Dynamics of heteromolecular filament formation

The self-assembly of molecular building blocks into linear filaments is a common form of self-organization in nature and underlies the formation of supra-molecular polymers in a variety of contexts, including in both functional and aberrant biology. To date, attention has focused mainly on homomolecular assembly phenomena; however, it has recently become apparent that heteromolecular assemblies can be common, and, for instance, pathological protein filaments such as amyloid aggregates form in vivo in environments supporting copolymerization. Here, we present a general kinetic scheme for heteromolecular filament formation and derive closed-form analytical expressions that describe the dynamics of such systems. Our results reveal the existence of a demixing transition time controlled by the relative rates of depletion of the different aggregating species, after which predominantly homomolecular polymers are formed even when the initial solution is heteromolecular. Furthermore, these results may be applied to the analysis of experimental kinetic data on the aggregation of mixtures of proteins, to determine which fundamental reaction steps occur between unlike proteins, and to provide accurate estimates of their rate constants.