Building differentiable kinetic models to improve yield of finite sized assemblies

The self-assembly of protein sub-units into a functional complex is an essential step in several cellular processes like transcription and virion formation. The formation of a functional complex can be carried out in specific pathways that involve a high degree of spatial and temporal organisation. However, the lack of these driving forces can lead to kinetic trapping that can reduce the final yield of the functional complex. In this work we use deterministic reaction simulations to quantify how kinetic trapping regimes can emerge in finite sized assemblies based on topology, size and interaction strengths. These kinetic models allow us to utilize the automatic differentiation technique to maxmize the yield while avoiding erroneous assembly pathways. We show that protein systems can exploit different strategies to avoid traps by introducing different degrees of heterogeneity in the kinetic parameters. Our results further show how certain biological limitations and toplogy of different sized assemblies can lead to emergence of a preferred pathway of assembly. The tuning of kinetic pathways to achieve a higher yield offers a high degree of robustness and flexibility in biological systems without the need to alter topologies or energetics.