# Criticality in cell differentiation

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## Abstract

Cell differentiation is an important process in living organisms. Differentiation is mostly based on binary decisions with the progenitor cells choosing between two specific lineages. The differentiation dynamics have both deterministic and stochastic components. Several theoretical studies suggest that cell differentiation is a bifurcation phenomenon, well-known in dynamical systems theory. The bifurcation point has the character of a critical point with the system dynamics exhibiting specific features in its vicinity. These include the critical slowing down, rising variance and lag-1 autocorrelation function, strong correlations between the fluctuations of key variables and non-Gaussianity in the distribution of fluctuations. Recent experimental studies provide considerable support to the idea of criticality in cell differentiation and in other biological processes like the development of the fruit fly embryo. In this review, an elementary introduction is given to the concept of criticality in cell differentiation. The correspondence between the signatures of criticality and experimental observations on blood cell differentiation in mice is further highlighted.

## Keywords

Bifurcation cell differentiation criticality signatures of criticality stochasticity## Notes

### Acknowledgements

IB acknowledges the support by CSIR, India, vide sanction Lett. No. 21(0956)/13-EMR-II dated 28.04.2014. MP acknowledges the support from Bose Institute, India, for carrying out the study. The Authors thank Achintya Singha for his help in preparing the manuscript. Figures 1, 2 and 3 are reprinted with permission from the paper titled “Non-genetic heterogeneity, criticality and cell differentiation” by Pal M, Ghosh S and Bose I 2015 *Phys. Biol.* **12** 016001 (IOP, UK).

## References

- Alon U 2007
*An introduction to systems biology: design principles of biological circuits*(New York: Chapman and Hall/CRC)Google Scholar - Cahan P and Daley GQ 2013 Origins and implications of pluripotent stem cell variability and heterogeneity.
*Nat. Rev. Mol. Cell Biol*.**14**357–368CrossRefPubMedPubMedCentralGoogle Scholar - Chang HH, Hemberg M, Barahona M, Ingber DE and Huang S 2008 Transcriptome-wide noise controls lineage choice in mammalian progenitor cells.
*Nature***453**544–547CrossRefPubMedPubMedCentralGoogle Scholar - Dai L, Vorselen D, Korolev KS and Gore J 2012 Generic indicators for loss of resilience before a tipping point leading to population collapse.
*Science***336**1175–1177CrossRefPubMedGoogle Scholar - Enver T, Pera M, Peterson C and Andrews PW 2009 Stem cell states, fates and the rules of attraction.
*Cell Stem Cell***4**387–397CrossRefPubMedGoogle Scholar - Erez A, Byrd TA, Vogel RM Altan-Bonnet G and Mugler A 2017 Criticality of biochemical feedback. arXiv: 1703.04194 v1 [physics. bio-ph]Google Scholar
- Ferrell JE 2012 Bistability, bifurcations and Waddington’s epigenetic landscape.
*Curr. Biol*.**22**R458–R466CrossRefPubMedPubMedCentralGoogle Scholar - Foster DV, Foster JG, Huang S and Kauffman SA 2009 A model of sequential branching in hierarchical cell fate determination.
*J. Theoret. Biol.***260**589–597CrossRefGoogle Scholar - Fox RF, Gatland IR, Roy R and Vemuri G 1988 Fast, accurate algorithm for numerical simulation of exponentially correlated coloured noise.
*Phys. Rev. A***38**5938–5940CrossRefGoogle Scholar - Furusawa C and Kaneko K 2012 A dynamical-systems view of stem cell biology.
*Science***338**215–217CrossRefPubMedGoogle Scholar - Garcia-Ojalvo J and Arias AM 2012 Towards a statistical mechanics of cell-fate decisions.
*Curr. Opin. Genet. Dev*.**22**619–626CrossRefPubMedGoogle Scholar - Gros C 2008
*Complex adaptive dynamical systems; a primer*(New York: Springer)CrossRefGoogle Scholar - Goldenfeld N 1992
*Lectures on phase transitions and the renormalization group*(Reading, MA: Addison-Wesley)Google Scholar - Heinäniemi M
*et al.*2013 Gene-pair expression signatures reveal lineage control.*Nat. Method*.**10**577CrossRefGoogle Scholar - Hidalgo J, Grilli J, Suweis S, Muñoz MA, Banavar JR and Maritan A 2014 Information-based fitness and the emergence of criticality in living systems.
*Proc. Natl. Acad. Sci. USA***111**10095–10100CrossRefPubMedPubMedCentralGoogle Scholar - Huang S, Eichler G, Bar-Yam Y and Ingber DE 2005 Cell fates as high-dimensional attractor states of a complex gene regulatory network.
*Phys. Rev. Lett*.**94**128701CrossRefPubMedGoogle Scholar - Huang S 2009a Reprogramming cell fates: reconciling rarity with robustness.
*BioEssays***31**546–560CrossRefPubMedGoogle Scholar - Huang S 2009b Non-genetic heterogeneity of cells in development: more than just noise.
*Development***136**3853–3862CrossRefPubMedPubMedCentralGoogle Scholar - Jaynes ET 1957 Information theory and statistical mechanics.
*Phys. Rev*.**106**620–630CrossRefGoogle Scholar - Kærn M, Elston TC, Blake WJ and Collins JJ 2005 Stochasticity in gene expression: from theories to phenotypes.
*Nat. Rev. Genet*.**6**451–464CrossRefPubMedGoogle Scholar - Kauffman SA 1993
*The origins of order: Self-organization and selection in evolution*(New York: Oxford University Press)Google Scholar - Kaufmann BB and van Oudenaarden A 2007 Stochastic gene expression: from single molecules to the proteome.
*Curr. Opin. Genet. Dev*.**17**107–112CrossRefPubMedGoogle Scholar - Krotov D, Dubuis JO, Gregor T and Bialek W 2014 Morphogenesis at criticality.
*Proc. Natl. Acad. Sci. USA***111**3683–3688CrossRefPubMedPubMedCentralGoogle Scholar - MacArthur BD, Ma’ayan A and Lemischka IR 2009 Systems biology of stem cell fate and cell reprogramming.
*Nat. Rev. Mol. Cell Biol.***10**672–681PubMedPubMedCentralGoogle Scholar - MacArthur BD and Lemischka IR 2013 Statistical mechanics of pluripotency.
*Cell***154**484–489CrossRefPubMedGoogle Scholar - Martinez Arias A and Brickman JM 2011 Gene expression heterogeneities in embryonic stem cell populations: origin and function.
*Curr. Opin. Cell Biol*.**23**1–7CrossRefGoogle Scholar - Mojtahedi M
*et al.*2016 Cell fate decision as high-dimensional critical state transition.*PLoS Biol*.**14**e2000640CrossRefPubMedPubMedCentralGoogle Scholar - Monod J and Jacob F 1961 Teleonomic mechanisms in cellular metabolism, growth and differentiation.
*Cold Spring Harb. Symp. Quant. Biol*.**26**389–401CrossRefPubMedGoogle Scholar - Mora T and Bialek W 2011 Are biological systems poised at criticality?
*J. Stat. Phys*.**144**268–302CrossRefGoogle Scholar - Moris N, Pina C and Arias AM 2016 Transition states and cell fate transitions in epigenetic landscapes.
*Nat. Rev. Genet*.**17**693–703CrossRefPubMedGoogle Scholar - Pal M, Pal AK, Ghosh S and Bose I 2013 Early signatures of regime shifts in gene expression dynamics.
*Phys. Biol*.**10**036010CrossRefPubMedGoogle Scholar - Pal M, Ghosh S and Bose I 2015 Non-genetic heterogeneity, criticality and cell differentiation.
*Phys. Biol*.**12**016001CrossRefGoogle Scholar - Peláez N
*et al.*2015 Dynamics and heterogeneity of a fate determinant during transition towards cell differentiation.*eLife***4**e08924Google Scholar - Podolskiy D
*et al.*2015 Critical dynamics of gene networks is a mechanism behind ageing and Gompertz law arXiv: 1502.04307 v1 [q-bio.MN]Google Scholar - Pomerening JR 2008 Uncovering mechanisms of bistability in biological systems. Curr. Opin. Biotechnol.
**19**381–388CrossRefPubMedGoogle Scholar - Raj A and van Oudenaarden A 2008 Nature, nurture or chance: stochastic gene expression and its consequences.
*Cell***135**216–226CrossRefPubMedPubMedCentralGoogle Scholar - Raj A and van Oudenaarden A 2009 Single-molecule approaches to stochastic gene expression.
*Ann. Rev. Biophys*.**38**255–270CrossRefGoogle Scholar - Richard A
*et al.*2016 Single-cell-based analysis highlights a surge in cell-to-cell molecular variability preceding irreversible commitment in a differentiation process.*PLoS Biol*.**14**e1002585CrossRefPubMedPubMedCentralGoogle Scholar - Ridden SJ, Chang HH, Zygalakis KC and MacArthur BD 2015 Entropy, ergodicity and stem cell multipotency.
*Phys. Rev. Lett*.**115**208103CrossRefPubMedGoogle Scholar - Rouault H and Hakim V 2012 Different cell fates from cell-cell interactions: core architectures of two-cell bistable networks.
*Biophys. J.***102**417–426CrossRefPubMedPubMedCentralGoogle Scholar - Scheffer M
*et al.*2009 Early-warning signals for critical transitions.*Nature***461**53–59CrossRefPubMedGoogle Scholar - Scheffer M
*et al.*2012 Anticipating critical transitions.*Science***338**344–348CrossRefPubMedGoogle Scholar - Semrau S and van Oudenaarden A 2015 Studying lineage decision-making in vitro: emerging concepts and novel tools.
*Annu. Rev. Cell Dev. Biol*.**31**317–345CrossRefPubMedGoogle Scholar - Sha W
*et al.*2003 Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts.*Proc. Natl. Acad. Sci.***100**975–980CrossRefPubMedGoogle Scholar - Strogatz SH 1994
*Nonlinear dynamics and chaos: With applications to physics, biology, chemistry and engineering*(Reading, MA: Addison-Wesley)Google Scholar - Thomas R 1978 Logical analysis of systems comprising feedback loops.
*J. Theor. Biol*.**73**631–656CrossRefPubMedGoogle Scholar - Torres-Padilla M-E and Chambers I 2014 Transcription factor heterogeneity in pluripotent stem cells: a stochastic advantage.
*Development***141**2173–2181CrossRefPubMedGoogle Scholar - Valverde S, Ohse S, Turalska M, West BJ and Garcia-Ojalvo J 2015 Structural determinants of criticality in biological networks.
*Front. Physiol*.**6**127CrossRefPubMedPubMedCentralGoogle Scholar - van Kampen NG 1992
*Stochastic processes in physics and chemistry*(Amsterdam: Elsevier)Google Scholar - Veraart AJ, Faassen EJ, Dakos V, van Nes EH, Lüring M and Scheffer M 2012 Recovery rates reflect distance to a tipping point in a living system.
*Nature***481**357–359Google Scholar - Wang J, Xu L, Wang E and Huang S 2010 The potential landscape of genetic circuits imposes the arrow of time in stem cell differentiation.
*Biophys.*J.**99**29–39CrossRefPubMedPubMedCentralGoogle Scholar - Weinberger LS, Dar RD and Simpsn ML 2008 Transient-mediated fate determination in a transcriptional circuit of HIV.
*Nat. Genet.***40**466–470CrossRefPubMedGoogle Scholar - Zhou JX and Huang S 2011 Understanding gene circuits at cell-fate branch points for rational cell reprogramming.
*Trends Genet*.**27**55–62CrossRefPubMedGoogle Scholar - Zhou JX, Aliyu MDS, Aurell E and Huang SJ 2012 Quasi-potential landscape in complex multi-stable systems.
*R. Soc. Interface***9**3539–3553CrossRefPubMedGoogle Scholar