Effects of linker flexibility on phase behavior and structure of linked colloidal gels

Neuromorphic Computing Primitives Using Polymer-Networked Nanoparticles

Nanoparticle networks have potential applications in brain-like computing yet their ability to adopt different states remains unexplored. In this work, we reveal the dynamics of the attachment of polyelectrolytes onto gold nanoparticles (AuNPs), using a bottom-up two-bead-monomer dissipative particle dynamics (TBM-DPD) model to show the heterogeneity of polymer coverage. We found that the use of one polyelectrolyte homopolymer limits the complexity of the possible engineered nanoparticle networks (ENPNs) that can be built. In addressing this challenge, we first found the commensurability rules between the numbers of AuNPs and poly(allylamine hydrochloride)s (PAHs). This gives rise to a well-defined valency of a AuNP which is the maximum number of PAHs that it can accommodate. We further use an engineered block copolymer, which has a conductive middle block to mediate the distance between a dimer of AuNP. We argue that by controlling the length of conductive block that is connecting the AuNPs and their respective topology, we can have ENPNs potentially adopt multiple states necessary for primitive neuromorphic computing.

Megamolecule Self-Assembly Networks: A Combined Computational and Experimental Design Strategy

This work describes the use of computational strategies to design megamolecule building blocks for the self-assembly of lattice networks. The megamolecules are prepared by attaching four Cutinase-SnapTag fusion proteins (CS fusions) to a four-armed linker, followed by functionalizing each fusion with a terpyridine linker. This functionality is designed to participate in a metal-mediated self-assembly process to give networks. This article describes a simulation-guided strategy for the design of megamolecules to optimize the peptide linker in the fusion protein to give conformations that are best suited for self-assembly and therefore streamlines the typically time-consuming and labor-intensive experimental process. We designed 11 candidate megamolecules and identified the most promising linker, (EAAAK)2, along with the optimal experimental conditions through a combination of all-atom molecular dynamics, enhanced sampling, and larger-scale coarse-grained molecular dynamics simulations. Our simulation findings were validated and found to be consistent with the experimental results. Significantly, this study offers valuable insight into the self-assembly of megamolecule networks and provides a novel and general strategy for large biomolecular material designs by using systematic bottom-up coarse-grained simulations.

Predicting the size and morphology of nanoparticle clusters driven by biomolecular recognition

Nanoparticle aggregation is a driving principle of innovative materials and biosensing methodologies, improving transduction capabilities displayed by optical, electrical or magnetic measurements. This aggregation can be driven by the biomolecular recognition between target biomolecules (analytes) and receptors bound onto nanoparticle surface. Despite theoretical advances on modelling the entropic interaction in similar systems, predictions of the fractal morphologies of the nanoclusters of bioconjugated nanoparticles are lacking. The morphology of resulting nanoclusters is sensitive to the location, size, flexibility, average number of receptors per particle f̄, and the analyte-particle concentration ratio. Here we considered bioconjugated iron oxide nanoparticles (IONPs) where bonds are mediated by a divalent protein that binds two receptors attached onto different IONPs. We developed a protocol combining analytical expressions for receptors and linker distributions, and Brownian dynamics simulations for bond formation, and validated it against experiments. As more bonds become available (e.g., by adding analytes), the aggregation deviates from the ideal Bethe's lattice scenario due to multivalence, loop formation, and steric hindrance. Generalizing Bethe's lattice theory with a (not-integer) effective functionality feff leads to analytical expressions for the cluster size distributions in excellent agreement with simulations. At high analyte concentration steric impediment imposes an accessible limit value facc to feff, which is bounded by facc < feff < f̄. A transition to gel phase, is correctly captured by the derived theory. Our findings offer new insights into quantifying analyte amounts by assessing nanocluster size, and predicting nanoassembly morphologies accurately is a first step towards understanding variations of physical properties in clusters formed after biomolecular recognition.

Rigidity-Induced Controlled Aggregation of Binary Colloids

Here, we report the proof-of-concept for controlled aggregation in a binary colloidal system. The binary systems are studied by varying bond flexibility of only one species, while the other species' bonds remain fully flexible. By establishing the underlying relation between gelation and bond rigidity, we demonstrate how the interplay among bond flexibility, critical concentration, and packing volume fraction influenced the aggregation kinetics. Our result shows that rigidity in bonds increases the critical concentration for gels to be formed in the binary mixture. Furthermore, the average number of bonded neighbor analyses reveal the influence of bond rigidity both above and below critical concentrations and show that variation in bond flexibility in only one species alters the kinetics of aggregation of both species. This finding improves our understanding of colloidal aggregation in soft and biological systems.

Effects of linker length on phase separation: lessons from the Rubisco-EPYC1 system of the algal pyrenoid

Biomolecular condensates are membraneless organelles formed via phase separation of macromolecules, typically consisting of bond-forming "stickers" connected by flexible "linkers". Linkers have diverse roles, such as occupying space and facilitating interactions. To understand how linker length relative to other lengths affects condensation, we focus on the pyrenoid, which enhances photosynthesis in green algae. Specifically, we apply coarse-grained simulations and analytical theory to the pyrenoid proteins of Chlamydomonas reinhardtii: the rigid holoenzyme Rubisco and its flexible partner EPYC1. Remarkably, halving EPYC1 linker lengths decreases critical concentrations by ten-fold. We attribute this difference to the molecular "fit" between EPYC1 and Rubisco. Varying Rubisco sticker locations reveals that the native sites yield the poorest fit, thus optimizing phase separation. Surprisingly, shorter linkers mediate a transition to a gas of rods as Rubisco stickers approach the poles. These findings illustrate how intrinsically disordered proteins affect phase separation through the interplay of molecular length scales.

Modelling network formation in folded protein hydrogels by cluster aggregation kinetics

Globular folded protein-based hydrogels are becoming increasingly attractive due to their specific biological functionality, as well as their responsiveness to stimuli. By modelling folded proteins as colloids, there are rich opportunities to explore network formation mechanisms in protein hydrogels that negate the need for computationally expensive simulations which capture the full complexity of proteins. Here we present a kinetic lattice-based model which simulates the formation of irreversibly chemically crosslinked, folded protein-based hydrogels. We identify the critical point of gel percolation, explore the range of network regimes covering diffusion-limited to reaction-limited cluster aggregation (DLCA and RLCA, respectively) network formation mechanisms and predict the final network structure, fractal dimensions and final gel porosity. We reveal a crossover between DLCA and RLCA mechanisms as a function of protein volume fraction and show how the final network structure is governed by the structure at the percolation point, regardless of the broad variation of non-percolating cluster masses observed across all systems. An analysis of the pore size distribution in the final network structures reveals that, approaching RLCA, gels have larger maximal pores than the DLCA counterparts for both volume fractions studied. This general kinetic model and the analysis tools generate predictions of network structure and concurrent porosity over a broad range of experimentally controllable parameters that are consistent with current expectations and understanding of experimental results.

Inhomogeneous steady shear dynamics of a three-body colloidal gel former

We investigate the stationary flow of a colloidal gel under an inhomogeneous external shear force using adaptive Brownian dynamics simulations. The interparticle forces are derived from the Stillinger-Weber potential, where the three-body term is tuned to enable network formation and gelation in equilibrium. When subjected to the shear force field, the system develops remarkable modulations in the one-body density profile. Depending on the shear magnitude, particles accumulate either in quiescent regions or in the vicinity of maximum net flow, and we deduce this strong non-equilibrium response to be characteristic of the gel state. Studying the components of the internal force parallel and perpendicular to the flow direction reveals that the emerging flow and structure of the stationary state are driven by significant viscous and structural superadiabatic forces. Thereby, the magnitude and nature of the observed non-equilibrium phenomena differ from the corresponding behavior of simple fluids. We demonstrate that a simple power functional theory reproduces accurately the viscous force profile, giving a rationale of the complex dynamical behavior of the system.

Modular mixing in plasmonic metal oxide nanocrystal gels with thermoreversible links

Gelation offers a powerful strategy to assemble plasmonic nanocrystal networks incorporating both the distinctive optical properties of constituent building blocks and customizable collective properties. Beyond what a single-component assembly can offer, the characteristics of nanocrystal networks can be tuned in a broader range when two or more components are intimately combined. Here, we demonstrate mixed nanocrystal gel networks using thermoresponsive metal-terpyridine links that enable rapid gel assembly and disassembly with thermal cycling. Plasmonic indium oxide nanocrystals with different sizes, doping concentrations, and shapes are reliably intermixed in linked gel assemblies, exhibiting collective infrared absorption that reflects the contributions of each component while also deviating systematically from a linear combination of the spectra for single-component gels. We extend a many-bodied, mutual polarization method to simulate the optical response of mixed nanocrystal gels, reproducing the experimental trends with no free parameters and revealing that spectral deviations originate from cross-coupling between nanocrystals with distinct plasmonic properties. Our thermoreversible linking strategy directs the assembly of mixed nanocrystal gels with continuously tunable far- and near-field optical properties that are distinct from those of the building blocks or mixed close-packed structures.

Ligand-modified nanocarriers for oral drug delivery: Challenges, rational design, and applications

Ligand-modified nanocarriers (LMNCs) specific to their targets have attracted increasing interest for enhanced oral drug delivery in recent decades. Although the design of LMNCs for enhanced endocytosis and improved exposure of the loaded drugs through the oral route has received abundant attention, it remains unclear how the design influences their transcellular process, especially the key factors affecting their functions. This review discusses the extracellular and cellular barriers to orally administered LMNCs in the gastrointestinal (GI) tract and new discoveries regarding the GI protein corona and the sequential transport barriers that impede the preplanned movements of LMNCs after oral administration. Furthermore, innovative progress in considering key factors (including target selection, ligand properties, and other important factors) in the rational design of LMNCs for oral drug delivery is presented. In particular, some factors that endow LMNCs with efficient transcytosis rather than only endocytosis are highlighted. Finally, the prospects of orally administered LMNCs in disease therapy for the enhanced oral/local bioavailability of active pharmaceutical ingredients, as well as emerging delivery routes, such as lymphatic drug delivery and systemic location-specific drug release based on oral transcellular LMNCs, are discussed.

Colorimetric quantification of linking in thermoreversible nanocrystal gel assemblies

Nanocrystal gels can be responsive, tunable materials, but designing their structure and properties is challenging. By using reversibly bonded molecular linkers, gelation can be realized under conditions predicted by thermodynamics. However, simulations have offered the only microscopic insights, with no experimental means to monitor linking leading to gelation. We introduce a metal coordination linkage with a distinct optical signature allowing us to quantify linking in situ and establish structural and thermodynamic bases for assembly. Because of coupling between linked indium tin oxide nanocrystals, their infrared absorption shifts abruptly at a chemically tunable gelation temperature. We quantify bonding spectroscopically and use molecular simulation to understand temperature-dependent bonding motifs, revealing that gel formation is governed by reaching a critical number of effective links that extend the nanocrystal network. Microscopic insights from our colorimetric linking chemistry enable switchable gels based on thermodynamic principles, opening the door to rational design of programmable nanocrystal networks.

Phase behavior of a binary mixture of patchy colloids: Effect of particle size and gravity

We study theoretically the effect of size difference and that of gravity in the phase behavior of a binary mixture of patchy particles. The species, 2A and 3B, have two A and three B patches, respectively, and only bonds between patches A and B (AB bonds) are allowed. This model describes colloidal systems where the aggregation of particles (3B) is mediated and controlled by a second species, the linkers (2A) to which they bind strongly. Thermodynamic calculations are performed using Wertheim's perturbation theory with a hard sphere reference term that accounts for the difference in the size of the two species. Percolation lines are determined employing a generalized Flory-Stockmayer theory, and the effects of gravity are included through a local density approximation. The bulk phase diagrams are calculated, and all the stacking sequences generated in the presence of gravity are determined and classified in a stacking diagram. The relative size of the particles can be used to control the phase behavior of the mixture. An increase in the size of particles 3B, relative to the size of the linkers 2A, is found to promote mixing while keeping the percolating structures and, in certain cases, leads to changes in the stacking sequence under gravity.

Colloidal Nanocrystal Gels from Thermodynamic Principles

Gels assembled from solvent-dispersed nanocrystals are of interest for functional materials because they promise the opportunity to retain distinctive properties of individual nanocrystals combined with tunable, structure-dependent collective behavior. By incorporating stimuli-responsive components, these materials could also be dynamically reconfigured between structurally distinct states. However, nanocrystal gels have so far been formed mostly through irreversible aggregation, which has limited the realization of these possibilities. Meanwhile, gelation strategies for larger colloidal microparticles have been developed using reversible physical or chemical interactions. These approaches have enabled the experimental navigation of theoretically predicted phase diagrams, helping to establish an understanding of how thermodynamic behavior can guide gel formation in these materials. However, the translation of these principles to the nanoscale poses both practical and fundamental challenges. The molecules guiding assembly can no longer be safely assumed to be vanishingly small compared to the particles nor large compared to the solvent.In this Account, we discuss recent progress toward the assembly of tunable nanocrystal gels using two strategies guided by equilibrium considerations: (1) reversible chemical bonding between functionalized nanocrystals and difunctional linker molecules and (2) nonspecific, polymer-induced depletion attractions. The effective nanocrystal attractions, mediated in both approaches by a secondary molecule, compete against stabilizing repulsions to promote reversible assembly. The structure and properties of the nanocrystal gels are controlled microscopically by the design of the secondary molecule and macroscopically by its concentration. This mode of control is compelling because it largely decouples nanocrystal synthesis and functionalization from the design of interactions that drive assembly. Statistical thermodynamic theory and computer simulation have been applied to simple models that describe the bonding motifs in these assembling systems, furnish predictions for conditions under which gelation is likely to occur, and suggest strategies for tuning and disassembling the gel networks. Insights from these models have guided experimental realizations of reversible gels with optical properties in the infrared range that are sensitive to the gel structure. This process avoids time-consuming and costly trial-and-error experimental investigations to accelerate the development of nanocrystal gel assemblies.These advances highlight the need to better understand interactions between nanocrystals, how interactions give rise to gel structure, and properties that emerge. Such an understanding could suggest new approaches for creating stimuli-responsive and dissipative assembled materials whose properties are tunable on demand through directed reconfiguration of the underlying gel microstructure. It may also make nanocrystal gels amenable to computationally guided design using inverse methods to rapidly optimize experimental parameters for targeted functionalities.