Assembly Factors Resolve Speed and Encoding Bottlenecks in Multifarious Self-Assembly

Cytoplasm is a heterogeneous mixture containing many types of proteins that self-assemble into a wide variety of complexes. The accuracy and speed of cytoplasmic self-assembly is astonishing because it involves the correct identification of components shared among different structures, despite pervasive thermal fluctuations. Typical toy models of self-assembly are based on the specificity of binding energies among components. However, kinetics plays a key role in biological self-assembly, often catalyzed by a plethora of assembly factors. Building on this observation, we extend a previous heteropolymer growth model to describe the retrieval of two-dimensional structures via quasi-two-dimensional growth. We find that the self-assembly of structures in this model is subject to strong speed and encoding bottlenecks. Moreover, we show that these bottlenecks can be suppressed by increasing the connectivity of a small fraction of components. This mechanism of kinetically controlling a small number of critical binding events provides a simple explanation for the timely assembly of large heteromeric protein complexes and suggests a unifying principle for the role of assembly factors.