Optimization of non-equilibrium self-assembly protocols using Markov state models

Discrete state model of a self-aggregating colloidal system with directional interactions

The construction of coarse-grained descriptions of a system's kinetics is well established in biophysics. One prominent example is Markov state models in protein folding dynamics. In this paper, we develop a coarse-grained, discrete state model of a self-aggregating colloidal particle system inspired by the concepts of Markov state modeling. The specific self-aggregating system studied here involves field-responsive colloidal particles in orthogonal electric and magnetic fields. Starting from particle-resolved (Brownian dynamics) simulations, we define the discrete states by categorizing each particle according to its local structure. We then describe the kinetics between these states as a series of stochastic, memoryless jumps. In contrast to other works on colloidal self-assembly, our coarse-grained approach describes the simultaneous formation and evolution of multiple aggregates from single particles. Our discrete model also takes into account the changes in transition dynamics between the discrete states as the size of the largest cluster grows. We validate the coarse-grained model by comparing the predicted population fraction in each of the discrete states with those calculated directly from the particle-resolved simulations as a function of the largest cluster size. We then predict population fractions in the presence of noise-averaging and in a situation where a model parameter is changed instantaneously after a certain time. Finally, we explore the validity of the detailed balance condition in the various stages of aggregation.

2D capsid formation within an oscillatory energy landscape: orderly self-assembly depends on the interplay between a dynamic potential and intrinsic relaxation times

Multiple dissipative self-assembly protocols designed to create novel structures or to reduce kinetic traps have recently emerged. Specifically, temporal oscillations of particle interactions have been shown effective at both aims, but investigations thus far have focused on systems of simple colloids or their binary mixtures. In this work, we expand our understanding of the effect of temporally oscillating interactions to a two-dimensional coarse-grained viral capsid-like model that undergoes a self-limited assembly. This model includes multiple intrinsic relaxation times due to the internal structure of the capsid subunits and, under certain interaction regimes, proceeds via a two-step nucleation mechanism. We find that oscillations much faster than the local intrinsic relaxation times can be described via a time averaged inter-particle potential across a wide range of interaction strengths, while oscillations much slower than these relaxation times result in structures that adapt to the attraction strength of the current half-cycle. Interestingly, oscillation periods similar to these relaxation times shift the interaction window over which orderly assembly occurs by enabling error correction during the half-cycles with weaker attractions. Our results provide fundamental insights to non-equilibrium self-assembly on temporally variant energy landscapes.

Adaptive nonequilibrium design of actin-based metamaterials: Fundamental and practical limits of control

The adaptive and surprising emergent properties of biological materials self-assembled in far-from-equilibrium environments serve as an inspiration for efforts to design nanomaterials. In particular, controlling the conditions of self-assembly can modulate material properties, but there is no systematic understanding of either how to parameterize external control or how controllable a given material can be. Here, we demonstrate that branched actin networks can be encoded with metamaterial properties by dynamically controlling the applied force under which they grow and that the protocols can be selected using multi-task reinforcement learning. These actin networks have tunable responses over a large dynamic range depending on the chosen external protocol, providing a pathway to encoding "memory" within these structures. Interestingly, we obtain a bound that relates the dissipation rate and the rate of "encoding" that gives insight into the constraints on control-both physical and information theoretical. Taken together, these results emphasize the utility and necessity of nonequilibrium control for designing self-assembled nanostructures.