J Theor Biol
July 21, 2014;
Two different network topologies yield bistability in models of mesoderm and anterior mesendoderm specification in amphibians.
Understanding the Gene Regulatory Networks (GRNs) that underlie development is a major question for systems biology. The establishment of the germ layers is amongst the earliest events of development and has been characterised in numerous model systems. The establishment of the mesoderm
is best characterised in the frog Xenopus laevis and has been well studied both experimentally and mathematically. However, the Xenopus network has significant differences from that in mouse and humans, including the presence of multiple copies of two key genes in the network, Mix and Nodal
. The axolotl, a urodele amphibian, provides a model with all the benefits of amphibian embryology but crucially only a single Mix and Nodal
gene required for the specification of the mesoderm
. Remarkably, the number of genes within the network is not the only difference. The interaction between Mix and Brachyury
, two transcription factors involved in the establishment of the endoderm
respectively, is not conserved. While Mix represses Brachyury
in Xenopus, it activates Brachyury
in axolotl. Thus, whilst the topology of the networks in the two species differs, both are able to form mesoderm
in vivo. Based on current knowledge of the structure of the mesendoderm GRN
we develop deterministic models that describe the time evolution of transcription factors in a single axolotl cell and compare numerical simulations with previous results from Xenopus. The models are shown to have stable steady states corresponding to mesoderm
and anterior mesendoderm
, with the in vitro model showing how the concentration of Activin can determine cell fate, while the in vivo model shows that β-catenin concentration can determine cell fate. Moreover, our analysis suggests that additional components must be important in the axolotl network in the specification of the full range of tissues.
J Theor Biol
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Fig. 1. A comparison of the axolotl and Xenopus mesendoderm GRNs. (a) The axolotl mesendoderm GRN and (b) the simplified Xenopus mesendoderm GRN. Arrow and bar heads represent, respectively, activation and repression. The ‘A’ indicates that an input is, in Boolean terms, an ‘AND’ gate. The ‘S’ indicates a synergy between the two transcription factors, i.e. β-catenin activates Nodal1 and this activation is enhanced by Nodal autoregulation. Otherwise, multiple inputs consisting of only one type (repression or activation) correspond to an ‘OR’ gate. When both types are present, the repression and activation inputs are treated as two ‘OR’ gates coupled by an ‘AND’ gate. Red lines show interactions which are the same in both networks and blue lines show those which differ. In (b) solid lines indicate experimentally verified links and dashed lines indicate links which are inferred from the Xenopus mesendoderm network, and which need to be verified experimentally. (c) Table summarising the main differences between the axolotl and Xenopus mesendoderm GRNs. Row 1: At least 6 Nodal genes are found in Xenopus, compared with 2 Nodal genes in axolotl. Row 2: There are seven Mix genes in Xenopus and one Mix gene in axolotl. Row 3: VegT acts to activate expression of Nodal, Mix and Brachyury in Xenopus, but in axolotl VegT does not activate these genes. Row 4: Siamois is a gene found in Xenopus but not axolotl. Row 5: In Xenopus, β-catenin acts in two different ways on Nodal: β-catenin enhances Nodal autoregulation of Xnr1 and Xnr2, and the expression of Xnr5 and Xnr6 is activated by β-catenin in the presence of VegT. In axolotl, Nodal1 can be activated by β-catenin alone and we also assume that it can enhance Nodal autoregulation. Row 6: Mix and Brachyury mutually repress each other in Xenopus, but, in axolotl, Mix is required for the expression of Brachyury. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)
Fig. 2. Mesoderm and anterior mesendoderm induction by Activin in animal cap explants (48 h after animal caps explants are cut from embryo). (A) Axolotl animal caps injected with 1pg Activin mRNA induce mesoderm, and 25pg of Activin induces anterior mesendoderm. (B) qPCR analysis of Brachyury, Mix, Sox17, Goosecoid, FGF8 and NCAM expression in animal caps.
Fig. 3. The axolotl in vitro network: Nodal signalling is simulated by bathing either whole or dissociated animal caps in Activin. Note that this network is identical to the simplified Xenopus in vitro network, except that Mix is required here for the expression of Brachyury.
Fig. 4. (a) Steady state solutions to (7) plotted against λAM,B for A=5. Thick solid lines represent the mesoderm steady state, thin solid lines represent the anterior mesendoderm steady state and dashed lines represent the unstable steady state. Fold bifurcations mark the appearance and the disappearance of the steady states. (b) Solution structure in terms of the bifurcation parameters λAM,B and λA,M, these representing the folds that determine the maximum rates of production of Brachyury and Mix in response to activation by Activin. (c) Solution structure in terms of the bifurcation parameters λAM,B and λM,G, these representing the folds that determine the maximum rates of production of Brachyury in response to activation by Activin and Goosecoid in response to Mix. Unless otherwise stated, parameters were chosen as in Table 2.
Fig. 5. Numerical solutions of the axolotl in vitro model. The responses of Brachyury (thin solid line), Mix (dashed line) and Goosecoid (dot-dashed line) are shown. Parameters were chosen as in Table 2.
Fig. 6. Numerical solutions of the axolotl in vitro model as functions of A for (a) A=4, (b) A=4.5, (c) A=6. The responses of Brachyury (thin solid line), Mix (dashed line) and Goosecoid (dot-dashed line) are shown. Parameters were chosen as in Table 2.
Fig. 7. Numerical solutions of the Xenopus in vitro model (Middleton et al., 2009) and the axolotl in vitro model (7), in the absence of Goosecoid, as functions of A. The responses of Brachyury (thin solid line), Mix (dashed line) and Goosecoid (dot-dashed line) are shown. Parameters used are given in Table 2 for the axolotl model and as given in Middleton et al. (2009) for the Xenopus. Values of λM,G, θG,G and λXM,B are higher in the axolotl model than in the Xenopus model, corresponding to higher rates of production of Mix and Brachyury and a higher threshold for Goosecoid negative autoregulation.
Fig. 8. Numerical solutions to (9) subject to initial conditions (10) with C0 as shown above. For sufficiently large C0, N tends to N⁎, first overshooting this value. Parameters were chosen as in Table 3.
Fig. 9. Numerical solutions of the axolotl model as functions of C0, for various values of τ. The response of Brachyury (thin solid line), eFGF (dotted line), Mix (dashed line), Goosecoid (dot-dashed line) and Nodal (blue solid line) are shown in response to an initial concentration of β-catenin. Parameters were chosen as in Table 3. (a) T=0.5, (b) T=1, (c) T=8 and (d) T=100. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)
Fig. 10. Gene regulatory networks which yield bistability. (A) Mutual negative regulation between X and Y drives differentiation of a cell to express either X or Y, with the indirect repression of X by Y (via Z) being dispensible. (B) An alternative network, where the indirect repression of X by Y (via Z) is necessary to drive differentiation of a cell to express Y.
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