Discovering optimal kinetic pathways for self-assembly using automatic differentiation.

Macromolecular complexes are frequently composed of diverse subunits. While evolution may favor repeated subunits and symmetry, we show how diversity in subunits generates an expansive parameter space that naturally improves the 'expressivity' of self-assembly, much like a deeper neural network. By using automatic differentiation algorithms commonly used in deep learning, we searched these parameter spaces to identify classes of kinetic protocols that mimic biological solutions for productive self-assembly. Our results reveal how high-yield complexes that easily become kinetically trapped in incomplete intermediates can instead be steered by internal design of rate constants or external and active control of subunits to efficiently assemble, exploiting nonequilibrium control of these ubiquitous dynamical systems.