Oscillatory Dynamics of Heterogeneous Stem Cell Regeneration

doi:10.1007/s42967-023-00263-z

Abstract

Abstract: Stem cell regeneration is an essential biological process in the maintenance of tissue homeostasis; dysregulation of stem cell regeneration may result in dynamic diseases that show oscillations in cell numbers. Cell heterogeneity and plasticity are necessary for the dynamic equilibrium of tissue homeostasis; however, how these features may affect the oscillatory dynamics of the stem cell regeneration process remains poorly understood. Here, based on a mathematical model of heterogeneous stem cell regeneration that includes cell heterogeneity and random transition of epigenetic states, we study the conditions to have oscillation solutions through bifurcation analysis and numerical simulations. Our results show various model system dynamics with changes in different parameters associated with kinetic rates, cellular heterogeneity, and plasticity. We show that introducing heterogeneity and plasticity to cells can result in oscillation dynamics, as we have seen in the homogeneous stem cell regeneration system. However, increasing the cell heterogeneity and plasticity intends to maintain tissue homeostasis under certain conditions. The current study is an initiatory investigation of how cell heterogeneity and plasticity may affect stem cell regeneration dynamics, and many questions remain to be further studied both biologically and mathematically.

Key words: Stem cell regeneration, Heterogenous, Hopf bifurcation, Hematopoietic dynamical disease

Xiyin Liang, Jinzhi Lei. Oscillatory Dynamics of Heterogeneous Stem Cell Regeneration[J]. Communications on Applied Mathematics and Computation, 2024, 6(1): 431-453.

TrendMD

References

[1] Atlasi, Y., Stunnenberg, H.G.:The interplay of epigenetic marks during stem cell differentiation and development. Nat. Rev. Genet. 18(11), 643-658 (2017)
[2] Bernard, S., Bélair, J., Mackey, M.C.:Oscillations in cyclical neutropenia:new evidence based on mathematical modeling. J. Theor. Biol. 223(3), 283-298 (2003)
[3] Burns, F.J., Tannock, I.F.:On the existence of a G0-phase in the cell cycle. Cell Prolif. 3(4), 321-334 (1970)
[4] Cao, J., Yan, Q.:Cancer epigenetics, tumor immunity, and immunotherapy. Trends Cancer 6(7), 580-592 (2020)
[5] Chisholm, R.H., Lorenzi, T., Lorz, A., Larsen, A.K., Almeida, LNd., Escargueil, A., Clairambault, J.:Emergence of drug tolerance in cancer cell populations:an evolutionary outcome of selection, nongenetic instability, and stress-induced adaptation. Cancer Res. 75(6), 930-939 (2015)
[6] Colijn, C., Mackey, M.:A mathematical model of hematopoiesis-I. Periodic chronic myelogenous leukemia. J. Theor. Biol. 237(2), 117-132 (2005)
[7] Colijn, C., Mackey, M.:A mathematical model of hematopoiesis:II. Cyclical neutropenia. J. Theor. Biol. 237(2), 133-146 (2005)
[8] Dale, D.C., Mackey, M.C.:Understanding, treating and avoiding hematological disease:better medicine through mathematics? Bull. Math. Biol. 77(5), 739-757 (2015)
[9] Denoth-Lippuner, A., Jaeger, B.N., Liang, T., Royall, L.N., Chie, S.E., Buthey, K., Machado, D., Korobeynyk, V.I., Kruse, M., Munz, C.M., Gerbaulet, A., Simons, B.D., Jessberger, S.:Visualization of individual cell division history in complex tissues using icount. Cell Stem Cell 28(11), 2020-2034 (2021)
[10] Foley, C., Mackey, M.C.:Dynamic hematological disease:a review. J. Math. Biol. 58(1), 285-322 (2009)
[11] Gupta, P.B., Fillmore, C.M., Jiang, G., Shapira, S.D., Tao, K., Kuperwasser, C., Lander, E.S.:Stochastic state transitions give rise to phenotypic equilibrium in populations of cancer cells. Cell 146(4), 633-644 (2010)
[12] Huang, R., Lei, J.:Dynamics of gene expression with positive feedback to histone modifications at bivalent domains. Int. J. Mod. Phys. B 4, 1850075 (2017)
[13] Huang, R., Lei, J.:Cell-type switches induced by stochastic histone modification inheritance. Discrete Contin. Dyn. Syst. Ser. B 22, 1-9 (2019)
[14] Lei, J.:A general mathematical framework for understanding the behavior of heterogeneous stem cell regeneration. J. Theor. Biol. 492, 110196 (2020)
[15] Lei, J.:Evolutionary dynamics of cancer:from epigenetic regulation to cell population dynamics-mathematical model framework, applications, and open problems. Sci. China Math. 63(3), 411-424 (2020)
[16] Lei, J., Levin, S.A., Nie, Q.:Mathematical model of adult stem cell regeneration with cross-talk between genetic and epigenetic regulation. Proc. Natl. Acad. Sci. USA 111, 880-887 (2014)
[17] Lei, J., Mackey, M.C.:Multistability in an age-structured model of hematopoiesis:cyclical neutropenia. J. Theor. Biol. 270(1), 143-153 (2011)
[18] Macaulay, I.C., Svensson, V., Labalette, C., Ferreira, L., Hamey, F., Voet, T., Teichmann, S.A., Cvejic, A.:Single-cell RNA-sequencing reveals a continuous spectrum of differentiation in hematopoietic cells. Cell Rep. 14(4), 1-13 (2016)
[19] Mackey, M.C.:Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. Blood 51(5), 941-956 (1978)
[20] Malta, T.M., Sokolov, A., Gentles, A.J., et al.:Machine learning identifies stemness features associated with oncogenic dedifferentiation. Cell 173, 338-354 (2008)
[21] Mohammad, H.P., Barbash, O., Creasy, C.L.:Targeting epigenetic modifications in cancer therapy:erasing the roadmap to cancer. Nat. Med. 25(3), 403-418 (2019)
[22] Nguyen, T.N., Clairambault, J., Jaffredo, T., Benoît Perthame, D.S.:Adaptive dynamics of hematopoietic stem cells and their supporting stroma:a model and mathematical analysis. Math. Biosci. Eng. 16(5), 4818-4845 (2019)
[23] Probst, A.V., Dunleavy, E., Almouzni, G.:Epigenetic inheritance during the cell cycle. Nat. Rev. Mol. Cell Biol. 10(3), 192-206 (2009)
[24] Quinn, J.J., Jones, M.G., Okimoto, R.A., Nanjo, S., Chan, M.M., Yosef, N., Bivona, T.G., Weissman, J.S.:Single-cell lineages reveal the rates, routes, and drivers of metastasis in cancer xenografts. Science 371(6532), eabc1944 (2021)
[25] Skrypek, N., Goossens, S., Smedt, E.D., Vandamme, N., Berx, G.:Epithelial-to-mesenchymal transition:epigenetic reprogramming driving cellular plasticity. TIG 33(12), 943-959 (2017)
[26] Souza, D.C.D., Humphries, A.R.:Dynamics of a mathematical hematopoietic stem-cell population model. SIAM J. Appl. Dyn. Syst. 18(2), 808-852 (2019)
[27] Su, Y., Wei, W., Robert, L., Xue, M., Tsoi, J., Garcia-Diaz, A., Moreno, B.H., Kim, J., Ng, R.H., Lee, J.W., Koya, R.C., Comin-Anduix, B., Graeber, T.G., Ribas, A., Heath, J.R.:Single-cell analysis resolves the cell state transition and signaling dynamics associated with melanoma drug-induced resistance. Proc. Natl. Acad. Sci. USA 114(52), 13679-13684 (2017)
[28] Wu, H., Zhang, Y.:Reversing DNA methylation:mechanisms, genomics, and biological functions. Cell 156(1/2), 45-68 (2014)
[29] Yang, J.-H., Hayano, M., Griffin, P.T., Amorim, J.A., Bonkowski, M.S., Apostolides, J.K., Salfati, E.L., Blanchette, M., Munding, E.M., Bhakta, M., Chew, Y.C., Guo, W., Yang, X., Maybury-Lewis, S., Tian, X., Ross, J.M., Coppotelli, G., Meer, M.V., Rogers-Hammond, R., Vera, D.L., Lu, Y.R., Pippin, J.W., Creswell, M.L., Dou, Z., Xu, C., Mitchell, S.J., Das, A., O'Connell, B.L., Thakur, S., Kane, A.E., Su, Q., Mohri, Y., Nishimura, E.K., Schaevitz, L., Garg, N., Balta, A.-M., Rego, M.A., Gregory-Ksander, M., Jakobs, T.C., Zhong, L., Wakimoto, H., El Andari, J., Grimm, D., Mostoslavsky, R., Wagers, A.J., Tsubota, K., Bonasera, S.J., Palmeira, C.M., Seidman, J.G., Seidman, C.E., Wolf, N.S., Kreiling, J.A., Sedivy, J.M., Murphy, G.F., Green, R.E., Garcia, B.A., Berger, S.L., Oberdoerffer, P., Shankland, S.J., Gladyshev, V.N., Ksander, B.R., Pfenning, A.R., Rajman, L.A., Sinclair, D.A.:Loss of epigenetic information as a cause of mammalian aging. Cell (2023). https://doi.org/10.1016/j.cell.2022.12.027
[30] Zhang, C., Shao, C., Jiao, X., Bai, Y., Li, M., Shi, H., Lei, J., Zhong, X.:Individual cell-based modeling of tumor cell plasticity-induced immune escape after CAR-T therapy. Comput. Syst. Oncol. 1(3), 21029 (2021)
[31] Zhuge, C., Mackey, M.C., Lei, J.:Origins of oscillation patterns in cyclical thrombocytopenia. J. Theor. Biol. 462, 432-445 (2019)