Neutral models of de novo gene emergence suggest that gene evolution has a preferred trajectory

New protein coding genes can emerge from genomic regions that previously did not contain any genes, via a process called \textit{de novo} gene emergence. To synthesize a protein, DNA must be transcribed as well as translated. Both processes need certain DNA sequence features. Stable transcription requires promoters and a polydenylation signal, while translation requires at least an open reading frame (ORF). We develop mathematical models based on mutation probabilities, and the assumption of neutral evolution, to find out how quickly genes emerge and are lost. We also investigate the effect of the order by which DNA features evolve, and if sequence composition is biased by mutation rate. We rationalize how genes are lost much more rapidly than they emerge, and how genes with long ORFs preferentially arise in regions that are already transcribed. Our study not only answers some fundamental questions on the topic of de novo emergence but also provides a modeling framework for future studies.