and survival, living systems should optimize survival strategies with adaptive interactions among molecules, cells, organs, individuals, and environments, which arises plasticity in survival curves of living systems. In general, survival dynamics in a population is mathematically depicted by a survival rate, which monotonically changes from 1 to 0 with age. It would be then useful to find an adequate function to describe complicated survival dynamics. Here we describe a flexible survival function, derived from the stretched exponential function by adopting an age-dependent shaping exponent. We note that the exponent is associated with the fractal-like scaling in cumulative mortality rate. The survival function well depicts general features in survival curves; healthy populations exhibit plasticity and evolve towards rectangular-like survival curves, as examples in humans or laboratory animals

Integrated Profiling of MicroRNAs and mRNAs: MicroRNAs Located on Xq27.3 Associate with Clear Cell Renal Cell Carcinoma

Background: With the advent of second-generation sequencing, the expression of gene transcripts can be digitally measured with high accuracy. The purpose of this study was to systematically profile the expression of both mRNA and miRNA genes in clear cell renal cell carcinoma (ccRCC) using massively parallel sequencing technology. Methodology: The expression of mRNAs and miRNAs were analyzed in tumor tissues and matched normal adjacent tissues obtained from 10 ccRCC patients without distant metastases. In a prevalence screen, some of the most interesting results were validated in a large cohort of ccRCC patients. Principal Findings: A total of 404 miRNAs and 9,799 mRNAs were detected to be differentially expressed in the 10 ccRCC patients. We also identified 56 novel miRNA candidates in at least two samples. In addition to confirming that canonical cancer genes and miRNAs (including VEGFA, DUSP9 and ERBB4; miR-210, miR-184 and miR-206) play pivotal roles in ccRCC development, promising novel candidates (such as PNCK and miR-122) without previous annotation in ccRCC carcinogenesis were also discovered in this study. Pathways controlling cell fates (e. g., cell cycle and apoptosis pathways) and cell communication (e. g., focal adhesion and ECM-receptor interaction) were found to be significantly more likely to be disrupted in ccRCC. Additionally, the results of the prevalence screen revealed that the expression of a miRNA gene cluster located on Xq27.3 was consistently downregulated in at least 76.7% of similar to 50 ccRCC patients. Conclusions: Our study provided a two-dimensional map of the mRNA and miRNA expression profiles of ccRCC using deep sequencing technology. Our results indicate that the phenotypic status of ccRCC is characterized by a loss of normal renal function, downregulation of metabolic genes, and upregulation of many signal transduction genes in key pathways. Furthermore, it can be concluded that downregulation of miRNA genes clustered on Xq27.3 is associated with ccRCC