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286534 occurrences (No.87 in the rank) during 5 years in the PubMed. [no cache] 500 found

382) We demonstrated that, for the model with constant kinetic rates, the concentration of free tau in the cytoplasm was determined by a single dimensionless parameter that represents the ratio of the diffusion time (the time it takes tau to diffuse from the axon hillock to the axon tip) to the half-life of tau.

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PMID:24573186 DOI:10.1093/imammb/dqu003

2015 Mathematical medicine and biology : a journal of the IMA

* A comparison between the diffusion-reaction and slow axonal transport models for predicting tau distribution along an axon.

- This paper developed equations describing steady-state tau distributions for three versions of the diffusion-reaction model of tau transport: a model with constant kinetic rates, a model that additionally accounts for tau diffusion along microtubules (MTs) and a model with a modulated rate of tau attachment to MTs. We demonstrated that, for the model with constant kinetic rates, the concentration of free tau in the cytoplasm was determined by a single dimensionless parameter that represents the ratio of the diffusion time (the time it takes tau to diffuse from the axon hillock to the axon tip) to the half-life of tau. We also developed a model based on the hypothesis that tau is actively transported. Analytical solutions for some special situations were obtained. The model predictions were compared with experimentally measured tau distributions in axons reported in Black et al. (1996, J. Neurosc., 16: , 3601-3619), and based on these comparisons, we discussed the performance of various models. We demonstrated the significance of modulation of the tau attachment rate to MTs in the diffusion-reaction model. On the other hand, the active transport model predictions were consistent with experimental data even with constant kinetic rates. For short axons (up to 600 μm in length) the predicted average transport velocity of tau was in the experimentally reported range for both the diffusion-reaction and active transport models, but for the active transport model the average tau velocity was larger.

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(1)158 that	(10)5 good	(19)3 excellent	(28)2 efficacy
(2)48 the	(11)5 increased	(20)3 more	(29)2 greater
(3)40 a	(12)5 significantly	(21)3 no	(30)2 how
(4)23 by	(13)4 as	(22)3 that,	(31)2 successful
(5)21 to	(14)4 better	(23)2 acceptable	(32)2 through
(6)13 in	(15)4 improved	(24)2 and	(33)2 using
(7)12 null	(16)4 its	(25)2 both
(8)11 an	(17)4 similar	(26)2 decreased
(9)8 for	(18)3 between	(27)2 differential

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--- WordNet output for demonstrated --- Overview of verb demonstrate The verb demonstrate has 4 senses (first 4 from tagged texts) 1. (24) show, demo, exhibit, present, demonstrate -- (give an exhibition of to an interested audience; "She shows her dogs frequently"; "We will demo the new software in Washington") 2. (22) prove, demonstrate, establish, show, shew -- (establish the validity of something, as by an example, explanation or experiment; "The experiment demonstrated the instability of the compound"; "The mathematician showed the validity of the conjecture") 3. (2) attest, certify, manifest, demonstrate, evidence -- (provide evidence for; stand as proof of; show by one's behavior, attitude, or external attributes; "His high fever attested to his illness"; "The buildings in Rome manifest a high level of architectural sophistication"; "This decision demonstrates his sense of fairness") 4. (1) demonstrate, march -- (march in protest; take part in a demonstration; "Thousands demonstrated against globalization during the meeting of the most powerful economic nations in Seattle") Overview of adj demonstrated The adj demonstrated has 1 sense (first 1 from tagged texts) 1. (1) demonstrated -- (having been demonstrated or verified beyond doubt) --- WordNet end ---