Elsevier

Biosystems

Volume 184, October 2019, 104013
Biosystems

The differentiation code

https://doi.org/10.1016/j.biosystems.2019.104013Get rights and content

Abstract

In code biology we seek a presumably arbitrary, and thus symbolic relationship between two or more entities, such as the relationship of the DNA triplet code to amino acids. Here we review the differentiation code from the code biology point of view. We observe that lineage trees of mosaic organisms can be subsumed as special cases of differentiation trees of regulating embryos. The latter can be empirically discovered as a bifurcating tree of contraction and expansion differentiation waves that recursively divide the embryo into its cell types. A binary digit, 0 or 1, assigned to each wave results in a binary number corresponding to each cell type, and may be called the differentiation code for that cell type. The differentiation tree has a correspondence in the genome, in terms of the genome’s logical structure. For a given cell type, the path to it from the zygote is marked epigenetically on the genome. Thus the differentiation code symbolically maps an epigenetically marked subset of the logical structure of the genome to the phenotype of a particular cell type. The waves involved and signal transduction from the cell state splitter to the genome are intermediaries in this relationship, and may also be arbitrary choices, and thus part of the code. In full, differentiation code ⇔ history along the differentiation tree of the differentiation wave types leading to a given cell type ⇔ contraction or expansion of the cell’s cell state splitter ⇔ activation of one of two signal transduction pathways from the cell state splitter to the nucleus ⇔ activation of one of two readied gene cascades (the “nuclear state splitter”) ⇔ epigenetic marking of the selected portion of the logical path. Each wave is in effect a cybernetic control system that results in differentiation of a set of cells and initiation of two new waves (cybernetic systems) as its goals. The differentiation code forms a basis for open evolution and its appearance was one of the major evolutionary transitions.

Introduction

It is generally possible to position each cell in a multicellular organism as a node on a cell lineage tree (except for syncytial cells such as muscle (Deng et al., 2017)). Below each node (cell) are its cellular ancestors, all deriving ultimately from a single cell, such as a fertilized egg. Above are all of its descendants, up to terminally differentiated cells and adult stem cells. The vertical scale is developmental time, which may vary with temperature. For mosaic organisms the lineage tree is usually the same for all individuals with the same genome (Fig. 1). For regulating embryos, it is anticipated that lineage trees should vary stochastically, as they obviously do for so-called “identical” twins and other clones (Casler, 1967). A few lineage trees have been constructed from direct (Bao et al., 2006; Nishida and Stach, 2014; Sulston et al., 1983) or indirect (Plass et al., 2018) observations. There is much to be learned from the analysis of lineage trees (Alicea and Gordon, 2016, 2018; Alicea et al., 2018a).

For regulating embryos we have proposed a specific kind of event, participation of a cell in a contraction or expansion differentiation wave, as the very first event triggering differentiation of a cell to a new cell type (Gordon and Gordon, 2016a; Gordon, 1999). At each step of differentiation we add one bit of information to the differentiation code: 0 = contraction wave, 1 = expansion wave (Fig. 2). This mechanochemical based model for cell differentiation was first proposed in 1985 and published by Gordon and Brodland (1987). The model uses the mechanically sensitive bistable organelle made of microtubules and microfilaments that occurs in the apical ends of cells within cell sheets when they are ready to differentiate. We call it the cell state splitter (Björklund and Gordon, 2006; Gordon and Gordon, 2016b) (Fig. 3). These cells are under mechanical tension with the microtubule mat and microfilament ring in radial mechanical opposition, metastabilized by a microfilament ring (Martin and Gordon, 1997). Depending on where the cell is within a sheet of cells and thus which wave traverses it, the tension is resolved by its apical end either contracting or expanding. Any so-called “organizer” is a place where a small subset of cells launches a contraction or expansion wave. This subsumes the classical embryological concept of an “inducer” (Gordon, 1999).

Once a wave begins, the contraction or expansion wave, which is visible in time-lapse microscopy (Gordon and Björklund, 1996), is propagated to adjacent cells. Termination of wave propagation may be caused by mechanical forces at boundaries or by the propagating signal reaching cells that do not have their bistable cell state splitter ready to respond. The first physical wave of contraction, predicted in Gordon and Brodland (1987), was found in 1990 (Fig. 59 in (Gordon, 1999); (Brodland et al., 1994)). It traverses the presumptive neural epithelium of the developing salamander, the axolotl (Ambystoma mexicanum). Additional waves were then discovered (Gordon et al., 1994), although not in the South African clawed toad Xenopus laevis, perhaps due to an overlying superficial epithelium (Nieuwkoop et al., 1996). The trajectory of each wave corresponds to differentiation of a different classically defined embryonic tissue (Gordon et al., 1994). Waves can begin at a point and expand outward, initiate along a line and travel as a moving furrow, or begin as a circle moving inward, depending on the mechanics of the cell sheet within the embryo as a whole. We have also observed entire regions of cell sheets contracting as a unit (Gordon and Gordon, 2016a). We regard the traveling furrow observed during Drosophila eye development (Alicea et al., 2018b; Gordon, 1999; Gordon and Björklund, 1993) as another example of a traveling wave and one which demonstrates the universality of the cell state splitter across phlya.

We assume that the cell state splitter evolved from specialization of the normal cell division in single cell organisms such as yeast where cell division produces a large cell with one function (mother cell) and a small cell with another (spore) (Gordon and Gordon, 2016a). We further generalize the cell state splitter model to Caenorhabditis elegans by assuming the when a cell division occurs, the larger call has experienced the equivalent of an expansion wave while the smaller cell has experienced the equivalent of a contraction wave (Alicea and Gordon, 2016; Gordon, 1999). The course of evolution may have been from single cell waves in mosaic embryos to waves that cross multiple cells in epithelia of regulating embryos (Gordon, 1999).

The trajectories of contraction and expansion waves were superimposed on the developmental anatomy of the axolotl over time (i.e., on its fate map (Cleine and Slack, 1985; Piekarski and Olsson, 2007; Vogt, 1925, 1929)). It was shown that there is a unique bifurcating sequence of expansion and contraction waves (called by us the differentiation tree (Alicea and Gordon, 2016; Martin and Gordon, 1995)) that correlates with all tissue types determined during gastrulation (Björklund and Gordon, 1994) (Fig. 4). Signal transduction pathways from the cell state splitter to the nucleus result in changes in gene expression (Björklund and Gordon, 1993; Gordon and Gordon, 2016a). Triggering this signal transduction pathway results in a genetic transduction of the biomechanical signal of the cytoskeleton via the activation of proteins such as FOXA1 (Yang et al., 2016). The one bit signal is a response to either a contraction wave or an expansion wave traversing the cells. The signal triggers changes in gene expression, one set of changes for contraction and another for expansion. Developmental checkpoints are therefore regulated by signaling from the cytoskeleton which prevents differentiation of a progenitor cell until it is in the correct cellular and tissue environment, as recently demonstrated by Zemke et al. (2019). We collectively refer to the components that participate in the changes in gene expression subsequent to the triggering of the cytoskeletal cell state splitter as the “nuclear state splitter” (Gordon and Gordon, 2016a). (See also “Signal transduction model for embryonic differentiation waves” (Wikipedia, 2019).) A temperature sensitive mutant that shows that wave propagation is separable from cell differentiation has been reported (Poodry et al., 1973; Suzuki, 1974) (Fig. 6.31 in.(Gordon and Gordon, 2016a)), suggesting that different processes are involved in the cell state splitter and the nuclear state splitter, i.e., that the link from the cell state splitter can be broken.

The signal transduction pathway trigger by the expansion or contraction wave consists of multiple elements such as wnt that are commonly invoked in diffusible morphogen models of embyrogenesis. The cell state splitter model places the presence such individual diffusible morphogens within the nuclear state splitter’s biomechanical transduction signal process. The spatiotemporally defined expression of these diffusible “morphogens” is governed by the trajectory of the contraction or expansion wave. According to the cell state splitter model, embryonic differentiation does not occur due to gradients. Embryonic differentiation is temporally and spatially directed by biochemical responses to mechanical differentiation waves in an active medium, a sheet of cells. The passage of the differentiation wave will produce a temporary gradient of cytoskeletal rearrangement, signal transduction and gene expression as a by-product. If the differentiation wave begins at a boundary and travels away from it, higher levels of specific gene expression can be expected since the boundary zone experienced the differentiation wave sooner and has had more time to up regulate production of the specific gene products being measured (Fig. 5). The reverse would be true with down regulation of a specific gene product. Cells in the cell state splitter model require no more than an epigenetic mechanism for keeping track of the number of contraction and expansion waves they participate in which can be based on well documented mechanisms such as changes of HOX gene expression as tissues differentiate. There is still a critically important role for the study of gradients in embryonic development: gradients can be used to plot the presence and trajectories of cell state splitter differentiation waves.

A differentiation tree of a regulating embryo can be regarded as a redrawing of a lineage tree so that all cells that have traversed the same sequence of differentiation waves are bundled together (Fig. 6). Note that the lineage tree of a mosaic organism in which there is only one cell of a given type at a given time is automatically a differentiation tree, and no bundling is necessary. Thus, from here on we will only talk about differentiation trees, subsuming lineage trees under the concept. The differentiation tree for the axolotl, the salamander Ambystoma mexicanum, has been worked out from the zygote through neural plate formation (Björklund and Gordon, 1994; Gordon and Gordon, 2016a) (Fig. 4).

Differentiation trees can be represented as planar graphs with nonoverlapping edges (the lines between nodes). In order to do this, some rule has to be used as to how to place each new node to the left or the right of its predecessor. For the mosaic nematode Caenorhabditis elegans each event of differentiation coincides with a cell division, and the usual choice is to place one daughter cell that is closest to the anterior end of the embryo in one horizontal direction and the daughter cell that is closest to the posterior end of the embryo to the opposite direction (Fig. 1). This is an arbitrary choice, unless one thinks there is something special about the anterior/posterior axis of the embryo in determining which daughter cell is closest to either end. While that may be the case, other choices are possible. For example, almost all ˜1000 cells in C. elegans undergo an asymmetric division, which results in one smaller (contraction) and one larger (expansion) daughter cell. We could thus order the cells left to right by relative sizes of the daughter cells resulting from a cell division (Alicea and Gordon, 2016). Such an ordering requires careful measurements of cell sizes, including choice of what is measured (characteristic diameter, volume, surface area, etc.), with attention to errors of measurement, which could flip which cell goes left or right. The 50 C. elegans cells that undergo equal divisions would either have to be kept together or placed left/right by another criterion. If we knew what to look for, other criteria could be used, such as different states of the cytoskeleton in the two daughter cells, different genes being activated or repressed, etc.

Once a criterion has been decided upon for placing differentiated cells to the left or the right, we can assign one bit of information to each node representing a branch point in the differentiation tree. If we assign 0 for cells on the left and 1 for cells on the right, then each cell can be assigned a binary number, a string of zeros and ones, indicating its state of differentiation. This string is what we call the cell’s differentiation code. Properly done, all cells of the same type would have the same differentiation code and vice versa. To make such codes more readable, we redundantly indicate the number of bits as a decimal number to the left of the “decimal” point (Fig. 2). (Unlike ordinary binary numbers, we cannot add trailing zeros to a differentiation code, as each 0 refers to a cell type instead of nothing.)

Section snippets

The logic of development: what determines a cell’s fate?

Before the vogue of calling DNA and later RNA (Brandhorst, 1985) “informational” macromolecules, Raven (1959) examined the logical contradictions involved in both of the two major approaches to embryogenesis: preformation and epigenesis. He proposed:

“Apparently, it is very difficult, not to say impossible, for the human mind to conceive of ordered spatial multiplicity arising "by itself" out of disorder. Although… the reverse process, disorder arising out of order, can quite easily be conceived

It’s not the environment

From the point of view of a single cell and its descendants, it has been puzzling how a cell “decides” which way to go as it traverses the differentiation tree. This cannot be an arbitrary decision, because the direction with respect to the rest of the embryo has morphogenetic consequences. Conrad Waddington externalized the genome in his “epigenetic landscape”, depicting a ball rolling down valleys whose shapes were determined by struts and wires connected to an unorganized set of genes below.

An hypothesis combining cell differentiation and morphogenesis via the differentiation code

As the differentiation tree is our mental construct, what is its representation in the cell making that differentiation decision? This question is at the heart of our (mis)understanding of how embryological development occurs. Our suggestion is that the genome itself has a hierarchical logical structure that represents the differentiation tree inside every cell. In Raven’s terms, the genome contains the blue-print, and the cytoplasm and cortex, along with the genome, execute the developmental

A cybernetic overview

If we ask: “What is a differentiation wave accomplishing?”, we see three functions:

  • 1

    It causes each cell it traverses to differentiate to a new cell type.

  • 2

    Its trajectory determines which cells undergo that particular step of differentiation.

  • 3

    It sets up the conditions for triggering another pair of differentiation waves within the tissue it traversed.

These three functions may be thought of as goals, a low level form of purpose as occurs in a simple cybernetic system, such as a thermostat (Gordon and

Continuing differentiation: the basis for the evolution and novelty in eukaryotes

Once we see development as the consequence of a playing out of the differentiation code as represented in the genome, we can ask how evolution might act upon a differentiation tree of a given species. The simplest answer is that now and then duplication of a subbranch of a differentiation tree could occur, and then the two copies could drift apart over subsequent evolutionary time (Gordon, 1999). The result would be growth of the differentiation tree, expansion of the differentiation code, and

Conclusion

We used to describe embryogenesis as a bifurcating syncopated interaction between the genome and the physics of differentiation waves (Gordon et al., 1994). Now we interpret embryogenesis as a bifurcating generation of cybernetic systems, each of which includes the goal of creating two more nested cybernetic systems (Gordon and Stone, 2016). It is not a simple top-down control system, but rather a nested bifurcating sequence of such control systems, where the “top” changes at each bifurcation.

Acknowledgements

Thanks to an anonymous reviewer for suggesting improvements, and to Marcello Barbieri for introducing RG to code biology with a preprint of Barbieri (2001).

References (92)

  • S.R. Mayoral et al.

    The environment rules: spatiotemporal regulation of oligodendrocyte differentiation

    Curr. Opin. Neurobiol.

    (2016)
  • C.A. Poodry et al.

    Temperature-sensitive mutations in Drosophila melanogaster. Part XV. Developmental properties of shibirets1: a pleiotropic mutation affecting larval and adult locomotion and development

    Dev. Biol.

    (1973)
  • J.E. Sulston et al.

    The embryonic cell lineage of the nematode Caenorhabditis elegans

    Dev. Biol.

    (1983)
  • M. Abolhasani et al.

    A rare case of duplication of chromosome 2 (q31.3q36.3) in a 4.5-year-old boy and review of the literature

    Int. J. Pediatr.-Masshad

    (2019)
  • B. Alicea et al.

    Quantifying mosaic development: towards an evo-devo postmodern synthesis of the evolution of development via differentiation trees of embryos [invited]

    Biology (Basel)

    (2016)
  • B. Alicea et al.

    Information Isometry Technique Reveals Organizational Features in Developmental Cell Lineages

    (2018)
  • Z.R. Bao et al.

    Automated cell lineage tracing in Caenorhabditis elegans

    Proc. Natl. Acad. Sci. U. S. A.

    (2006)
  • M. Barbieri

    The Organic Codes: The Birth of Semantic Biology

    (2001)
  • E. Bates et al.

    Boston, Massachusetts, July 26–30, 2019Developmental Bioelectricity, Satellite Symposium, 78th Annual Society for Developmental Biology Meeting2019

    Developmental Bioelectricity, Satellite Symposium, 78th Annual Society for Developmental Biology Meeting

    (2019)
  • L.V. Beloussov et al.

    Effects of relaxation of mechanical tensions upon the early morphogenesis of Xenopus laevis embryos [English]

    Int. J. Dev. Biol.

    (1990)
  • J.J. Bezem et al.

    A simple model for the estimation of the cytoplasmic information content of the animal egg

    Proceedings Nederlandse Akademie van Wetenschappen Amsterdam

    (1961)
  • N.K. Björklund et al.

    Nuclear state splitting: a working model for the mechanochemical coupling of differentiation waves to master genes

    Russ. J. Dev. Biol.

    (1993)
  • N.K. Björklund et al.

    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)
  • N.P. Bordzilovskaya et al.

    Developmental-stage series of axolotl embryos [Erratum: Staging Table 19-1 is for 20°C, not 29°C]

  • E.C. Boterenbrood et al.

    The direction of cleavage waves and the regional variation in the duration of cleavage cycles on the dorsal side of the Xenopus laevis blastula

    Roux’s Arch. Dev. Biol.

    (1986)
  • E.C. Boterenbrood et al.

    Duration of cleavage cycles and asymmetry in the direction of cleavage waves prior to gastrulation in Xenopus laevis

    Roux’s Arch. Dev. Biol.

    (1983)
  • A. Bradley et al.

    Formation of germ-line chimaeras from embryo-derived teratocarcinoma cell lines

    Nature

    (1984)
  • B.P. Brandhorst

    Informational content of the echinoderm egg

    Dev. Biol.

    (1985)
  • G.W. Brodland et al.

    Furrowing surface contraction wave coincident with primary neural induction in amphibian embryos

    J. Morphol.

    (1994)
  • C.B. Cameron

    The emergence of shape. Review of: Mechanisms of morphogenesis: The creation of biological form by Jamie A. Davies

    Bioscience

    (2006)
  • D. Carey

    Star Trek® Final Frontier

    (1988)
  • E. Casler

    Pattern variation in isogenic frogs

    J. Exp. Zool.

    (1967)
  • J.H. Cleine et al.

    Normal fates and states of specification of different regions in the axolotl gastrula

    J. Embryol. Exp. Morphol.

    (1985)
  • M. Coppola et al.

    Provable self-organizing pattern formation by a swarm of robots with limited knowledge

    Swarm Intell.

    (2019)
  • S.M. Dancoff et al.

    The information content and error rate of living things

  • C. Darwin

    On the Origin of Species by Means of Natural Selection, Or, The Preservation of Favoured Races in the Struggle for Life

    (1859)
  • A. De Loof

    Differentiation: “keep the genome constant but change over and over again its ionic and or macromolecular environment”? A conceptual synthesis

    Belg. J. Zool.

    (1993)
  • S.V. Evsikov et al.

    Role of ooplasmic segregation in mammalian development

    Roux’s Arch. Dev. Biol.

    (1994)
  • T. Fujimori

    Preimplantation development of mouse: a view from cellular behavior

    Dev. Growth Diff.

    (2010)
  • R.L. Gardner et al.

    Environmental factors and the stability of differentiation in mammalian development

    Comptes Rendus de L’Academie des Sciences. Serie III, Sciences de la vie

    (1992)
  • N.K. Gordon et al.

    Differentiation waves versus French flag gradients [invited] [NFLG]

    Math. Biosci.

    (2019)
  • N.K. Gordon et al.

    Embryogenesis Explained

    (2016)
  • N.K. Gordon et al.

    The organelle of differentiation in embryos: the cell state splitter [invited review]

    Theor. Biol. Med. Model.

    (2016)
  • R. Gordon

    The Hierarchical Genome and Differentiation Waves: Novel Unification of Development, Genetics and Evolution

    (1999)
  • R. Gordon

    Mechanics in embryogenesis and embryonics: prime mover or epiphenomenon?

    Int. J. Dev. Biol.

    (2006)
  • R. Gordon

    Epilogue: the diseased breast lobe in the context of X-chromosome inactivation and differentiation waves

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