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Cell-Level Model to Predict the Spatiotemporal Dynamics of Neurodegenerative Disease

Shih-Huan Huang (黃士桓)1,2, Matthew W. Cotton1,2, Tuomas P. J. Knowles1,3, David Klenerman1,2, and Georg Meisl1,2,*

  • *Contact author: gm373@cam.ac.uk
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PRX Life 4, 013021 – Published 17 February, 2026

DOI: https://doi.org/10.1103/f9hz-xvpr

Abstract

A central challenge in modeling neurodegenerative diseases is connecting cellular-level mechanisms to tissue-level pathology, in particular to determine whether pathology is driven primarily by cell-autonomous triggers or by propagation from cells that are already in a pathological, runaway aggregation state. To bridge this gap, we develop here a bottom-up physical model that explicitly incorporates these two fundamental cell-level drivers of protein aggregation dynamics. We show that our model naturally explains the characteristic long, slow development of pathology followed by a rapid acceleration, a hallmark of many neurodegenerative diseases. Furthermore, the model reveals the existence of a critical switch point at which the system's dynamics transition from being dominated by slow, spontaneous formation of diseased cells to being driven by fast propagation. We explore the different limiting behaviours of this model, derive approximate analytical solutions for several observables, and demonstrate the parallels to models used in population epidemiology. This framework offers a method to simulate disease propagation and intervention in silico and provides a robust physical foundation for interpreting pathological data.

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References (43)

  1. F. Chiti and C. M. Dobson, Protein misfolding, amyloid formation, and human disease: A summary of progress over the last decade, Annu. Rev. Biochem. 86, 27 (2017).
  2. C. R. Jack, D. S. Knopman, W. J. Jagust, L. M. Shaw, P. S. Aisen, M. W. Weiner, R. C. Petersen, and J. Q. Trojanowski, Hypothetical model of dynamic biomarkers of the Alzheimer's pathological cascade, Lancet Neurol. 9, 119 (2010).
  3. G. Meisl, T. P. Knowles, and D. Klenerman, The molecular processes underpinning prion-like spreading and seed amplification in protein aggregation, Curr. Opin. Neurobiol. 61, 58 (2020).
  4. T. P. J. Knowles, C. A. Waudby, G. L. Devlin, S. I. A. Cohen, A. Aguzzi, M. Vendruscolo, E. M. Terentjev, M. E. Welland, and C. M. Dobson, An analytical solution to the kinetics of breakable filament assembly, Science 326, 1533 (2009).
  5. S. I. A. Cohen, M. Vendruscolo, M. E. Welland, C. M. Dobson, E. M. Terentjev, and T. P. J. Knowles, Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments, J. Chem. Phys. 135, 065105 (2011).
  6. G. Meisl, J. B. Kirkegaard, P. Arosio, T. C. T. Michaels, M. Vendruscolo, C. M. Dobson, S. Linse, and T. P. J. Knowles, Molecular mechanisms of protein aggregation from global fitting of kinetic models, Nat. Protoc. 11, 252 (2016).
  7. J. W. Vogel, N. Corriveau-Lecavalier, N. Franzmeier, J. B. Pereira, J. A. Brown, A. Maass, H. Botha, W. W. Seeley, D. S. Bassett, D. T. Jones, and M. Ewers, Connectome-based modeling of neurodegenerative diseases: Towards precision medicine and mechanistic insight, Nat. Rev. Neurosci. 24, 620 (2023).
  8. S. Fornari, A. Schäfer, E. Kuhl, and A. Goriely, Spatially-extended nucleation-aggregation-fragmentation models for the dynamics of prion-like neurodegenerative protein-spreading in the brain and its connectome, J. Theor. Biol. 486, 110102 (2020).
  9. A. Mudher, M. Colin, S. Dujardin, M. Medina, I. Dewachter, S. M. Alavi Naini, E.-M. Mandelkow, E. Mandelkow, L. Buée, M. Goedert, and J.-P. Brion, What is the evidence that tau pathology spreads through prion-like propagation?, Acta Neuropathol. Commun. 5, 99 (2017).
  10. F. Clavaguera, T. Bolmont, R. A. Crowther, D. Abramowski, S. Frank, A. Probst, G. Fraser, A. K. Stalder, M. Beibel, M. Staufenbiel, M. Jucker, M. Goedert, and M. Tolnay, Transmission and spreading of tauopathy in transgenic mouse brain, Nat. Cell Biol. 11, 909 (2009).
  11. G. Meisl, E. Hidari, K. Allinson, T. Rittman, S. L. DeVos, J. S. Sanchez, C. K. Xu, K. E. Duff, K. A. Johnson, J. B. Rowe, B. T. Hyman, T. P. J. Knowles, and D. Klenerman, In vivo rate-determining steps of tau seed accumulation in Alzheimer's disease, Sci. Adv. 7, eabh1448 (2021).
  12. K. Amunts, H. Mohlberg, S. Bludau, S. Caspers, S. B. Eickhoff, and P. Pieperhoff, Whole-brain parcellation of the Julich-Brain cytoarchitectonic atlas (v2.9) [Dataset], EBRAINS (2021).
  13. S. Brenner, Sequences and consequences, Philos. Trans. R. Soc. B 365, 207 (2010).
  14. G. Meisl, The thermodynamics of neurodegenerative disease, Biophys. Rev. 5, 011303 (2024).
  15. M. W. Cotton, A. Goriely, D. Klenerman, and G. Meisl, A universal phase-plane model for in vivo protein aggregation, arXiv:2511.18893.
  16. T. P. J. Knowles, D. A. White, A. R. Abate, J. J. Agresti, S. I. A. Cohen, R. A. Sperling, E. J. D. Genst, C. M. Dobson, and D. A. Weitz, Observation of spatial propagation of amyloid assembly from single nuclei, Proc. Natl. Acad. Sci. USA 108, 14746 (2011).
  17. T. Sinnige, G. Meisl, T. C. T. Michaels, M. Vendruscolo, T. P. J. Knowles, and R. I. Morimoto, Kinetic analysis reveals that independent nucleation events determine the progression of polyglutamine aggregation in C. elegans, Proc. Natl. Acad. Sci. USA 118, e2021888118 (2021).
  18. T. Bae, L. Fasching, Y. Wang, J. H. Shin, M. Suvakov, Y. Jang, S. Norton, C. Dias, J. Mariani, A. Jourdon, F. Wu, A. Panda, R. Pattni, Y. Chahine, R. Yeh, R. C. Roberts, A. Huttner, J. E. Kleinman, T. M. Hyde, R. E. Straub, et al., Analysis of somatic mutations in 131 human brains reveals aging-associated hypermutability, Science 377, 511 (2022).
  19. J. Hardy, V. Escott-Price, The genetics of neurodegenerative diseases is the genetics of age-related damage clearance failure, Molecular Psychiatry 30, 2748 (2025).
  20. T. B. Thompson, G. Meisl, T. P. J. Knowles, and A. Goriely, The role of clearance mechanisms in the kinetics of pathological protein aggregation involved in neurodegenerative diseases, J. Chem. Phys. 154, 125101 (2021).
  21. J. Weickenmeier, E. Kuhl, and A. Goriely, Multiphysics of prionlike diseases: Progression and atrophy, Phys. Rev. Lett. 121, 158101 (2018).
  22. B. Frost, R. L. Jacks, and M. I. Diamond, Propagation of tau misfolding from the outside to the inside of a cell, J. Biol. Chem. 284, 12845 (2009).
  23. See Supplemental Material at http://link.aps.org/supplemental/10.1103/f9hz-xvpr for additional simulation results.
  24. S.-H. Huang, A. Quaegebeur, T. Pansuwan, T. Rittman, R. Wang, T. P. Knowles, J. B. Rowe, D. Klenerman, and G. Meisl, A mathematical model of cellular aggregation predicts patterns of tau accumulation in neurodegenerative disease, Adv. Sci. 13, e11297 (2026).
  25. D. Böken, D. Cox, M. Burke, J. Y. L. Lam, T. Katsinelos, J. S. H. Danial, E. Fertan, W. A. McEwan, J. B. Rowe, and D. Klenerman, Single-molecule characterization and super-resolution imaging of Alzheimer's disease-relevant tau aggregates in human samples, Angew. Chem. Int. Ed. 63, e202317756 (2024).
  26. R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugenics 7, 355 (1937).
  27. M. S. Bartlett, Measles periodicity and community size, J. R. Stat. Soc. A 120, 48 (1957).
  28. D. G. Kendall, Mathematical models of the spread of infection, Math. Comput. Sci. Biol. Med., H.M. Stationary Off, London 213 (1965).
  29. J. Medlock and M. Kot, Spreading disease: Integro-differential equations old and new, Math. Biosci. 184, 201 (2003).
  30. S. I. A. Cohen, L. Rajah, C. H. Yoon, A. K. Buell, D. A. White, R. A. Sperling, M. Vendruscolo, E. M. Terentjev, C. M. Dobson, D. A. Weitz, and T. P. J. Knowles, Spatial propagation of protein polymerization, Phys. Rev. Lett. 112, 098101 (2014).
  31. S. B. Prusiner, Novel proteinaceous infectious particles cause scrapie, Science 216, 136 (1982).
  32. G. Banerjee, S. F. Farmer, H. Hyare, Z. Jaunmuktane, S. Mead, N. S. Ryan, J. M. Schott, D. J. Werring, P. Rudge, and J. Collinge, Iatrogenic Alzheimer's disease in recipients of cadaveric pituitary-derived growth hormone, Nat. Med. 30, 394 (2024).
  33. G. G. Kovacs, M. I. Lutz, G. Ricken, T. Stroebel, R. Hoeftberger, M. Preusser, G. Regelsberger, S. Hoenigschnabl, A. Reiner, P. Fischer, H. Budka, and J. A. Hainfellner, Dura mater is a potential source of aβ seeds, Acta Neuropathol. 131, 911 (2016).
  34. P. Arosio, T. P. J. Knowles, and S. Linse, On the lag phase in amyloid fibril formation, Phys. Chem. Chem. Phys. 17, 7606 (2015).
  35. B. Bulic, M. Pickhardt, E.-M. Mandelkow, and E. Mandelkow, Tau protein and tau aggregation inhibitors, Neuropharmacology 59, 276 (2010).
  36. M. Bourdenx, A. Martin-Segura, A. Scrivo, J. A. Rodriguez-Navarro, S. Kaushik, I. Tasset, A. Diaz, N. J. Storm, Q. Xin, Y. R. Juste, E. Stevenson, E. Luengo, C. C. Clement, S. J. Choi, N. J. Krogan, E. Mosharov, V., L. Santambrogio, F. Grueninger, L. Collin, D. L. Swaney, et al., Chaperone-mediated autophagy prevents collapse of the neuronal metastable proteome, Cell 184, 2696 (2021).
  37. G. Yadollahikhales and J. C. Rojas, Anti-amyloid immunotherapies for Alzheimer's disease: A 2023 clinical update, Neurotherapeutics 20, 914 (2023).
  38. J. Cummings, L. Apostolova, G. D. Rabinovici, A. Atri, P. Aisen, S. Greenberg, S. Hendrix, D. Selkoe, M. Weiner, R. C. Petersen, and S. Salloway, Lecanemab: Appropriate use recommendations, J. Preven. Alzheimers Dis. 10, 362 (2023).
  39. M. Vaz and S. Silvestre, Alzheimer's disease: Recent treatment strategies, Eur. J. Pharmacol. 887, 173554 (2020).
  40. K. Chung, J. Wallace, S.-Y. Kim, S. Kalyanasundaram, A. S. Andalman, T. J. Davidson, J. J. Mirzabekov, K. A. Zalocusky, J. Mattis, A. K. Denisin, S. Pak, H. Bernstein, C. Ramakrishnan, L. Grosenick, V. Gradinaru, and K. Deisseroth, Structural and molecular interrogation of intact biological systems, Nature (London) 497, 332 (2013).
  41. N. Renier, Z. Wu, D. J. Simon, J. Yang, P. Ariel, and M. Tessier-Lavigne, idisco: A simple, rapid method to immunolabel large tissue samples for volume imaging, Cell 159, 896 (2014).
  42. K. Jellinger, Cell death mechanisms in neurodegeneration, J. Cell. Mol. Med. 5, 1 (2001).
  43. S.-H. Huang, M. W. Cotton, T. P. Knowles, D. Klenerman, and G. Meisl, Dataset for: A cell-level model to predict spatiotemporal dynamics of neurodegenerative disease, Apollo–University of Cambridge Repository, https://doi.org/10.17863/CAM.120852 (2025).

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PRX Life 4, 013021– Published 17 February, 2026
  • Received 22 August 2025
  • Accepted 14 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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