Designing the timing and time of macromolecular assembly processes

Living systems are extraordinarily effective at assembling higher order macromolecular complexes with 3 or 300 subunits. The self-assembly process is a necessary step in the formation of obligate structures, but the process itself can also play a functional role in sensing and decision making. In both cases, the timing of the assembly process represents an optimizable dimension that can thus benefit from the innate time-dependence or activity in nonequilibrium systems. Using theory, kinetic rate equations, and automatic differentiation, we show here how optimizing the self-assembly timescales of 3-7 subunit macromolecular systems can enhance not only efficiency for high-yield, but robustness under perturbations to subunit concentrations or binding energies. Selecting for the time-dependence of subunit concentrations or actively recycling intermediates through enzyme activity provide general strategies for efficient assembly regardless of the evolved pairwise interactions, also working effectively for virus assembly. To control when and where these assemblies form, we designed a biochemical oscillator that exploits membrane localization and dimensional reduction to drive up subunit concentrations, triggering assembly. By using enzymes to modify the membrane rather than the assembly subunits, this mechanism can be coupled to a variety of macromolecular complexes. Our analysis uses optimization, rate equations, and reaction-diffusion simulations to demonstrate how asymmetries in the enzyme kinetics are essential to support oscillations, along with a sufficiently large volume-to-surface area ratio. This mechanism ensures that assembly only occurs at the membrane and promotes sensing and response to changes to the membrane composition, similar to steps in signaling and membrane trafficking. We discuss the tunability and design constraints of these timescales for both efficient and targeted assembly.