Fractional Modeling of Neurotransmitter Transport in the presence of Receptor and Transporter

Author(s):  
S.Ruban raj ◽  
◽  
Sheena Mathew
Author(s):  
G. C. Ruben ◽  
K. Iqbal ◽  
I. Grundke-Iqbal ◽  
H. Wisniewski ◽  
T. L. Ciardelli ◽  
...  

In neurons, the microtubule associated protein, tau, is found in the axons. Tau stabilizes the microtubules required for neurotransmitter transport to the axonal terminal. Since tau has been found in both Alzheimer neurofibrillary tangles (NFT) and in paired helical filaments (PHF), the study of tau's normal structure had to preceed TEM studies of NFT and PHF. The structure of tau was first studied by ultracentrifugation. This work suggested that it was a rod shaped molecule with an axial ratio of 20:1. More recently, paraciystals of phosphorylated and nonphosphoiylated tau have been reported. Phosphorylated tau was 90-95 nm in length and 3-6 nm in diameter where as nonphosphorylated tau was 69-75 nm in length. A shorter length of 30 nm was reported for undamaged tau indicating that it is an extremely flexible molecule. Tau was also studied in relation to microtubules, and its length was found to be 56.1±14.1 nm.


2020 ◽  
Vol 23 (6) ◽  
pp. 1647-1662
Author(s):  
Ravshan Ashurov ◽  
Sabir Umarov

Abstract The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation with an arbitrary second order elliptic differential operator. We prove that the additional information about the solution at a fixed time instant at a monitoring location, as “the observation data”, identifies uniquely the order of the fractional derivative.


Author(s):  
Abhaya Pal Singh ◽  
Dipankar Deb ◽  
Himanshu Agrawal ◽  
Valentina E. Balas

Author(s):  
Mohamed M. Khader

AbstractThis paper is devoted to introduce a numerical treatment using the generalized Adams-Bashforth-Moulton method for some of the variable-order fractional modeling dynamics problems, such as Riccati and Logistic differential equations. The fractional derivative is described in Caputo variable-order fractional sense. The obtained numerical results of the proposed models show the simplicity and efficiency of the proposed method. Moreover, the convergence order of the method is also estimated numerically.


2016 ◽  
Vol 323 ◽  
pp. 219-242 ◽  
Author(s):  
Yue Yu ◽  
Paris Perdikaris ◽  
George Em Karniadakis

2021 ◽  
Author(s):  
Abhaya Pal Singh ◽  
Dipankar Deb ◽  
Himanshu Agrawal ◽  
Valentina E. Balas

Genome ◽  
2007 ◽  
Vol 50 (10) ◽  
pp. 877-897 ◽  
Author(s):  
Shiva M. Singh ◽  
Julie Treadwell ◽  
Morgan L. Kleiber ◽  
Michelle Harrison ◽  
Raihan K. Uddin

Most familial behavioral phenotypes result from the complex interaction of multiple genes. Studies of such phenotypes involving human subjects are often inconclusive owing to complexity of causation and experimental limitations. Studies of animal models argue for the use of established genetic strains as a powerful tool for genetic dissection of behavioral disorders and have led to the identification of rare genes and genetic mechanisms implicated in such phenotypes. We have used microarrays to study global gene expression in adult brains of four genetic strains of mice (C57BL/6J, DBA/2J, A/J, and BALB/c). Our results demonstrate that different strains show expression differences for a number of genes in the brain, and that closely related strains have similar patterns of gene expression as compared with distantly related strains. In addition, among the 24 000 genes and ESTs on the microarray, 77 showed at least a 1.5-fold increase in the brains of C57BL/6J mice as compared with those of DBA/2J mice. These genes fall into such functional categories as gene regulation, metabolism, cell signaling, neurotransmitter transport, and DNA/RNA binding. The importance of these findings as a novel genetic resource and their use and application in the genetic analysis of complex behavioral phenotypes, susceptibilities, and responses to drugs and chemicals are discussed.


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