The SOC control landscape as revealed by a sandpile-to-sandpile transition in mouse embryo development.

<p>The development of a sandpile transitional behavior between sequential cell states suggests the existence of an SOC control landscape (first row: schematic picture of a valley-ridge-valley transition; <i>x</i>-axis: cell state; <i>y</i>-axis: degree of SOC control). The second and third rows show that a sandpile-to-sandpile transition occurs in mouse embryo development from the zygote single-cell stage to the morula cell state: <b>I</b>: a sandpile (i.e., critical transition) develops from the zygote single-cell stage to the early 2-cell state = > <b>II:</b> a sandpile is destroyed from the middle to the late 2-cell state, which exhibits stochastic expression (i.e., no critical transition; refer to the random mouse expression matrix in <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0167912#pone.0167912.s002" target="_blank">S2 Fig</a></b>) = > <b>III:</b> a sandpile again develops from the 8-cell state to the morula state. These results show that a significant perturbation (reprogramming) in self-organization occurs from the middle stage to the late 2-cell stage through a stochastic overall expression (refer to <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0167912#pone.0167912.g007" target="_blank">Fig 7</a></b>). Note: Qualitatively, there is a high degree of SOC control for a well-developed shape of the sandpile-type transition (SOC control), an intermediate degree of SOC control for a weakened (broken) sandpile, and a low degree for non-SOC control. The latter is due to stochastic expression. The linear behavior (absence of a critical point) in mouse embryo development is also reflected in the low Pearson correlation (<i>r</i> ~0.21 after the 8-cell state) (<b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0167912#pone.0167912.g007" target="_blank">Fig 7A and 7C</a></b>).