Neural control of body-plan axis in regenerating planaria
Fig 3
Key concepts underlying the Markov Chain Model of Regeneration used to predict regeneration outcomes from modeled steady-state morphogen concentrations averaged at the wound sites of the model.
Concentrations of key instructive morphogens (ERK and β-Cat) were sampled and averaged at each model cut line (A). The base Markov Chain assumed possible transitions of the blastema at the cutting site into a potential head or tail, with the additional case that failure to transition to head or tail represents a failed regeneration (B). Head, tail, or blastema (failed) probabilities were represented by pH, pT, and pB, respectively (B, C). Transition rates from blastema to head (αBH) were assumed to be increased by ERK concentrations at the wound (B, Eq 3), while transitions from blastema to tail (αBT) were assumed to be increased by β-Cat concentrations at the wound (B, Eq 4). Regeneration outcomes at cut-lines were calculated probabilistically, where existing head and tail remained unchanged on top and bottommost fragments (C). To determine the frequencies of heteromorphoses in a particular fragment appearing in a population of regenerates, the probabilities of each possible outcome at each cut line of the fragment were multiplied (D). The respective predicted fraction of heteromorphoses appearing in the population were inferred from the combinations shown in (D), where the possible heteromorphoses and their net probabilities are shown in (E).