Deterministic and stochastic naive T cell population dynamics: symmetric and asymmetric cell division

References

• Freitas , AA and Rocha , B . 2000 . Population biology of lymphocytes: The flight for survival . Ann. Rev. Immunol. , 18 : 83 – 111 .
   PubMed Web of Science ®Google Scholar
• Takada , K and Jameson , SC . 2009 . Naive T cell homeostasis: From awareness of space to a sense of place . Nat. Rev. Immunol. , 9 : 823 – 832 .
   PubMed Web of Science ®Google Scholar
• Yates , A , Chan , CCW , Callard , RE , George , AJT and Stark , J . 2001 . An approach to modelling in immunology . Brief. Bioinform. , 2 : 245
   PubMedGoogle Scholar
• Callard , RE , Stark , J and Yates , AJ . 2003 . Fratricide: A mechanism for T memory-cell homeostasis . Trends Immunol. , 24 : 370 – 375 .
   PubMed Web of Science ®Google Scholar
• Hardy , K and Stark , J . 2002 . Mathematical models of the balance between apoptosis and proliferation . Apoptosis , 7 : 373 – 381 .
   PubMed Web of Science ®Google Scholar
• Yates , A , Stark , J , Klein , N , Antia , R and Callard , R . 2007 . Understanding the slow depletion of memory CD4+ T cells in HIV infection . PLoS Med. , 4 : e177
   PubMed Web of Science ®Google Scholar
• Grossman , Z , Meier-Schellersheim , M , Sousa , AE , Victorino , RMM and Paul , WE . 2002 . CD 4+ T-cell depletion in HIV infection: Are we closer to understanding the cause? . Nat. Med. , 8 : 319 – 323 .
   PubMed Web of Science ®Google Scholar
• Yates , A and Callard , R . 2001 . Cell death and the maintenance of immunological memory . Discr. Contin. Dyn. Syst. Ser. B. , 1 : 43 – 60 .
   Web of Science ®Google Scholar
• Yates , A , Bergmann , C , Leo Van Hemmen , J , Stark , J and Callard , R . 2000 . Cytokine-modulated regulation of helper T cell populations . J. Theor. Biol. , 206 : 539 – 560 .
   PubMed Web of Science ®Google Scholar
• Carneiro , J , Paixão , T , Milutinovic , D , Sousa , J , Leon , K , Gardner , R and Faro , J . 2005 . Immunological self-tolerance: Lessons from mathematical modeling . J. Comput. Appl. Math. , 184 : 77 – 100 .
   Web of Science ®Google Scholar
• De Boer , RJ . 2002 . Mathematical models of human CD4 T-cell population kinetics . The Netherlands J. Med. , 60 : 17 – 26 .
   PubMed Web of Science ®Google Scholar
• Thomas-Vaslin , V , Altes , HK , De Boer , RJ and Klatzmann , D . 2008 . Comprehensive assessment and mathematical modeling of T cell population dynamics and homeostasis . J. Immunol. , 180 : 2240
   PubMed Web of Science ®Google Scholar
• Antia , R , Ganusov , VV and Ahmed , R . 2005 . The role of models in understanding CD8+ T-cell memory . Nat. Rev. Immunol. , 5 : 101 – 111 .
   PubMed Web of Science ®Google Scholar
• Murray , JM , Kaufmann , GR , Hodgkin , PD , Lewin , SR , Kelleher , AD , Davenport , MP and Zaunders , JJ . 2003 . Naive T cells are maintained by thymic output in early ages but by proliferation without phenotypic change after age twenty . Immunol. Cell Biol. , 81 : 487 – 495 .
   PubMed Web of Science ®Google Scholar
• Dowling , MR and Hodgkin , PD . 2009 . Modelling naive T-cell homeostasis: Consequences of heritable cellular lifespan during ageing . Immunol. Cell Biol. , 87 : 445 – 456 .
   PubMed Web of Science ®Google Scholar
• Chang , JT , Palanivel , VR , Kinjyo , I , Schambach , F , Intlekofer , AM , Banerjee , A , Longworth , SA , Vinup , KE , Mrass , P and Oliaro , J . 2007 . Asymmetric T lymphocyte division in the initiation of adaptive immune responses . Science , 315 : 1687
   PubMed Web of Science ®Google Scholar
• Harty , JT and Badovinac , VP . 2008 . Shaping and reshaping CD8+ T-cell memory . Nat. Rev. Immunol. , 8 : 107 – 119 .
   PubMed Web of Science ®Google Scholar
• Reiner , SL , Sallusto , F and Lanzavecchia , A . 2007 . Division of labor with a workforce of one: Challenges in specifying effector and memory T cell fate . Science , 317 : 622
   PubMed Web of Science ®Google Scholar
• Yates , A , Chan , C , Strid , J , Moon , S , Callard , R , George , A and Stark , J . 2007 . Reconstruction of cell population dynamics using CFSE . BMC Bioinform. , 8 : 196
   PubMed Web of Science ®Google Scholar
• Lynch , HE , Goldberg , GL , Chidgey , A , Van den Brink , MRM , Boyd , R and Sempowski , GD . 2009 . Thymic involution and immune reconstitution . Trends Immunol. , 30 : 366 – 373 .
   PubMed Web of Science ®Google Scholar
• Bains , I , Antia , R , Callard , R and Yates , AJ . 2009 . Quantifying the development of the peripheral naive CD4+ T-cell pool in humans . Blood , 113 : 5480
   PubMed Web of Science ®Google Scholar
• Yates , A , Saini , M , Mathiot , A and Seddon , B . 2008 . Mathematical modeling reveals the biological program regulating lymphopenia-induced proliferation . J. Immunol. , 180 : 1414
   PubMed Web of Science ®Google Scholar
• Quigley , MF , Greenaway , HY , Venturi , V , Lindsay , R , Quinn , KM , Seder , RA , Douek , DC , Davenport , MP and Price , DA . 2010 . Convergent recombination shapes the clonotypic landscape of the naïve T-cell repertoire . Proc. Nat. Acad. Sci. , 107 : 19414
   PubMed Web of Science ®Google Scholar
• Allen , LJS . 2003 . An introduction to stochastic processes with applications to biology , Upper Saddle River , NJ : Pearson/Prentice Hall .
   Google Scholar
• Lyons , AB and Parish , CR . 1994 . Determination of lymphocyte division by flow cytometry . J. Immunol. Methods , 171 : 131 – 137 .
   PubMed Web of Science ®Google Scholar
• Miao , H , Jin , X , Perelson , AS and Wu , H . 2011 . Evaluation of Multitype Mathematical Models for CFSE-Labeling Experiment Data . Bull. Math. Biol. , . Available at http://dx.doi.org/10.1007/s11538-011-9668-y
   Web of Science ®Google Scholar
• Zilman , A , Ganusov , VV and Perelson , AS . 2010 . Stochastic models of lymphocyte proliferation and death . PLoS One , 5 : e12775
   Web of Science ®Google Scholar
• Banks , HT , Sutton , KL , Thompson , WC , Bocharov , G , Doumic , M , Schenkel , T , Argilaguet , J , Giest , S , Peligero , C and Meyerhans , A . 2011 . A new model for the estimation of cell proliferation dynamics using CFSE data . J. Immunol. Methods , 373 : 143 – 160 .
   PubMed Web of Science ®Google Scholar
• Markham , JF , Wellard , CJ , Hawkins , ED , Duffy , KR and Hodgkin , PD . 2010 . A minimum of two distinct heritable factors are required to explain correlation structures in proliferating lymphocytes . J. R. Soc. Interface , 7 : 1049 – 1059 .
   PubMed Web of Science ®Google Scholar
• Hawkins , ED , Markham , JF , McGuinness , LP and Hodgkin , PD . 2009 . A single-cell pedigree analysis of alternative stochastic lymphocyte fates . Proc. Nat. Acad. Sci. , 106 : 13457 – 13462 .
   PubMed Web of Science ®Google Scholar
• Subramanian , VG , Duffy , KR , Turner , ML and Hodgkin , PD . 2008 . Determining the expected variability of immune responses using the cyton model . J. Math. Biol. , 56 : 861 – 892 .
   PubMed Web of Science ®Google Scholar
• Van Kampen , NG . 1976 . Stochastic differential equations . Phys. Rep. , 24 : 171 – 228 .
   Google Scholar
• Stirk , ER , Molina-París , C and van den Berg , HA . 2008 . Stochastic niche structure and diversity maintenance in the T cell repertoire . J. Theor. Biol. , 255 : 237 – 249 .
   PubMed Web of Science ®Google Scholar
• Stirk , ER , Lythe , G , van den Berg , HA , Hurst , GAD and Molina-París , C . 2010 . The limiting conditional probability distribution in a stochastic model of T cell repertoire maintenance . Math. Biosci. , 224 : 74 – 86 .
   PubMed Web of Science ®Google Scholar
• Stirk , ER , Lythe , G , van den Berg , HA and Molina-París , C . 2010 . Stochastic competitive exclusion in the maintenance of the naïve T cell repertoire . J. Theor. Biol. , 265 : 396 – 410 .
   PubMed Web of Science ®Google Scholar