Mechanism of Micelle Birth and Death

Molecularly informed field theory for estimating critical micelle concentrations of intrinsically disordered protein surfactants

The critical micelle concentration (CMC) is a crucial parameter in understanding the self-assembly behavior of surfactants. In this study, we combine simulation and experiment to demonstrate the predictive capability of molecularly informed field theories in estimating the CMC of biologically based protein surfactants. Our simulation approach combines the relative entropy coarse-graining of small-scale atomistic simulations with large-scale field-theoretic simulations, allowing us to efficiently compute the free energy of micelle formation necessary for the CMC calculation while preserving chemistry-specific information about the underlying surfactant building blocks. We apply this methodology to a unique intrinsically disordered protein platform capable of a wide variety of tailored sequences that enable tunable micelle self-assembly. The computational predictions of the CMC closely match experimental measurements, demonstrating the potential of molecularly informed field theories as a valuable tool to investigate self-assembly in bio-based macromolecules systematically.

A molecularly informed field-theoretic study of the complexation of polycation PDADMA with mixed micelles of sodium dodecyl sulfate and ethoxylated surfactants

The self-assembly and phase separation of mixtures of polyelectrolytes and surfactants are important to a range of applications, from formulating personal care products to drug encapsulation. In contrast to systems of oppositely charged polyelectrolytes, in polyelectrolyte-surfactant systems the surfactants micellize into structures that are highly responsive to solution conditions. In this work, we examine how the morphology of micelles and degree of polyelectrolyte adsorption dynamically change upon varying the mixing ratio of charged and neutral surfactants. Specifically, we consider a solution of the cationic polyelectrolyte polydiallyldimethylammonium, anionic surfactant sodium dodecyl sulfate, neutral ethoxylated surfactants (C[Formula: see text]EO[Formula: see text]), sodium chloride salt, and water. To capture the chemical specificity of these species, we leverage recent developments in constructing molecularly informed field theories via coarse-graining from all-atom simulations. Our results show how changing the surfactant mixing ratios and the identity of the nonionic surfactant modulates micelle size and surface charge, and as a result dictates the degree of polyelectrolyte adsorption. These results are in semi-quantitative agreement with experimental observations on the same system.

Diffusion of surfactant from a micellar solution to a bare interface. 1. Absorbing boundary

We analyze dynamic adsorption of surfactant from a micellar solution to a rapidly created surface that acts as an absorbing boundary for surfactant monomers (single molecules), along which the monomer concentration vanishes, with no direct micelle adsorption. This somewhat idealized situation is analyzed as a prototype for situations in which strong suppression of monomer concentration accelerates micelle dissociation, and will be used as a starting point for analysis of more realistic boundary conditions in subsequent work. We present scaling arguments and approximate models for particular time and parameter regimes and compare the resulting predictions to numerical simulations of the reaction-diffusion equations for a polydisperse system containing surfactant monomers and clusters of arbitrary aggregation number. The model considered here exhibits an initial period of rapid shrinkage and ultimate dissociation of micelles within a narrow region near the interface. This opens a micelle-free region near the interface after some time τ_e, the width of which increases as t^1/2 at times t≫τ_e. In systems that exhibit disparate fast and slow bulk relaxation times τ₁ and τ₂ in response to small perturbations, τ_e is usually comparable to or greater than τ₁ but much less than τ₂. Such systems exhibit a wide intermediate time regime τ_e<t<τ₂ in which the remaining micellar region reaches a state of partial local equilibrium, followed by a final stage t≫τ₂ in which full local equilibrium is established.

Predicting surfactant phase behavior with a molecularly informed field theory

HYPOTHESIS

The computational study of surfactants and self-assembly is challenging because 1) models need to reflect chemistry-specific interactions, and 2) self-assembled structures are difficult to equilibrate with conventional molecular dynamics. We propose to overcome these challenges with a multiscale simulation approach where relative entropy minimization transfers chemically-detailed information from all-atom (AA) simulations to coarse-grained (CG) models that can be simulated using field-theoretic methods. Field-theoretic simulations are not limited by intrinsic physical time scales like diffusion and allow for rigorous equilibration via free energy minimization. This approach should enable the study of properties that are difficult to obtain by particle-based simulations.

SIMULATION WORK

We apply this workflow to sodium dodecylsulfate. To ensure chemical fidelity we present an AA force field calibrated against interfacial tension experiments. We generate CG models from AA simulation trajectories and show that particle-based and field-theoretic simulations of the CG model reproduce AA simulations and experimental measurements.

FINDINGS

The workflow captures the complex balance of interactions in a multicomponent system ultimately described by an atomistic model. The resulting CG models can study complex 3D phases like double or alternating gyroids, and reproduce salt effects on properties like aggregation number and shape transitions.

Dynamics and Equilibration Mechanisms in Block Copolymer Particles

Self-assembly of block copolymers into interesting and useful nanostructures, in both solution and bulk, is a vibrant research arena. While much attention has been paid to characterization and prediction of equilibrium phases, the associated dynamic processes are far from fully understood. Here, we explore what is known and not known about the equilibration of particle phases in the bulk, and spherical micelles in solution. The presumed primary equilibration mechanisms are chain exchange, fusion, and fragmentation. These processes have been extensively studied in surfactants and lipids, where they occur on subsecond time scales. In contrast, increased chain lengths in block copolymers create much larger barriers, and time scales can become prohibitively slow. In practice, equilibration of block copolymers is achievable only in proximity to the critical micelle temperature (in solution) or the order-disorder transition (in the bulk). Detailed theories for these processes in block copolymers are few. In the bulk, the rate of chain exchange can be quantified by tracer diffusion measurements. Often the rate of equilibration, in terms of number density and aggregation number of particles, is much slower than chain exchange, and consequently observed particle phases are often metastable. This is particularly true in regions of the phase diagram where Frank-Kasper phases occur. Chain exchange in solution has been explored quantitatively by time-resolved SANS, but the results are not well captured by theory. Computer simulations, particularly via dissipative particle dynamics, are beginning to shed light on the chain escape mechanism at the molecular level. The rate of fragmentation has been quantified in a few experimental systems, and TEM images support a mechanism akin to the anaphase stage of mitosis in cells, via a thin neck that pinches off to produce two smaller micelles. Direct measurements of micelle fusion are quite rare. Suggestions for future theoretical, computational, and experimental efforts are offered.

Triblock copolymer micelle model of spherical paraspeckles

Paraspeckles are nuclear bodies scaffolded by RNP complexes of NEAT1_2 RNA transcripts and multiple RNA-binding proteins. The assembly of paraspeckles is coupled with the transcription of NEAT1_2. Paraspeckles form the core-shell structure, where the two terminal regions of NEAT1_2 RNP complexes compose the shell of the paraspeckle and the middle regions of these complexes compose the core. We here construct a theoretical model of paraspeckles by taking into account the transcription of NEAT1_2 in an extension of the theory of block copolymer micelles. This theory predicts that the core-shell structure of a paraspeckle is assembled by the association of the middle region of NEAT1_2 RNP complexes due to the multivalent interactions between RBPs bound to these regions and by the relative affinity of the terminal regions of the complexes to the nucleoplasm. The latter affinity results in the effective repulsive interactions between terminal regions of the RNA complexes and limits the number of complexes composing the paraspeckle. In the wild type, the repulsive interaction between the middle and terminal block dominates the thermal fluctuation. However, the thermal fluctuation can be significant in a mutant, where a part of the terminal regions of NEAT1_2 is deleted, and distributes the shortened terminal regions randomly between the shell and the core, consistent with our recent experiments. With the upregulated transcription, the shortened terminal regions of NEAT1_2 in a deletion mutant is localized to the core to decrease the repulsive interaction between the terminal regions, while the structure does not change with the upregulation in the wild type. The robustness of the structure of paraspeckles in the wild type results from the polymeric nature of NEAT1_2 complexes.

Micellar Composition Affects Lipid Accretion Kinetics in Molecular Dynamics Simulations: Support for Lipid Network Reproduction

Mixed lipid micelles were proposed to facilitate life through their documented growth dynamics and catalytic properties. Our previous research predicted that micellar self-reproduction involves catalyzed accretion of lipid molecules by the residing lipids, leading to compositional homeostasis. Here, we employ atomistic Molecular Dynamics simulations, beginning with 54 lipid monomers, tracking an entire course of micellar accretion. This was done to examine the self-assembly of variegated lipid clusters, allowing us to measure entry and exit rates of monomeric lipids into pre-micelles with different compositions and sizes. We observe considerable rate-modifications that depend on the assembly composition and scrutinize the underlying mechanisms as well as the energy contributions. Lastly, we describe the measured potential for compositional homeostasis in our simulated mixed micelles. This affirms the basis for micellar self-reproduction, with implications for the study of the origin of life.

Nonlinear dynamics in micellar surfactant solutions. I. Kinetics

This is the first of a pair of articles that present the theory of kinetic and transport phenomena in micelle-forming surfactant solutions in a form that facilitates discussion of large deviations from equilibrium. Our goal is to construct approximate but robust reduced models for both homogeneous and inhomogeneous systems as differential equations for unimer concentration c_{1}, micelle number concentration c_{m}, average micelle aggregation number q and (optionally) aggregation number variance σ_{m}^{2}. This first article discusses kinetics in homogeneous solutions. We focus particularly on developing models that can describe both weakly perturbed states and states in which c_{1} is suppressed significantly below the critical micelle concentration, which leads to rapid shrinkage and dissociation of any remaining micelles. This focus is motivated by the strong local suppression of c_{1} that is predicted to occur near interfaces during some adsorption processes that are considered in the second article. Toward this end, we develop a general nonlinear theory of fast stepwise processes for systems that may be subjected to large changes in q and c_{1}. This is combined with the existing nonlinear theory of slow association and dissociation processes to construct a general model for systems governed by stepwise reaction kinetics. We also consider situations in which the slow process of micelle creation and destruction instead occurs primarily by micelle fission and fusion, and analyze the dependencies of micelle lifetime and the slow relaxation time upon surfactant concentration in systems controlled by either association-dissociation or fission-fusion mechanisms.

Universal Scaling for the Exit Dynamics of Block Copolymers from Micelles at Short and Long Time Scales

The correlation function for the exit of poloxamer copolymers from equilibrated micelles is found to show up to four regimes depending on the chain flexibility: an initial fast reorganization, a logarithmic intermediate regime, followed by an exponential intermediate regime, and a final exponential decay. The logarithmic intermediate regime has been observed experimentally and attributed to the polydispersity of the polymer samples. However, we present dynamic single-chain mean-field theory simulations with chains of variable flexibility which show the same logarithmic relaxation but with strictly monodisperse systems. In agreement with our previous studies, we propose that this logarithmic response arises from a degeneracy of energy states of the hydrophobic block in the micelle core. For this to occur, a sufficiently large number of degenerate conformational states are required, which depend on the polymer flexibility and therefore should not be present for rigid polymers. Experimental results for monodisperse polymeric samples claiming the absence of such a logarithmic response may also lack a sufficient number of hydrophobic blocks for the required number of configurational states for this type of response to be seen. The insight gained from analyzing the simulation results allows us to propose a modified Eyring equation capable of reproducing the observed dynamic behavior. On scaling experimental results from different sources and systems according to this equation, we find a unique master curve showing a universal nature of the intermediate regimes: the logarithmic regime together with the secondary exponential decay. The terminal exponential regime at long times proposed by the standard Halperin and Alexander model is beyond the range of the data analyzed in this article. The universality observed suggests an entropic origin of the short-time dynamic response of this class of systems rather than the polydispersity.

Structural Insights into Self-Assembled Aerosol-OT Aggregates in Aqueous Media Using Atomistic Molecular Dynamics

In water, the surfactant dioctyl sulfosuccinate (Aerosol-OT or AOT) exhibits diverse aggregate structures, ranging from micelles to lamella. An atomic-level understanding, however, of the formation and structure of these aggregates is lacking. Herein, using atomistic molecular dynamics (MD) with microsecond-long simulations, self-assembly of AOT in water is studied for concentrations of 1, 7.2, and 20 wt % at 293 K and for 7.2 wt % at 353 K. Assembly proceeds through stepwise association and dissociation of single AOT molecules, and the fusion and fission of AOT clusters. At 293 K, AOT self-assembles into either (i) spherical micelles (1 wt %), (ii) biphasic systems consisting of rod-like and prolate spheroidal micelles (7.2 wt %), or (iii) bilayers (20 wt %). We hypothesize that the observed rod-like structure is a precursor to lamellar microdomains found experimentally in biphasic dispersions. Increasing temperature to 353 K at 7.2 wt % results in a system consisting of prolate micelles but no rod-like micelles. Simulated phase behavior agrees with previously published experimental observations. Individual aggregates formed during self-assembly are identified using graph theory. Structural metrics of these aggregates like the radius of gyration, shape anisotropy, and prolateness are presented. Trends in structural metrics quantitatively reflect how shapes and sizes of AOT aggregates vary with surfactant concentration and temperature. These simulations provide deeper insight into open questions in the scientific community and demonstrate a method to generate physics-based micelle structures that can be used to rationalize experimental observations.

Critical Micelle Concentrations in Surfactant Mixtures and Blends by Simulation

We explore the use of coarse-grained dissipative particle dynamics simulations to predict critical micelle concentrations (CMCs) in polydisperse surfactant mixtures and blends. By fitting pseudo-phase separation models (PSMs) to aqueous solutions of binary surfactant mixtures at selected compositions above the CMC, we avoid the need for expensive simulations of more complex multicomponent mixtures performed as a function of dilution. The approach is demonstrated for sodium laureth sulfate (SLES) surfactants with polydispersity in the ethoxylate spacer. For this system, we find a modest degree of cooperativity in micelle formation, which we attribute to the reduced repulsion between charged headgroups for surfactants with dissimilar ethoxylate spacer lengths. However, this is insufficient to explain the lowered CMC often observed in commercial SLES samples, which we attribute to the presence of small amounts of unsulfated alkyl ethoxylates and/or traces of salt.

Simulation of diblock copolymer surfactants. III. Equilibrium interfacial adsorption

Monte Carlo simulations are used to study adsorption of highly asymmetric diblock copolymers to a polymer-polymer interface, and the results compared to self-consistent field theory (SCFT) predictions. The simulation model used here is a bead-spring model that has been used previously to study equilibrium and kinetic properties of spherical micelles [J. A. Mysona et al., Phys. Rev. E 100, 012602 (2019)2470-004510.1103/PhysRevE.100.012602; Phys. Rev. E 100, 012603 (2019)10.1103/PhysRevE.100.012603; Phys. Rev. Lett. 123, 038003 (2019)10.1103/PhysRevLett.123.038003]. Interfacial copolymer concentration Γ and interfacial tension γ are measured as functions of bulk copolymer concentration at concentrations up to the critical micelle concentration over a range of values of the Flory-Huggins χ parameter. The dependence of interfacial pressure Π = γ_{0}-γ on Γ (where γ_{0} is the interfacial tension in the absence of copolymer) is found to be almost independent of χ and to be accurately predicted by SCFT. The bare interfacial tension γ_{0} and total interfacial tension γ(Γ) can also be accurately predicted by SCFT using an estimate of χ obtained from independent analysis of properties of symmetric diblock copolymer melts. SCFT predictions obtained with this estimate of χ do not, however, adequately describe the thermodynamics of the coexisting bulk copolymer solution, as a result of contraction of the strongly interacting core block of dissolved copolymers. Accurate predictions of the relationship between bulk and interfacial properties can thus only be obtained for this system by combining SCFT predictions of the interfacial equation of state with a fit to the measured equation of state for the bulk solution.

Inflammation product effects on dilatational mechanics can trigger the Laplace instability and acute respiratory distress syndrome

In the lungs, the Laplace pressure, ΔP = 2γ/R, would be higher in smaller alveoli than larger alveoli unless the surface tension, γ decreases with alveolar interfacial area, A, such that 2ε > γ in which ε = A(dγ/dA) is the dilatational modulus. In Acute Respiratory Distress Syndrome (ARDS), lipase activity due to the immune response to an underlying trauma or disease causes single chain lysolipid concentrations to increase in the alveolar fluids via hydrolysis of double-chain phospholpids in bacterial, viral, and normal cell membranes. Increasing lysolipid concentrations decrease the dilatational modulus dramatically at breathing frequencies if the soluble lysolipid has sufficient time to diffuse off the interface, causing 2ε < γ, thereby potentially inducing the "Laplace Instability", in which larger alveoli have a lower internal pressure than smaller alveoli. This can lead to uneven lung inflation, alveolar flooding, and poor gas exchange, typical symptoms of ARDS. While the ARDS lung contains a number of lipid and protein species in the alveolar fluid in addition to lysolipids, the surface activity and frequency dependent dilatational modulus of lysolipid suggest how inflammation may lead to the lung instabilities associated with ARDS. At high frequencies, even at high lysolipid concentrations, 2ε - γ > 0, which may explain the benefits ARDS patients receive from high frequency oscillatory ventilation.

NMR Studies of Block Copolymer-Based Supramolecules in Solution

Hierarchical assemblies from block copolymer (BCP)-based supramolecules have shown immense potential as programmable materials owing to their versatility for incorporating functional molecules and provide access to arrays of hierarchical structures. However, there remains a knowledge gap on the formation of the supramolecule in solution. Here, we applied NMR techniques to investigate the solution-phase behavior of the most studied supramolecular systems, polystyrene-block-poly(4-vinylpyridine)(3-pentadecylphenol) (PS-b-P4VP(PDP)_r). The results show that the supramolecule likely adopts a coil-comb conformation, despite the small molecule's (PDP) rapid exchange between the bonded and free states. The exchange rate (>10⁴ s^-1) exceeds the NMR time scale at the frequency of interest. The supramolecules form under dilute conditions (∼2 vol %) and are attributed to the enthalpic gain of the hydrogen bonding between the PDP and 4VP. As the solute concentration increases (>10 vol %), the supramolecule forms micelle-like aggregates with PDP accumulated within the comb-block's pervaded volume based on analysis of the apparent molecular weight, viscosity, and chain dynamics. This work sheds light on the long-standing question regarding the evolution of the constituents in the BCP-based supramolecule in solution and provides valuable guidance toward their solution-based processing and morphological control.

A Surface Site Interaction Point Method for Dissipative Particle Dynamics Parametrization: Application to Alkyl Ethoxylate Surfactant Self-Assembly

Dissipative particle dynamics (DPD) is a coarse-grained approach to the simulation of large supramolecular systems, but one limitation has been that the parameters required to describe the noncovalent interactions between beads are not readily accessible. A first-principles computational method has been developed so that bead interaction parameters can be calculated directly from ab initio gas-phase molecular electrostatic potential surfaces of the molecular fragments that represent the beads. A footprinting algorithm converts the molecular electrostatic potential surfaces into a discrete set of surface site interaction points (SSIPs), and these SSIPs are used in the SSIMPLE (surface site interaction model for the properties of liquids at equilibrium) algorithm to calculate the free energies of transfer of one bead into a solution of any other bead. The bead transfer free energies are then converted into the required DPD interaction parameters for all pairwise combinations of different beads. The reliability of the parameters was demonstrated using DPD simulations of a range of alkyl ethoxylate surfactants. The simulations reproduce the experimentally determined values of the critical micelle concentration and mean aggregation number well for all 22 surfactants studied.