Theory for sequence selection via phase separation and oligomerization

Nonequilibrium selection pressures were proposed for forming oligonucleotides with rich functionalities encoded in their sequences, such as catalysis. Since phase separation was shown to direct various chemical processes, we ask whether condensed phases can provide mechanisms for sequence selection. To answer this question, we use nonequilibrium thermodynamics and describe the reversible oligomerization of different monomers to sequences at nondilute conditions prone to phase separation. We find that as sequences form, their interactions can trigger phase separation, which in turn enriches some sequences while depleting others. Our main result is that phase separation creates a selection pressure leading to specific sequence patterns when fragmentation maintains the system away from equilibrium. When fragmentation is slow, alternating sequences that interact more cooperatively with their surroundings are preferred. When fragmentation is fast, sequences with longer repeating motifs capable of more specific interactions are selected instead. Our finding that out-of-equilibrium condensed phases can provide a selection mechanism highlights their potential as versatile hubs for the evolution of functional sequences, a question relevant to the molecular origin of life and de novo life.