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By NMR-guided simulations, amyloid beta 1-40 and amyloid beta 1-42 also seem to feature highly different conformational states, [66] with the C-terminus of amyloid beta 1-42 being more structured than that of the 1-40 fragment. Low-temperature and low-salt conditions allowed to isolate pentameric disc-shaped oligomers devoid of beta structure. [67]
Amyloid beta (Aβ) is a small protein, most often 40 or 42 amino acids in length, that is released from a longer parent protein called the Aβ-precursor protein (APP). [24] APP is produced by many types of cell in the body, but it is especially abundant in neurons. It is a single-pass transmembrane protein, passing once through cellular ...
p3 peptide also known as amyloid β- peptide (Aβ) 17–40/42 is the peptide resulting from the α-and γ-secretase cleavage from the amyloid precursor protein . It is known to be the major constituent of diffuse plaques observed in Alzheimer's disease (AD) brains and pre- amyloid plaques in people affected by Down syndrome .
Amyloid-beta precursor protein (APP) is an integral membrane protein expressed in many tissues and concentrated in the synapses of neurons. It functions as a cell surface receptor [ 5 ] and has been implicated as a regulator of synapse formation , [ 6 ] neural plasticity , [ 7 ] antimicrobial activity, [ 8 ] and iron export . [ 9 ]
The notions of completely and absolutely monotone function/sequence play an important role in several areas of mathematics. For example, in classical analysis they occur in the proof of the positivity of integrals involving Bessel functions or the positivity of Cesàro means of certain Jacobi series. [ 6 ]
If Y is a metric space, then the compact-open topology is equivalent to the topology of compact convergence, [1] and we obtain a definition which is closer to the classical one: A collection F of continuous functions is called a normal family if every sequence of functions in F contains a subsequence which converges uniformly on compact subsets ...
Let {f n} be a sequence of functions analytic on a simply-connected domain S. Suppose there exists a compact set Ω ⊂ S such that for each n , f n ( S ) ⊂ Ω. Forward (inner or right) Compositions Theorem — { F n } converges uniformly on compact subsets of S to a constant function F ( z ) = λ .
The snake lemma is a tool used in mathematics, particularly homological algebra, to construct long exact sequences.The snake lemma is valid in every abelian category and is a crucial tool in homological algebra and its applications, for instance in algebraic topology.