Optimal control strategies for inhibition of protein aggregation

Thomas C. T. Michaels, Christoph A. Weber, and L. Mahadevan
PNAS July 16, 2019 116 (29) 14593-14598; first published June 28, 2019 https://doi.org/10.1073/pnas.1904090116

  1. Edited by William A. Eaton, National Institutes of Health, Bethesda, MD, and approved June 3, 2019 (received for review March 08, 2019)

This article requires a subscription to view the full text. If you have a subscription you may use the login form below to view the article. Access to this article can also be purchased.

Significance

A range of medical conditions, such as Alzheimer’s disease, Parkinson’s disease, and type II diabetes, are linked to protein aggregation. Thus, it is imperative to develop effective therapeutic strategies to combat protein aggregation. Here, we lay out a general approach for optimizing inhibition strategies based on small molecules that suppress nucleation or growth of aggregates. Our model reveals that the optimal timing of drug administration crucially depends on whether the compound inhibits primary nucleation, secondary nucleation, or the growth of aggregates. This approach could guide the rational design of therapeutic strategies to target protein aggregation diseases.

Abstract

Protein aggregation has been implicated in many medical disorders, including Alzheimer’s and Parkinson’s diseases. Potential therapeutic strategies for these diseases propose the use of drugs to inhibit specific molecular events during the aggregation process. However, viable treatment protocols require balancing the efficacy of the drug with its toxicity, while accounting for the underlying events of aggregation and inhibition at the molecular level. To address this key problem, we combine here protein aggregation kinetics and control theory to determine optimal protocols that prevent protein aggregation via specific reaction pathways. We find that the optimal inhibition of primary and fibril-dependent secondary nucleation require fundamentally different drug administration protocols. We test the efficacy of our approach on experimental data for the aggregation of the amyloid-β(1-42) peptide of Alzheimer’s disease in the model organism Caenorhabditis elegans. Our results pose and answer the question of the link between the molecular basis of protein aggregation and optimal strategies for inhibiting it, opening up avenues for the design of rational therapies to control pathological protein aggregation.

Footnotes

  • ↵1T.C.T.M. and C.A.W. contributed equally to this work.

  • ↵2To whom correspondence may be addressed. Email: lmahadev{at}g.harvard.edu.

  • Author contributions: L.M. conceived the research and approach; T.C.T.M. and C.A.W. performed research; T.C.T.M., C.A.W., and L.M. contributed new reagents/analytic tools; T.C.T.M., C.A.W., and L.M. analyzed data; and T.C.T.M., C.A.W., and L.M. wrote the paper.

  • This article is a PNAS Direct Submission.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1904090116/-/DCSupplemental.

Published under the PNAS license.

References

  1. ↵
    1. T. P. J. Knowles,
    2. M. Vendruscolo,
    3. C. M. Dobson
    , The amyloid state and its association with protein misfolding diseases. Nat. Rev. Mol. Cell Biol. 15, 384–396 (2014).
    OpenUrlCrossRefPubMed
  2. ↵
    1. F. Chiti,
    2. C. M. Dobson
    , Protein misfolding, functional amyloid, and human disease: A summary of progress over the last decade. Annu. Rev. Biochem. 86, 27–68 (2017).
    OpenUrlCrossRefPubMed
  3. ↵
    1. C. M. Dobson
    , The amyloid phenomenon and its links with human disease. Cold. Spring. Harb. Perspect. Biol. 9, a023648 (2017).
    OpenUrlAbstract/FREE Full Text
  4. ↵
    1. C. M. Dobson
    , Protein folding and misfolding. Nature 426, 884–890 (2003).
    OpenUrlCrossRefPubMed
  5. ↵
    1. D. J. Selkoe,
    2. J. Hardy
    , The amyloid hypothesis of Alzheimer’s disease at 25 years. EMBO Mol. Med. 8, 595–608 (2016).
    OpenUrlAbstract/FREE Full Text
  6. ↵
    1. J. Hardy,
    2. D. J. Selkoe
    , The amyloid hypothesis of Alzheimer’s disease: Progress and problems on the road to therapeutics. Science 297, 353–356 (2002).
    OpenUrlAbstract/FREE Full Text
  7. ↵
    1. E. Karran,
    2. J. Hardy
    , A critique of the drug discovery and phase 3 clinical programs targeting the amyloid hypothesis for Alzheimer disease. Ann. Neurol. 76, 185–205 (2014).
    OpenUrlCrossRefPubMed
  8. ↵
    1. R. J. O’Brien,
    2. P. C. Wong
    , Amyloid precursor protein processing and Alzheimer’s disease. Annu. Rev. Neurosci. 34, 185–204 (2011).
    OpenUrlCrossRefPubMed
  9. ↵
    1. P. Arosio,
    2. M. Vendruscolo,
    3. C. M. Dobson,
    4. T. P. J. Knowles
    , Chemical kinetics for drug discovery to combat protein aggregation diseases. Trends Pharmacol. Sci. 35, 127–135 (2014).
    OpenUrlCrossRefPubMed
  10. ↵
    1. J. Habchi et al.
    , An anticancer drug suppresses the primary nucleation reaction that initiates the production of the toxic Aβ42 aggregates linked with Alzheimer’s disease. Sci. Adv. 2, e1501244 (2016).
    OpenUrlFREE Full Text
  11. ↵
    1. J. Habchi et al.
    , Systematic development of small molecules to inhibit specific microscopic steps of Aβ42 aggregation in Alzheimer’s disease. Proc. Natl. Acad. Sci. U.S.A. 114, E200–E208 (2017).
    OpenUrlAbstract/FREE Full Text
  12. ↵
    1. S. Chia et al.
    , SAR by kinetics for drug discovery for protein misfolding diseases. Proc. Natl. Acad. Sci. U.S.A. 115, 10245–10250 (2018).
    OpenUrlAbstract/FREE Full Text
  13. ↵
    1. S. I. A. Cohen et al.
    , A molecular chaperone breaks the catalytic cycle that generates toxic Aβ oligomers. Nat. Struct. Mol. Biol. 22, 207–213 (2015).
    OpenUrlCrossRefPubMed
  14. ↵
    1. P. Arosio et al.
    , Kinetic analysis reveals the diversity of microscopic mechanisms through which molecular chaperones suppress amyloid formation. Nat. Commun. 7, 10948 (2016).
    OpenUrlCrossRefPubMed
  15. ↵
    1. F. A. Aprile et al.
    , Selective targeting of primary and secondary nucleation pathways in Aβ42 aggregation using a rational antibody scanning method. Sci. Adv. 3, e1700488 (2017).
    OpenUrlFREE Full Text
  16. ↵
    1. T. C. T. Michaels et al.
    , Chemical kinetics for bridging molecular mechanisms and macroscopic measurements of amyloid fibril formation. Annu. Rev. Phys. Chem. 69, 273–298 (2018).
    OpenUrl
  17. ↵
    1. L. M. Hocking
    , “The Pontryagin maximum principle” in Optimal Control: An Introduction to the Theory with Applications (Oxford University Press, Oxford, UK, 1991), pp. 85–88.
  18. ↵
    1. F. Oosawa,
    2. S. Asakura
    , “Kinetics of polymerization” in Thermodynamics of the Polymerization of Protein (Academic, London, UK, 1975), pp. 41–55.
  19. ↵
    1. T. P. J. Knowles et al.
    , An analytical solution to the kinetics of breakable filament assembly. Science 326, 1533–1537 (2009).
    OpenUrlAbstract/FREE Full Text
  20. ↵
    1. G. Ramachandran,
    2. J. B. Udgaonkar
    , Evidence for the existence of a secondary pathway for fibril growth during the aggregation of tau. J. Mol. Biol. 421, 296–314 (2012).
    OpenUrlCrossRefPubMed
  21. ↵
    1. A. M. Ruschak,
    2. A. D. Miranker
    , Fiber-dependent amyloid formation as catalysis of an existing reaction pathway. Proc. Natl. Acad. Sci. U.S.A. 104, 12341–12346(2007).
    OpenUrlAbstract/FREE Full Text
  22. ↵
    1. S. I. A. Cohen et al.
    , Proliferation of amyloid-β42 aggregates occurs through a secondary nucleation mechanism. Proc. Natl. Acad. Sci. U.S.A. 110, 9758–9763 (2013).
    OpenUrlAbstract/FREE Full Text
  23. ↵
    1. G. Meisl et al.
    , Differences in nucleation behavior underlie the contrasting aggregation kinetics of the Aβ40 and Aβ42 peptides. Proc. Natl. Acad. Sci. U.S.A. 111, 9384–9389 (2014).
    OpenUrlAbstract/FREE Full Text
  24. ↵
    1. A. Sarić et al.
    , Physical determinants of the self-replication of protein fibrils. Nat. Phys. 12, 874–880 (2016).
    OpenUrl
  25. ↵
    1. F. A. Ferrone,
    2. J. Hofrichter,
    3. W. A. Eaton
    , Kinetics of sickle hemoglobin polymerization. II. A double nucleation mechanism. J. Mol. Biol. 183, 611–631 (1985).
    OpenUrlCrossRefPubMed
  26. ↵
    1. S. I. A. Cohen et al.
    , Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments. J. Chem. Phys. 135, 065105 (2011).
    OpenUrlCrossRefPubMed
  27. ↵
    1. I. Benilova,
    2. E. Karran,
    3. B. De Strooper
    , The toxic Aβ oligomer and Alzheimer’s disease: An emperor in need of clothes. Nat. Neurosci. 15, 349–357 (2012).
    OpenUrlCrossRefPubMed
  28. ↵
    1. S. Campioni et al.
    , A causative link between the structure of aberrant protein oligomers and their toxicity. Nat. Chem. Biol. 6, 140–147 (2010).
    OpenUrlCrossRefPubMed
  29. ↵
    1. G. Fusco et al.
    , Structural basis of membrane disruption and cellular toxicity by α-synuclein oligomers. Science 358, 1440–1443 (2017).
    OpenUrlAbstract/FREE Full Text
  30. ↵
    1. P. Arosio,
    2. T. P. J. Knowles,
    3. S. Linse
    , On the lag phase in amyloid fibril formation. Phys. Chem. Chem. Phys. 17, 7606–7618 (2015).
    OpenUrlCrossRefPubMed
  31. ↵
    1. G. McColl et al.
    , Utility of an improved model of amyloid-beta (Aβ1−42) toxicity in Caenorhabditis elegans for drug screening for Alzheimer’s disease. Mol. Neurodegener. 7, 57 (2012).
    OpenUrlCrossRefPubMed
  32. ↵
    1. C. A. Weber,
    2. T. C. T. Michaels,
    3. L. Mahadevan
    , Spatial control of irreversible protein aggregation. eLife 8, e4231 (2019).
    OpenUrl
  33. ↵
    1. R. F. Stengel
    , Optimal Control and Estimation (Dover Publications, 1994).
View Full Text

Purchase access

You may purchase access to this article. This will require you to create an account if you don't already have one.
Back to top
Article Alerts
Email Article
Citation Tools
Request Permissions
Optimal control strategies for inhibition of protein aggregation
Thomas C. T. Michaels, Christoph A. Weber, L. Mahadevan
Proceedings of the National Academy of Sciences Jul 2019, 116 (29) 14593-14598; DOI: 10.1073/pnas.1904090116
del.icio.us logo Digg logo Reddit logo Twitter logo CiteULike logo Facebook logo Google logo Mendeley logo
Proceedings of the National Academy of Sciences: 116 (38)
Current Issue

Submit

Article Classifications

Jump to section

You May Also be Interested in

Habituation and training of the ravens in the experimental compartments, Haidlhof Research Station, Austria. Image courtesy of Jessie E. C. Adriaense.
Shared emotional states in ravens
Researchers report negative emotional contagion, or the coordination of emotional states between multiple individuals, in common ravens, suggesting convergent emotional evolution in birds and mammals.
Image courtesy of Jessie E. C. Adriaense.
Fishing fleet. Image courtesy of Pixabay/3282700.
Increase in global fishing fleets
A study examines trends in global fishing fleets and finds that by 2015, 68% of the global fishing fleet became motorized, and that the overall number of fleet vessels increased to 3.7 million, despite a consistent decrease in the catch per unit of effort.
Image courtesy of Pixabay/3282700.
Magnified views of fingerprints found on fragments of 11th-century AD jars from the U S Southwest enabled archaeologists to determine the sex of the potter. Image courtesy of John Kantner.
Fingerprints reveal gender roles in ancient society
A method to determine gender from fingerprints suggests pottery making was not a primarily female activity in ancient Puebloan society, challenging previous assumptions about gendered divisions of labor in ancient societies.
Image courtesy of John Kantner.

Similar Articles