Single-cell lineage tracking strategies enabled by recent experimental technologies have produced significant insights into cell fate decisions, but lack the quantitative framework necessary for rigorous statistical analysis of mechanistic models describing cell division and differentiation. In this paper, we develop such a framework with corresponding moment-based parameter estimation techniques for continuous-time, multi-type branching processes. Such processes provide a probabilistic model of how cells divide and differentiate, and we apply our method to study hematopoiesis, the mechanism of blood cell production. We derive closed-form expressions for higher moments in a general class of such models. These analytical results allow us to efficiently estimate parameters of much richer statistical models of hematopoiesis than those used in previous statistical studies. To our knowledge, the method provides the first rate inference procedure for fitting such models to time series data generated from cellular barcoding experiments. After validating the methodology in simulation studies, we apply our estimator to hematopoietic lineage tracking data from rhesus macaques. Our analysis provides a more complete understanding of cell fate decisions during hematopoiesis in nonhuman primates, which may be more relevant to human biology and clinical strategies than previous findings from murine studies. For example, in addition to previously estimated hematopoietic stem cell self-renewal rate, we are able to estimate fate decision probabilities and to compare structurally distinct models of hematopoiesis using cross validation. These estimates of fate decision probabilities and our model selection results should help biologists compare competing hypotheses about how progenitor cells differentiate. The methodology is transferrable to a large class of stochastic compartmental and multi-type branching models, commonly used in studies of cancer progression, epidemiology and many other fields.
References
Abkowitz, J. L., Linenberger, M. L., Newton, M. A., Shelton, G. H., Ott, R. L. and Guttorp, P. (1990). Evidence for the maintenance of hematopoiesis in a large animal by the sequential activation of stem-cell clones. Proc. Natl. Acad. Sci. USA 87 9062–9066.Abkowitz, J. L., Linenberger, M. L., Newton, M. A., Shelton, G. H., Ott, R. L. and Guttorp, P. (1990). Evidence for the maintenance of hematopoiesis in a large animal by the sequential activation of stem-cell clones. Proc. Natl. Acad. Sci. USA 87 9062–9066.
Bailey, N. T. J. (1964). The Elements of Stochastic Processes with Applications to the Natural Sciences. Wiley, New York. 0127.11203Bailey, N. T. J. (1964). The Elements of Stochastic Processes with Applications to the Natural Sciences. Wiley, New York. 0127.11203
Becker, A. J., McCulloch, E. A. and Till, J. E. (1963). Cytological demonstration of the clonal nature of spleen colonies derived from transplanted mouse marrow cells. Nature 197 452–454.Becker, A. J., McCulloch, E. A. and Till, J. E. (1963). Cytological demonstration of the clonal nature of spleen colonies derived from transplanted mouse marrow cells. Nature 197 452–454.
Biasco, L., Pellin, D., Scala, S., Dionisio, F., Basso-Ricci, L., Leonardelli, L., Scaramuzza, S., Baricordi, C., Ferrua, F. et al. (2016). In vivo tracking of human hematopoiesis reveals patterns of clonal dynamics during early and steady-state reconstitution phases. Cell Stem Cell 19 107–119.Biasco, L., Pellin, D., Scala, S., Dionisio, F., Basso-Ricci, L., Leonardelli, L., Scaramuzza, S., Baricordi, C., Ferrua, F. et al. (2016). In vivo tracking of human hematopoiesis reveals patterns of clonal dynamics during early and steady-state reconstitution phases. Cell Stem Cell 19 107–119.
Buchholz, V. R., Flossdorf, M., Hensel, I., Kretschmer, L., Weissbrich, B., Gräf, P., Verschoor, A., Schiemann, M., Höfer, T. et al. (2013). Disparate individual fates compose robust CD8+ T cell immunity. Science 340 630–635.Buchholz, V. R., Flossdorf, M., Hensel, I., Kretschmer, L., Weissbrich, B., Gräf, P., Verschoor, A., Schiemann, M., Höfer, T. et al. (2013). Disparate individual fates compose robust CD8+ T cell immunity. Science 340 630–635.
Catlin, S. N., Abkowitz, J. L. and Guttorp, P. (2001). Statistical inference in a two-compartment model for hematopoiesis. Biometrics 57 546–553. 1209.62264 10.1111/j.0006-341X.2001.00546.xCatlin, S. N., Abkowitz, J. L. and Guttorp, P. (2001). Statistical inference in a two-compartment model for hematopoiesis. Biometrics 57 546–553. 1209.62264 10.1111/j.0006-341X.2001.00546.x
Catlin, S. N., Busque, L., Gale, R. E., Guttorp, P. and Abkowitz, J. L. (2011). The replication rate of human hematopoietic stem cells in vivo. Blood 117 4460–4466.Catlin, S. N., Busque, L., Gale, R. E., Guttorp, P. and Abkowitz, J. L. (2011). The replication rate of human hematopoietic stem cells in vivo. Blood 117 4460–4466.
Dorman, K. S., Sinsheimer, J. S. and Lange, K. (2004). In the garden of branching processes. SIAM Rev. 46 202–229. 1069.60072 10.1137/S0036144502417843Dorman, K. S., Sinsheimer, J. S. and Lange, K. (2004). In the garden of branching processes. SIAM Rev. 46 202–229. 1069.60072 10.1137/S0036144502417843
Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96 1348–1360. 1073.62547 10.1198/016214501753382273Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96 1348–1360. 1073.62547 10.1198/016214501753382273
Fong, Y., Guttorp, P. and Abkowitz, J. (2009). Bayesian inference and model choice in a hidden stochastic two-compartment model of hematopoietic stem cell fate decisions. Ann. Appl. Stat. 3 1695–1709. 1184.62035 10.1214/09-AOAS269 euclid.aoas/1267453960Fong, Y., Guttorp, P. and Abkowitz, J. (2009). Bayesian inference and model choice in a hidden stochastic two-compartment model of hematopoietic stem cell fate decisions. Ann. Appl. Stat. 3 1695–1709. 1184.62035 10.1214/09-AOAS269 euclid.aoas/1267453960
Gerrits, A., Dykstra, B., Kalmykowa, O. J., Klauke, K., Verovskaya, E., Broekhuis, M. J. C., de Haan, G. and Bystrykh, L. V. (2010). Cellular barcoding tool for clonal analysis in the hematopoietic system. Blood 115 2610–2618.Gerrits, A., Dykstra, B., Kalmykowa, O. J., Klauke, K., Verovskaya, E., Broekhuis, M. J. C., de Haan, G. and Bystrykh, L. V. (2010). Cellular barcoding tool for clonal analysis in the hematopoietic system. Blood 115 2610–2618.
Golinelli, D., Guttorp, P. and Abkowitz, J. A. (2006). Bayesian inference in a hidden stochastic two-compartment model for feline hematopoiesis. Math. Med. Biol. 23 153–172. 1098.62145 10.1093/imammb/dql008Golinelli, D., Guttorp, P. and Abkowitz, J. A. (2006). Bayesian inference in a hidden stochastic two-compartment model for feline hematopoiesis. Math. Med. Biol. 23 153–172. 1098.62145 10.1093/imammb/dql008
Goyal, S., Kim, S., Chen, I. S. Y. and Chou, T. (2015). Mechanisms of blood homeostasis: Lineage tracking and a neutral model of cell populations in rhesus macaques. BMC Biol. 13 85.Goyal, S., Kim, S., Chen, I. S. Y. and Chou, T. (2015). Mechanisms of blood homeostasis: Lineage tracking and a neutral model of cell populations in rhesus macaques. BMC Biol. 13 85.
Griffin, J. E. and Brown, P. J. (2013). Some priors for sparse regression modelling. Bayesian Anal. 8 691–702. 1329.62132 10.1214/13-BA827Griffin, J. E. and Brown, P. J. (2013). Some priors for sparse regression modelling. Bayesian Anal. 8 691–702. 1329.62132 10.1214/13-BA827
Guttorp, P. (1995). Stochastic Modeling of Scientific Data. Stochastic Modeling Series. CRC Press, London. 0862.60034Guttorp, P. (1995). Stochastic Modeling of Scientific Data. Stochastic Modeling Series. CRC Press, London. 0862.60034
Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica 50 1029–1054. 0502.62098 10.2307/1912775Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica 50 1029–1054. 0502.62098 10.2307/1912775
Hellerstein, M., Hanley, M. B., Cesar, D., Siler, S., Papageorgopoulos, C., Wieder, E., Schmidt, D., Hoh, R., Neese, R. et al. (1999). Directly measured kinetics of circulating T lymphocytes in normal and HIV-1-infected humans. Nat. Med. 5 83–89.Hellerstein, M., Hanley, M. B., Cesar, D., Siler, S., Papageorgopoulos, C., Wieder, E., Schmidt, D., Hoh, R., Neese, R. et al. (1999). Directly measured kinetics of circulating T lymphocytes in normal and HIV-1-infected humans. Nat. Med. 5 83–89.
Hyrien, O., Peslak, S. A., Yanev, N. M. and Palis, J. (2015). Stochastic modeling of stress erythropoiesis using a two-type age-dependent branching process with immigration. J. Math. Biol. 70 1485–1521. 1368.92032 10.1007/s00285-014-0803-xHyrien, O., Peslak, S. A., Yanev, N. M. and Palis, J. (2015). Stochastic modeling of stress erythropoiesis using a two-type age-dependent branching process with immigration. J. Math. Biol. 70 1485–1521. 1368.92032 10.1007/s00285-014-0803-x
Kaur, A., Di Mascio, M., Barabasz, A., Rosenzweig, M., McClure, H. M., Perelson, A. S., Ribeiro, R. M. and Johnson, R. P. (2008). Dynamics of T-and B-lymphocyte turnover in a natural host of simian immunodeficiency virus. J. Virol. 82 1084–1093.Kaur, A., Di Mascio, M., Barabasz, A., Rosenzweig, M., McClure, H. M., Perelson, A. S., Ribeiro, R. M. and Johnson, R. P. (2008). Dynamics of T-and B-lymphocyte turnover in a natural host of simian immunodeficiency virus. J. Virol. 82 1084–1093.
Kawamoto, H., Wada, H. and Katsura, Y. (2010). A revised scheme for developmental pathways of hematopoietic cells: The myeloid-based model. Int. Immunol. 22 65–70.Kawamoto, H., Wada, H. and Katsura, Y. (2010). A revised scheme for developmental pathways of hematopoietic cells: The myeloid-based model. Int. Immunol. 22 65–70.
Kimmel, M. and Axelrod, D. E. (2002). Branching Processes in Biology. Interdisciplinary Applied Mathematics 19. Springer, New York. 0994.92001Kimmel, M. and Axelrod, D. E. (2002). Branching Processes in Biology. Interdisciplinary Applied Mathematics 19. Springer, New York. 0994.92001
Koelle, S. J., Espinoza, D. A., Wu, C., Xu, J., Lu, R., Li, B., Donahue, R. E. and Dunbar, C. E. (2017). Quantitative stability of hematopoietic stem and progenitor cell clonal output in rhesus macaques receiving transplants. Blood 129 1448–1457.Koelle, S. J., Espinoza, D. A., Wu, C., Xu, J., Lu, R., Li, B., Donahue, R. E. and Dunbar, C. E. (2017). Quantitative stability of hematopoietic stem and progenitor cell clonal output in rhesus macaques receiving transplants. Blood 129 1448–1457.
Lange, K. (2010). Applied Probability. Springer, New York. 1216.62001Lange, K. (2010). Applied Probability. Springer, New York. 1216.62001
Laslo, P., Pongubala, J. M. R., Lancki, D. W. and Singh, H. (2008). Gene regulatory networks directing myeloid and lymphoid cell fates within the immune system. Semin. Immunol. 20 228–235.Laslo, P., Pongubala, J. M. R., Lancki, D. W. and Singh, H. (2008). Gene regulatory networks directing myeloid and lymphoid cell fates within the immune system. Semin. Immunol. 20 228–235.
Liepe, J., Kirk, P., Filippi, S., Toni, T., Barnes, C. P. and Stumpf, M. P. H. (2014). A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. Nat. Protoc. 9 439–456.Liepe, J., Kirk, P., Filippi, S., Toni, T., Barnes, C. P. and Stumpf, M. P. H. (2014). A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. Nat. Protoc. 9 439–456.
Lu, R., Neff, N. F., Quake, S. R. and Weissman, I. L. (2011). Tracking single hematopoietic stem cells in vivo using high-throughput sequencing in conjunction with viral genetic barcoding. Nat. Biotechnol. 29 928–933.Lu, R., Neff, N. F., Quake, S. R. and Weissman, I. L. (2011). Tracking single hematopoietic stem cells in vivo using high-throughput sequencing in conjunction with viral genetic barcoding. Nat. Biotechnol. 29 928–933.
Marciniak-Czochra, A., Stiehl, T., Ho, A. D., Jäger, W. and Wagner, W. (2009). Modeling of asymmetric cell division in hematopoietic stem cells-regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev. 18 377–386.Marciniak-Czochra, A., Stiehl, T., Ho, A. D., Jäger, W. and Wagner, W. (2009). Modeling of asymmetric cell division in hematopoietic stem cells-regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev. 18 377–386.
Marjoram, P., Molitor, J., Plagnol, V. and Tavaré, S. (2003). Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. USA 100 15324–15328.Marjoram, P., Molitor, J., Plagnol, V. and Tavaré, S. (2003). Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. USA 100 15324–15328.
Notta, F., Zandi, S., Takayama, N., Dobson, S., Gan, O. I., Wilson, G., Kaufmann, K. B., McLeod, J., Laurenti, E. et al. (2016). Distinct routes of lineage development reshape the human blood hierarchy across ontogeny. Science aab2116.Notta, F., Zandi, S., Takayama, N., Dobson, S., Gan, O. I., Wilson, G., Kaufmann, K. B., McLeod, J., Laurenti, E. et al. (2016). Distinct routes of lineage development reshape the human blood hierarchy across ontogeny. Science aab2116.
Pakes, A. and Pollard, D. (1989). Simulation and the asymptotics of optimization estimators. Econometrica 57 1027–1057. 0698.62031 10.2307/1913622Pakes, A. and Pollard, D. (1989). Simulation and the asymptotics of optimization estimators. Econometrica 57 1027–1057. 0698.62031 10.2307/1913622
Park, T. and Casella, G. (2008). The Bayesian lasso. J. Amer. Statist. Assoc. 103 681–686. 1330.62292 10.1198/016214508000000337Park, T. and Casella, G. (2008). The Bayesian lasso. J. Amer. Statist. Assoc. 103 681–686. 1330.62292 10.1198/016214508000000337
Perié, L., Hodgkin, p., Naik, S. H., Schumacher, T. N., de Boer, R. J. and Duffy, K. R. (2014). Determining lineage pathways from cellular barcoding experiments. Cell Rep. 6 617–624.Perié, L., Hodgkin, p., Naik, S. H., Schumacher, T. N., de Boer, R. J. and Duffy, K. R. (2014). Determining lineage pathways from cellular barcoding experiments. Cell Rep. 6 617–624.
Pudlo, P., Marin, J. M., Estoup, A., Cornuet, J. M., Gautier, M. and Robert, C. P. (2016). Reliable ABC model choice via random forests. Bioinformatics 32 859–866.Pudlo, P., Marin, J. M., Estoup, A., Cornuet, J. M., Gautier, M. and Robert, C. P. (2016). Reliable ABC model choice via random forests. Bioinformatics 32 859–866.
Shepherd, B. E., Kiem, H. P., Lansdorp, P. M., Dunbar, C. E., Aubert, G., LaRochelle, A., Seggewiss, R., Guttorp, P. and Abkowitz, J. L. (2007). Hematopoietic stem-cell behavior in nonhuman primates. Blood 110 1806–1813.Shepherd, B. E., Kiem, H. P., Lansdorp, P. M., Dunbar, C. E., Aubert, G., LaRochelle, A., Seggewiss, R., Guttorp, P. and Abkowitz, J. L. (2007). Hematopoietic stem-cell behavior in nonhuman primates. Blood 110 1806–1813.
Siminovitch, L., McCulloch, E. A. and Till, J. E. (1963). The distribution of colony-forming cells among spleen colonies. J. Cell. Comp. Physiol. 62 327–336.Siminovitch, L., McCulloch, E. A. and Till, J. E. (1963). The distribution of colony-forming cells among spleen colonies. J. Cell. Comp. Physiol. 62 327–336.
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 267–288. 0850.62538 10.1111/j.2517-6161.1996.tb02080.xTibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 267–288. 0850.62538 10.1111/j.2517-6161.1996.tb02080.x
Till, J. E., McCulloch, E. A. and Siminovitch, L. (1964). A stochastic model of stem cell prolifiration, based on the growth of spleen colony-forming cells. Proc. Natl. Acad. Sci. USA 51 29–36. 1355.92026 10.1073/pnas.51.1.29Till, J. E., McCulloch, E. A. and Siminovitch, L. (1964). A stochastic model of stem cell prolifiration, based on the growth of spleen colony-forming cells. Proc. Natl. Acad. Sci. USA 51 29–36. 1355.92026 10.1073/pnas.51.1.29
Toni, T., Welch, D., Strelkowa, N., Ipsen, A. and Stumpf, M. P. H. (2009). Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface 6 187–202.Toni, T., Welch, D., Strelkowa, N., Ipsen, A. and Stumpf, M. P. H. (2009). Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface 6 187–202.
van der Vaart, A. W. (1998). Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics 3. Cambridge Univ. Press, Cambridge.van der Vaart, A. W. (1998). Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics 3. Cambridge Univ. Press, Cambridge.
Velten, L., Haas, S. F., Raffel, S., Blaszkiewicz, S., Islam, S., Hennig, B. P., Hirche, C., Lutz, C., Buss, E. C. et al. (2017). Human haematopoietic stem cell lineage commitment is a continuous process. Nat. Cell Biol. 19 271.Velten, L., Haas, S. F., Raffel, S., Blaszkiewicz, S., Islam, S., Hennig, B. P., Hirche, C., Lutz, C., Buss, E. C. et al. (2017). Human haematopoietic stem cell lineage commitment is a continuous process. Nat. Cell Biol. 19 271.
Wakefield, J. (2013). Bayesian and Frequentist Regression Methods. Springer Series in Statistics. Springer, New York. 1281.62014Wakefield, J. (2013). Bayesian and Frequentist Regression Methods. Springer Series in Statistics. Springer, New York. 1281.62014
Wu, C., Li, B., Lu, R., Koelle, S. J., Yang, Y., Jares, A., Krouse, A. E., Metzger, M., Liang, F. et al. (2014). Clonal tracking of rhesus macaque hematopoiesis highlights a distinct lineage origin for natural killer cells. Cell Stem Cell 14 486–499.Wu, C., Li, B., Lu, R., Koelle, S. J., Yang, Y., Jares, A., Krouse, A. E., Metzger, M., Liang, F. et al. (2014). Clonal tracking of rhesus macaque hematopoiesis highlights a distinct lineage origin for natural killer cells. Cell Stem Cell 14 486–499.
Xu, J., Koelle, S., Guttorp, P., Wu, C., Dunbar, C., Abkowitz, J. L. and Minin, V. N. (2019). Supplement to “Statistical inference for partially observed branching processes with application to cell lineage tracking of in vivo hematopoiesis.” DOI:10.1214/19-AOAS1272SUPP.Xu, J., Koelle, S., Guttorp, P., Wu, C., Dunbar, C., Abkowitz, J. L. and Minin, V. N. (2019). Supplement to “Statistical inference for partially observed branching processes with application to cell lineage tracking of in vivo hematopoiesis.” DOI:10.1214/19-AOAS1272SUPP.
Zhang, Y., Wallace, D. L., De Lara, C. M., Ghattas, H., Asquith, B., Worth, A., Griffin, G. E., Taylor, G. P., Tough, D. F. et al. (2007). In vivo kinetics of human natural killer cells: The effects of ageing and acute and chronic viral infection. Immunology 121 258–265.Zhang, Y., Wallace, D. L., De Lara, C. M., Ghattas, H., Asquith, B., Worth, A., Griffin, G. E., Taylor, G. P., Tough, D. F. et al. (2007). In vivo kinetics of human natural killer cells: The effects of ageing and acute and chronic viral infection. Immunology 121 258–265.
