×

zbMATH — the first resource for mathematics

Bayesian multivariate Poisson abundance models for T-cell receptor data. (English) Zbl 1322.92014
Summary: A major feature of an adaptive immune system is its ability to generate B- and T-cell clones capable of recognizing and neutralizing specific antigens. These clones recognize antigens with the help of the surface molecules, called antigen receptors, acquired individually during the clonal development process. In order to ensure a response to a broad range of antigens, the number of different receptor molecules is extremely large, resulting in a huge clonal diversity of both B- and T-cell receptor populations and making their experimental comparisons statistically challenging. To facilitate such comparisons, we propose a flexible parametric model of multivariate count data and illustrate its use in a simultaneous analysis of multiple antigen receptor populations derived from mammalian T-cells. The model relies on a representation of the observed receptor counts as a multivariate Poisson abundance mixture (\(m\) PAM). A Bayesian parameter fitting procedure is proposed, based on the complete posterior likelihood, rather than the conditional one used typically in similar settings. The new procedure is shown to be considerably more efficient than its conditional counterpart (as measured by the Fisher information) in the regions of \(m\) PAM parameter space relevant to model T-cell data.

MSC:
92C50 Medical applications (general)
62F15 Bayesian inference
Software:
JAGS; R; sedaR
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aitchison, J.; Ho, C., The multivariate Poisson-log normal distribution, Biometrika, 76, 643, (1989) · Zbl 0679.62040
[2] Andrieu, C.; De-Freitas, N.; Doucet, A.; Jordan, M., An introduction to MCMC for machine learning, Mach. Learn., 50, 5-43, (2003) · Zbl 1033.68081
[3] Barger, K.; Bunge, J., Bayesian estimation of the number of species using noninformative priors, Biom. J., 50, 1064-1076, (2008)
[4] Bolotin, D. A.; Mamedov, I. Z.; Britanova, O. V.; Zvyagin, I. V.; Shagin, D.; Ustyugova, S. V.; Turchaninova, M. A.; Lukyanov, S.; Lebedev, Y. B.; Chudakov, D. M., Next generation sequencing for TCR repertoire profiling: platform-specific features and correction algorithms, Eur. J. Immunol., 42, 11, 3073-3083, (2012)
[5] Bulmer, M., On Fitting the Poisson lognormal distribution to species-abundance data, Biometrics, 30, 101-110, (1974) · Zbl 0276.62088
[6] Chao, A., Species richness estimation, (Balakrishnan, N.; Read, C.; Vidakovic, B., Encyclopedia of Statistical Sciences, (2006), Wiley New York)
[7] Correia-Neves, M.; Waltzinger, C.; Mathis, D.; Benoist, C., The shaping of the T-cell repertoire, Immunity, 14, 21-32, (2001)
[8] Davis, M. M.; Bjorkman, P. J., T-cell antigen receptor genes and T-cell recognition, Nature, 334, 395-402, (1988)
[9] Engen, S.; Lande, R.; Walla, T.; DeVries, P., Analyzing spatial structure of communities using the two-dimensional Poisson lognormal species abundance model, Am. Nat., 160, 60-73, (2002)
[10] Fisher, R. A.; Corbet, A. S.; Williams, C. B., The relation between the number of species and the number of individuals in a random sample of an animal population, J. Anim. Ecol., 12, 42-58, (1943)
[11] Gelman, A.; Rubin, D., Inference from iterative simulation using multiple sequences, Stat. Sci., 7, 457-472, (1992) · Zbl 1386.65060
[12] Golub, G.; Van Loan, C., Matrix computations, (1996), Johns Hopkins University Press · Zbl 0865.65009
[13] Hastie, T.; Tibshirani, R.; Friedman, J., Elements of statistical learningdata mining, inference, and prediction, (2009), Springer-Verlag New York
[14] Ignatowicz, L.; Kappler, J.; Parker, D. C.; Marrack, P., The responses of mature T-cells are not necessarily antagonized by their positively selecting peptide, J. Immunol., 157, 1827-1831, (1996)
[15] Johnson, V., A Bayesian \(\chi^2\) test for goodness-of-fit, Ann. Stat., 32, 2361-2384, (2004) · Zbl 1068.62028
[16] Kawano, T.; Cui, J.; Koezuka, Y.; Toura, I.; Kaneko, Y.; Motoki, K.; Ueno, H.; Nakagawa, R.; Sato, H.; Kondo, E., CD1D-restricted and TCR-mediated activation of \(\operatorname{v} \alpha 14\) nkt-cells by glycosylceramides, Science, 278, 1626-1629, (1997)
[17] Kedzierska, K.; La Gruta, N. L.; Stambas, J.; Turner, S. J.; Doherty, P. C., Tracking phenotypically and functionally distinct T-cell subsets via T-cell repertoire diversity, Mol. Immunol., 45, 607-618, (2008)
[18] Lai, B.; Ding, R.; Li, Y.; Duan, L.; Zhu, H., A de novo metagenomic assembly program for shotgun DNA reads, Bioinformatics, 28, 1455-1462, (2012)
[19] Legendre, P., Legendre, L., 1998. Numerical ecology. Developments in Environmental Modelling, English edition, vol. 20, Elsevier Science B.V., Amsterdam (translated and revised from the second French (1984) edition). · Zbl 1033.92036
[20] Lunn, D.; Spiegelhalter, D.; Thomas, A.; Best, N., The BUGS projectevolution, critique and future directions, Stat. Med., 28, 3049-3067, (2009)
[21] Magurran, A. E., Biological diversity, Curr. Biol., 15, R116-R118, (2005)
[22] Mamedov, I. Z.; Britanova, O. V.; Bolotin, D. A.; Chkalina, A. V.; Staroverov, D. B.; Zvyagin, I. V.; Kotlobay, A. A.; Turchaninova, M. A.; Fedorenko, D. A.; Novik, A. A.; Sharonov, G. V.; Lukyanov, S.; Chudakov, D. M.; Lebedev, Y. B., Quantitative tracking of T-cell clones after haematopoietic stem cell transplantation, EMBO Mol. Med., 3, 201-207, (2011)
[23] Murphy, K.; Travers, P.; Walport, M., Janeway’s immunobiology, (2011), Taylor & Francis
[24] Nayak, T., Estimating the number of component processes of a superimposed process, Biometrika, 78, 75-81, (1991) · Zbl 0717.62076
[25] Pacholczyk, R.; Ignatowicz, H.; Kraj, P.; Ignatowicz, L., Origin and T-cell receptor diversity of foxp3+CD4+CD25+ T-cells, Immunity, 25, 249-259, (2006)
[26] Pacholczyk, R.; Kern, J.; Singh, N.; Iwashima, M.; Kraj, P.; Ignatowicz, L., Nonself-antigens are the cognate specificities of foxp3+ regulatory T-cells, Immunity, 27, 493-504, (2007)
[27] Plummer, M., 2003. JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling. In: Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003), March, pp. 20-22.
[28] R Team, 2010. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
[29] Rempala, G. A.; Seweryn, M.; Ignatowicz, L., Model for comparative analysis of antigen receptor repertoires, J. Theor. Biol., 269, 1-15, (2011) · Zbl 1307.92089
[30] Rodrigues, J.; Milan, L.; Leite, J., Hierarchical Bayesian estimation for the number of species, Biom. J., 43, 737-746, (2001) · Zbl 0988.62069
[31] Sanathanan, L., Estimating the size of a multinomial population, Ann. Math. Stat., 142-152, (1972) · Zbl 0241.62007
[32] SepĂșlveda, N.; Paulino, C. D.; Carneiro, J., Estimation of T-cell repertoire diversity and clonal size distribution by Poisson abundance models, J. Immunol. Methods, 353, 124-137, (2010)
[33] Thalamuthu, A.; Mukhopadhyay, I.; Zheng, X.; Tseng, G. C., Evaluation and comparison of gene clustering methods in microarray analysis, Bioinformatics, 22, 2405-2412, (2006)
[34] Venturi, V.; Chin, H. Y.; Asher, T. E.; Ladell, K.; Scheinberg, P.; Bornstein, E.; van-Bockel, D.; Kelleher, A. D.; Douek, D. C.; Price, D. A.; Davenport, M. P., TCR \(\beta \operatorname{-} \operatorname{chain}\) sharing in human CD8+ T-cell responses to cytomegalovirus and EBV, J. Immunol., 181, 7853-7862, (2008)
[35] Venturi, V.; Quigley, M. F.; Greenaway, H. Y.; Ng, P. C.; Ende, Z. S.; McIntosh, T.; Asher, T. E.; Almeida, J. R.; Levy, S.; Price, D. A.; Davenport, M. P.; Douek, D. C., A mechanism for TCR sharing between T-cell subsets and individuals revealed by pyrosequencing, J. Immunol., 186, 4285-4294, (2011)
[36] Wang, C.; Sanders, C.; Yang, Q.; Schroeder, H.; Wang, E.; Babrzadeh, F.; Gharizadeh, B.; Myers, R.; Hudson, J.; Davis, R., High throughput sequencing reveals a complex pattern of dynamic interrelationships among human T-cell subsets, Proc. Natl. Acad. Sci., 107, 1518-1523, (2010)
[37] Wang, Z.; Gerstein, M.; Snyder, M., RNA-seqa revolutionary tool for transcriptomics, Nat. Rev. Genet., 10, 57-63, (2009)
[38] Warren, R.; Nelson, B.; Holt, R., Profiling model T-cell metagenomes with short reads, Bioinformatics, 25, 458, (2009)
[39] Wong, F. S.; Janeway, C. A., The role of CD4 vs. CD8 T-cells in IDDM, J. Autoimmun., 13, 290-295, (1999)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.