Parameter Identifiability in PDE Models of Fluorescence Recovery After Photobleaching.
FRAP
Parameter identifiability
Partial differential equations
Profile likelihood
RNA binding proteins
Journal
Bulletin of mathematical biology
ISSN: 1522-9602
Titre abrégé: Bull Math Biol
Pays: United States
ID NLM: 0401404
Informations de publication
Date de publication:
02 Mar 2024
02 Mar 2024
Historique:
received:
27
07
2023
accepted:
02
02
2024
medline:
2
3
2024
pubmed:
2
3
2024
entrez:
2
3
2024
Statut:
epublish
Résumé
Identifying unique parameters for mathematical models describing biological data can be challenging and often impossible. Parameter identifiability for partial differential equations models in cell biology is especially difficult given that many established in vivo measurements of protein dynamics average out the spatial dimensions. Here, we are motivated by recent experiments on the binding dynamics of the RNA-binding protein PTBP3 in RNP granules of frog oocytes based on fluorescence recovery after photobleaching (FRAP) measurements. FRAP is a widely-used experimental technique for probing protein dynamics in living cells, and is often modeled using simple reaction-diffusion models of the protein dynamics. We show that current methods of structural and practical parameter identifiability provide limited insights into identifiability of kinetic parameters for these PDE models and spatially-averaged FRAP data. We thus propose a pipeline for assessing parameter identifiability and for learning parameter combinations based on re-parametrization and profile likelihoods analysis. We show that this method is able to recover parameter combinations for synthetic FRAP datasets and investigate its application to real experimental data.
Identifiants
pubmed: 38430382
doi: 10.1007/s11538-024-01266-4
pii: 10.1007/s11538-024-01266-4
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
36Subventions
Organisme : Division of Mathematical Sciences
ID : 174429
Organisme : Division of Mathematical Sciences
ID : 2038039
Organisme : Division of Mathematical Sciences
ID : 2106566
Organisme : Foundation for the National Institutes of Health
ID : R01GM07104
Informations de copyright
© 2024. The Author(s), under exclusive licence to Society for Mathematical Biology.
Références
Alexander AM, Lawley SD (2022) Inferences from FRAP data are model dependent: a subdiffusive analysis. Biophys J 121(20):3795–3810
doi: 10.1016/j.bpj.2022.09.015
pubmed: 36127879
pmcid: 9674994
Audoly S, Bellu G, D’Angio L, Saccomani MP, Cobelli C (2001) Global identifiability of nonlinear models of biological systems. IEEE Trans Biomed Eng 48(1):55–65
doi: 10.1109/10.900248
pubmed: 11235592
Browning AP, Tască M, Falcó C, Baker RE (2023) Structural identifiability analysis of linear reaction-advection-diffusion processes in mathematical biology. arXiv preprint arXiv:2309.15326
Cabral SE, Otis JP, Mowry KL (2022) Multivalent interactions with RNA drive recruitment and dynamics in biomolecular condensates in Xenopus oocytes. iScience 25:104811
doi: 10.1016/j.isci.2022.104811
pubmed: 35982794
pmcid: 9379569
Chis O-T, Banga JR, Balsa-Canto E (2011) Structural identifiability of systems biology models: a critical comparison of methods. PloS ONE 6(11):27755
doi: 10.1371/journal.pone.0027755
Cintrón-Arias A, Banks HT, Capaldi A, Lloyd AL (2009) A sensitivity matrix based methodology for inverse problem formulation
Ciocanel M-V, Kreiling JA, Gagnon JA, Mowry KL, Sandstede B (2017) Analysis of active transport by fluorescence recovery after photobleaching. Biophys J 112(8):1714–1725
doi: 10.1016/j.bpj.2017.02.042
pubmed: 28445762
pmcid: 5406284
Cobelli C, Distefano JJ 3rd (1980) Parameter and structural identifiability concepts and ambiguities: a critical review and analysis. Am J Physiol-Regul Integr Comp Physiol 239(1):7–24
doi: 10.1152/ajpregu.1980.239.1.R7
Cox SM, Matthews PC (2002) Exponential time differencing for stiff systems. J Comput Phys 176(2):430–455
doi: 10.1006/jcph.2002.6995
Deschout H, Hagman J, Fransson S, Jonasson J, Rudemo M, Lorén N, Braeckmans K (2010) Straightforward FRAP for quantitative diffusion measurements with a laser scanning microscope. Opt Express 18(22):22886–22905
doi: 10.1364/OE.18.022886
pubmed: 21164628
Eisenberg M (2019) Input-output equivalence and identifiability: some simple generalizations of the differential algebra approach. arXiv preprint arXiv:1302.5484
Eisenberg MC, Hayashi MA (2014) Determining identifiable parameter combinations using subset profiling. Math Biosci 256:116–126
doi: 10.1016/j.mbs.2014.08.008
pubmed: 25173434
Eisenberg MC, Robertson SL, Tien JH (2013) Identifiability and estimation of multiple transmission pathways in cholera and waterborne disease. J Theor Biol 324:84–102
doi: 10.1016/j.jtbi.2012.12.021
pubmed: 23333764
Evans ND, Chappell MJ (2000) Extensions to a procedure for generating locally identifiable reparameterisations of unidentifiable systems. Math Biosci 168(2):137–159
doi: 10.1016/S0025-5564(00)00047-X
pubmed: 11121562
Geweke JF et al (1991) Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Technical report, Federal Reserve Bank of Minneapolis
GitHub: Sample Matlab code for estimating parameters from FRAP microscopy data. GitHub (2020)
Gutenkunst RN, Waterfall JJ, Casey FP, Brown KS, Myers CR, Sethna JP (2007) Universally sloppy parameter sensitivities in systems biology models. PLoS Computat Biol 3(10):189
doi: 10.1371/journal.pcbi.0030189
Haario H, Laine M, Mira A, Saksman E (2006) DRAM: efficient adaptive MCMC. Stat Comput 16(4):339–354
doi: 10.1007/s11222-006-9438-0
Hengl S, Kreutz C, Timmer J, Maiwald T (2007) Data-based identifiability analysis of non-linear dynamical models. Bioinformatics 23(19):2612–2618
doi: 10.1093/bioinformatics/btm382
pubmed: 17660526
Hines KE, Middendorf TR, Aldrich RW (2014) Determination of parameter identifiability in nonlinear biophysical models: a Bayesian approach. J General Physiol 143(3):401–416
doi: 10.1085/jgp.201311116
Hong H, Ovchinnikov A, Pogudin G, Yap C (2020) Global identifiability of differential models. Commun Pure Appl Math 73(9):1831–1879
doi: 10.1002/cpa.21921
Ishikawa-Ankerhold HC, Ankerhold R, Drummen GP (2012) Advanced fluorescence microscopy techniques-FRAP, FLIP, FLAP, FRET and FLIM. Molecules 17(4):4047–4132
doi: 10.3390/molecules17044047
pubmed: 22469598
pmcid: 6268795
Kassam A-K, Trefethen LN (2005) Fourth-order time-stepping for stiff PDEs. SIAM J Sci Comput 26(4):1214–1233
doi: 10.1137/S1064827502410633
Kenworthy AK (2023) What’s past is prologue: FRAP keeps delivering 50 years later. Biophys J 122:P3577-3586
doi: 10.1016/j.bpj.2023.05.016
Ljung L, Glad T (1994) On global identifiability for arbitrary model parametrizations. Automatica 30(2):265–276
doi: 10.1016/0005-1098(94)90029-9
Miao H, Xia X, Perelson AS, Wu H (2011) On identifiability of nonlinear ode models and applications in viral dynamics. SIAM Rev 53(1):3–39
doi: 10.1137/090757009
Murphy SA, Van der Vaart AW (2000) On profile likelihood. J Am Stat Assoc 95(450):449–465
doi: 10.1080/01621459.2000.10474219
Neil CR, Jeschonek SP, Cabral SE, O’Connell LC, Powrie EA, Otis JP, Wood TR, Mowry KL (2021) L-bodies are RNA-protein condensates driving RNA localization in Xenopus oocytes. Mol Biol Cell 32(22):37
doi: 10.1091/mbc.E21-03-0146-T
Ollivier F (1990) Le problème de l’identifiabilité structurelle globale: approche théorique, méthodes effectives et bornes de complexité. PhD thesis, Palaiseau, Ecole polytechnique
Powrie EA, Ciocanel V, Kreiling JA, Gagnon JA, Sandstede B, Mowry KL (2016) Using in vivo imaging to measure RNA mobility in Xenopus laevis oocytes. Methods 98:60–65
doi: 10.1016/j.ymeth.2015.11.003
pubmed: 26546269
Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, Klingmüller U, Timmer J (2009) Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics 25(15):1923–1929
doi: 10.1093/bioinformatics/btp358
pubmed: 19505944
Raue A, Kreutz C, Theis FJ, Timmer J (2013) Joining forces of Bayesian and frequentist methodology: a study for inference in the presence of non-identifiability. Philos Trans R Soc A Math Phys Eng Sci 371(1984):20110544
doi: 10.1098/rsta.2011.0544
Reid J (1977) Structural identifiability in linear time-invariant systems. IEEE Trans Autom Control 22(2):242–246
doi: 10.1109/TAC.1977.1101474
Renardy M, Kirschner D, Eisenberg M (2022) Structural identifiability analysis of age-structured PDE epidemic models. J Math Biol 84(1):1–30
Siekmann I, Sneyd J, Crampin EJ (2012) MCMC can detect nonidentifiable models. Biophys J 103(11):2275–2286
doi: 10.1016/j.bpj.2012.10.024
pubmed: 23283226
pmcid: 3514526
Simpson MJ, Baker RE, Vittadello ST, Maclaren OJ (2020) Practical parameter identifiability for spatio-temporal models of cell invasion. J R Soc Interface 17(164):20200055
doi: 10.1098/rsif.2020.0055
pubmed: 32126193
pmcid: 7115235
Sprague BL, Pego RL, Stavreva DA, McNally JG (2004) Analysis of binding reactions by fluorescence recovery after photobleaching. Biophys J 86(6):3473–3495
doi: 10.1529/biophysj.103.026765
pubmed: 15189848
pmcid: 1304253