Mapping the configurational landscape and aggregation phase behavior of the tau protein fragment PHF6.

The PHF6 (Val-Gln-Ile-Val-Tyr-Lys) motif, found in all isoforms of the microtubule-associated protein tau, forms an integral part of ordered cores of amyloid fibrils formed in tauopathies and is thought to play a fundamental role in tau aggregation. Because PHF6 as an isolated hexapeptide assembles into ordered fibrils on its own, it is investigated as a minimal model for insight into the initial stages of aggregation of larger tau fragments. Even for this small peptide, however, the large length and time scales associated with fibrillization pose challenges for simulation studies of its dynamic assembly, equilibrium configurational landscape, and phase behavior. Here, we develop an accurate, bottom-up coarse-grained model of PHF6 for large-scale simulations of its aggregation, which we use to uncover molecular interactions and thermodynamic driving forces governing its assembly. The model, not trained on any explicit information about fibrillar structure, predicts coexistence of formed fibrils with monomers in solution, and we calculate a putative equilibrium phase diagram in concentration-temperature space. We also characterize the configurational and free energetic landscape of PHF6 oligomers. Importantly, we demonstrate with a model of heparin that this widely studied cofactor enhances the aggregation propensity of PHF6 by ordering monomers during nucleation and remaining associated with growing fibrils, consistent with experimentally characterized heparin-tau interactions. Overall, this effort provides detailed molecular insight into PHF6 aggregation thermodynamics and pathways and, furthermore, demonstrates the potential of modern multiscale modeling techniques to produce predictive models of amyloidogenic peptides simultaneously capturing sequence-specific effects and emergent aggregate structures.

A microcanonical approach to temperature-transferable coarse-grained models using the relative entropy.

Bottom-up coarse-graining methods provide systematic tools for creating simplified models of molecular systems. However, coarse-grained (CG) models produced with such methods frequently fail to accurately reproduce all thermodynamic properties of the reference atomistic systems they seek to model and, moreover, can fail in even more significant ways when used at thermodynamic state points different from the reference conditions. These related problems of representability and transferability limit the usefulness of CG models, especially those of strongly state-dependent systems. In this work, we present a new strategy for creating temperature-transferable CG models using a single reference system and temperature. The approach is based on two complementary concepts. First, we switch to a microcanonical basis for formulating CG models, focusing on effective entropy functions rather than energy functions. This allows CG models to naturally represent information about underlying atomistic energy fluctuations, which would otherwise be lost. Such information not only reproduces energy distributions of the reference model but also successfully predicts the correct temperature dependence of the CG interactions, enabling temperature transferability. Second, we show that relative entropy minimization provides a direct and systematic approach to parameterize such classes of temperature-transferable CG models. We calibrate the approach initially using idealized model systems and then demonstrate its ability to create temperature-transferable CG models for several complex molecular liquids.

Temperature-Controlled Reconfigurable Nanoparticle Binary Superlattices.

The presence of diffusionless transformations during the assembly of DNA-functionalized particles (DFPs) is highly significant in designing reconfigurable materials whose structure and functional properties are tunable with controllable variables. In this paper, we first use a variety of computational models and techniques (including free energy methods) to address the nature of such transformations between face-centered cubic (FCC) and body-centered cubic (BCC) structures in a three-dimensional binary system of multiflavored DFPs. We find that the structural rearrangements between BCC and FCC structures are thermodynamically reversible and dependent on crystallite size. Smaller nuclei favor nonclose-packed BCC structures, whereas close-packed FCC structures are observed during the growth stage once the crystallite size exceeds a threshold value. Importantly, we show that a similar reversible transformation between BCC/FCC structures can be driven by changing temperature without introducing additional solution components, highlighting the feasibility of creating reconfigurable crystalline materials. Lastly, we validate this thermally responsive switching behavior in a DFP system with explicit DNA (un)hybridization, demonstrating our findings' applicability to experimentally realizable systems.

Deep learning for characterizing the self-assembly of three-dimensional colloidal systems.

Creating a systematic framework to characterize the structural states of colloidal self-assembly systems is crucial for unraveling the fundamental understanding of these systems' stochastic and non-linear behavior. The most accurate characterization methods create high-dimensional neighborhood graphs that may not provide useful information about structures unless these are well-defined reference crystalline structures. Dimensionality reduction methods are thus required to translate the neighborhood graphs into a low-dimensional space that can be easily interpreted and used to characterize non-reference structures. We investigate a framework for colloidal system state characterization that employs deep learning methods to reduce the dimensionality of neighborhood graphs. The framework next uses agglomerative hierarchical clustering techniques to partition the low-dimensional space and assign physically meaningful classifications to the resulting partitions. We first demonstrate the proposed colloidal self-assembly state characterization framework on a three-dimensional in silico system of 500 multi-flavored colloids that self-assemble under isothermal conditions. We next investigate the generalizability of the characterization framework by applying the framework to several independent self-assembly trajectories, including a three-dimensional in silico system of 2052 colloidal particles that undergo evaporation-induced self-assembly.

Grand canonical inverse design of multicomponent colloidal crystals.

Inverse design methods are powerful computational approaches for creating colloidal systems which self-assemble into a target morphology by reverse engineering the Hamiltonian of the system. Despite this, these optimization procedures tend to yield Hamiltonians which are too complex to be experimentally realized. An alternative route to complex structures involves the use of several different components, however, conventional inverse design methods do not explicitly account for the possibility of phase separation into compositionally distinct structures. Here, we present an inverse design scheme for multicomponent colloidal systems by combining active learning with a method to directly compute their ground state phase diagrams. This explicitly accounts for phase separation and can locate stable regions of Hamiltonian parameter space which grid-based surveys are prone to miss. Using this we design low-density, binary structures with Lennard-Jones-like pairwise interactions that are simpler than in the single component case and potentially realizable in an experimental setting. This reinforces the concept that ground states of simple, multicomponent systems might be rich with previously unappreciated diversity, enabling the assembly of non-trivial structures with only few simple components instead of a single complex one.

Symmetry-Based Crystal Structure Enumeration in Two Dimensions.

The accurate prediction of stable crystalline phases is a long-standing problem encountered in the study of conventional atomic and molecular solids as well as soft materials. One possible solution involves enumerating a reasonable set of candidate structures and then screening them to identify the one(s) with the lowest (free) energy. Candidate structures in this set can also serve as starting points for other routines, such as genetic algorithms, which search via optimization. Here, we present a framework for crystal structure enumeration of two-dimensional systems that utilizes a combination of symmetry- and stoichiometry-imposed constraints to compute valid configurations of particles that tile Euclidean space. With mild assumptions, this produces a computationally tractable total number of proposed candidates, enabling multicomponent systems to be screened by direct enumeration of possible crystalline ground states. The python code that enables these calculations is available at https://github.com/usnistgov/PACCS.

Size-dependent thermodynamic structural selection in colloidal crystallization.

Nucleation and growth of crystalline phases play an important role in a variety of physical phenomena, ranging from freezing of liquids to assembly of colloidal particles. Understanding these processes in the context of colloidal crystallization is of great importance for predicting and controlling the structures produced. In many systems, crystallites that nucleate have structures differing from those expected from bulk equilibrium thermodynamic considerations, and this is often attributed to kinetic effects. In this work, we consider the self-assembly of a binary mixture of colloids in two dimensions, which exhibits a structural transformation from a non-close-packed to a close-packed lattice during crystal growth. We show that this transformation is thermodynamically driven, resulting from size dependence of the relative free energy between the two structures. We demonstrate that structural selection can be entirely thermodynamic, in contrast to previously considered effects involving growth kinetics or interaction with the surrounding fluid phase.

Using symmetry to elucidate the importance of stoichiometry in colloidal crystal assembly.

We demonstrate a method based on symmetry to predict the structure of self-assembling, multicomponent colloidal mixtures. This method allows us to feasibly enumerate candidate structures from all symmetry groups and is many orders of magnitude more computationally efficient than combinatorial enumeration of these candidates. In turn, this permits us to compute ground-state phase diagrams for multicomponent systems. While tuning the interparticle potentials to produce potentially complex interactions represents the conventional route to designing exotic lattices, we use this scheme to demonstrate that simple potentials can also give rise to such structures which are thermodynamically stable at moderate to low temperatures. Furthermore, for a model two-dimensional colloidal system, we illustrate that lattices forming a complete set of 2-, 3-, 4-, and 6-fold rotational symmetries can be rationally designed from certain systems by tuning the mixture composition alone, demonstrating that stoichiometric control can be a tool as powerful as directly tuning the interparticle potentials themselves.

Assembly of three-dimensional binary superlattices from multi-flavored particles.

Binary superlattices constructed from nano- or micron-sized colloidal particles have a wide variety of applications, including the design of advanced materials. Self-assembly of such crystals from their constituent colloids can be achieved in practice by, among other means, the functionalization of colloid surfaces with single-stranded DNA sequences. However, when driven by DNA, this assembly is traditionally premised on the pairwise interaction between a single DNA sequence and its complement, and often relies on particle size asymmetry to entropically control the crystalline arrangement of its constituents. The recently proposed "multi-flavoring" motif for DNA functionalization, wherein multiple distinct strands of DNA are grafted in different ratios to different colloids, can be used to experimentally realize a binary mixture in which all pairwise interactions are independently controllable. In this work, we use various computational methods, including molecular dynamics and Wang-Landau Monte Carlo simulations, to study a multi-flavored binary system of micron-sized DNA-functionalized particles modeled implicitly by Fermi-Jagla pairwise interactions. We show how self-assembly of such systems can be controlled in a purely enthalpic manner, and by tuning only the interactions between like particles, demonstrate assembly into various morphologies. Although polymorphism is present over a wide range of pairwise interaction strengths, we show that careful selection of interactions can lead to the generation of pure compositionally ordered crystals. Additionally, we show how the crystal composition changes with the like-pair interaction strengths, and how the solution stoichiometry affects the assembled structures.