Random aggregation models for the formation and evolution of coding and non-coding DNA

A random aggregation model with influx is proposed for the formation of the non-coding DNA regions via random co-aggregation and influx of biological macromolecules such as viruses, parasite DNA, and replication segments. The constant mixing (transpositions) and influx drives the system in an out-of-equilibrium steady state characterised by a power law size distribution. The model predicts the long range distributions found in the noncoding eucaryotic DNA and explains the observed correlations. For the formation of coding DNA a random closed aggregation model is proposed which predicts short range coding size distributions. The closed aggregation process drives the system in an almost “frozen” stable state which is robust to external perturbations and which is characterised by well defined space and time scales, as observed in coding sequences.