Sequential vs. parallel complexity in simple gene assembly

We investigate some differences between the general intramolecular model for gene assembly and its restricted simple model. Although both models satisfactorily sort all current experimental data, we show that the general model offers assembly strategies for a given string that vary in both assembly length and the operations used, while the simple model will always use the same number of each type of operation to sort a gene. When simple operations are applied in parallel this is given a new twist. We prove that for any n≥1, there exists a string having maximally parallel assemblies of any length between n and 2n.