378
Views
5
CrossRef citations to date
0
Altmetric
Articles

Estimating the rate of prion aggregate amplification in yeast with a generation and structured population model

, , , &
Pages 257-279 | Received 27 Mar 2017, Accepted 31 Mar 2017, Published online: 18 Apr 2017

References

  • Knowles TPJ , Vendruscolo M , Dobson CM . The amyloid state and its association with protein misfolding diseases. Nat Rev Mol Cell Biol. 2014;15(6):384–396.
  • Aguzzi A , Polymenidou M . Mammalian prion biology: one century of evolving concepts. Cell. 2004;116(2):313–327.
  • Collinge J . Prion diseases of humans and animals: their causes and molecular basis. Ann Rev Neurosci. 2001;24(1):519–550.
  • Sindi SS , Serio TR . Prion dynamics and the quest for the genetic determinant in protein-only inheritance. Curr Opin Microbiol. 2009;12(6):623–630.
  • Tuite MF , Serio TR . The prion hypothesis: from biological anomaly to basic regulatory mechanism. Nat Rev Mol Cell Biol. 2010;11(12):823–833.
  • Palmer KJ , Ridout MS , Morgan BJT . Kinetic models of guanidine hydrochloride-induced curing of the yeast [psi+] prion. J Theor Biol. 2011;274(1):1–11.
  • Olofsson P , Sindi SS . A crump-mode-jagers branching process model of prion loss in yeast. J Appl Probab. 2014;51(2):453–465.
  • Ridout M , Giagos V , Morgan B , et al. Modelling prion dynamics in yeast. International Statistical Institute Proceedings of the 58th World Statistical Congress, Dublin (Session IPS020). 2011.
  • Pöschel T , Brilliantov NV , Frömmel C . Kinetics of prion growth. Biophys J. 2003;85(6):3460–3474.
  • Greer ML , Pujo-Menjouet L , Webb GF . A mathematical analysis of the dynamics of prion proliferation. J Theor Biol. 2006;242(3):598–606.
  • Davis JK , Sindi SS . A mathematical model of the dynamics of prion aggregates with chaperone-mediated fragmentation. J Math Biol. 2016;72(6):1555–1578.
  • Prüss J , Pujo-Menjouet L , Webb G , et al . Analysis of a model for the dynamics of prions. Discrete Contin Dyn Syst Ser B. 2006;6(1):225–235.
  • Engler H , Prüss J , Webb GF . Analysis of a model for the dynamics of prions ii. J Math Anal Appl. 2006;324(1):98–117.
  • Tanaka M , Collins SR , Toyama BH , et al . The physical basis of how prion conformations determine strain phenotypes. Nature. 2006;442(7102):585–589.
  • Derdowski A , Sindi SS , Klaips CL , et al . A size threshold limits prion transmission and establishes phenotypic diversity. Science. 2010;330(6004):680–683.
  • Klaips CL , Hochstrasser ML , Langlois CR , et al. Spatial quality control bypasses cell-based limitations on proteostasis to promote prion curing. eLife. 2014;3:e04288
  • Masel J , Jansen VAA , Nowak MA . Quantifying the kinetic parameters of prion replication. Biophys Chem. 1999;77(2):139–152.
  • Davis JK , Sindi SS . A study in nucleated polymerization models of protein aggregation. Appl Math Lett. 2015;40:97–101.
  • Calvez V , Lenuzza N , Doumic M , et al . Prion dynamics with size dependency-strain phenomena. J Biol Dyn. 2010;4(1):28–42.
  • Banks HT , Flores KB , Sindi SS . On analytical and numerical approaches to division and label structured population models. Appl Math Lett. 2016;60:81–88.
  • Banks HT , Sutton KL , Thompson WC , et al . Estimation of cell proliferation dynamics using cfse data. Bull Math Biol. 2011;73(1):116–150.
  • Thompson WC . Partial differential equation modeling of flow cytometry data from CFSE-based proliferation assays. Raleigh (NC): North Carolina State University; 2011.
  • Hasenauer J , Schittler D , Allgöwer F . Analysis and simulation of division-and label-structured population models. Bull Math Biol. 2012;74(11):2692–2732.
  • Cole DJ , Morgan BJT , Ridout MS , et al . Estimating the number of prions in yeast cells. Math Med Biol. 2004;21(4):369–395.
  • Byrne LJ , Cole DJ , Cox BS , et al . The number and transmission of [psi+] prion seeds (propagons) in the yeast saccharomyces cerevisiae. PLoS One. 2009;4(3):e4670–e4670.
  • Byrne LJ , Cox BS , Cole DJ , et al . Cell division is essential for elimination of the yeast [psi+] prion by guanidine hydrochloride. Proc Nat Acad Sci. 2007;104(28):11688–11693.
  • Langlois CR , Pei F , Sindi SS , et al . Distinct prion domain sequences ensure efficient amyloid propagation by promoting chaperone binding or processing In vivo. In Review.
  • Cipollina C , Vai M , Porro D , et al . Towards understanding of the complex structure of growing yeast populations. J Biotechnol. 2007;128(2):393–402.
  • Gyllenberg M . The size and scar distributions of the yeast saccharomyces cerevisiae. J Math Biol. 1986;24(1):81–101.
  • Banks HT , Fitzpatrick BG . Estimation of growth rate distributions in size structured population models. Q Appl Math. 1991;49:215–235.
  • Banks HT , Fitzpatrick BG , Potter Y , et al . Estimation of probability distributions for individual parameters using aggregate population data. Stochastic analysis, control, optimization and applications. Springer; 1999. p. 353–371.
  • Billingsley P . Convergence of probability measures. Wiley; 2013.
  • Banks HT . A functional analysis framework for modeling, estimation and control in science and engineering. CRC Press; 2012.
  • Banks HT , Hu S , Thompson WC . Modeling and inverse problems in the presence of uncertainty. CRC Press; 2014.
  • Banks HT , Bihari KL . Modeling and estimating uncertainty in parameter estimation. Inverse Prob. 2001;17:95–111.
  • Banks HT , Kunisch Karl . Estimation techniques for distributed parameter systems. Boston (MA): Birkhausen; 1989.
  • Banks HT , Davis JL . A comparison of approximation methods for the estimation of probability distributions on parameters. Appl Numer Math. 2007;57(5):753–777.
  • Banks HT , Fitzpatrick BG . Statistical methods for model comparison in parameter estimation problems for distributed systems. J Math Biol. 1990;28(5):501–527.
  • Banks HT , Tran HT . Mathematical and experimental modeling of physical and biological processes. CRC Press; 2009.
  • Martins JRRA , Kroo IM , Alonso JJ . An automated method for sensitivity analysis using complex variables. AIAA paper 2000–0689, 38th Aerospace Sciences Meeting. Reno (NC); 2000. p. 2000–0689.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.