Nonequilibrium associative retrieval of multiple stored self-assembly targets

Driven Self-Assembly of Patchy Particles Overcoming Equilibrium Limitations

Bridging biological complexity and synthetic material design, we investigate dissipative self-assembly in patchy particle systems. Utilizing Monte Carlo and Molecular Dynamics simulations, we demonstrate how external driving forces mitigate equilibrium trade-offs between assembly time and structural stability, traditionally encountered in self-assembly processes. Our findings also extend to biological-mimicking environments, where we explore the dynamics of patchy particles under crowded conditions. This comprehensive analysis offers insights into advanced material design, opening avenues for innovations in nanotechnology applications.

Escaping Kinetic Traps Using Nonreciprocal Interactions

Kinetic traps are a notorious problem in equilibrium statistical mechanics, where temperature quenches ultimately fail to bring the system to low energy configurations. Using multifarious self-assembly as a model system, we introduce a mechanism to escape kinetic traps by utilizing nonreciprocal interactions between components. Introducing nonequilibrium effects offered by broken action-reaction symmetry in the system pushes the trajectory of the system out of arrested dynamics. The dynamics of the model is studied using tools from the physics of interfaces and defects. Our proposal can find applications in self-assembly, glassy systems, and systems with arrested dynamics to facilitate escape from local minima in rough energy landscapes.

Nanocrystal Assemblies: Current Advances and Open Problems

We explore the potential of nanocrystals (a term used equivalently to nanoparticles) as building blocks for nanomaterials, and the current advances and open challenges for fundamental science developments and applications. Nanocrystal assemblies are inherently multiscale, and the generation of revolutionary material properties requires a precise understanding of the relationship between structure and function, the former being determined by classical effects and the latter often by quantum effects. With an emphasis on theory and computation, we discuss challenges that hamper current assembly strategies and to what extent nanocrystal assemblies represent thermodynamic equilibrium or kinetically trapped metastable states. We also examine dynamic effects and optimization of assembly protocols. Finally, we discuss promising material functions and examples of their realization with nanocrystal assemblies.

Non-reciprocal multifarious self-organization

A hallmark of living systems is the ability to employ a common set of building blocks that can self-organize into a multitude of different structures. This capability can only be afforded in non-equilibrium conditions, as evident from the energy-consuming nature of the plethora of such dynamical processes. To achieve automated dynamical control of such self-assembled structures and transitions between them, we need to identify the fundamental aspects of non-equilibrium dynamics that can enable such processes. Here we identify programmable non-reciprocal interactions as a tool to achieve such functionalities. The design rule is composed of reciprocal interactions that lead to the equilibrium assembly of the different structures, through a process denoted as multifarious self-assembly, and non-reciprocal interactions that give rise to non-equilibrium dynamical transitions between the structures. The design of such self-organized shape-shifting structures can be implemented at different scales, from nucleic acids and peptides to proteins and colloids.

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

The promise of self-assembly to enable the bottom-up formation of materials with prescribed architectures and functions has driven intensive efforts to uncover rational design principles for maximizing the yield of a target structure. Yet, despite many successful examples of self-assembly, ensuring kinetic accessibility of the target structure remains an unsolved problem in many systems. In particular, long-lived kinetic traps can result in assembly times that vastly exceed experimentally accessible timescales. One proposed solution is to design non-equilibrium assembly protocols in which system parameters change over time to avoid such kinetic traps. Here, we develop a framework to combine Markov state model (MSM) analysis with optimal control theory to compute a time-dependent protocol that maximizes the yield of the target structure at a finite time. We present an adjoint-based gradient descent method that, in conjunction with MSMs for a system as a function of its control parameters, enables efficiently optimizing the assembly protocol. We also describe an interpolation approach to significantly reduce the number of simulations required to construct the MSMs. We demonstrate our approach with two examples; a simple semi-analytic model for the folding of a polymer of colloidal particles, and a more complex model for capsid assembly. Our results show that optimizing time-dependent protocols can achieve significant improvements in the yields of selected structures, including equilibrium free energy minima, long-lived metastable structures, and transient states.

Density-tunable pathway complexity in a minimalistic self-assembly model

An open challenge in self-assembly is learning how to design systems that can be conditionally guided towards different target structures depending on externally-controlled conditions. Using a theoretical and numerical approach, here we discuss a minimalistic self-assembly model that can be steered towards different types of ordered constructs at the equilibrium by solely tuning a facile selection parameter, namely the density of building blocks. Metadynamics and Langevin dynamics simulations allow us to explore the behavior of the system in and out of equilibrium conditions. We show that the density-driven tunability is encoded in the pathway complexity of the system, and specifically in the competition between two different main self-assembly routes. A comprehensive set of simulations provides insight into key factors allowing to make one self-assembling pathway prevailing on the other (or vice versa), determining the selection of the final self-assembled products. We formulate and validate a practical criterion for checking whether a specific molecular design is predisposed for such density-driven tunability of the products, thus offering a new, broader perspective to realize and harness this facile extrinsic control of conditional self-assembly.

A simple solution to the problem of self-assembling cubic diamond crystals

The self-assembly of colloidal diamond (CD) crystals is considered as one of the most coveted goals of nanotechnology, both from the technological and fundamental points of view. For applications, colloidal diamond is a photonic crystal which can open new possibilities of manipulating light for information processing. From a fundamental point of view, its unique symmetry exacerbates a series of problems that are commonly faced during the self-assembly of target structures, such as the presence of kinetic traps and the formation of crystalline defects and alternative structures (polymorphs). Here we demonstrate that all these problems can be systematically addressed via SAT-assembly, a design framework that converts self-assembly into a Boolean satisfiability problem (SAT). Contrary to previous solutions (requiring four or more components), we prove that the assembly of the CD crystal only requires a binary mixture. Moreover, we use molecular dynamics simulations of a system composed by nearly a million nucleotides to test a DNA nanotechnology design that constitutes a promising candidate for experimental realization.

Temperature protocols to guide selective self-assembly of competing structures

Multicomponent self-assembly mixtures offer the possibility of encoding multiple target structures with the same set of interacting components. Selective retrieval of one of the stored structures has been attempted by preparing an initial state that favors the assembly of the required target, through seeding, concentration patterning, or specific choices of interaction strengths. This may not be possible in an experiment where on-the-fly reconfiguration of the building blocks to switch functionality may be required. In this paper, we explore principles of inverse design of a multicomponent, self-assembly mixture capable of encoding two competing structures that can be selected through simple temperature protocols. We design the target structures to realize the generic situation in which one of the targets has the lower nucleation barrier, while the other is globally more stable. We observe that, to avoid the formation of spurious or chimeric aggregates, the number of neighboring component pairs that occur in both structures should be minimal. Our design also requires the inclusion of components that are part of only one of the target structures. We observe, however, that to maximize the selectivity of retrieval, the component library itself should be maximally shared by the two targets, within such a constraint. We demonstrate that temperature protocols can be designed that lead to the formation of either one of the target structures with high selectivity. We discuss the important role played by secondary aggregation products in improving selectivity, which we term "vestigial aggregates."

Self-assembly of two-dimensional, amorphous materials on a liquid substrate

Recent experimental utilization of liquid substrate in the production of two-dimensional crystals, such as graphene, together with a general interest in amorphous materials, raises the following question: is it beneficial to use a liquid substrate to optimize amorphous material production? Inspired by epitaxial growth, we use a two-dimensional coarse-grained model of interacting particles to show that introducing a motion for the substrate atoms improves the self-assembly process of particles that move on top of the substrate. We find that a specific amount of substrate liquidity (for a given sample temperature) is needed to achieve optimal self-assembly. Our results illustrate the opportunities that the combination of different degrees of freedom provides to the self-assembly processes.

Nonequilibrium self-assembly of multiple stored targets in a dimer-based system

Nonequilibrium self-assembly can be found in various biological processes where chemical potential gradients are exploited to steer the system to a desired organized structure with a particular function. Microtubules, for example, are composed of two globular protein subunits, α-tubulin and β-tubulin, which bind together to form polar dimers that self-assemble a hollow cylinder structure in a process driven by GTPase activity. Inspired by this process, we define a generic self-assembly lattice model containing particles of two subunits, which is driven out-of-equilibrium by a dimer-favoring local driving force. Using Monte Carlo simulations, we characterize the ability of this system to restore pre-encoded target structures as a function of the initial seed size, interaction energy, chemical potential, number of target structures, and strength of the nonequilibrium drive. We demonstrate some intriguing consequences of the drive, such as a smaller critical seed and an improved target assembly stability, compared to the equilibrium scenario. Our results can expand the theoretical basis of nonequilibrium self-assembly and provide deeper understanding of how nonequilibrium driving can overcome equilibrium constraints.

Kinetic Monte Carlo Algorithms for Active Matter Systems

We study kinetic Monte Carlo (KMC) descriptions of active particles. We show that, when they rely on purely persistent, active steps, their continuous-time limit is ill-defined, leading to the vanishing of trademark behaviors of active matter such as the motility-induced phase separation, ratchet effects, as well as to a diverging mechanical pressure. We then show how, under an appropriate scaling, mixing passive steps with active ones leads to a well-defined continuous-time limit that however differs from standard active dynamics. Finally, we propose new KMC algorithms whose continuous-time limits lead to the dynamics of active Ornstein-Uhlenbeck, active Brownian, and run-and-tumble particles.

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. These two objectives are known to be typically in competition, but it is not known how to simultaneously optimize them. 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 short-ranged interaction energies. We use a coarse-grained model for the particles' dynamics that allows us to efficiently search over parameters, for systems small enough to be enumerated. For most target states there is a tradeoff when the number of types of particles 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 short-ranged isotropic interactions should generically have a tradeoff, and avoiding it in larger systems will require orientation-dependent interactions.

Thermodynamics of structure-forming systems

Structure-forming systems are ubiquitous in nature, ranging from atoms building molecules to self-assembly of colloidal amphibolic particles. The understanding of the underlying thermodynamics of such systems remains an important problem. Here, we derive the entropy for structure-forming systems that differs from Boltzmann-Gibbs entropy by a term that explicitly captures clustered states. For large systems and low concentrations the approach is equivalent to the grand-canonical ensemble; for small systems we find significant deviations. We derive the detailed fluctuation theorem and Crooks' work fluctuation theorem for structure-forming systems. The connection to the theory of particle self-assembly is discussed. We apply the results to several physical systems. We present the phase diagram for patchy particles described by the Kern-Frenkel potential. We show that the Curie-Weiss model with molecule structures exhibits a first-order phase transition.

Programming Dynamic Assembly of Viral Proteins with DNA Origami

Biomolecular assembly in biological systems is typically a complex dynamic process regulated by the exchange of molecular information between biomolecules such as proteins and nucleic acids. Here, we demonstrate a nucleic-acid-based system that can program the dynamic assembly process of viral proteins. Tobacco mosaic virus (TMV) genome-mimicking RNA is anchored on DNA origami nanostructures via hybridization with a series of DNA strands which also function as locks that prevent the packaging of RNA by the TMV proteins. The selective, sequential releasing of the RNA via toehold-mediated strand displacement allows us to program the availability of RNA and subsequently the TMV growth in situ. Furthermore, the programmable dynamic assembly of TMV on DNA templates also enables the production of new DNA-protein hybrid nanostructures, which are not attainable by using previous assembly methods.

Lessons from equilibrium statistical physics regarding the assembly of protein complexes

In order to carry out their functions, most proteins assemble into multicomponent complexes. In the process of assembly, complexes need to discriminate their specific components from a mixture of hundreds of different proteins present in the cell. To assess some of the implications of this requirement, we develop a minimal model of self-assembly based on equilibrium statistical physics. We argue that the need to assemble reliably imposes fundamental constraints on the characteristics of complexes, which we support with analysis of available structural and compositional data. Our work constitutes only a step toward future theory of protein complex assembly, which will have to incorporate also nonequilibrium and kinetic aspects of this fundamental and rich, yet theoretically neglected, problem.

Cellular functions are established through biological evolution, but are constrained by the laws of physics. For instance, the physics of protein folding limits the lengths of cellular polypeptide chains. Consequently, many cellular functions are carried out not by long, isolated proteins, but rather by multiprotein complexes. Protein complexes themselves do not escape physical constraints, one of the most important being the difficulty of assembling reliably in the presence of cellular noise. In order to lay the foundation for a theory of reliable protein complex assembly, we study here an equilibrium thermodynamic model of self-assembly that exhibits 4 distinct assembly behaviors: diluted protein solution, liquid mixture, “chimeric assembly,” and “multifarious assembly.” In the latter regime, different protein complexes can coexist without forming erroneous chimeric structures. We show that 2 conditions have to be fulfilled to attain this regime: 1) The composition of the complexes needs to be sufficiently heterogeneous, and 2) the use of the set of components by the complexes has to be sparse. Our analysis of publicly available databases of protein complexes indicates that cellular protein systems might have indeed evolved so as to satisfy both of these conditions.