Abstract
Time efficiency of self-assembly is crucial for many biological processes. Moreover, with the advances of nanotechnology, time efficiency in artificial self-assembly becomes ever more important. While structural determinants and the final assembly yield are increasingly well understood, kinetic aspects concerning the time efficiency, however, remain much more elusive. In computer science, the concept of time complexity is used to characterize the efficiency of an algorithm and describes how the algorithm's runtime depends on the size of the input data. Here we characterize the time complexity of nonequilibrium self-assembly processes by exploring how the time required to realize a certain, substantial yield of a given target structure scales with its size. We identify distinct classes of assembly scenarios, i.e., "algorithms" to accomplish this task, and show that they exhibit drastically different degrees of complexity. Our analysis enables us to identify optimal control strategies for nonequilibrium self-assembly processes. Furthermore, we suggest an efficient irreversible scheme for the artificial self-assembly of nanostructures, which complements the state-of-the-art approach using reversible binding reactions and requires no fine-tuning of binding energies.
Highlights
Time efficiency of self-assembly is crucial for many biological processes
How exactly does the assembly time scale with the size of the target structure, and how does this scaling depend on the selfassembly scheme? What kinds of schemes optimize the assembly time? Answers to these questions will enable assembly strategies to be identified that are optimally suited for the production of large, functionally complex macromolecular structures via artificial self-assembly, a major goal in nanotechnology [4, 5, 11,12,13]
We address these questions by studying the time complexity [14,15,16,17] of four prototypical self-assembly scenarios, using scaling arguments and in silico modeling of the stochastic dynamics
Summary
Time efficiency of self-assembly is crucial for many biological processes. with the advances of nanotechnology, time efficiency in artificial self-assembly becomes ever more important. Answers to these questions will enable assembly strategies to be identified that are optimally suited for the production of large, functionally complex macromolecular structures via artificial self-assembly, a major goal in nanotechnology [4, 5, 11,12,13]. The fourth strategy is a distinct idea conceptualized to achieve efficient self-assembly in a technological context by effectively regulating the supply of building blocks To explore these questions in their simplest form, we consider an assembly process involving N identical copies of S different species of building blocks (monomers) and assume chemical reaction kinetics in a well-mixed fluid environment.
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