Methods for diversity and overlap analysis in T-cell receptor populations

Journal of Mathematical Biology

Volumn 67, Issue 6-7, 2013, Pages 1339-1368

  Rempala, Grzegorz A ^a   Seweryn, Michal ^a,b  

^a MEDICAL COLLEGE OF GEORGIA   (United States)

^b UNIVERSITY OF LODZ   (Poland)

Author keywords

Antigen receptors; Contingency tables; Renyi's divergence; Renyi's entropy; Richness and diversity estimation

Indexed keywords

MAMMALIA; MUS;

LYMPHOCYTE ANTIGEN RECEPTOR;

ANIMAL; ARTICLE; GENETIC VARIABILITY; GENETICS; IMMUNOLOGY; MOUSE; STATISTICAL ANALYSIS; T LYMPHOCYTE; T LYMPHOCYTE SUBPOPULATION;

ANIMALS; DATA INTERPRETATION, STATISTICAL; GENETIC VARIATION; MICE; RECEPTORS, ANTIGEN, T-CELL; T-LYMPHOCYTE SUBSETS; T-LYMPHOCYTES;

EID: 84887425111     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-012-0589-7     Document Type: Article

References (41)

1. Agresti A (2002) Categorical data analysis, 2nd edn. In: Wiley series in probability and statistics. Wiley, New York.
2. Antos A, Kontoyiannis I (2001) Convergence properties of functional estimates for discrete distributions. Random Struct Algorithms 19(3-4): 163-193.
3. Arstila T, Casrouge A, Baron V, Even J, Kanellopoulos J, Kourilsky P (1999) A direct estimate of the human α β T-cell receptor diversity. Science 286(5441): 958.
4. Baum P, McCune J (2006) Direct measurement of T-cell receptor repertoire diversity with amplicot. Nat methods 3(11): 895-901.
5. Butz EA, Bevan MJ (1998) Massive expansion of antigen-specific cd8+ T-cells during an acute virus infection. Immunity 8(2): 167-75.
6. Chao A, Shen T (2003) Nonparametric estimation of Shannon's index of diversity when there are unseen species in sample. Environ Ecol Stat 10(4): 429-443.
7. Chao A, Chazdon RL, Colwell RK, Shen TJ (2005) A new statistical approach for assessing similarity of species composition with incidence and abundance data. Ecol Lett 8: 148-159.
8. Chen W, Jin W, Hardegen N, Lei KJ, Li L, Marinos N, McGrady G, Wahl SM (2003) Conversion of peripheral cd4+cd25- naive T-cells to cd4+cd25+ regulatory T cells by tgf-beta induction of transcription factor foxp3. J Exp Med 198(12): 1875-86. doi: 10. 1084/jem. 20030152.
9. Davis MM, Bjorkman PJ (1988) T-cell antigen receptor genes and T-cell recognition. Nature 334(6181): 395-402. doi: 10. 1038/334395a0.
10. Esteban MD, Morales D (1995) A summary on entropy statistics. Kybernetika 31(4): 337-346.
11. Esty W (1983) A normal limit law for a nonparametric estimator of the coverage of a random sample. Ann Stat 11: 905-912.
12. Esty W (1986) The efficiency of Good's nonparametric coverage estimator. Ann Stat 3: 1257-1260.
13. Good I (1953) The population frequencies of species and the estimation of population parameters. Biometrika 40(3-4): 237-264.
14. Gras S, Kjer-Nielsen L, Burrows S, McCluskey J, Rossjohn J (2008) T-cell receptor bias and immunity. Curr Opin Immunol 20(1): 119-125.
15. Hsieh CS, Zheng Y, Liang Y, Fontenot JD, Rudensky AY (2006) An intersection between the self-reactive regulatory and nonregulatory T-cell receptor repertoires. Nat Immunol 7(7): 401-410. doi: 10. 1038/ni1318.
16. Hsieh CS, Lee HM, Lio CWJ (2012) Selection of regulatory T-cells in the thymus. Nat Rev Immunol 12(3): 157-167. doi: 10. 1038/nri3155.
17. Janeway C (2005) Immunobiology: the immune system in health and disease, 6th edn. Garland Science, New York.
18. Jost L (2006) Entropy and diversity. Oikos 113(2): 363-375.
19. Keylock C (2005) Simpson diversity and the shannon-wiener index as special cases of a generalized entropy. Oikos 109(1): 203-207.
20. Komatsu N, Mariotti-Ferrandiz ME, Wang Y, Malissen B, Waldmann H, Hori S (2009) Heterogeneity of natural foxp3+ T-cells: a committed regulatory T-cell lineage and an uncommitted minor population retaining plasticity. Proc Natl Acad Sci USA 106(6): 1903-1908. doi: 10. 1073/pnas. 0811556106.
21. Magurran AE (2005) Biological diversity. Curr Biol 15(4): R116-R118. doi: 10. 1016/j. cub. 2005. 02. 006.
22. Mao C, Lindsay B (2002) A poisson model for the coverage problem with a genomic application. Biometrika 89(3): 669-682.
23. Memon SA, Sportès C, Flomerfelt FA, Gress RE, Hakim FT (2012) Quantitative analysis of T-cell receptor diversity in clinical samples of human peripheral blood. J Immunol Methods 375(1-2): 84-92. doi: 10. 1016/j. jim. 2011. 09. 012.
24. Mohebtash M, Tsang KY, Madan RA, Huen NY, Poole DJ, Jochems C, Jones J, Ferrara T, Heery CR, Arlen PM, Steinberg SM, Pazdur M, Rauckhorst M, Jones EC, Dahut WL, Schlom J, Gulley JL (2011) A pilot study of muc-1/cea/tricom poxviral-based vaccine in patients with metastatic breast and ovarian cancer. Clin Cancer Res 17(22): 7164-7173. doi: 10. 1158/1078-0432. CCR-11-0649.
25. Nayak T (1986) An analysis of diversity using Rao's quadratic entropy. Sankhyā. Indian J Stat Ser B 48: 315-330.
26. Nielsen R, Paul J, Albrechtsen A, Song Y (2011) Genotype and SNP calling from next-generation sequencing data. Nat Rev Genet 12(6): 443-451.
27. Orlitsky A, Santhanam N, Zhang J (2003) Always Good-Turing: asymptotically optimal probability estimation. Science 302(5644): 427-431.
28. Orlitsky A, Santhanam N, Zhang J (2004) Universal compression of memoryless sources over unknown alphabets. IEEE Trans Inf Theory 50(7): 1469-1481.
29. Pacholczyk R, Ignatowicz H, Kraj P, Ignatowicz L (2006) Origin and T-cell receptor diversity of foxp3+cd4+cd25+ T-cells. Immunity 25(2): 249-259. doi: 10. 1016/j. immuni. 2006. 05. 016.
30. Pacholczyk R, Kern J, Singh N, Iwashima M, Kraj P, Ignatowicz L (2007) Nonself-antigens are the cognate specificities of foxp3+ regulatory T-cells. Immunity 27(3): 493-504. doi: 10. 1016/j. immuni. 2007. 07. 019.
31. Rempala GA, Seweryn M, Ignatowicz L (2011) Model for comparative analysis of antigen receptor repertoires. J Theor Biol 269(1): 1-15. doi: 10. 1016/j. jtbi. 2010. 10. 001.
32. Rényi P (1961) On measures of information and entropy. In: Proceedings of the 4th Berkeley symposium on mathematics, statistics and probability, pp 547-561.
33. Ricotta C (2005) Through the jungle of biological diversity. Acta Biotheoret 53(1): 29-38.
34. Salameire D, Le Bris Y, Fabre B, Fauconnier J, Solly F, Pernollet M, Bonnefoix T, Leroux D, Plumas J, Jacob MC (2009) Efficient characterization of the tcr repertoire in lymph nodes by flow cytometry. Cytometry A 75(9): 743-753. doi: 10. 1002/cyto. a. 20767.
35. Spellerberg I, Fedor P (2003) A tribute to claude shannon (1916-2001) and a plea for more rigorous use of species richness, species diversity and the Shannon-Wiener index. Global Ecol Biogeogr 12(3): 177-179.
36. Staveley-O'Carroll K, Sotomayor E, Montgomery J, Borrello I, Hwang L, Fein S, Pardoll D, Levitsky H (1998) Induction of antigen-specific T-cell anergy: an early event in the course of tumor progression. Proc Natl Acad Sci USA 95(3): 1178-1183.
37. Tóthmérész B (1995) Comparison of different methods for diversity ordering. J Veget Sci 6(2): 283-290.
38. Valiant P (2008) Testing symmetric properties of distributions. PhD thesis, MIT.
39. van Den Berg HA, Molina-París C, Sewell AK (2011) Specific T-cell activation in an unspecific t-cell repertoire. Sci Prog 94(Pt 3): 245-64.
40. Vu VQ, Yu B, Kass RE (2007) Coverage-adjusted entropy estimation. Stat Med 26(21): 4060. doi: 10. 1002/sim. 2942.
41. Zhang CH, Zhang Z (2009) Asymptotic normality of a nonparametric estimator of sample coverage. Ann Stat 37: 2582-2595.