AmyloidAmyloids are aggregates of proteins characterised by a fibrillar morphology of typically 7–13 nm in diameter, a β-sheet secondary structure (known as cross-β) and ability to be stained by particular dyes, such as Congo red. In the human body, amyloids have been linked to the development of various diseases. Pathogenic amyloids form when previously healthy proteins lose their normal structure and physiological functions (misfolding) and form fibrous deposits within and around cells.
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.
Amyloid betaAmyloid beta (Aβ or Abeta) denotes peptides of 36–43 amino acids that are the main component of the amyloid plaques found in the brains of people with Alzheimer's disease. The peptides derive from the amyloid-beta precursor protein (APP), which is cleaved by beta secretase and gamma secretase to yield Aβ in a cholesterol-dependent process and substrate presentation. Aβ molecules can aggregate to form flexible soluble oligomers which may exist in several forms.
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.
FibrilFibrils (from the Latin fibra) are structural biological materials found in nearly all living organisms. Not to be confused with fibers or filaments, fibrils tend to have diameters ranging from 10–100 nanometers (whereas fibers are micro to milli-scale structures and filaments have diameters approximately 10–50 nanometers in size). Fibrils are not usually found alone but rather are parts of greater hierarchical structures commonly found in biological systems.
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.
ProteinopathyIn medicine, proteinopathy ([pref. protein]; -pathy [suff. disease]; proteinopathies pl.; proteinopathic adj), or proteopathy, protein conformational disorder, or protein misfolding disease, is a class of diseases in which certain proteins become structurally abnormal, and thereby disrupt the function of cells, tissues and organs of the body. Often the proteins fail to fold into their normal configuration; in this misfolded state, the proteins can become toxic in some way (a toxic gain-of-function) or they can lose their normal function.
Amyloid plaquesAmyloid plaques (also known as neuritic plaques, amyloid beta plaques or senile plaques) are extracellular deposits of the amyloid beta (Aβ) protein mainly in the grey matter of the brain. Degenerative neuronal elements and an abundance of microglia and astrocytes can be associated with amyloid plaques. Some plaques occur in the brain as a result of aging, but large numbers of plaques and neurofibrillary tangles are characteristic features of Alzheimer's disease. Abnormal neurites in amyloid plaques are tortuous, often swollen axons and dendrites.
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).
Alzheimer's diseaseAlzheimer's disease (AD) is a neurodegenerative disease that usually starts slowly and progressively worsens, and is the cause of 60–70% of cases of dementia. The most common early symptom is difficulty in remembering recent events. As the disease advances, symptoms can include problems with language, disorientation (including easily getting lost), mood swings, loss of motivation, self-neglect, and behavioral issues. As a person's condition declines, they often withdraw from family and society.
