A Size-Dependent Multiple-Loop Negative Feedback System Describes Biological Segment Formation Based on the Clock and Wavefront Mechanism

We proposed a new mathematical model for biological segment formation based on the clock and wavefront mechanism suggested in 1970s. Here, we chose an invertebrate, Enchytraeus japonensis, as a model animal and adopted multiple-loop negative feedback system based on its physiological features. We numerically showed the segment number of the model animal is autopoietically controlled by a size-dependent function. Additionally, we discussed two cases of the irregular oscillations by applying the biological conditions for abnormal development. The present model showed robustness under local noise perturbations like many other biological oscillators and qualitatively described unique development of the model animal. As a result, we suggested that a global interaction of chemical signals in the body can also drive “segmentation clock”.