Literature DB >> 24146290

Alzheimer's disease: analysis of a mathematical model incorporating the role of prions.

Mohamed Helal1, Erwan Hingant, Laurent Pujo-Menjouet, Glenn F Webb.   

Abstract

We introduce a mathematical model of the in vivo progression of Alzheimer's disease with focus on the role of prions in memory impairment. Our model consists of differential equations that describe the dynamic formation of β-amyloid plaques based on the concentrations of Aβ oligomers, PrP(C) proteins, and the Aβ-x-Aβ-PrP(C)complex, which are hypothesized to be responsible for synaptic toxicity. We prove the well-posedness of the model and provided stability results for its unique equilibrium, when the polymerization rate of Aβ-amyloid is constant and also when it is described by a power law.

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Year:  2013        PMID： 24146290     DOI： 10.1007/s00285-013-0732-0

Source DB:  PubMed          Journal:  J Math Biol        ISSN： 0303-6812            Impact factor:   2.259


  30 in total

1.  Memory impairment in transgenic Alzheimer mice requires cellular prion protein.

Authors:  David A Gimbel; Haakon B Nygaard; Erin E Coffey; Erik C Gunther; Juha Laurén; Zachary A Gimbel; Stephen M Strittmatter
Journal:  J Neurosci       Date:  2010-05-05       Impact factor: 6.167

2.  Determining the critical nucleus and mechanism of fibril elongation of the Alzheimer's Abeta(1-40) peptide.

Authors:  Nicolas Lux Fawzi; Yuka Okabe; Eng-Hui Yap; Teresa Head-Gordon
Journal:  J Mol Biol       Date:  2006-10-07       Impact factor: 5.469

3.  The cellular prion protein mediates neurotoxic signalling of β-sheet-rich conformers independent of prion replication.

Authors:  Ulrike K Resenberger; Anja Harmeier; Andreas C Woerner; Jessica L Goodman; Veronika Müller; Rajaraman Krishnan; R Martin Vabulas; Hans A Kretzschmar; Susan Lindquist; F Ulrich Hartl; Gerd Multhaup; Konstanze F Winklhofer; Jörg Tatzelt
Journal:  EMBO J       Date:  2011-03-25       Impact factor: 11.598

4.  Scrapie-infected spleens: analysis of infectivity, scrapie-associated fibrils, and protease-resistant proteins.

Authors:  R Rubenstein; P A Merz; R J Kascsak; C L Scalici; M C Papini; R I Carp; R H Kimberlin
Journal:  J Infect Dis       Date:  1991-07       Impact factor: 5.226

Review 5.  Insoluble cellular prion protein and its association with prion and Alzheimer diseases.

Authors:  Wen-Quan Zou; Xiaochen Zhou; Jue Yuan; Xiangzhu Xiao
Journal:  Prion       Date:  2011-07-01       Impact factor: 3.931

6.  Amyloid beta-protein fibrillogenesis. Detection of a protofibrillar intermediate.

Authors:  D M Walsh; A Lomakin; G B Benedek; M M Condron; D B Teplow
Journal:  J Biol Chem       Date:  1997-08-29       Impact factor: 5.157

7.  Interaction between prion protein and toxic amyloid β assemblies can be therapeutically targeted at multiple sites.

Authors:  Darragh B Freir; Andrew J Nicoll; Igor Klyubin; Silvia Panico; Jessica M Mc Donald; Emmanuel Risse; Emmanuel A Asante; Mark A Farrow; Richard B Sessions; Helen R Saibil; Anthony R Clarke; Michael J Rowan; Dominic M Walsh; John Collinge
Journal:  Nat Commun       Date:  2011-06-07       Impact factor: 14.919

8.  Anti-PrPC monoclonal antibody infusion as a novel treatment for cognitive deficits in an Alzheimer's disease model mouse.

Authors:  Erika Chung; Yong Ji; Yanjie Sun; Richard J Kascsak; Regina B Kascsak; Pankaj D Mehta; Stephen M Strittmatter; Thomas Wisniewski
Journal:  BMC Neurosci       Date:  2010-10-14       Impact factor: 3.288

9.  Prion dynamics with size dependency-strain phenomena.

Authors:  V Calvez; N Lenuzza; M Doumic; J-P Deslys; F Mouthon; B Perthame
Journal:  J Biol Dyn       Date:  2010-01       Impact factor: 2.179

Review 10.  The amyloid hypothesis of Alzheimer's disease: progress and problems on the road to therapeutics.

Authors:  John Hardy; Dennis J Selkoe
Journal:  Science       Date:  2002-07-19       Impact factor: 47.728
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  5 in total

1.  Stability analysis of a steady state of a model describing Alzheimer's disease and interactions with prion proteins.

Authors:  Mohammed Helal; Angélique Igel-Egalon; Abdelkader Lakmeche; Pauline Mazzocco; Angélique Perrillat-Mercerot; Laurent Pujo-Menjouet; Human Rezaei; Léon M Tine
Journal:  J Math Biol       Date:  2018-08-11       Impact factor: 2.259

2.  A physical model for dementia.

Authors:  O Sotolongo-Costa; L M Gaggero-Sager; J T Becker; F Maestu; O Sotolongo-Grau
Journal:  Physica A       Date:  2017-01-04       Impact factor: 3.263

3.  Mathematical model on Alzheimer's disease.

Authors:  Wenrui Hao; Avner Friedman
Journal:  BMC Syst Biol       Date:  2016-11-18

4.  The development of a stochastic mathematical model of Alzheimer's disease to help improve the design of clinical trials of potential treatments.

Authors:  Christoforos Hadjichrysanthou; Alison K Ower; Frank de Wolf; Roy M Anderson
Journal:  PLoS One       Date:  2018-01-29       Impact factor: 3.240

5.  Mathematical Model Shows How Sleep May Affect Amyloid-β Fibrillization.

Authors:  Masoud Hoore; Sahamoddin Khailaie; Ghazal Montaseri; Tanmay Mitra; Michael Meyer-Hermann
Journal:  Biophys J       Date:  2020-07-22       Impact factor: 4.033
  5 in total

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