Mathematical modeling of cell-fate specification: From simple to complex epigenetics

Jomar Fajardo Rabajante, Ariel Lagdameo Babierra, Jerrold Maranan Tubay, Editha Carreon Jose


Modern biology will never be the same without mathematical and computational tools. Using mind map with “epigenetics” as the root, we discuss the current advancement in the field of biomathematics for modeling cell-fate specification. In the discussions, we also present possible directions for future research.

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Bruin JE, Saber N, Braun N, Fox JK, Mojibian M, Asadi A et al. Treating diet-induced diabetes and obesity with human embryonic stem cell-derived pancreatic progenitor cells and antidiabetic drugs. Stem Cell Reports 2015; 4:1-16.

Baxter E, Windloch K, Gannon F, Lee JS. Epigenetic regulation in cancer progression. Cell & Bioscience 2014; 4:45.

Benitah SA, Bracken A, Dou Y, Huangfu D, Ivanova N, Koseki H et al. Stem cell epigenetics: looking forward. Cell Stem Cell 2014; 14:706-209.

David L, Polo JM. Phases of reprogramming. Stem Cell Res 2014; 12(3):754-761.

Ogliari KS, Brum DE, Marinowic D, Loth F. Stem cells in dermatology. An Bras Dermatol 2014; 89(2):286-291.

Tonge PD, Corso AJ, Monetti C, Hussein SM, Puri MC, Michael IP et al. Divergent reprogramming routes lead to alternative stem-cell states. Nature 2014; 516:192-197.

Buganim Y, Faddah DA, Jaenisch R. Mechanisms and models of somatic cell reprogramming. Nat Rev Genet 2013; 14:427-439.

Reece JB, Urry LA, Cain ML, Wasserman SA, Minorsky PV, Jackson RB. Campbell Biology. 10th Edition. San Francisco: Pearson Benjamin Cummings; 2013.

Eguizabal C, Montserrat N, Veiga A, Belmonte JCI. Dedifferentiation, transdifferentiation, and reprogramming: future directions in regenerative medicine. Semin Reprod Med 2013; 31(1):82-94.

Harding J, Roberts RM, Mirochnitchenko O. Large animal models for stem cell therapy. Stem Cell Res Ther 2013; 4:23.

Malik N, Rao MS. A review of the methods for human iPSC derivation. Methods Mol Biol 2013; 997:23-33.

Feil R, Fraga MF. Epigenetics and the environment: emerging patterns and implications. Nat Rev Genet 2012; 13:97-109.

Yamanaka S. Induced pluripotent stem cells: past, present, and future. Cell Stem Cell 2012; 10:678-684.

Gupta PK, Das AK, Chullikana A, Majumdar AS. Mesenchymal stem cells for cartilage repair in osteoarthritis. Stem Cell Res Ther 2012; 3:25.

Balazsi G, van Oudenaarden A, Collins JJ. Cellular decision making and biological noise: from microbes to mammals. Cell 2011; 144:910-925.

Fortier LA, Travis AJ. Stem cells in veterinary medicine. Stem Cell Res Ther 2011; 2:9.

Zhou JX, Huang, S. Understanding gene circuits at cell-fate branch points for rational cell reprogramming. Trends Genet 2011; 27(2):55-62.

Christen B, Robles V, Raya M, Paramanov I, Belmonte JCI. Regeneration and reprogramming compared. BMC Biology 2010; 8:5.

Dantuma E, Merchant S, Sugaya K. Stem cells for the treatment of neurodegenerative diseases. Stem Cell Res Ther 2010; 1:37.

Hanna JH, Saha K, Jaenisch R. Pluripotency and cellular reprogramming: facts, hypotheses, unresolved issues. Cell 2010; 143:508-525.

Pera MF, Tam PPL. Extrinsic regulation of pluripotent stem cells. Nature 2010; 465:713–720.

Weake VM, Workman JL. Inducible gene expression: diverse regulatory mechanisms. Nat Rev Genet 2010; 11(6):426-437.

Enver T, Pera M, Peterson C, Andrews PW. Stem cell states, fates and the rules of attraction. Cell Stem Cell 2009; 4:387-397.

Nadig RR. Stem cell therapy – hype or hope? A review. J Conserv Dent 2009; 12(4):131-138.

Yamanaka S. Elite and stochastic models for induced pluripotent stem cell generation. Nature 2009; 460:49-52.

Magnus T, Liu Y, Parker GC, Rao MS. Stem cell myths. Phil Trans R Soc B 2008; 363:9-22.

Takahashi K, Yamanaka S. Induction of pluripotent stem cells from mouse embryonic and adult fibroblast cultures by defined factors. Cell 2006; 126:663-676.

Stocum DL. Amphibian Regeneration and Stem Cells. In Regeneration: Stem Cells and Beyond. Current Topics in Microbiology and Immunology Volume 280. 1st Edition. Edited by Heber-Katz E. Berlin/Heidelberg: Springer; 2004:1-70.

Giles KL. Dedifferentiation and regeneration in bryophytes: A selective review. New Zeal J Bot 1971; 9:689-694.

The National Academies. Understanding Stem Cells: An Overview of the Science and Issues from the National Academies []

Waddington CH. The Strategy of the Genes. London: George Allen & Unwin; 1957.

Rabajante JF, Babierra AL. Branching and oscillations in the epigenetic landscape of cell-fate determination. Prog Biophys Mol Biol 2015; doi: 10.1016/j.pbiomolbio.2015.01.006.

Li C, Wang J. Quantifying the underlying landscape and paths of cancer. J R Soc Interface 2014; 11:20140774.

Banerji CR, Miranda-Saavedra D, Severini S, Widschwendter M, Enver T, Zhou JX et al. Cellular network entropy as the energy potential in Waddington’s differentiation landscape. Sci. Rep. 2013; 3:3039.

Ladewig J, Koch P, Brüstle O. Leveling Waddington: the emergence of direct programming and the loss of cell fate hierarchies. Nat Rev Mol Cell Biol 2013; 14:225-236.

Li C, Wang J. Quantifying Waddington landscapes and paths of non-adiabatic cell fate decisions for differentiation, reprogramming and transdifferentiation. J R Soc Interface 2013; 10(89):20130787.

Ferrell JE Jr. Bistability, bifurcations, and Waddington’s epigenetic landscape. Curr Biol 2012; 22(11):R458-R466.

Li M, Liu G-H, Belmonte JCI. Navigating the epigenetic landscape of pluripotent stem cells. Nat Rev Mol Cell Biol 2012; 13:524-535.

Pujadas E, Feinberg AP. Regulated noise in the epigenetic landscape of development and disease. Cell 2012; 148(6):1123-1131.

Takahashi K. Cellular reprogramming – lowering gravity on Waddington’s epigenetic landscape. J Cell Sci 2012; 125(11):2553-2560.

Bhattacharya S, Zhang Q, Andersen ME. A deterministic map of Waddington’s epigenetic landscape for cell fate specification. BMC Syst Biol 2011; 5:85.

Huang S. The molecular and mathematical basis of Waddington’s epigenetic landscape: A framework for post-Darwinian biology? Bioessays 2011; 34:149–157.

Wang J, Zhang K, Xu L, Wang E. Quantifying the Waddington landscape and biological paths for development and differentiation. Proc Natl Acad Sci USA 2011; 108(20):8257-8262.

Wang J, Xu L, Wang E, Huang S. The potential landscape of genetic circuits imposes the arrow of time in stem cell differentiation. Biophys J 2010; 99(1):29-39.

Wang P, Song C, Zhang H, Wu Z, Tian XJ, Xing J. Epigenetic state network approach for describing cell phenotypic transitions. Interface Focus 2014; 4(3):20130068.

Wolkenhauer O. Why model? Front Physiol. 2014; 5:21.

Bernot B, Comet JP, Richard A, Chaves M, Gouze JL, Dayan F. Modeling and Analysis of Gene Regulatory Networks. In Modeling and Computational Biology and Biomedicine: A Multidisciplinary Endeavor. Volume 28. 1st Edition. Edited by Cazals F, Kornprobst P. Heidelberg: Springer-Verlag; 2013:47-80.

Creixell P, Schoof EM, Erler JT, Linding R. Navigating cancer network attractors for tumor-specific therapy. Nat Biotechnol 2012; 30:842-848.

Voit EO. A First Course in Systems Biology. New York: Garland Science; 2012.

Huang S. Systems biology of stem cells: three useful perspectives to help overcome the paradigm of linear pathways. Phil Trans R Soc B 2011; 366:2247–2259.

Radde N. The role of feedback mechanisms in biological network models. Asian J Control 2011; 13(5):597-610.

Lim SJ, Tan TW, Tong JC. Computational Epigenetics: the new scientific paradigm. Bioinformation 2010; 4(7):331-337.

Liu E, Lauffenburger D (Eds). Systems Biomedicine: Concepts and Perspectives. Massachusetts: Academic Press; 2009.

Shmulevich I, Aitchison JD. Deterministic and Stochastic Models of Genetic Regulatory Networks. In Methods in Enzymology. Volume 467. 1st Edition. Edited by Johnson ML, Brand L. Amsterdam: Elsevier BV; 2009:335-356.

McArthur BD, Ma’ayan A, Lemischka IR. Systems biology of stem cell fate and cellular reprogramming. Nat Rev Mol Cell Biol 2009; 10:672-681.

Tracik G, Bialek W. Cell Biology: Networks, Regulation and Pathways. In Encyclopedia of Complexity and Systems Science. Edited by Meyers RA. New York: Springer; 2009:719-741.

Aguda BD, Friedman A. Models of Cellular Regulation. New York: Oxford Univ. Press; 2008.

Bock C, Lengauer T. Computational epigenetics. Bioinformatics 2008; 24(1):1-10.

Voit EO, Qi Z, Miller GW. Steps of modeling complex biological systems. Pharmacopsychiatry 2008; 41(Suppl 1):S78– S84

Schlitt T, Brazma A. Current approaches to gene regulatory network modelling. BMC Bioinformatics 2007; 8(Suppl 6):S9.

Rabajante JF, Talaue CO. Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation. Chaos Soliton Fract 2015; 73:166–182.

Anink-Groenen LCM, Maarleveld TR, Verschure PJ, Bruggeman FJ. Mechanistic stochastic model of histone modification pattern formation. Epigenet Chromatin 2014; 7:30.

Bogdan P, Deasy BM, Gharaibeh B, Roehrs T, Marculescu R. Heterogeneous structure of stem cells dynamics: statistical models and quantitative predictions. Sci Rep 2014; 4:4826.

Chung KM, Kolling FW 4th, Gajdosik MD, Burger S, Russell AC, Nelson CE. Single Cell Analysis Reveals the Stochastic Phase of Reprogramming to Pluripotency Is an Ordered Probabilistic Process. PLoS ONE 2014; 9(4): e95304.

El Baroudi M, La Sala D, Cinti C, Capobianco E. Pathway landscapes and epigenetic regulation in breast cancer and melanoma cell lines. Theor Biol Med Model 2014; 11(1):S8.

Huether R, Dong L, Chen X, Wu G, Parker M, Wei L et al. The landscape of somatic mutations in epigenetic regulators across 1,000 pediatric cancer genomes. Nat Commun 2014; 5:3630.

Lang AH, Li H, Collins JJ, Mehta P. Epigenetic Landscapes Explain Partially Reprogrammed Cells and Identify Key Reprogramming Genes. PLoS Comput Biol 2014; 10(8):e1003734.

Morris R, Sancho-Martinez I, Sharpee TO, Izpisua Belmonte JC. Mathematical approaches to modeling development and reprogramming. Proc Natl Acad Sci USA 2014; 111(14):5076–5082.

Nikolov S, Wolkenhauer O, Vera J. Tumors as chaotic attractors. Mol Biosyst 2014; 10:172-179.

Przybilla J, Rohlf T, Loeffler M, Galle J. Understanding epigenetic changes in aging stem cells – a computational model approach. Aging Cell 2014; 13:320-328.

Shi SH, Cai YP, Cai XJ, Zheng XY, Cao DS, Ye FQ et al. A Network Pharmacology Approach to Understanding the Mechanisms of Action of Traditional Medicine: Bushenhuoxue Formula for Treatment of Chronic Kidney Disease. PLoS ONE 2014; 9(3):e89123.

Verd B, Crombach A, Jaeger J. Classification of transient behaviours in a time-dependent toggle switch model. BMC Syst Biol 2014; 8:43.

Foster DV, Rorick MM, Gesell T, Feeney LM, Foster JG. Dynamic landscapes: A model of context and contingency in evolution. J Theor Biol 2013; 334:162-172.

Huang S, Kauffman S. How to escape the cancer attractor: Rationale and limitations of multi-target drugs. Semin Cancer Biol 2013; 23:270-278.

Sasai M, Kawabata Y, Makishi K, Itoh K, Terada TP. Time scales in epigenetic dynamics and phenotypic heterogeneity of embryonic stem cells. PLoS Comput Biol 2013; 9(12):e1003380.

Teles J, Pina C, Edén P, Ohlsson M, Enver T, Peterson C. Transcriptional regulation of lineage commitment – a stochastic model of cell fate decisions. PLoS Comput Biol 2013; 9(8):e1003197.

Wu M, Su RQ, Li X, Ellis T, Lai YC, Wang X. Engineering of regulated stochastic cell fate determination. Proc Natl Acad Sci USA 2013; 110(26):10610-10615.

Flöttmann M, Scharp T, Klipp E. A stochastic model of epigenetic dynamics in somatic cell reprogramming. Front Physiol 2012; 3:216.

Kim KH, Sauro HM. Adjusting phenotype by noise control. PLoS Comput Biol 2012; 8(1):e1002344.

Nené NR, Zaikin A. Interplay between path and speed in decision making by high-dimensional stochastic gene regulatory networks. PLoS ONE 2012; 7(7):e40085.

Andrecut M, Halley JD, Winkler DA, Huang S. A general model for binary cell fate decision gene circuits with degeneracy: indeterminacy and switch behavior in the absence of cooperativity. PLoS ONE 2011; 6(5):e19358.

Suzuki N, Furusawa C, Kaneko K. Oscillatory protein expression dynamics endows stem cells with robust differentiation potential. PLoS ONE 2011; 6(11):e27232.

Nordon RE, Ko KH, Odell R, Schroeder T. Multi-type branching models to describe cell differentiation programs. J Theor Biol 2011; 277:7-18.

Zhang L, Zheng Y, Li D, Zhong Y. Self-organizing map of gene regulatory networks for cell phenotypes during reprogramming. Comput Biol Chem 2011; 35:211–217.

Gonze D. Coupling oscillations and switches in genetic networks. BioSystems 2010; 99:60–69.

Graham TGW, Tabei SMA, Dinner AR, Rebay I. Modeling bistable cell-fate choices in the Drosophila eye: qualitative and quantitative perspectives. Development 2010; 137:2265-78.

Huang S. Cell Lineage Determination in State Space: A Systems View Brings Flexibility to Dogmatic Canonical Rules. PLoS Biol 2010; 8(5):e1000380.

Ito Y, Uchida K. Formulas for intrinsic noise evaluation in oscillatory genetic networks. . J Theor Biol 2010; 267:223–234.

Micheelsen MA, Mitarai N, Sneppen K, Dodd IB. Theory for stability and regulation of epigenetic landscapes. Phys Biol 2010; 7:026010.

Zhdanov VP. Periodic perturbation of the bistable kinetics of gene expression. Phys A 2010; 390(1):57-64.

Foster DV, Foster JG, Huang S, Kauffman SA. A model of sequential branching in hierarchical cell fate determination. J Theor Biol 2009; 260(4):589-597.

Furusawa C, Kaneko K. Chaotic expression dynamics implies pluripotency: when theory and experiment meet. Biol Direct 2009 4:17.

Huang S. Reprogramming cell fates: reconciling rarity with robustness. Bioessays 2009; 31:546–560.

Huang S, Ernberg I, Kauffman S. Cancer attractors: A systems view of tumors from a gene network dynamics and developmental perspective. Semin Cell Dev Biol 2009; 20(7):869-876.

Alvarez-Buylla ER, Chaos A, Aldana M, Benítez M, Cortes-Poza Y, Espinosa-Soto C et al. Floral Morphogenesis: Stochastic Explorations of a Gene Network Epigenetic Landscape. PLoS ONE 2008; 3(11):e3626.

Andrecut M, Cloud D, Kauffman SA. Monte Carlo simulation of a simple gene network yields new evolutionary insights. J Theor Biol 2008; 250:468-474.

MacArthur BD, Please CP, Oreffo ROC. Stochasticity and the molecular mechanisms of induced pluripotency. PLoS ONE 2008; 3(8):e3086.

Ribeiro A, Kauffman SA. Noisy attractors and ergodic sets in models of gene regulatory networks. J Theor Biol 2007; 247:743-755.

Huang S, Eichler G, Bar-Yam Y, Ingber DE. Cell fates as high-dimensional attractor states of a complex gene regulatory network. Phys Rev Lett 2005; 94:128701.

Ledford H. Language: Disputed definitions. Nature 2008; 455:1023-1028.

The Nobel Prize in Physiology or Medicine 2012 Press Release []

The Japan Times: Haruko Obokata []

Hughes V. Epigenetics: The sins of the father. The roots of inheritance may extend beyond the genome, but the mechanisms remain a puzzle []

Institute for Systems Biology, Sui Huang group []



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