Tau proteinThe tau proteins (abbreviated from tubulin associated unit) are a group of six highly soluble protein isoforms produced by alternative splicing from the gene MAPT (microtubule-associated protein tau). They have roles primarily in maintaining the stability of microtubules in axons and are abundant in the neurons of the central nervous system (CNS), where the cerebral cortex has the highest abundance. They are less common elsewhere but are also expressed at very low levels in CNS astrocytes and oligodendrocytes.
Neurofibrillary tangleNeurofibrillary tangles (NFTs) are aggregates of hyperphosphorylated tau protein that are most commonly known as a primary biomarker of Alzheimer's disease. Their presence is also found in numerous other diseases known as tauopathies. Little is known about their exact relationship to the different pathologies. Neurofibrillary tangles are formed by hyperphosphorylation of a microtubule-associated protein known as tau, causing it to aggregate, or group, in an insoluble form.
Protein phosphorylationProtein phosphorylation is a reversible post-translational modification of proteins in which an amino acid residue is phosphorylated by a protein kinase by the addition of a covalently bound phosphate group. Phosphorylation alters the structural conformation of a protein, causing it to become either activated or deactivated, or otherwise modifying its function. Approximately 13000 human proteins have sites that are phosphorylated. The reverse reaction of phosphorylation is called dephosphorylation, and is catalyzed by protein phosphatases.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
O-GlcNAcO-GlcNAc (short for O-linked GlcNAc or O-linked β-N-acetylglucosamine) is a reversible enzymatic post-translational modification that is found on serine and threonine residues of nucleocytoplasmic proteins. The modification is characterized by a β-glycosidic bond between the hydroxyl group of serine or threonine side chains and N-acetylglucosamine (GlcNAc).
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
Contrast agentA contrast agent (or contrast medium) is a substance used to increase the contrast of structures or fluids within the body in medical imaging. Contrast agents absorb or alter external electromagnetism or ultrasound, which is different from radiopharmaceuticals, which emit radiation themselves. In x-ray imaging, contrast agents enhance the radiodensity in a target tissue or structure. In magnetic resonance imaging, contrast agents shorten (or in some instances increase) the relaxation times of nuclei within body tissues in order to alter the contrast in the image.
Magnetic resonance imagingMagnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio waves to generate images of the organs in the body. MRI does not involve X-rays or the use of ionizing radiation, which distinguishes it from computed tomography (CT) and positron emission tomography (PET) scans.
