Multiscale Models for Fibril Formation: Rare Events Methods, Microkinetic Models, and Population Balances

Amyloid fibrils are thought to grow by a two-step dock-lock mechanism. However, previous simulations of fibril formation (i) overlook the bi-molecular nature of the docking step and obtain rates with first-order units, or (ii) superimpose the docked and locked states when computing the potential of mean force for association and thereby muddle the docking and locking steps. Here, we developed a simple microkinetic model with separate locking and docking steps and with the appropriate concentration dependences for each step. We constructed a simple model comprised of chiral dumbbells that retains qualitative aspects of fibril formation. We used rare events methods to predict separate docking and locking rate constants for the model. The rate constants were embedded in the microkinetic model, with the microkinetic model embedded in a population balance model for “bottom-up” multiscale fibril growth rate predictions. These were compared to “top-down” results using simulation data with the same model and multiscale framework to obtain maximum likelihood estimates of the separate lock and dock rate constants. We used the same procedures to extract separate docking and locking rate constants from experimental fibril growth data. Our multiscale strategy, embedding rate theories, and kinetic models in conservation laws should help to extract docking and locking rate constants from experimental data or long molecular simulations with correct units and without compromising the molecular description.

Reaction Monitoring and Structural Characterisation of Coordination Driven Self-Assembled Systems by Ion Mobility-Mass Spectrometry

Nature creates exquisite molecular assemblies, required for the molecular-level functions of life, via self-assembly. Understanding and harnessing these complex processes presents an immense opportunity for the design and fabrication of advanced functional materials. However, the significant industrial potential of self-assembly to fabricate highly functional materials is hampered by a lack of knowledge of critical reaction intermediates, mechanisms, and kinetics. As we move beyond the covalent synthetic regime, into the domain of non-covalent interactions occupied by self-assembly, harnessing and embracing complexity is a must, and non-targeted analyses of dynamic systems are becoming increasingly important. Coordination driven self-assembly is an important subtype of self-assembly that presents several wicked analytical challenges. These challenges are "wicked" due the very complexity desired confounding the analysis of products, intermediates, and pathways, therefore limiting reaction optimisation, tuning, and ultimately, utility. Ion Mobility-Mass Spectrometry solves many of the most challenging analytical problems in separating and analysing the structure of both simple and complex species formed via coordination driven self-assembly. Thus, due to the emerging importance of ion mobility mass spectrometry as an analytical technique tackling complex systems, this review highlights exciting recent applications. These include equilibrium monitoring, structural and dynamic analysis of previously analytically inaccessible complex interlinked structures and the process of self-sorting. The vast and largely untapped potential of ion mobility mass spectrometry to coordination driven self-assembly is yet to be fully realised. Therefore, we also propose where current analytical approaches can be built upon to allow for greater insight into the complexity and structural dynamics involved in self-assembly.

Vibrational Sum-Frequency Generation Hyperspectral Microscopy for Molecular Self-Assembled Systems

In this review, we discuss the recent developments and applications of vibrational sum-frequency generation (VSFG) microscopy. This hyperspectral imaging technique can resolve systems without inversion symmetry, such as surfaces, interfaces and noncentrosymmetric self-assembled materials, in the spatial, temporal, and spectral domains. We discuss two common VSFG microscopy geometries: wide-field and confocal point-scanning. We then introduce the principle of VSFG and the relationships between hyperspectral imaging with traditional spectroscopy, microscopy, and time-resolved measurements. We further highlight crucial applications of VSFG microscopy in self-assembled monolayers, cellulose in plants, collagen fibers, and lattice self-assembled biomimetic materials. In these systems, VSFG microscopy reveals relationships between physical properties that would otherwise be hidden without being spectrally, spatially, and temporally resolved. Lastly, we discuss the recent development of ultrafast transient VSFG microscopy, which can spatially measure the ultrafast vibrational dynamics of self-assembled materials. The review ends with an outlook on the technical challenges of and scientific potential for VSFG microscopy.

Equilibrium mechanisms of self-limiting assembly

Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of equilibrium assembly processes give rise to two states: one consisting of dispersed disassociated subunits, and the other, a bulk-condensed state of unlimited size. This review focuses on the more specialized class of self-limiting assembly, which describes equilibrium assembly processes resulting in finite-size structures. These systems pose a generic and basic question, how do thermodynamic processes involving non-covalent interactions between identical subunits "measure" and select the size of assembled structures? In this review, we begin with an introduction to the basic statistical mechanical framework for assembly thermodynamics, and use this to highlight the key physical ingredients that ensure equilibrium assembly will terminate at finite dimensions. Then, we introduce examples of self-limiting assembly systems, and classify them within this framework based on two broad categories: self-closing assemblies and open-boundary assemblies. These include well-known cases in biology and synthetic soft matter - micellization of amphiphiles and shell/tubule formation of tapered subunits - as well as less widely known classes of assemblies, such as short-range attractive/long-range repulsive systems and geometrically-frustrated assemblies. For each of these self-limiting mechanisms, we describe the physical mechanisms that select equilibrium assembly size, as well as potential limitations of finite-size selection. Finally, we discuss alternative mechanisms for finite-size assemblies, and draw contrasts with the size-control that these can achieve relative to self-limitation in equilibrium, single-species assemblies.

A dissipative particle dynamics model for studying dynamic phenomena in colloidal rod suspensions

A dissipative particle dynamics (DPD) model is developed and demonstrated for studying dynamics in colloidal rod suspensions. The solvent is modeled as conventional DPD particles, while individual rods are represented by a rigid linear chain consisting of overlapping solid spheres, which interact with solvent particles through a hard repulsive potential. The boundary condition on the rod surface is controlled using a surface friction between the solid spheres and the solvent particles. In this work, this model is employed to study the diffusion of a single colloid in the DPD solvent and compared with theoretical predictions. Both the translational and rotational diffusion coefficients obtained at a proper surface friction show good agreement with calculations based on the rod size defined by the hard repulsive potential. In addition, the system-size dependence of the diffusion coefficients shows that the Navier-Stokes hydrodynamic interactions are correctly included in this DPD model. Comparing our results with experimental measurements of the diffusion coefficients of gold nanorods, we discuss the ability of the model to correctly describe dynamics in real nanorod suspensions. Our results provide a clear reference point from which the model could be extended to enable the study of colloid dynamics in more complex situations or for other types of particles.

In Situ Quantification of Interactions between Charged Nanorods in a Predefined Potential Energy Landscape

Quantitative understanding of nanoscale interactions is a prerequisite for harnessing the remarkable collective properties of nanoparticle systems. Here, we report the combined use of liquid-phase transmission electron microscopy and electron beam lithography to elucidate the interactions between charged nanorods in a predefined potential energy landscape. In situ site-selective lift-off of surface-functionalized lithographed gold nanorods is achieved by patterning them with adhesion layer materials that undergo etching at different rates. Analysis of the subsequent nanorod motion, which is two-dimensionally confined as a result of the particle-substrate attraction, allows quantification of interparticle interactions in a lithographically engineered environment. For lithographed nanorods patterned with the same adhesion layer material, their self-assembly behavior following lift-off is tuned by changing their starting spatial arrangement. Our approach facilitates investigation of interparticle interactions in designed nanoparticle systems and affords fundamental insights into the role of the potential energy landscape in determining the kinetic pathway for nanoparticle self-assembly.

Metastable Zr/Hf-MOFs: the hexagonal family of EHU-30 and their water-sorption induced structural transformation

Four new EHU-30 isoreticular compounds, based on amino-functionalized linkers and Zr and Hf metal centres are reported, in which H2O adsorption isotherms show an anomalous behaviour due to a localized structural transformation from EHU-30 to UiO-66.

Probing Self-Assembly in Arginine-Oleic Acid Solutions with Terahertz Spectroscopy and X-ray Scattering

A study of the formation of microstructures in the reaction of oleic acid with arginine elucidates dynamical self-assembly processes at the molecular level. Terahertz spectroscopy combined with density functional calculations reveals the initial hydrogen-bonding motifs in the assembly process, leading to the formation of micelles and vesicles. Small-angle X-ray scattering measurements allow for kinetic analysis of the growth processes of these nanostructures, revealing a prenucleation pathway of vesicles and micelles which lead to spongelike structures. This final stage of the assembly into spongelike aggregates is investigated with optical microscopy. The formed structures only occur at pH > 8 and are resistant to extreme acidic and basic conditions. A mechanistic pathway to the formation of the spongelike aggregates is described.

Rapid prediction of crucial hotspot interactions for icosahedral viral capsid self-assembly by energy landscape atlasing validated by mutagenesis

Icosahedral viruses are under a micrometer in diameter, their infectious genome encapsulated by a shell assembled by a multiscale process, starting from an integer multiple of 60 viral capsid or coat protein (VP) monomers. We predict and validate inter-atomic hotspot interactions between VP monomers that are important for the assembly of 3 types of icosahedral viral capsids: Adeno Associated Virus serotype 2 (AAV2) and Minute Virus of Mice (MVM), both T = 1 single stranded DNA viruses, and Bromo Mosaic Virus (BMV), a T = 3 single stranded RNA virus. Experimental validation is by in-vitro, site-directed mutagenesis data found in literature. We combine ab-initio predictions at two scales: at the interface-scale, we predict the importance (cruciality) of an interaction for successful subassembly across each interface between symmetry-related VP monomers; and at the capsid-scale, we predict the cruciality of an interface for successful capsid assembly. At the interface-scale, we measure cruciality by changes in the capsid free-energy landscape partition function when an interaction is removed. The partition function computation uses atlases of interface subassembly landscapes, rapidly generated by a novel geometric method and curated opensource software EASAL (efficient atlasing and search of assembly landscapes). At the capsid-scale, cruciality of an interface for successful assembly of the capsid is based on combinatorial entropy. Our study goes all the way from resource-light, multiscale computational predictions of crucial hotspot inter-atomic interactions to validation using data on site-directed mutagenesis' effect on capsid assembly. By reliably and rapidly narrowing down target interactions, (no more than 1.5 hours per interface on a laptop with Intel Core i5-2500K @ 3.2 Ghz CPU and 8GB of RAM) our predictions can inform and reduce time-consuming in-vitro and in-vivo experiments, or more computationally intensive in-silico analyses.

Designing Patchy Interactions to Self-Assemble Arbitrary Structures

One of the fundamental goals of nanotechnology is to exploit selective and directional interactions between molecules to design particles that self-assemble into desired structures, from capsids, to nanoclusters, to fully formed crystals with target properties (e.g., optical, mechanical, etc.). Here, we provide a general framework which transforms the inverse problem of self-assembly of colloidal crystals into a Boolean satisfiability problem for which solutions can be found numerically. Given a reference structure and the desired number of components, our approach produces designs for which the target structure is an energy minimum, and also allows us to exclude solutions that correspond to competing structures. We demonstrate the effectiveness of our approach by designing model particles that spontaneously nucleate milestone structures such as the cubic diamond, the pyrochlore, and the clathrate lattices.

Universal reshaping of arrested colloidal gels via active doping

Colloids that interact via a short-range attraction serve as the primary building blocks for a broad range of self-assembled materials. However, one of the well-known drawbacks to this strategy is that these building blocks rapidly and readily condense into a metastable colloidal gel. Using computer simulations, we illustrate how the addition of a small fraction of purely repulsive self-propelled colloids, a technique referred to as active doping, can prevent the formation of this metastable gel state and drive the system toward its thermodynamically favored crystalline target structure. The simplicity and robust nature of this strategy offers a systematic and generic pathway to improving the self-assembly of a large number of complex colloidal structures. We discuss in detail the process by which this feat is accomplished and provide quantitative metrics for exploiting it to modulate the self-assembly. We provide evidence for the generic nature of this approach by demonstrating that it remains robust under a number of different anisotropic short-ranged pair interactions in both two and three dimensions. In addition, we report on a novel microphase in mixtures of passive and active colloids. For a broad range of self-propelling velocities, it is possible to stabilize a suspension of fairly monodisperse finite-size crystallites. Surprisingly, this microphase is also insensitive to the underlying pair interaction between building blocks. The active stabilization of these moderately sized monodisperse clusters is quite remarkable and should be of great utility in the design of hierarchical self-assembly strategies. This work further bolsters the notion that active forces can play a pivotal role in directing colloidal self-assembly.

Kinetics of actin networks formation measured by time resolved particle-tracking microrheology

Actin is one of the most studied cytoskeleton proteins showing a very rich span of structures and functions. For example, adenosine triphosphate (ATP)-assisted polymerization of actin is used to push protrusions forward in a mechanism that enables cells to crawl on a substrate. In this process, the chemical energy released from the hydrolysis of ATP is what enables force generation. We study a minimal model system comprised of actin monomers in an excess of ATP concentration. In such a system polymerization proceeds in three stages: nucleation of actin filaments, elongation, and network formation. While the kinetics of filament growth was characterized previously, not much is known about the kinetics of network formation and the evolution of networks towards a steady-state structure. In particular, it is not clear how the non-equilibrium nature of this ATP-assisted polymerization manifests itself in the kinetics of self-assembly. Here, we use time-resolved microrheology to follow the kinetics of the three stages of self-assembly as a function of initial actin monomer concentration. Surprisingly, we find that at high enough initial monomer concentrations the effective elastic modulus of the forming actin networks overshoots and then relaxes with a -2/5 power law. We attribute the overshoot to the non-equilibrium nature of the polymerization and the relaxation to rearrangements of the network into a steady-state structure.

Equilibrium clustering of colloidal particles at an oil/water interface due to competing long-range interactions

HYPOTHESIS

Colloids at fluid interfaces organize according to inter-particle interactions. The main contributions to an effective interaction potential are expected to be electrostatic dipole-dipole repulsion and capillary attraction due to fluid interface deformation. When these interactions are weak, a secondary minimum in the particle pair interaction potential is expected.

EXPERIMENTS

Clean bare silica particles were deposited at an oil/water interface and their organization as well as dynamics were observed under a light microscope and analyzed in terms of radial distribution function and mean squared displacement.

FINDINGS

Weak long-range competing interactions between colloids at an oil/water interface result in cluster formation. The clusters have a liquid-like structure and grow with increasing particle packing fraction. System 'ergodicity' suggests near-equilibrium assembly, which is confirmed by free particle dynamics outside the clusters. The interplay between dipole-dipole repulsion and capillary attraction responsible for the cluster formation is reflected in a secondary minimum of the effective interaction potential predicted theoretically but inaccessible experimentally from collective particle properties prior to this work.

Equilibrium size distribution and phase separation of multivalent, molecular assemblies in dilute solution

Multivalent molecules can bind a limited number of multiple neighbors via specific interactions. In this paper, we investigate theoretically the self-assembly and phase separation of such molecules in dilute solution. We show that the equilibrium size (n) distributions of linear or branched assemblies qualitatively differ; the former decays exponentially with the relative size n/N[combining macron] (N[combining macron] = n), while the latter decays as a power law, with an exponential cutoff only for n ⪆ N[combining macron]2 ≫ N[combining macron]. In some cases, finite, branched assemblies are unstable and show a sol-gel transition at a critical concentration. In dilute solutions, non-specific interactions result in phase separation, whose critical point is described by an effective Flory Huggins theory that is sensitive to the nature of these distributions.

Leveraging Hierarchical Self-Assembly Pathways for Realizing Colloidal Photonic Crystals

Colloidal open crystals are attractive materials, especially for their photonic applications. Self-assembly appeals as a bottom-up route for structure fabrication, but self-assembly of colloidal open crystals has proven to be elusive for their mechanical instability due to being low-coordinated. For such a bottom-up route to yield a desired colloidal open crystal, the target structure is required to be thermodynamically favored for designer building blocks and also kinetically accessible via self-assembly pathways in preference to metastable structures. Additionally, the selection of a particular polymorph poses a challenge for certain much sought-after colloidal open crystals for their applications as photonic crystals. Here, we devise hierarchical self-assembly pathways, which, starting from designer triblock patchy particles, yield in a cascade of well-separated associations first tetrahedral clusters and then tetrastack crystals. The designed pathways avoid trapping into an amorphous phase. Our analysis reveals how such a two-stage self-assembly pathway via tetrahedral clusters promotes crystallization by suppressing five- and seven-membered rings that hinder the emergence of the ordered structure. We also find that slow annealing promotes a bias toward the cubic polymorph relative to the hexagonal counterpart. Finally, we calculate the photonic band structures, showing that the cubic polymorph exhibits a complete photonic band gap for the dielectric filling fraction directly realizable from the designer triblock patchy particles. Unexpectedly, we find that the hexagonal polymorph also supports a complete photonic band gap, albeit only for an increased filling fraction, which can be realized via postassembly processing.

Learning to grow: Control of material self-assembly using evolutionary reinforcement learning

We show that neural networks trained by evolutionary reinforcement learning can enact efficient molecular self-assembly protocols. Presented with molecular simulation trajectories, networks learn to change temperature and chemical potential in order to promote the assembly of desired structures or choose between competing polymorphs. In the first case, networks reproduce in a qualitative sense the results of previously known protocols, but faster and with higher fidelity; in the second case they identify strategies previously unknown, from which we can extract physical insight. Networks that take as input the elapsed time of the simulation or microscopic information from the system are both effective, the latter more so. The evolutionary scheme we have used is simple to implement and can be applied to a broad range of examples of experimental self-assembly, whether or not one can monitor the experiment as it proceeds. Our results have been achieved with no human input beyond the specification of which order parameter to promote, pointing the way to the design of synthesis protocols by artificial intelligence.

3D Self-Assembled Microelectronic Devices: Concepts, Materials, Applications

Modern microelectronic systems and their components are essentially 3D devices that have become smaller and lighter in order to improve performance and reduce costs. To maintain this trend, novel materials and technologies are required that provide more structural freedom in 3D over conventional microelectronics, as well as easier parallel fabrication routes while maintaining compatability with existing manufacturing methods. Self-assembly of initially planar membranes into complex 3D architectures offers a wealth of opportunities to accommodate thin-film microelectronic functionalities in devices and systems possessing improved performance and higher integration density. Existing work in this field, with a focus on components constructed from 3D self-assembly, is reviewed, and an outlook on their application potential in tomorrow's microelectronics world is provided.

Programming colloidal bonding using DNA strand-displacement circuitry

As a strategy for regulating entropy, thermal annealing is a commonly adopted approach for controlling dynamic pathways in colloid assembly. By coupling DNA strand-displacement circuits with DNA-functionalized colloid assembly, we developed an enthalpy-mediated strategy for achieving the same goal while working at a constant temperature. Using this tractable approach allows colloidal bonding to be programmed for synchronization with colloid assembly, thereby realizing the optimal programmability of DNA-functionalized colloids. We applied this strategy to conditionally activate colloid assembly and dynamically switch colloid identities by reconfiguring DNA molecular architectures, thereby achieving orderly structural transformations; leveraging the advantage of room-temperature assembly, we used this method to prepare a lattice of temperature-sensitive proteins and gold nanoparticles. This approach bridges two subfields: dynamic DNA nanotechnology and DNA-functionalized colloid programming.

Assembling Magnetic Nanoparticles on Nanomechanical Resonators for Torque Magnetometry

We report a highly compliant process for patterning nanoparticle arrays on micro- and nanomechanical devices. The distinctive step involves the single layer self-assembled nanoparticles on top of released nanomechanical devices. We demonstrate the process by fabricating sizable arrays of nanomechanical devices on silicon-on-insulator substrates, acting as nanomechanical torque magnetometers. Later, the nanoparticles were self-assembled in geometrical shapes on top of the devices by a unique combination of top-down and bottom-up methods. The self-assembled array of nanoparticles successfully showed a magnetic torque signal by magnetic actuation of the magnetometer. This patterning process can be generalized for any shape and for a wide range of nanoparticles on the nanomechanical resonators.

From atoms to aerosols: probing clusters and nanoparticles with synchrotron based mass spectrometry and X-ray spectroscopy

Synchrotron radiation provides insight into spectroscopy and dynamics in clusters and nanoparticles.

Refocusing in Situ Electron Microscopy: Moving beyond Visualization of Nanoparticle Self-Assembly To Gain Practical Insights into Advanced Material Fabrication

Despite incredible progress in preparing extended nanoparticle superlattices by self-assembly, theoretically predicted collective properties of extended nanoparticle superlattices are rarely correlated to observations due to the presence of defects. Enhanced fundamental understanding of the kinetics involved in nanoparticle superlattice self-assembly, specifically defect formation and annealing kinetics and mechanisms, is needed to prepare defect-free nanoparticle superlattices. In situ transmission electron microscopy (TEM) enables direct visualization of nanoparticle self-assembly phenomena in real time and at atomic spatial resolution; however, effective translation of in situ TEM data into new predictive models and material synthesis design rules remains a persistent challenge. Recent work by Ondry et al. in this issue of ACS Nano utilized atomic resolution in situ TEM to establish defect removal kinetics in epitaxially attached CdSe nanocrystal pairs, revealing a set of practical guidelines for minimizing defect formation in extended nanoparticle solids. Motivated by this work, in this Perspective, I explore and discuss the most effective and impactful uses of in situ TEM for nanoscience research and the associated technical barriers for performing in situ TEM measurements that are meaningful to bulk-scale self-assembly experiments.

Catalystlike role of impurities in speeding layer-by-layer growth

Molecular self-assembly is usually done at low supersaturation, leading to low rates of growth, in order to allow time for binding mistakes to anneal. However, such conditions can lead to prohibitively long assembly times where growth proceeds by the slow nucleation of successive layers. Here we use a lattice model of molecular self-assembly to show that growth in this regime can be sped up by impurities, which lower the free-energy cost of layer nucleation. Under certain conditions impurities behave almost as a catalyst in that they are present at high concentration at the surface of the assembling structure, but at low concentration in the bulk of the assembled structure. Extrapolation of our numerics using simple analytic arguments suggests that this mechanism can reduce growth times by orders of magnitude in parameter regimes applicable to molecular systems.

Effects of non-pairwise repulsion on nanoparticle assembly

Electrostatic interactions provide a convenient way to modulate interactions between nanoparticles, colloids, and biomolecules because they can be adjusted by the solution pH or salt concentration. While the presence of salt provides an easy method to control the net interparticle interaction, the nonlinearities arising from electrostatic screening make it difficult to quantify the strength of the interaction. In particular, when charged particles assemble into clusters or aggregates, nonlinear effects render the interactions strongly non-pairwise. Here, we report Brownian dynamics simulations to investigate the effect that the non-pairwise nature of electrostatic interactions has on nanoparticle assembly. We compare these simulations to a system in which the electrostatics are modeled by a strictly pairwise Yukawa potential. We find that both systems show a narrow range in parameter space where the particles form well-ordered crystals. Bordering this range are regions where the net interactions are too weak to stabilize aggregated structures or strong enough that the system becomes kinetically trapped in a gel. The non-pairwise potential differs from the pairwise system in the appearance of an amorphous state for strongly charged particles. This state appears because the many-body electrostatic interactions limit the maximum density achievable in an assembly.

Mechanistic Insights into Statistical Co-Assembly of Metal Complexes

Statistical copolymerization plays a key role in many biological and technological processes; however, mechanistic understanding of the formation of analogous supramolecular counterparts remains limited. Herein, we report detailed insights into the supramolecular co-assembly of two π-conjugated PdII and PtII complexes, which in isolation self-assemble into flexible fibers and nanodisks, respectively. An efficient single-step co-assembly into only one type of nanostructure (fibers or nanodisks) takes place if any of the components is in excess. In contrast, equimolar mixtures lead to PdII -rich fiber-like co-assemblies by a statistical co-nucleation event along with a residual amount of self-sorted nanodisks in a stepwise manner.

A versatile simulation method for studying phase behavior and dynamics in colloidal rod and rod-polymer suspensions

Here, we present an implicit-solvent model for dynamic simulations of hard-rod and rod-polymer suspensions. Individual rods are represented by a rigid linear chain consisting of overlapping spheres which interact through a pseudohard-core potential based on the cut-and-shifted Mie (generalized Lennard-Jones) potential with exponents (50, 49). In the rod-polymer suspensions, the polymers are modeled as freely interpenetrable spheres with respect to each other, while there is the pseudohard-core repulsion between the polymer and rod spheres. Dynamic simulations with this model are carried out with a dissipative particle dynamics (DPD) thermostat-each sphere is put in a larger DPD sphere and thus interacts with others via additional pairwise frictional and random forces-which captures the effects of Brownian forces due to the solvent while conserving local momentum. The phase behavior of these models, obtained from continuous compression and expansion simulations, reproduces previous predictions based on theoretical calculations and Monte Carlo simulations. Our method is suited to study dynamic processes in these suspensions, including nucleation and self-assembly, and can be readily extended to colloidal particles of different shapes and chemistry.

Typical Stochastic Paths in the Transient Assembly of Fibrous Materials

When chemically fueled, molecular self-assembly can sustain dynamic aggregates of polymeric fibers-hydrogels-with tunable properties. If the fuel supply is finite, the hydrogel is transient, as competing reactions switch molecular subunits between active and inactive states, drive fiber growth and collapse, and dissipate energy. Because the process is away from equilibrium, the structure and mechanical properties can reflect the history of preparation. As a result, the formation of these active materials is not readily susceptible to a statistical treatment in which the configuration and properties of the molecular building blocks specify the resulting material structure. Here, we illustrate a stochastic-thermodynamic and information-theoretic framework for this purpose and apply it to these self-annihilating materials. Among the possible paths, the framework variationally identifies those that are typical-loosely, the minimum number with the majority of the probability. We derive these paths from computer simulations of experimentally-informed stochastic chemical kinetics and a physical kinetics model for the growth of an active hydrogel. The model reproduces features observed by confocal microscopy, including the fiber length, lifetime, and abundance as well as the observation of fast fiber growth and stochastic fiber collapse. The typical mesoscopic paths we extract are less than 0.23% of those possible, but they accurately reproduce material properties such as mean fiber length.

Conformation Dependence of Diphenylalanine Self-Assembly Structures and Dynamics: Insights from Hybrid-Resolution Simulations

The molecular design of peptide-assembled nanostructures relies on extensive knowledge pertaining to the relationship between conformational features of peptide constituents and their behavior regarding self-assembly, and characterizing the conformational details of peptides during their self-assembly is experimentally challenging. Here, we demonstrate that a hybrid-resolution modeling method can be employed to investigate the role that conformation plays during the assembly of terminally capped diphenylalanines (FF) through microsecond simulations of hundreds or thousands of peptides. Our simulations discovered tubular or vesicular nanostructures that were consistent with experimental observation while reproducing critical self-assembly concentration and secondary structure contents in the assemblies that were measured in our experiments. The atomic details provided by our method allowed us to uncover diverse FF conformations and conformation dependence of assembled nanostructures. We found that the assembled morphologies and the molecular packing of FFs in the observed assemblies are linked closely with side-chain angle and peptide bond orientation, respectively. Of various conformations accessible to soluble FFs, only a select few are compatible with the assembled morphologies in water. A conformation resembling a FF crystal, in particular, became predominant due to its ability to permit highly ordered and energetically favorable FF packing in aqueous assemblies. Strikingly, several conformations incompatible with the assemblies arose transiently as intermediates, facilitating key steps of the assembly process. The molecular rationale behind the role of these intermediate conformations were further explained. Collectively, the structural details reported here advance the understanding of the FF self-assembly mechanism, and our method shows promise for studying peptide-assembled nanostructures and their rational design.

The Pathway to Intelligence: Using Stimuli-Responsive Materials as Building Blocks for Constructing Smart and Functional Systems

Systems that are intelligent have the ability to sense their surroundings, analyze, and respond accordingly. In nature, many biological systems are considered intelligent (e.g., humans, animals, and cells). For man-made systems, artificial intelligence is achieved by massively sophisticated electronic machines (e.g., computers and robots operated by advanced algorithms). On the other hand, freestanding materials (i.e., not tethered to a power supply) are usually passive and static. Hence, herein, the question is asked: can materials be fabricated so that they are intelligent? One promising approach is to use stimuli-responsive materials; these "smart" materials use the energy supplied by a stimulus available from the surrounding for performing a corresponding action. After decades of research, many interesting stimuli-responsive materials that can sense and perform smart functions have been developed. Classes of functions discussed include practical functions (e.g., targeting and motion), regulatory functions (e.g., self-regulation and amplification), and analytical processing functions (e.g., memory and computing). The pathway toward creating truly intelligent materials can involve incorporating a combination of these different types of functions into a single integrated system by using stimuli-responsive materials as the basic building blocks.

Why Enveloped Viruses Need Cores-The Contribution of a Nucleocapsid Core to Viral Budding

During the lifecycle of many enveloped viruses, a nucleocapsid core buds through the cell membrane to acquire an outer envelope of lipid membrane and viral glycoproteins. However, the presence of a nucleocapsid core is not required for assembly of infectious particles. To determine the role of the nucleocapsid core, we develop a coarse-grained computational model with which we investigate budding dynamics as a function of glycoprotein and nucleocapsid interactions, as well as budding in the absence of a nucleocapsid. We find that there is a transition between glycoprotein-directed budding and nucleocapsid-directed budding that occurs above a threshold strength of nucleocapsid interactions. The simulations predict that glycoprotein-directed budding leads to significantly increased size polydispersity and particle polymorphism. This polydispersity can be explained by a theoretical model accounting for the competition between bending energy of the membrane and the glycoprotein shell. The simulations also show that the geometry of a budding particle leads to a barrier to subunit diffusion, which can result in a stalled, partially budded state. We present a phase diagram for this and other morphologies of budded particles. Comparison of these structures against experiments could establish bounds on whether budding is directed by glycoprotein or nucleocapsid interactions. Although our model is motivated by alphaviruses, we discuss implications of our results for other enveloped viruses.

Self-assembled pearl-necklace patterned upconverting nanocrystals with highly efficient blue and ultraviolet emission: femtosecond laser based upconversion properties

This work reports new findings on the formation of a pearl-necklace pattern in self-assembled upconverting nanocrystals (UCN-PNs) which exhibit strong upconversion emission under an NIR excitation source of a femtosecond laser (Fs-laser). Each nano-necklace consists of several upconversion nanoparticles (UCNPs) having a size ca. 10 ± 1 nm. UCN-PNs are arranged in a self-organized manner to form necklace type chains with an average length of 140 nm of a single row of nanoparticles. Furthermore, UCN-PNs are comprised of UCNPs with an average interparticle separation of ca. 4 nm in each of the nanonecklace chains. Interestingly, these UCN-PNs exhibit high energy upconversion especially in the UV region on interaction with a 140 Fs-laser pulse duration at 80 MHz repetition rate and intense blue emission at 450 nm on interaction with a 900 nm excitation source is obtained. The preparation of self-assembled UCNPs is easy and they are very stable for a longer period of time. The emission (fluorescence/luminescence) intensity is very high which can make them unique in innumerable industrial and bio-applications such as for disease diagnosis and therapeutic applications by targeting the infected cells with enhanced efficiency.

Self-assembled pearl necklace patterned-upconverting nanoparticles and their femtosecond laser based upconversion properties.

Self-assembling outside equilibrium: emergence of structures mediated by dissipation

Self-assembly under non-equilibrium conditions may give rise to the formation of structures not available at equilibrium.

Information generating, sharing, and manipulating Source-Reservoir-Sink model of self-organizing dissipative structures

The evolution of self-organizing ensembles of fullerenes and the emergence of the Buckyball are described by information generating, sharing, and manipulating Source-Reservoir-Sink model. Shannon's information-theoretic model of signal transmitter, channel, and receiver that preserves and retains the original signal is extended to our model that maps the transformations of chemical and physical components of the self-organizing dissipative structures into Source, Reservoir, and Sink. The information generated by Source is manipulated by controlling the flow of information to Reservoir before being transmitted to Sink. It is demonstrated in a Box-model. The role of Reservoir in building up the manipulative capacity for information storage and selective sharing is illustrated by the asymmetric exchange of material and information. The number of boxes and the flow rates are varied to evaluate the information-theoretic diagnostic tools of Shannon entropy, complexity, fractal dimension, relative entropy, and the entropic cost of the emerging dissipative structures.

Nonequilibrium associative retrieval of multiple stored self-assembly targets

Many biological systems rely on the ability to self-assemble different target structures using the same set of components. Equilibrium self-assembly suffers from a limited capacity in such cases, due to an increasing number of decoy states that grows rapidly with the number of targets encoded. Moreover, improving the kinetic stability of a target at equilibrium carries the price of introducing kinetic traps, leading to slower assembly. Using a toy physical model of interacting particles, we demonstrate that local driving can improve both the assembly time and kinetic stability of multitarget self-assembly, as well as reduce fluctuations around the target configuration. We further show that the local drive can result in a steady-state probability distribution over target structures that deviates from the Boltzmann distribution in a way that depends on the types of interactions that stabilize the targets. Our results illustrate the role that nonequilibrium driving plays in overcoming tradeoffs that are inherent to equilibrium assemblies.

Self-Assembly of Nanocubic Molecular Capsules via Solvent-Guided Formation of Rectangular Blocks

We investigate the mechanism underlying the self-assembly of gear-shaped amphiphilic molecules into a highly ordered nanocubic capsule ("nanocube") in aqueous methanol. Simulation results show that the solvent molecules play a significant role in the assembly process by directing the primitive intermediates to orthogonal/rectangular shapes, thus creating appropriate building blocks for cubic assembly while avoiding off-pathway stacked aggregates. Free-energy analyses reveal that the interplay of the direct intermonomer interaction and the solvent-mediated repulsion between large aromatic cores (via preferential solvation of methanol on hydrophobic surfaces) leads to the strong trend for perpendicular binding of monomers and hence the solvent-guided formation of rectangular blocks. Furthermore, we report the self-assembly simulation of the nanocube using replica exchange with solute tempering and demonstrate that the simulation can predict a highly ordered nanocapsule structure, assembly intermediates, and encapsulated molecules, which helps promote computer-aided design of functional molecular self-assemblies in explicit solvent.

Nonequilibrium self-assembly dynamics of icosahedral viral capsids packaging genome or polyelectrolyte

The survival of viruses partly relies on their ability to self-assemble inside host cells. Although coarse-grained simulations have identified different pathways leading to assembled virions from their components, experimental evidence is severely lacking. Here, we use time-resolved small-angle X-ray scattering to uncover the nonequilibrium self-assembly dynamics of icosahedral viral capsids packaging their full RNA genome. We reveal the formation of amorphous complexes via an en masse pathway and their relaxation into virions via a synchronous pathway. The binding energy of capsid subunits on the genome is moderate (~7k_BT₀, with k_B the Boltzmann constant and T₀ = 298 K, the room temperature), while the energy barrier separating the complexes and the virions is high (~ 20k_BT₀). A synthetic polyelectrolyte can lower this barrier so that filled capsids are formed in conditions where virions cannot build up. We propose a representation of the dynamics on a free energy landscape.

The mechanism by which virus capsules assemble around RNA to package their genetic material is not clear. Here, the authors observed the assembly of the cowpea chlorotic mottle virus capsid around viral RNA or poly(styrene sulfonic acid) using time-resolved small-angle X-ray scattering measurements.

Programming hierarchical self-assembly of colloids: matching stability and accessibility

Encoding hierarchical self-assembly in colloidal building blocks is a promising bottom-up route to high-level structural complexity often observed in biological materials. However, harnessing this promise faces the grand challenge of bridging hierarchies of multiple length- and time-scales, associated with structure and dynamics respectively along the self-assembly pathway. Here we report on a case study, which examines the kinetic accessibility of a series of hollow spherical structures with a two-level structural hierarchy self-assembled from charge-stabilized colloidal magnetic particles. By means of a variety of computational methods, we find that for a staged assembly pathway, the structure, which derives the strongest energetic stability from the first stage of assembly and the weakest from the second stage, is most kinetically accessible. Such a striking correspondence between energetics and kinetics for optimal design principles should have general implications for programming hierarchical self-assembly pathways for nano- and micro-particles, while matching stability and accessibility.

Energy-Landscape-Independent Kinetic Trap of an Incomplete Cage in the Self-Assembly of a Pd2 L4 Cage

A kinetic trap is the metastable species that is transiently or constantly produced during the reaction by trapping in a deep energy well. In most cases, the reactivity of kinetically trapped species is relatively low under the reaction conditions. Herein, we report another type of kinetically trapped species that is an incomplete cage (IC) intermediate produced during the self-assembly of a Pd₂ L₄ cage from ditopic ligand (L) and Pd^II ions with a certain lifetime, although IC has a high enough reactivity to be converted into the cage with the reaction of free L, which was confirmed by the reaction of the isolated IC and L under the self-assembly conditions. IC was kinetically trapped not because IC lies on the bottom of a deep energy well but because the conversion of the intermediates essential for the conversion of IC to the cage preferentially takes place; IC was kinetically trapped independently of the shape of the energy landscape of the self-assembly.

Direct observation and rational design of nucleation behavior in addressable self-assembly

Current efforts aimed at constructing complex supramolecular structures often suffer from low yields or require long assembly protocols. We address these problems by demonstrating a facile strategy for optimizing the nucleation step of a multicomponent self-assembly reaction. By tracking the formation of multisubunit clusters in situ, our experiments show that modifying the critical nucleus required to initiate structure growth can broaden the range of conditions over which self-assembly occurs and, consequently, can dramatically improve the final yield of correctly formed structures. Since varying the design of only a small portion of the target structure optimizes its yield, this strategy provides a practical route to improve the speed and accuracy of self-assembly in biomolecular, colloidal, and nanoparticle systems.

To optimize a self-assembly reaction, it is essential to understand the factors that govern its pathway. Here, we examine the influence of nucleation pathways in a model system for addressable, multicomponent self-assembly based on a prototypical “DNA-brick” structure. By combining temperature-dependent dynamic light scattering and atomic force microscopy with coarse-grained simulations, we show how subtle changes in the nucleation pathway profoundly affect the yield of the correctly formed structures. In particular, we can increase the range of conditions over which self-assembly occurs by using stable multisubunit clusters that lower the nucleation barrier for assembling subunits in the interior of the structure. Consequently, modifying only a small portion of a structure is sufficient to optimize its assembly. Due to the generality of our coarse-grained model and the excellent agreement that we find with our experimental results, the design principles reported here are likely to apply generically to addressable, multicomponent self-assembly.

In vivo production of RNA nanostructures via programmed folding of single-stranded RNAs

Programmed self-assembly of nucleic acids is a powerful approach for nano-constructions. The assembled nanostructures have been explored for various applications. However, nucleic acid assembly often requires chemical or in vitro enzymatical synthesis of DNA or RNA, which is not a cost-effective production method on a large scale. In addition, the difficulty of cellular delivery limits the in vivo applications. Herein we report a strategy that mimics protein production. Gene-encoded DNA duplexes are transcribed into single-stranded RNAs, which self-fold into well-defined RNA nanostructures in the same way as polypeptide chains fold into proteins. The resulting nanostructure contains only one component RNA molecule. This approach allows both in vitro and in vivo production of RNA nanostructures. In vivo synthesized RNA strands can fold into designed nanostructures inside cells. This work not only suggests a way to synthesize RNA nanostructures on a large scale and at a low cost but also facilitates the in vivo applications.

RNA nanostructures have been demonstrated in a range of biological applications, but their assembly and delivery to cells is difficult. Here the authors demonstrate the in vivo assembly of a RNA nanostructure from a single transcript inside the cellular environment.

Robust nonequilibrium pathways to microcompartment assembly

Cyanobacteria sequester photosynthetic enzymes into microcompartments which facilitate the conversion of carbon dioxide into sugars. Geometric similarities between these structures and self-assembling viral capsids have inspired models that posit microcompartments as stable equilibrium arrangements of the constituent proteins. Here we describe a different mechanism for microcompartment assembly, one that is fundamentally nonequilibrium and yet highly reliable. This pathway is revealed by simulations of a molecular model resolving the size and shape of a cargo droplet and the extent and topography of an elastic shell. The resulting metastable microcompartment structures closely resemble those of carboxysomes, with a narrow size distribution and faceted shells. The essence of their assembly dynamics can be understood from a simpler mathematical model that combines elements of classical nucleation theory with continuum elasticity. These results highlight important control variables for achieving nanoscale encapsulation in general and for modulating the size and shape of carboxysomes in particular.

Direct Visualization of Planar Assembly of Plasmonic Nanoparticles Adjacent to Electrodes in Oscillatory Electric Fields

Electric field-directed assembly of colloidal nanoparticles (NPs) has been widely adopted for fabricating functional thin films and nanostructured surfaces. While first-order electrokinetic effects on NPs are well-understood in terms of classical models, effects of second-order electrokinetics that involve induced surface charge are still poorly understood. Induced charge electroosmotic phenomena, such as electrohydrodynamic (EHD) flow, have long been implicated in electric field-directed NP assembly with little experimental basis. Here, we use in situ dark-field optical microscopy and plasmonic NPs to directly observe the dynamics of planar assembly of colloidal NPs adjacent to a planar electrode in low-frequency (<1 kHz) oscillatory electric fields. We exploit the change in plasmonic NP color resulting from interparticle plasmonic coupling to visualize the assembly dynamics and assembly structure of silver NPs. Planar assembly of NPs is unexpected because of strong electrostatic repulsion between NPs and indicates that there are strong attractive interparticle forces oriented perpendicular to the electric field direction. A parametric investigation of the voltage- and frequency-dependent phase behavior reveals that planar NP assembly occurs over a narrow frequency range below which irreversible ballistic deposition occurs. Two key experimental observations are consistent with EHD flow-induced NP assembly: (1) NPs remain mobile during assembly and (2) electron microscopy observations reveal randomly close-packed planar assemblies, consistent with strong interparticle attraction. We interpret planar assembly in terms of EHD fluid flow and develop a scaling model that qualitatively agrees with the measured phase regions. Our results are the first direct in situ observations of EHD flow-induced NP assembly and shed light on long-standing unresolved questions concerning the formation of NP superlattices during electric field-induced NP deposition.