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Computational modeling of assembly is challenging for many systems, because their timescales can vastly exceed those accessible to simulations. This article describes the multiMSM, which is a general framework that uses Markov state models (MSMs) to enable simulating self-assembly and self-organization of finite-sized structures on timescales that are orders of magnitude longer than those accessible to brute-force dynamics simulations. As with traditional MSM approaches, the method efficiently overcomes free energy barriers and other dynamical bottlenecks. In contrast to previous MSM approaches to simulating assembly, the framework describes simultaneous assembly of many clusters and the consequent depletion of free subunits or other small oligomers. The algorithm accounts for changes in transition rates as concentrations of monomers and intermediates evolve over the course of the reaction. Using two model systems, we show that the multiMSM accurately predicts the concentrations of the full ensemble of intermediates on timescales required to reach equilibrium. Importantly, after constructing a multiMSM for one system concentration, yields at other concentrations can be approximately calculated without any further sampling. This capability allows for orders of magnitude additional speedup. In addition, the method enables highly efficient calculation of quantities such as free energy profiles, nucleation timescales, flux along the ensemble of assembly pathways, and entropy production rates. Identifying contributions of individual transitions to entropy production rates reveals sources of kinetic traps. The method is broadly applicable to systems with equilibrium or nonequilibrium dynamics and is trivially parallelizable and, thus, highly scalable. Published by the American Physical Society2024 

Programmable self-assembly has seen an explosion in the diversity of synthetic crystalline materials, but developing strategies that target “self-limiting” assemblies has remained a challenge. Among these, self-closing structures, in which the local curvature defines the finite global size, are prone to polymorphism due to thermal bending fluctuations, a problem that worsens with increasing target size. Here, we show that assembly complexity can be used to eliminate this source of polymorphism in the assembly of tubules. Using many distinct components, we prune the local density of off-target geometries, increasing the selectivity of the tubule width and helicity to nearly 100%. We further show that by reducing the design constraints to target either the pitch or the width alone, fewer components are needed to reach complete selectivity. Combining experiments with theory, we reveal an economical limit, which determines the minimum number of components required to create arbitrary assembly sizes with full selectivity. 

This review accompanies the Special Issue on the subject of physical virology, which features work presented at the recent Gordon Research Conference (GRC) on this topic [...] 

We propose and investigate an extension of the Caspar–Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies—in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)—is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly. 

Self-assembly of complex and functional materials remains a grand challenge in soft material science. Efficient assembly depends on a delicate balance between thermodynamic and kinetic effects, requiring fine-tuning affinities and concentrations of subunits. By contrast, we introduce an assembly paradigm that allows large error-tolerance in the subunit affinity and helps avoid kinetic traps. Our combined experimental and computational approach uses a model system of triangular subunits programmed to assemble intoT= 3 icosahedral capsids comprising 60 units. The experimental platform uses DNA origami to create monodisperse colloids whose three-dimensional geometry is controlled to nanometer precision, with two distinct bonds whose affinities are controlled tok_BTprecision, quantified in situ by static light scattering. The computational model uses a coarse-grained representation of subunits, short-ranged potentials, and Langevin dynamics. Experimental observations and modeling reveal that when the bond affinities are unequal, two distincthierarchicalassembly pathways occur, in which the subunits first form dimers in one case and pentamers in another. These hierarchical pathways produce complete capsids faster and are more robust against affinity variation than egalitarian pathways, in which all binding sites have equal strengths. This finding suggests that hierarchical assembly may be a general engineering principle for optimizing self-assembly of complex target structures.