Thermodynamic stability versus Kinetic Accessibility: Pareto Fronts for Programmable Self-Assembly.

A challenge in designing self-assembling building blocks is to ensure the target state is both thermodynamically stable and kinetically accessible. Little is known about the tradeoff between these two objectives as design parameters are varied, nor how to choose parameters to avoid a tradeoff. We consider this problem through the lens of multi-objective optimization theory: we develop a genetic algorithm to compute the Pareto fronts characterizing the tradeoff between equilibrium probability and folding rate, for a model system of small polymers of colloids with tunable interaction energies. We use a coarse-grained model for the particles' dynamics that allows us to efficiently search over parameters. For most target states there is a tradeoff when the number of particle types is small, with medium-weak bonds favouring fast folding, and strong bonds favouring high equilibrium probability. The tradeoff disappears when the number of particle types reaches a value $m_*$, that is usually much less than the total number of particles. This general approach of computing Pareto fronts allows one to identify the minimum number of design parameters to avoid a thermodynamic-kinetic tradeoff. However, we argue, by contrasting our coarse-grained model's predictions with those of Brownian dynamics simulations, that particles with isotropic interactions should generically have a tradeoff, and avoiding it in larger systems will require orientation-dependent interactions.