An extended steepness model for leg-size determination based on Dachsous/Fat trans-dimer system

What determines organ size has been a long-standing biological question. Lawrence et al. (2008) proposed the steepness hypothesis suggesting that the protocadherin Dachsous/Fat (Ds/Ft) system may provide some measure of dimension to the cells in relation to the gradient. In this paper we extended the model as a means of interpreting experimental results in cricket leg regeneration. We assumed that (1) Ds/Ft trans-heterodimers or trans-homodimers are redistributed during cell division, and (2) growth would cease when a differential of the dimer across each cell decreases to a certain threshold. We applied our model to simulate the results obtained by leg regeneration experiments in a cricket model. The results were qualitatively consistent with the experimental data obtained for cricket legs by RNA interference methodology. Using our extended steepness model, we provided a molecular-based explanation for leg size determination even in intercalary regeneration and for organ size determination.