The time complexity of self-assembly

Abstract

SignificanceAn important limiting factor for self-assembly processes is the time it takes to assemble large structures with high yield. While equilibrium self-assembly systems slowly relax toward a state of minimal free energy, nonequilibrium systems offer various ways to control assembly processes and to optimize their time efficiency. We show that these different control scenarios can informatively be characterized by their time complexity, i.e., their scaling of the assembly time with the structure size, analogous to algorithms for computational problems. Especially for large structures, differences in the time complexity of the scenarios lead to strongly diverging time efficiencies. Most significantly, we show that by effectively regulating the supply of constituents, high resource and time efficiency can be achieved for self-assembly processes.