Introduction to Differentiation Waves

Richard Gordon,
Gulf Specimen Marine Laboratory
Presented in the Embryo Physics Course, January 9, 2013


A cytoskeletal structure (the cell state splitter) at the apical end of epithelial cells, that we predicted [1] and observed [2], may be set up in a metastable state and explain the binary nature of cell differentiations due to its predicted bistability. A differentiation wave is a propagation of expansion or contraction of a cell’s cell state splitter to cell state splitters in adjacent cells. For example, a contraction differentiation wave was predicted in 1985 [1] as being what conveys planar induction of the neural plate in urodele amphibians (salamanders and newts) from cell to cell in the ectoderm. This wave was found in axolotl embryos in 1990 [3, 4], and proved easy to observe [5]. Signal transduction from the cell state splitter to the nucleus need only involve transmission of one bit of information: whether the cell has just participated in a contraction (0) or expansion (1) differentiation wave. The signal presumably triggers one of two gene cascades, depending on whether the wave was a contraction or an expansion wave, changing the cell’s phenotype. The history of bits for a given cell is its differentiation code [6]. Numerous other paired expansion and contraction waves with complementary trajectories, that correlate with classically defined steps of differentiation [6, 7], suggest that the “genetic program” for embryogenesis consists of a bifurcating alternation of differentiation waves and specific gene expression triggered by the waves. The genetic program can be represented as a bifurcating differentiation tree, in which the differentiation waves become the modules of development [8]. The nucleus is postulated to be a finite state machine that responds to the signal from the cell state splitter by changing its configuration to one of two new accessible states. A ratcheting mechanism would prevent return to a previous state. This can be approximated by a toy model, the Wurfel [9]. Mosaic development can be addressed by postulating single cell differentiation waves  [4]. Application of these concepts to the origin [10] and differentiation [11, 12] of stem cells will be left for Lu Kai’s talk. Differentiation waves provide a working model for solving “…the grand problem of biology, how out of a single cell arises the complex multicellular organism” [13]. Outstanding problems include the mechanisms for triggering and halting differentiation waves [4, 14], the relationships of differentiation waves to the mechanics of embryogenesis [14], to birth defects [15], to molecular developmental biology [4], to the logical, chromosomal and synteny organization of the genome [4], to tissue-specific drug development, and to macroevolution, microevolution and progressive evolution [4]. The origin of differentiation waves may be interwoven with the origin of life [16].


1.       Gordon, R.; Brodland, G.W. The cytoskeletal mechanics of brain morphogenesis. Cell state splitters cause primary neural induction. Cell Biophys 1987, 11, 177-238.
2.       Martin, C.C.; Gordon, R. Ultrastructural analysis of the cell state splitter in ectoderm cells differentiating to neural plate and epidermis during gastrulation in embryos of the axolotl Ambystoma mexicanum. Russian J. Dev. Biol. 1997, 28, 71-80.
3.       Brodland, G.W.; Gordon, R.; Scott, M.J.; Björklund, N.K.; Luchka, K.B.; Martin, C.C.; Matuga, C.; Globus, M.; Vethamany-Globus, S.; Shu, D. Furrowing surface contraction wave coincident with primary neural induction in amphibian embryos. J. Morphol. 1994, 219, 131-142.
4.       Gordon, R. The Hierarchical Genome and Differentiation Waves: Novel Unification of Development, Genetics and Evolution; World Scientific & Imperial College Press: Singapore & London, 1999.
5.       Gordon, R.; Björklund, N.K. How to observe surface contraction waves on axolotl embryos. Int J Dev Biol 1996, 40, 913-914.
6.       Björklund, N.K.; Gordon, R. Surface contraction and expansion waves correlated with differentiation in axolotl embryos. I. Prolegomenon and differentiation during the plunge through the blastopore, as shown by the fate map. Computers & Chemistry 1994, 18, 333-345.
7.       Gordon, R.; Björklund, N.K.; Nieuwkoop, P.D. Dialogue on embryonic induction and differentiation waves. International Review of Cytology 1994, 150, 373-420.
8.       Gordon, R. Walking the tightrope: the dilemmas of hierarchical instabilities in Turing’s morphogenesis [invited]. In The Once and Future Turing – Computing the World; Cooper, S. B.; Hodges, A., Eds.; Cambridge University Press: 2012; in press.
9.       Tromp, J.T.; Gordon, R. The number of 3D configurations of a labeled size 2*n “Wurfel” [A117613: The On-Line Encyclopedia of Integer Sequences]. Available online:
10.     Gordon, R. Epilogue: the diseased breast lobe in the context of X-chromosome inactivation and differentiation waves. In Breast Cancer: A Lobar Disease; Tot, T., Ed. Springer: London, 2011; pp. 205-210.
11.     Lu, K.; Gordon, R.; Cao, T. Embryonic stem cell morphogenesis: a pathway to in vitro organogenesis? Journal of Tissue Engineering and Regenerative Medicine 2012, in press.
12.     Lu, K.; Tong, C.; Gordon, R. A cell state splitter and differentiation wave working-model for embryonic stem cell development and somatic cell epigenetic reprogramming. BioSystems 2012, 109, 390-396.
13.     Just, E.E. The Biology of the Cell Surface; Blakiston: Philadelphia, 1939.
14.     Fleury, V.; Gordon, R. Coupling of growth, differentiation and morphogenesis: an integrated approach to design in embryogenesis. In Origin(s) of Design in Nature: A Fresh, Interdisciplinary Look at How Design Emerges in Complex Systems, Especially Life; Swan, L.; Gordon, R.; Seckbach, J., Eds.; Springer: Dordrecht, 2012; pp. 385-428.
15.     Björklund, N.K.; Gordon, R. A hypothesis linking low folate intake to neural tube defects due to failure of post-translation methylations of the cytoskeleton. Int. J. Dev. Biol. 2006, 50, 135-141.
16.     Gordon, N.K.; Gordon, R. Embryogenesis Explained [in preparation]; World Scientific Publishing Company: Singapore, 2013.






Richard Gordon, A Tale of Two Papers
Richard Gordon, University of Manitoba & Gulf Specimen Marine Laboratory, Walking the tightrope: The dilemmas of hierarchical instabilities in Turing’s morphogenesis
Dick Gordon, Cause and Effect in the Interaction between Embryogenesis and the Genome

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