Open Access
Issue
Math. Model. Nat. Phenom.
Volume 19, 2024
Article Number 19
Number of page(s) 23
Section Population dynamics and epidemiology
DOI https://doi.org/10.1051/mmnp/2023028
Published online 07 October 2024
  1. M. Adimy, L. Babin and L. Pujo-Menjouet, Neuron scale modeling of prion production with the unfolded protein response. SIAM J. Appl. Dyn. Syst. 21 (2022) 2487–2517. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Andrade-Restrepo, P. Lemarre, L. Pujo-Menjouet, L.M. Tine and S.I. Ciuperca, Modeling the spatial propagation of aβ oligomers in Alzheimer's disease. ESAIM Proc. Surv. 67 (2020) 30–45. [CrossRef] [EDP Sciences] [Google Scholar]
  3. D.R. Brown, Oligomeric alpha-synuclein and its role in neuronal death. IUBMB Life 62 (2010) 334–339. [CrossRef] [PubMed] [Google Scholar]
  4. G. Chavent, Nonlinear Least Squares for Inverse Problems: Theoretical Foundations and Step-by-Step Guide for Applications. Scientific Computation. Springer Netherlands (2010). [CrossRef] [Google Scholar]
  5. I.S. Ciuperca, M. Dumont, A. Lakmeche, P. Mazzocco, L. Pujo-Menjouet, H. Rezaei and L.M. Tine, Alzheimer's disease and prion: analysis of an in vitro mathematical model. Discrete Continuous Dyn. Syst. B 24 (2018) 5225–5260. [Google Scholar]
  6. P. Čižas, A. Jekabsone, V. Borutaite and R. Morkūmene, Prevention of amyloid-beta oligomer-induced neuronal death by EGTA, estradiol, and endocytosis inhibitor. Medicina 47 (2011) 15. [CrossRef] [Google Scholar]
  7. S.I.A. Cohen, S. Linse, L.M. Luheshi, E. Hellstrand, D.A. White, L. Rajah, D.E. Otzen, M. Vendruscolo, C.M. Dobson and T.P.J. Knowles, Proliferation of Amyloid-β42 aggregates occurs through a secondary nucleation mechanism. Proc. Natl. Acad. Sci. U.S.A. 110 (2013) 9758–9763. [CrossRef] [PubMed] [Google Scholar]
  8. M. Eigen, Prionics or the kinetic basis of prion diseases. Biophys. Chem. 63 (1996) A1–A18. [CrossRef] [Google Scholar]
  9. S. Eleuteri, S. Di Giovanni, E. Rockenstein, M. Mante, A. Adame, M. Trejo, W. Wrasidlo, F. Wu, P.C. Fraering, E. Masliah, et al., Blocking Aβ seeding-mediated aggregation and toxicity in an animal model of Alzheimer's Disease: a novel therapeutic strategy for neurodegeneration. Neurobiol. Dis. 74 (2015) 144. [CrossRef] [Google Scholar]
  10. M.L. Greer, L. Pujo-Menjouet and G.F. Webb, A mathematical analysis of the dynamics of prion proliferation. J. Theoret. Biol. 242 (2006) 598–606. [CrossRef] [MathSciNet] [Google Scholar]
  11. C. Haass and D.J. Selkoe, Soluble protein oligomers in neurodegeneration: lessons from the Alzheimer's amyloid β-peptide. Nat. Rev. Mol. Cell Biol. 8 (2017) 101. [Google Scholar]
  12. J. Hardy and D.J. Selkoe, The amyloid hypothesis of Alzheimer's disease: progress and problems on the road to therapeutics. Science 297 (2002) 353–356. [CrossRef] [PubMed] [Google Scholar]
  13. J.A. Hardy and G.A. Higgins, Alzheimer's disease: the amyloid cascade hypothesis. Science 256 (1992) 184–186. [CrossRef] [PubMed] [Google Scholar]
  14. J.D. Harper and P.T. Lansbury Jr., Models of amyloid seeding in Alzheimer's disease and scrapie: mechanistic truths and physiological consequences of the time-dependent solubility of amyloid proteins. Annu. Rev. Biochem. 66 (1997) 385–407. [CrossRef] [PubMed] [Google Scholar]
  15. M. Helal, A. Lakmeche, P. Mazzocco, A. Perrillat-Mercerot, L. Pujo-Menjouet, H. Rezaei and L.M. Tine, Stability analysis of a steady state of a model describing Alzheimer's disease and interactions with prion proteins. J. Math. Biol., in press. [Google Scholar]
  16. C. Hughes, M.-L. Choi, J. Yi, S.C. Kim, A. Drews, P. George-Hyslop, C. Bryant, S. Gandhi, K. Cho and D. Klenerman, Beta amyloid aggregates induce sensitised tlr4 signalling causing long-term potentiation deficit and rat neuronal cell death. Commun. Biol. 3 (2020) 02. [CrossRef] [Google Scholar]
  17. L.M Ittner and J. Götz, Amyloid-β and tau—a toxic pas de deux in Alzheimer's disease. Nat. Rev. Neurosci. 12 (2011) 67. [CrossRef] [Google Scholar]
  18. C.R. Jack Jr., D.S. Knopman, W.J. Jagust, R.C. Petersen, M.W. Weiner, P.S. Aisen, L.M. Shaw, P. Vemuri, H.J. Wiste, S.D. Weigand, et al., Tracking pathophysiological processes in Alzheimer's disease: an updated hypothetical model of dynamic biomarkers. Lancet Neurol. 12 (2013) 207–216. [CrossRef] [Google Scholar]
  19. F. Matthäus, Diffusion versus network models as descriptions for the spread of prion diseases in the brain. J. Theoret. Biol. 240 (2006) 104–113. [CrossRef] [MathSciNet] [Google Scholar]
  20. M.A. Nowak, D.C. Krakauer, A. Klug and R.M. May, Prion infection dynamics. Integr. Biol. Issues News Rev. 1 (1998) 3–15. [CrossRef] [Google Scholar]
  21. T. Oda, G.M. Pasinetti, H.H. Osterburg, C. Anderson, S.A. Johnson and C.E. Finch, Purification and characterization of brain clusterin. Biochem. Biophys. Res. Commun. 204 (1994) 1131–1136. [CrossRef] [Google Scholar]
  22. T.G. Ohm, H. Müller, H. Braak and J. Bohl, Close-meshed prevalence rates of different stages as a tool to uncover the rate of Alzheimer's disease-related neurofibrillary changes. Neuroscience 64 (1995) 209–217. [CrossRef] [PubMed] [Google Scholar]
  23. R.J. Perrin, A.M. Fagan and D.M. Holtzman, Multimodal techniques for diagnosis and prognosis of Alzheimer's disease. Nature 461 (2009) 916. [CrossRef] [PubMed] [Google Scholar]
  24. U. Sengupta, A.N. Nilson and R. Kayed, The role of amyloid-β oligomers in toxicity, propagation, and immunotherapy. EBioMedicine 6 (2016) 42–49. [CrossRef] [PubMed] [Google Scholar]
  25. R.D.E. Sewell, Protein Misfolding in Neurodegenerative Diseases: Mechanisms and Therapeutic Strategies. Enzyme Inhibitors Series. CRC Press (2007). [Google Scholar]
  26. A.D. Smith, Imaging the progression of Alzheimer pathology through the brain. Proc. Natl. Acad. Sci. U.S.A. 99 (2002) 4135–4137. [CrossRef] [PubMed] [Google Scholar]
  27. C. Soto, Unfolding the role of protein misfolding in neurodegenerative diseases. Nat. Rev. Neurosci. 4 (2003) 49. [CrossRef] [PubMed] [Google Scholar]
  28. M. Storandt, E.A. Grant, J.P. Miller and J.C. Morris, Rates of progression in mild cognitive impairment and early Alzheimer's disease. Neurology 59 (2002) 1034–1041. [CrossRef] [PubMed] [Google Scholar]
  29. M.P.H. Stumpf and D.C. Krakauer, Mapping the parameters of prion-induced neuropathology. Proc. Natl. Acad. Sci. U.S.A. 97 (2000) 10573–10577. [CrossRef] [PubMed] [Google Scholar]
  30. R.H. Takahashi, T. Nagao and G.K. Gouras, Plaque formation and the intraneuronal accumulation of β-amyloid in Alzheimer's disease. Pathol. Int. 67 (2017) 185–193. [CrossRef] [PubMed] [Google Scholar]
  31. T. Umeda, T. Tomiyama, N. Sakama, S. Tanaka, M.P. Lambert, W.L. Klein and H. Mori, Intraneuronal amyloid β-oligomers cause cell death via endoplasmic reticulum stress, endosomal/lysosomal leakage, and mitochondrial dysfunction in vivo. J. Neurosci. Res. 89 (2011) 1031–1042. [CrossRef] [PubMed] [Google Scholar]
  32. L.N. Zhao, H.W. Long, Y. Mu and L.Y. Chew, The toxicity of amyloid β oligomers. Int. J. Mol. Sci. 13 (2012) 7303–7327. [CrossRef] [Google Scholar]

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