Nonequilibrium Assembly Research Articles

Role of Thermolysin in Catalytic-Controlled Self-Assembly of Fmoc-Dipeptides

In recent years, short peptide self-assembled materials, prepared under the control of the thermolysin catalyst, have been investigated extensively and shown to acquire various morphologies and fun...

Clustering and self-organization in small-scale natural and artificial systems.

Physical properties of clusters, i.e. systems composed of a 'small' number of particles, are qualitatively different from those of infinite systems. The general approach to the problem of clustering is suggested. Clusters, as they are seen in the graphs theory, are discussed. Various physical mechanisms of clustering are reviewed. Dimensional properties of clusters are addressed. The dimensionality of clusters governs to a great extent their properties. Weakly and strongly coupled clusters are discussed. Hydrodynamic and capillary interactions giving rise to clusters formation are surveyed. Levitating droplet clusters, turbulent clusters and droplet clusters responsible for the breath-figures self-assembly are considered. Entropy factors influencing clustering are considered. Clustering in biological systems results in non-equilibrium multi-scale assembly, where at each scale, self-driven components come together by consuming energy in order to form the hierarchical structure. This article is part of the theme issue 'Bioinspired materials and surfaces for green science and technology (part 3)'.

Assembly of heteropolymers via a network of reaction coordinates.

In biochemistry, heteropolymers encoding biological information are assembled out of equilibrium by sequentially incorporating available monomers found in the environment. Current models of polymerization treat monomer incorporation as a sequence of discrete chemical reactions between intermediate metastable states. In this paper, we use ideas from reaction rate theory and describe nonequilibrium assembly of a heteropolymer via a continuous reaction coordinate. Our approach allows for estimating the copy error and incorporation speed from the Gibbs free energy landscape of the process. We apply our theory to several examples from a simple reaction characterized by a free energy barrier to more complex cases incorporating error correction mechanisms, such as kinetic proofreading.

Jonathan Steed to helm Crystal Growth and Design

Jonathan W. Steed, professor of inorganic chemistry at Durham University, has been named the new editor in chief of the American Chemical Society journal Crystal Growth and Design. He takes the helm from Robin Rogers, who has served as inaugural editor in chief of the journal since its founding in 2001. Crystal Growth and Design publishes theoretical and experimental studies of the physical, chemical, and biological phenomena and processes related to the design, growth, and application of crystalline materials. “As editor in chief I will look to reach out to a broad range of scientists interested in nonequilibrium assembly and make the journal a home for their cross-disciplinary work,” Steed says. “This offers tremendous scope for joint initiatives with other ACS journals. I will also look to further build the industry integration of the journal.” Steed’s research at Durham University is at the interface of crystallization and soft materials chemistry.

Non-equilibrium steady-state colloidal assembly dynamics.

Simulations and experiments are reported for nonequilibrium steady-state assembly of small colloidal crystal clusters in rotating magnetic fields vs frequency and amplitude. High-dimensional trajectories of particle coordinates from image analysis of experiments and from Stokesian Dynamic computer simulations are fit to low-dimensional reaction coordinate based Fokker-Planck and Langevin equations. The coefficients of these equations are effective energy and diffusivity landscapes that capture configuration-dependent energy and friction for nonequilibrium steady-state dynamics. Two reaction coordinates that capture condensation and anisotropy of dipolar chains folding into crystals are sufficient to capture high-dimensional experimental and simulated dynamics in terms of first passage time distributions. Our findings illustrate how field-mediated nonequilibrium steady-state colloidal assembly dynamics can be modeled to interpret and design pathways toward target microstructures and morphologies.

Electrostatic Forces in Field-Perturbed Equilibria: Nanopore Analysis of Cage Complexes

Summary Molecular recognition has been widely investigated under equilibrium conditions, but little is known about such processes when perturbed by external forces. Here, we investigate the influence of electric fields on complexes formed between metallosupramolecular cages and a protein nanopore at the single-molecule level. Association rates were dominated by the applied voltage, whereas local electrostatic interactions between the cage and the nanopore more greatly influenced the dissociation kinetics. By exploiting these principles, we showed that the externally applied voltage could be used to selectively bind a specific cage from a mixture containing a large excess of other cages. Moreover, the applied voltage could also be used to drive supramolecular enantio-inversion of the chiral cages or, occasionally, the non-equilibrium capture and disassembly of cages deep within the nanopore. Similar principles might be exploited in the design of other molecular devices that operate within externally applied electric fields or biogenic transmembrane potentials.

Systems protobiology: origin of life in lipid catalytic networks.

Life is that which replicates and evolves, but there is no consensus on how life emerged. We advocate a systems protobiology view, whereby the first replicators were assemblies of spontaneously accreting, heterogeneous and mostly non-canonical amphiphiles. This view is substantiated by rigorous chemical kinetics simulations of the graded autocatalysis replication domain (GARD) model, based on the notion that the replication or reproduction of compositional information predated that of sequence information. GARD reveals the emergence of privileged non-equilibrium assemblies (composomes), which portray catalysis-based homeostatic (concentration-preserving) growth. Such a process, along with occasional assembly fission, embodies cell-like reproduction. GARD pre-RNA evolution is evidenced in the selection of different composomes within a sparse fitness landscape, in response to environmental chemical changes. These observations refute claims that GARD assemblies (or other mutually catalytic networks in the metabolism first scenario) cannot evolve. Composomes represent both a genotype and a selectable phenotype, anteceding present-day biology in which the two are mostly separated. Detailed GARD analyses show attractor-like transitions from random assemblies to self-organized composomes, with negative entropy change, thus establishing composomes as dissipative systems—hallmarks of life. We show a preliminary new version of our model, metabolic GARD (M-GARD), in which lipid covalent modifications are orchestrated by non-enzymatic lipid catalysts, themselves compositionally reproduced. M-GARD fills the gap of the lack of true metabolism in basic GARD, and is rewardingly supported by a published experimental instance of a lipid-based mutually catalytic network. Anticipating near-future far-reaching progress of molecular dynamics, M-GARD is slated to quantitatively depict elaborate protocells, with orchestrated reproduction of both lipid bilayer and lumenal content. Finally, a GARD analysis in a whole-planet context offers the potential for estimating the probability of life's emergence. The invigorated GARD scrutiny presented in this review enhances the validity of autocatalytic sets as a bona fide early evolution scenario and provides essential infrastructure for a paradigm shift towards a systems protobiology view of life's origin.

Large-Scale Noniridescent Structural Color Printing Enabled by Infiltration-Driven Nonequilibrium Colloidal Assembly.

Structural colors originating from interaction of light with intricately arranged micro-/nanostructures have stimulated considerable interest because of their inherent photostability and energy efficiency. In particular, noniridescent structural color with wide viewing angle has been receiving increasing attention recently. However, no method is yet available for rapid and large-scale fabrication of full-spectrum structural color patterns with wide viewing angles. Here, infiltration-driven nonequilibrium assembly of colloidal particles on liquid-permeable and particle-excluding substrates is demonstrated to direct the particles to form amorphous colloidal arrays (ACAs) within milliseconds. The infiltration-assisted (IFAST) colloidal assembly opens new possibilities for rapid manufacture of noniridescent structural colors of ACAs and straightforward structural color mixing. Full-spectrum noniridescent structural colors are successfully produced by mixing primary structural colors of red, blue, and yellow using a commercial office inkjet printer. Rapid fabrication of large-scale structural color patterns with sophisticated color combination/layout by IFAST printing is realized. The IFAST technology is versatile for developing structural color patterns with wide viewing angles, as colloidal particles, inks, and substrates are flexibly designable for diverse applications.

Associative Pattern Recognition Through Macro-molecular Self-Assembly

We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of $N$ distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical attractors to recognize and reconstruct partially corrupted patterns. Traditional parameters of pattern recognition theory, such as sparsity, fidelity, and capacity are related to physical parameters, such as nucleation barriers, interaction range, and non-equilibrium assembly forces. Notably, we find that self-assembly bears greater similarity to continuous attractor neural networks, such as place cell networks that store spatial memories, rather than discrete memory networks. This relationship suggests that features and trade-offs seen here are not tied to details of self-assembly or neural network models but are instead intrinsic to associative pattern recognition carried out through short-ranged interactions.

Using active colloids as machines to weave and braid on the micrometer scale

Controlling motion at the microscopic scale is a fundamental goal in the development of biologically inspired systems. We show that the motion of active, self-propelled colloids can be sufficiently controlled for use as a tool to assemble complex structures such as braids and weaves out of microscopic filaments. Unlike typical self-assembly paradigms, these structures are held together by geometric constraints rather than adhesive bonds. The out-of-equilibrium assembly that we propose involves precisely controlling the 2D motion of active colloids so that their path has a nontrivial topology. We demonstrate with proof-of-principle Brownian dynamics simulations that, when the colloids are attached to long semiflexible filaments, this motion causes the filaments to braid. The ability of the active particles to provide sufficient force necessary to bend the filaments into a braid depends on a number of factors, including the self-propulsion mechanism, the properties of the filament, and the maximum curvature in the braid. Our work demonstrates that nonequilibrium assembly pathways can be designed using active particles.

Landscape of kinetically trapped binary assemblies.

For two-component assemblies, an inherent structure diagram (ISD) is the relationship between set inter-subunit energies and the types of kinetic traps (inherent structures) one may obtain from those energies. It has recently been shown that two-component ISDs are apportioned into regions or plateaux within which inherent structures display uniform features (e.g., stoichometries and morphologies). Interestingly, structures from one of the plateaux were also found to be robust outcomes of one type of non-equilibrium growth, which indicates the usefulness of the two-component ISD in predicting outcomes of some types of far-from-equilibrium growth. However, little is known as to how the ISD is apportioned into distinct plateaux. Also, while each plateau displays classes of structures that are morphologically distinct, little is known about the source of these distinct morphologies. This article outlines an analytic treatment of the two-component ISD and shows that the manner in which any ISD is apportioned arises from a single unitless order parameter. Additionally, the analytical framework allows for the characterization of local properties of the trapped structures within each ISD plateau. This work may prove to be useful in the design of novel classes of robust nonequilibrium assemblies.

Association-dissociation process with aging subunits: Recursive solution.

The coupling of stochastic growth and shrinkage of one-dimensional structures to random aging of the constituting subunits defines the simple association-dissociation-aging process which captures the essential features of the nonequilibrium assembly of cytoskeletal filaments. Because of correlations, previously employed mean-field methods fail to correctly describe filament growth. We study an alternative formulation of the full master equation of the stochastic process. An ansatz for the steady-state solution leads to a recursion relation which allows for the calculation of all emergent quantities with increasing accuracy and in excellent agreement with stochastic simulations.

Model-driven optimization of multicomponent self-assembly processes

Here, we report an engineering approach toward multicomponent self-assembly processes by developing a methodology to circumvent spurious, metastable assemblies. The formation of metastable aggregates often hampers self-assembly of molecular building blocks into the desired nanostructures. Strategies are explored to master the pathway complexity and avoid off-pathway aggregates by optimizing the rate of assembly along the correct pathway. We study as a model system the coassembly of two monomers, the R- and S-chiral enantiomers of a π-conjugated oligo(p-phenylene vinylene) derivative. Coassembly kinetics are analyzed by developing a kinetic model, which reveals the initial assembly of metastable structures buffering free monomers and thereby slows the formation of thermodynamically stable assemblies. These metastable assemblies exert greater influence on the thermodynamically favored self-assembly pathway if the ratio between both monomers approaches 1:1, in agreement with experimental results. Moreover, competition by metastable assemblies is highly temperature dependent and hampers the assembly of equilibrium nanostructures most effectively at intermediate temperatures. We demonstrate that the rate of the assembly process may be optimized by tuning the cooling rate. Finally, it is shown by simulation that increasing the driving force for assembly stepwise by changing the solvent composition may circumvent metastable pathways and thereby force the assembly process directly into the correct pathway.

Non-equilibrium ionic assemblies of oppositely charged nanoparticles

Structure and evolution kinetics of non-equilibrium clusters formed in a solution of oppositely charged nanoparticles are studied using a recently developed kinetic Monte Carlo simulation scheme (Jha et al., Soft Matter, 2012, 8, 227–234). A diverse range of dynamic cluster configurations are obtained by varying the interaction strength between nanoparticles, screening length, and packing density of nanoparticles. Structural details of the resulting clusters are obtained using the correlations of local bond orientational order parameters. At low-salt concentrations (weak screening), clusters with structures ranging from NaCl-type cubic aggregates to fibril-like chains are observed, while at high-salt concentrations (strong screening), disordered compact clusters are observed. A chain-folding barrier model is proposed to explain the kinetically trapped fibril-like assemblies. In higher-density solutions, large ionic clusters or percolated gel structures are observed. Our work demonstrates the structural richness of non-equilibrium ionic assemblies of oppositely charged nanoparticles and elucidates the effect of ion correlations on the determination of the structure of assemblies of oppositely charged nanoparticles. These “nanoionic composites” hold great promise in a variety of emerging applications such as templated polymerization of charged molecules and assembly of charged nano-objects.

Topological Interaction by Entangled DNA Loops

We have discovered a new type of interaction between micro- or nanoscale particles that results from the entanglement of strands attached to their surfaces. Self-complementary DNA single strands on a particle can hybridize to form loops. A similar proximal particle can have its loops catenate with those of the first. Unlike conventional thermodynamic interparticle interactions, the catenation interaction is strongly history and protocol dependent, allowing for nonequilibrium particle assembly. The interactions can be controlled by an interesting combination of forces, temperature, light sensitive cross-linking and enzymatic unwinding of the topological links. This novel topological interaction may lead to new materials and phenomena such as particles strung on necklaces, confined motions on designed contours and surfaces, and colloidal Olympic gels.

Interfacial templating of inorganic nanostructures using a growth directing and reducing peptide

The rational design of interfacially confined peptides allows for the direct examination of biomimetic processes for materials synthesis, where non-equilibrium interfacial assembly engenders complexity in metallic nano-structures. Here we report our recent progress towards applying surface-active peptides to precisely control the spatial distribution of amino acids. In order to engineer multiple length scales in inorganic materials, our periodically sequenced peptide is designed to be trifunctional: (1) self-assembling at the air–water interface, (2) reducing gold in the subphase, and (3) directing growth of the inorganic phase under confinement. We use the Langmuir trough, Brewster angle microscopy, atomic force microscopy, transmission electron microscopy and electron diffraction to characterize control over inorganic structure as a function of the surface pressure of the organic material at the interface. Single crystalline triangular nanoplatelets of gold form at a surface pressure of 30 mN m−1 or less. At higher surface pressures, when binding sites are in closer proximity, a mosaic of more complex structures are formed. This work demonstrates that self-assembling surface confined peptides can be applied to define a bio-inspired tectonic process, leading to hierarchical structures at phase boundaries.

Nonequilibirum Assembly, Retroviruses, and Conical Structures

We study the spontaneous assembly of viral shells composed of several identical subunits under nonequilibrium conditions. We find that within the basic continuum elasticity framework, the nonequilibrium assembly process is able to predict the formation of structures pertinent to retroviruses. Our minimal model of assembly yields a unified one-dimensional phase diagram in which the appearance of spherical, irregular, conical and cylindrical structures of retroviruses is seen to be governed by the spontaneous curvature of protein subunits.

Nonequilibrium statistical mechanical models for cytoskeletal assembly: Towards understanding tensegrity in cells

The cytoskeleton is not an equilibrium structure. To develop theoretical tools to investigate such nonequilibrium assemblies, we study a statistical physical model of motorized spherical particles. Though simple, it captures some of the key nonequilibrium features of the cytoskeletal networks. Variational solutions of the many-body master equation for a set of motorized particles accounts for their thermally induced Brownian motion as well as for the motorized kicking of the structural elements. These approximations yield stability limits for crystalline phases and for frozen amorphous structures. The methods allow one to compute the effects of nonequilibrium behavior and adhesion (effective cross-linking) on the mechanical stability of localized phases as a function of density, adhesion strength, and temperature. We find that nonequilibrium noise does not necessarily destabilize mechanically organized structures. The nonequilibrium forces strongly modulate the phase behavior and have comparable effect as the adhesion due to cross-linking. Modeling transitions such as these allows the mechanical properties of cytoskeleton to rapidly and adaptively change. The present model provides a statistical mechanical underpinning for a tensegrity picture of the cytoskeleton.

Nonequilibrium Synthesis and Assembly of Hybrid Inorganic−Protein Nanostructures Using an Engineered DNA Binding Protein

We show that a protein with no intrinsic inorganic synthesis activity can be endowed with the ability to control the formation of inorganic nanostructures under thermodynamically unfavorable (nonequilibrium) conditions, reproducing a key feature of biological hard-tissue growth and assembly. The nonequilibrium synthesis of Cu(2)O nanoparticles is accomplished using an engineered derivative of the DNA-binding protein TraI in a room-temperature precursor electrolyte. The functional TraI derivative (TraIi1753::CN225) is engineered to possess a cysteine-constrained 12-residue Cu(2)O binding sequence, designated CN225, that is inserted into a permissive site in TraI. When TraIi1753::CN225 is included in the precursor electrolyte, stable Cu(2)O nanoparticles form, even though the concentrations of [Cu(+)] and [OH(-)] are at 5% of the solubility product (K(sp,Cu2O)). Negative control experiments verify that Cu(2)O formation is controlled by inclusion of the CN225 binding sequence. Transmission electron microscopy and electron diffraction reveal a core-shell structure for the nonequilibrium nanoparticles: a 2 nm Cu(2)O core is surrounded by an adsorbed protein shell. Quantitative protein adsorption studies show that the unexpected stability of Cu(2)O is imparted by the nanomolar surface binding affinity of TraIi1753::CN225 for Cu(2)O (K(d) = 1.2 x 10(-)(8) M), which provides favorable interfacial energetics (-45 kJ/mol) for the core-shell configuration. The protein shell retains the DNA-binding traits of TraI, as evidenced by the spontaneous organization of nanoparticles onto circular double-stranded DNA.

Profilin Promotes Barbed-end Actin Filament Assembly without Lowering the Critical Concentration

The mechanism of profilin-promoted actin polymerization has been systematically reinvestigated. Rates of barbed-end elongation onto Spectrin.4.1. Actin seeds were measured by right angle light scattering to avoid confounding effects of pyrenyl-actin, and KINSIM was used to analyze elongation progress curves. Without thymosin-beta4, both actin and Profilin. Actin (P.A) are competent in barbed-end polymerization, and kinetic simulations yielded the same bimolecular rate constant ( approximately 10 x 10(6) M(-1) s(-1)) for actin monomer or Profilin. Actin. When measured in the absence of profilin, actin assembly curves over a 0.7-4 microM thymosin-beta4 concentration range fit a simple monomer sequestering model (1 microM K(D) for Thymosin-beta4. Actin). The corresponding constant for thymosin-beta4.pyrenyl-Actin, however, was significantly higher ( approximately 9-10 microM), suggesting that the fluorophore markedly weakens binding to thymosin-beta4. With solutions of actin (2 microM) and thymosin-beta4 (2 or 4 microM), the barbed-end assembly rate rose with increasing profilin concentration (0.7-2 microM). Actin assembly in presence of thymosin-beta4 and profilin fit a simple thermodynamic energy cycle, thereby disproving an earlier claim (D. Pantaloni and M.-F. Carlier (1993) Cell 75, 1007-1014) that profilin promotes nonequilibrium filament assembly by accelerating hydrolysis of filament-bound ATP. Our findings indicate that profilin serves as a polymerization catalyst that captures actin monomers from Thymosin-beta4. Actin and ushers actin as a Profilin. Actin complex onto growing barbed filament ends.