Session Q07: Mechanisms of Self-Assembly: Biology and Beyond I

Chain flexibility effect on complex coacervate core micelles

Complex coacervate core micelles (C3Ms) have been investigated in a wide range of applications owing to stimuli-responsiveness and hydrophilic cores. Assembly of two oppositely charged block copolyelectrolytes leads to the formation of C3Ms based on the chain length recognition. Therefore, it was limited to form various structures by mixing block copolyelectrolytes having different lengths. In this study, we investigated the structure of C3Ms formed by mixing of block copolyelectrolytes having different lengths characterized by dynamic light scattering (DLS) and small angle X-ray scattering (SAXS) measurements. A well-defined poly(ethylene oxide-b-allyl glycidyl ether) (PEO-PAGE) was synthesized and functionalized with charged moieties including ammonium (A) and sulfonate (S). The C3M is formed by mixing of oppositely charged block copolyelectrolyte solutions of different lengths due to the degree of conformational freedom of the ether backbone. The relatively shorter chains are stretched to the center of the C3Ms core, because of core-corona junction alignment at interface. The core dimensions are associated with the average number of charged block, and it is captured by free energy theory for block copolymer micelle systems.   

Surface Layer Adsorption and Bulk Association of Mucins in Human Airway Mucus

The airway surface layer lines the respiratory tract, simultaneously trapping inhaled particulates and facilitating their removal from the lung. Secreted gel-forming mucins, which possess both hydrophilic glycosylated domains and hydrophobic globular domains, interact with a wide range of proteins and nucleic acids and are responsible for the characteristic biophysical properties of mucus. The mucin hydrophobic domains promote: 1) self-association in the bulk phase; and 2) strong adsorption at the air-mucus interface with formation of a thin, viscoelastic skin layer that effectively separates the mucus layer itself into two distinct sublayers. Measuring the modulus of mucus using multiple rheometric geometries with varying surface-to-volume ratios, we measure different apparent viscosities with different contributions of surface to bulk. A simple model deconvolutes these contributions, permitting assessment of the bulk and surface properties. Surfactants are shown to reduce the associative interactions of mucins, lowering the degree of association/adsorption and overall viscoelastic modulus. Understanding of the structural organization of mucus in the airway and resultant mechanical properties will enable the development of therapeutic approaches to improve mucus clearance in muco-obstructive lung diseases.   

Membrane-mediated interactions between deformable nanoparticles on membranes

Adsorption of nanoparticles onto a membrane can cause membrane deformations that give rise to effective interactions between the particles. Previous studies have focused on rigid nanoparticles with well-defined shapes, but DNA origami technology has enabled the creation of deformable nanostructures with precisely controllable shapes and mechanical properties. Here we use computer simulations to investigate the interactions between deformable, hinge-like nanostructures and lipid membranes. We employ coarse-grained molecular dynamics simulations to characterize the mutual deformations of cholesterol-tagged particles anchored to a membrane as a function of the hinge stiffness. We then determine the effective membrane-mediated interactions between two hinges adsorbed onto a bilayer using umbrella sampling methods. The resulting potentials of mean force show that sufficiently stiff hinges experience an attractive force that can lead to membrane mediated self-assembly. Our results suggest new avenues to modulate interactions between membrane-associated nanoparticles and to sculpt biological membranes using deformable particles with controlled mechanical properties.

    

Relaxational dynamics of the size interconversion of virus capsids

Recent experiments show that a modified coat protein of a simple icosahedral plant virus forms capsids of different sizes, or T-numbers, under different solution conditions, and that by changing the solution conditions one T-number can be converted into the other albeit that the kinetics of the process is rather slow. We apply a simple relaxational model that ignores the impact of any nucleation barriers, and finds a reasonable agreement between theory and experiment with a minimal number of adjustable parameters. We conclude that following a sudden change in pH or salinity, and starting off from a solution dominated by one of the T-numbers, the initial response must be driven by an increase in mixing entropy giving rise to a mixture of sizes. In the late stages, the impact of minimizing the binding free energy kicks in and the solution relaxes to thermodynamic equilibrium. We find that the concentration of free protein subunits, or dimers, relaxes very swiftly and that their concentration remains virtually constant for most of the T-number conversion.   

Thermal stability and secondary aggregation in geometrically-frustrated assembly

Geometric frustration has emerged as a paradigm for potentially engineering self-limiting structures with finite, well-controlled sizes much larger than a single subunit. Frustrated assemblies often escape to unlimited sizes through elastic shape deformations or through the inclusion of defects or broken bonds within the assembled structures. Understanding how to prevent these modes of escape is crucial to controlling assembly size. While the zero-temperature mechanics of geometrically-frustrated assemblies is well-studied, less is known about the role of temperature. In the absence of thermal fluctuations, any partial bonding between subunits, regardless of how weak, will always lower the energy of the system, resulting in an unlimited aggregate of weakly-bonded structures. Thus, thermal fluctuations must play an important role in the stability of self-limiting structures. We here consider a simple model of a frustrated 1D incommensurate chain at finite temperature. We show that a quantity termed the "defectability", which characterizes the tendency for defect formation, determines whether there exists a range of subunit concentrations and temperatures in which self-limiting assembly can occur. In particularly, we find that there is a frustration-dependent minimum temperature required for self-limiting assembly. Low-temperature condensation of finite-aggregates is likely the generic result of weak-binding possible in any physical frustrated assembly. Hence, our analysis highlights key principles needed for targeting, designing and stabilizing experimental systems that regain robust self-limiting regimes.   

Biophysical Modeling of SARS-CoV-2 Assembly: Genome Condensation and Budding

The COVID-19 pandemic caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has spurred unprecedented and concerted worldwide research to curtail and eradicate this pathogen. SARS-CoV-2 has four structural proteins: Envelope (E), Membrane (M), Nucleocapsid (N), and Spike (S), which self-assemble along with its RNA into the infectious virus by budding from intracellular lipid membranes. Here, we develop a model to explore the mechanisms of RNA condensation by structural proteins, protein oligomerization and cellular membrane–protein interactions that control the budding process and the ultimate virus structure. Using molecular dynamics simulations, we have deciphered how the positively charged N proteins interact and condense the very long genomic RNA resulting in its packaging by a lipid envelope decorated with structural proteins inside a host cell. Furthermore, considering the length of RNA and the size of the virus, we find that the intrinsic curvature of M proteins is essential for virus budding. While most current research has focused on the S protein, which is responsible for viral entry, and it has been motivated by the need to develop efficacious vaccines, the development of resistance through mutations in this crucial protein makes it essential to elucidate the details of the viral life cycle to identify other drug targets for future therapy. Our simulations will provide insight into the viral life cycle through the assembly of viral particles de novo and potentially identify therapeutic targets for future drug development.   

Impact of cross-linking on the structural and interfacial properties of surfactant micelles

Structural properties of self-assembled formulations composed of Tyloxapol and Triton X-100 surfactants were investigated using all-atomic molecular dynamics simulations. Tyloxapol is a polymerized version of the Triton X-100 non-ionic surfactant. Multiple systems were investigated and compared – pure Tyloxapol or Triton X-100 systems and mixed systems containing different concentrations of the two surfactants. We find that crosslinking of monomers greatly affects the overall structure and stability of the resulting micellar structure. Structural analysis shows that pure tyloxapol systems are relatively spherical in shape and become more aspherical by replacing tyloxapol molecules with a corresponding number of Triton X-100 monomers. Interestingly, the initial analysis shows the most stable of the mixed systems has a 50:50 ratio of Tyloxapol and Triton X-100. Finally, a novel method was developed to calculate volumes of the micelles as well as the intrinsic density profiles of the different species regardless of the nanoparticle's shape.   

Aggregation vs. Condensation in a Lattice Model of Geometrically Frustrated Assembly

Geometrically frustrated assembly (GFA) has proven to be a useful framework for understanding a wide range of self-assembling systems whose behavior is governed by global constraints that obstruct the uniform extension of some locally preferred order across the entire system. One common response to these imposed constraints is the formation of a state of self-limited assembly where at least one dimension of the equilibrium structure is restricted to a certain finite length that is controlled by the ratio of frustration and inter-particle binding energy. We consider a minimal lattice model of geometrically frustrated assembly and use it to study the statistical mechanics of GFA at variable temperature and concentration. In this talk, we focus on how these systems can escape this size limitation via a condensation transition to a macroscopic bulk phase that is characterized by a finite density of topological defects. Using a combination of numerical and analytical methods, we show that this transition occurs at a critical ratio of frustration and binding energy and that this critical point is largely independent of concentration, consistent with scaling argument comparing dimensions of self-limiting to multi-defect ground states. We conclude with an examination of the affect of temperature on the critical frustration and discuss how the assembly morphologies are impacted by increasing conformational entropy.   

High-precision measurement and inference of short-ranged colloidal interactions

Understanding the interactions between colloidal particles is essential for controlling self-assembly. Methods to characterize these interactions generally rely on imaging the particles, usually within an optical potential, and inferring the distribution of distances between them to extract the potential. Such methods must account for how the scattering of light from the particles changes as a function of distance, as well as how out-of-plane fluctuations affect the inferred distance distribution. We demonstrate an alternative method based on holographic microscopy and Bayesian inference. This method rigorously accounts for scattering effects, works in three dimensions, and does not require the particles to be trapped in an optical potential. With this method, we precisely track pairs of freely-diffusing spheres in three dimensions and at high frame rates. We show that the method can measure separation distances as small as a few nanometers between micrometer scale particles to 3 nm precision. We infer the pair potential from measurements of fluctuations in the particle separation distances in two ways: by analyzing uncorrelated samples of the separation distance, and by fitting equations of motions to the full three-dimensional trajectories of the two particles. We validate the results by comparison to indirect measurements of the interaction.   

End-to-end base stacking drives liquid crystalline phase formation in "gapped" DNA constructs

Small-angle/wide-angle x-ray scattering (SAXS/WAXS) and polarizing optical microscopy (POM) are used to study the liquid crystalline phases of “gapped” DNA (GDNA) constructs in an aqueous solution. In our previous studies, smectic liquid crystalline (LC) phases, which depend on temperature, DNA concentration (C_DNA), and the number of single thymine bases constituting the “gap” between the DNA duplexes, were observed [1,2]. At sufficiently high C_DNA, we observe a smectic-B phase wherein spontaneous end-to-end stacking of the DNA duplexes is accompanied by their in-plane ordering. By performing SAXS/WAXS measurements for temperatures in the range of 5 to 65°C, we determined the thermal melting temperature (T_m)  of the end-to-end and side-by-side interactions that stabilize the positional order for DNA constructs, which differ in their terminal base pairs (AT-AT, AT-GC, or GC-GC) but are otherwise identical. We report remarkable variations in thermal stability (up to 25 °C shift in T_m) of these interactions, and the accompanying smectic order, due to these single base-pair alterations. Analysis of the melting data enables a comparison of relative enthalpic and entropic contributions to the interaction of free energy in each case.   

Dynamically tuning the membrane lipid composition can control macromolecular assembly

Clathrin-mediated endocytosis (CME) is an essential process for transport

into the cell, requiring hundreds of protein components to assemble into

large macromolecular structures on the cell membrane. The composition of

the plasma membrane is critical for initiating assembly, as proteins bind

specifically only to subpopulations of lipids. Two opposing lipid-modifying

enzymes can dynamically tune these lipid populations, and it is not known to

what extent these enzymes help promote or inhibit protein recruitment at

specific places and times. This dynamical complexity of CME makes it not

only an interesting process to study for its own sake, but for the potential to

reveal general principles for controlling self-assembly on a 2D surface.

However, this very complexity and the fast time scales make CME difficult to

interrogate in vivo with sufficient resolution, thus the relationships between

environmental variables and the dynamics of clathrin-coated vesicle

formation are yet to be fully characterized. Here, we use computational

modeling to quantify how macromolecular self-assembly can be dynamically

tuned via the composition of the plasma membrane and protein

stoichiometry. Our models solve differential equations with the structure-

resolved reaction-diffusion software NERDSS, as well as non-spatial ordinary

differential equations that are amenable to efficient parameter optimization

and sensitivity analysis. We found a novel mechanism for biochemical

feedback loops allowing for switch-like lipid remodeling and oscillatory

behavior. We discuss how the principles established here for controlling

membrane composition are informative for a broader range of processes

across biological systems.

    

The role of inter-particle cohesive stiffness in determining the size and nature of self-limiting, geometrically-frustrated assemblies

Geometrically frustrated assemblies are an emerging class of systems where local inter-subunit misfits propagate to large-scale strain gradients in an assembly, giving rise to anomalous self-limiting thermodynamics under certain conditions.  Recently, the “curvamer” model was introduced to study self-limitation in 1D stacks of deformable, shell-like particles, where an elastic energy emerges from bending costs in stacks of uniformly spaced particles.  In general, elastic strains will also be borne by the stretching of cohesive bonds between particles.  Here, we generalize the curvamer model to consider the effect of inter-particle bond stiffness, or alternatively the effect of finite attraction range between particles.  We find that the ratio of intra-particle (bending elasticity) to inter-particle stiffness not only controls the regimes of self-limitation but also the nature of frustration propagation.  We develop and study a continuum elastic description as well as a numerical coarse-grained model of curvamers from which we deduce critical parameter regimes separating uniformly spaced stacks from quasi-uniform (gap-opened) stacks.  We conclude that the self-limiting stack size is unbounded for an infinitely short-range of attraction while a finite range of attraction yields a maximum self-limiting size.  These predictions provide critical guidance for experimental realizations of frustrated particle systems designed to exhibit self-limitation at especially large multi-particle scales.

    

Frustrated Self-Assembly of Hyperbolic Crystals from Icosahedral Nanoparticles

Simple building blocks such as polyhedral nanoparticles (NPs) can self-organize into complex assemblies that resemble structures observed in biology. Previous study showed that the complex order of tetrahedral NP assemblies can be understood based on their crystal structures on the 3-sphere. Icosahedra, however, cannot tile the 3-sphere and is beyond this theory. In this talk, we present an analytical theory of icosahedral NP self-assembly based on the non-Euclidean crystal {3,5,3} in 3-hyperbolic space. Following the assumption that geometric frustration will favor low dimensional morphology of assembled clusters, we show that the local order of the self-assembly is determined by the crystal order on a flat surface in 3-hyperbolic space and icosahedral NPs self-organized into part of cylindrical or spherical shells.   

Controlled 2D and 3D Self-assembly of short fibers for additive manufacturing

A common issue with thermosetting resins is the relatively weak mechanical properties of the pure polymer materials. Thus, 3D-printed parts using thermoset chemistries are restricted to rapid prototyping.  For thermoset 3D manufacturing to be useful in user-end parts, reinforcements must be incorporated to improve mechanical properties such as modulus and strength. Carbon and glass continuous mats or short fibers are examples of reinforcement materials commonly used in traditional composite manufacturing. However, fiber mats are difficult to incorporate into 3D printing technologies, and short fiber is limited to very low loadings in resins for printing. Here we present an inexpensive method of aligning and consolidating short fibers into different shapes, such as discs, spheres, triangles, and needles. The method consists of flow-induced self-assembly of fibers using complex flow fields.   The self-assembled shapes are shown to depend on the length of the short fibers, the concentration of fibers, and flow field parameters. We envision that the self-assembled shapes can be used in VAT polymerization methods via placement and consolidation.  3D printed test specimens are discussed and the results are compared to neat resin and traditional composite manufacturing methods.