Molecular dynamics study of the formation mechanisms of ionic SDS and nonionic C12E8 micelles and n-dodecane droplets

Phase Behavior of Alkyl Ethoxylate Surfactants in a Dissipative Particle Dynamics Model

We present a dissipative particle dynamics (DPD) model capable of capturing the liquid state phase behavior of nonionic surfactants from the alkyl ethoxylate (C_nE_m) family. The model is based upon our recent work [Anderson et al. J. Chem. Phys. 2017, 147, 094503] but adopts tighter control of the molecular structure by setting the bond angles with guidance from molecular dynamics simulations. Changes to the geometry of the surfactants were shown to have little effect on the predicted micelle properties of sampled surfactants, or the water-octanol partition coefficients of small molecules, when compared to the original work. With these modifications the model is capable of reproducing the binary water-surfactant phase behavior of nine surfactants (C₈E₄, C₈E₅, C₈E₆, C₁₀E₄, C₁₀E₆, C₁₀E₈, C₁₂E₆, C₁₂E₈, and C₁₂E₁₂) with a good degree of accuracy.

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.

Model for the Simulation of the CnEm Nonionic Surfactant Family Derived from Recent Experimental Results

Using a comprehensive set of recently published experimental results for training and validation, we have developed computational models appropriate for simulations of aqueous solutions of poly(ethylene oxide) alkyl ethers, an important class of micelle-forming nonionic surfactants, usually denoted C_nE_m. These models are suitable for use in simulations that employ a moderate amount of coarse graining and especially for dissipative particle dynamics (DPD), which we adopt in this work. The experimental data used for training and validation were reported earlier and produced in our laboratory using dynamic light scattering (DLS) measurements performed on 12 members of the C_nE_m compound family yielding micelle size distribution functions and mass-weighted mean aggregation numbers at each of several surfactant concentrations. The range of compounds and quality of the experimental results were designed to support the development of computational models. An essential feature of this work is that all simulation results were analyzed in a way that is consistent with the experimental data. Proper account is taken of the fact that a broad distribution of micelle sizes exists, so mass-weighted averages (rather than number-weighted averages) over this distribution are required for the proper comparison of simulation and experimental results. The resulting DPD force field reproduces several important trends seen in the experimental critical micelle concentrations and mass-averaged mean aggregation numbers with respect to surfactant characteristics and concentration. We feel it can be used to investigate a number of open questions regarding micelle sizes and shapes and their dependence on surfactant concentration for this important class of nonionic surfactants.

Protein unfolding by SDS: the microscopic mechanisms and the properties of the SDS-protein assembly

The effects of detergent sodium dodecyl sulfate (SDS) on protein structure and dynamics are fundamental to the most common laboratory technique used to separate proteins and determine their molecular weights: polyacrylamide gel electrophoresis. However, the mechanism by which SDS induces protein unfolding and the microstructure of protein-SDS complexes remain largely unknown. Here, we report a detailed account of SDS-induced unfolding of two proteins-I27 domain of titin and β-amylase-obtained through all-atom molecular dynamics simulations. Both proteins were found to spontaneously unfold in the presence of SDS at boiling water temperature on the time scale of several microseconds. The protein unfolding was found to occur via two distinct mechanisms in which specific interactions of individual SDS molecules disrupt the protein's secondary structure. In the final state of the unfolding process, the proteins are found to wrap around SDS micelles in a fluid necklace-and-beads configuration, where the number and location of bound micelles changes dynamically. The global conformation of the protein was found to correlate with the number of SDS micelles bound to it, whereas the number of SDS molecules directly bound to the protein was found to define the relaxation time scale of the unfolded protein. Our microscopic characterization of SDS-protein interactions sets the stage for future refinement of SDS-enabled protein characterization methods, including protein fingerprinting and sequencing using a solid-state nanopore.

Protobiotic Systems Chemistry Analyzed by Molecular Dynamics

Systems chemistry has been a key component of origin of life research, invoking models of life's inception based on evolving molecular networks. One such model is the graded autocatalysis replication domain (GARD) formalism embodied in a lipid world scenario, which offers rigorous computer simulation based on defined chemical kinetics equations. GARD suggests that the first pre-RNA life-like entities could have been homeostatically-growing assemblies of amphiphiles, undergoing compositional replication and mutations, as well as rudimentary selection and evolution. Recent progress in molecular dynamics has provided an experimental tool to study complex biological phenomena such as protein folding, ligand-receptor interactions, and micellar formation, growth, and fission. The detailed molecular definition of GARD and its inter-molecular catalytic interactions make it highly compatible with molecular dynamics analyses. We present a roadmap for simulating GARD's kinetic and thermodynamic behavior using various molecular dynamics methodologies. We review different approaches for testing the validity of the GARD model by following micellar accretion and fission events and examining compositional changes over time. Near-future computational advances could provide empirical delineation for further system complexification, from simple compositional non-covalent assemblies towards more life-like protocellular entities with covalent chemistry that underlies metabolism and genetic encoding.

Molecular dynamics study of the potential of mean force of SDS aggregates

In our previous study, all-atomistic molecular dynamics (MD) calculations have been carried out for the aggregation of ionic sodium dodecyl sulfate in water [S. Kawada et al., Chem. Phys. Lett. 646, 36 (2016)]. Aggregates of 20-30 dodecyl sulfate ions were formed within a short MD run for 10 ns. However, further aggregation did not occur despite a long MD calculation for more than 100 ns. This suggests that strong electrostatic repulsive interactions between the aggregates prevent the fusion of the aggregates. In the present study, mean force and potential of mean force acting between two aggregates with aggregation number N = 30 were evaluated as a function of their separation by MD calculations. The repulsive force becomes strong with decreasing distance between the two aggregates before they merge into one. An origin of the repulsive force is an electric double layer formed by the sulfate group and counter sodium ions. Strength of the repulsive force is in good agreement with the theoretical value given by the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Once the aggregates establish contact, the force between them turns to be a large attractive force that can be explained by the interfacial tension. In order to form a single micelle from the two aggregates, it is necessary for them to climb over a free energy barrier of 23 kJ/mol. Once, the barrier is overcome, the micelle is stabilized by ∼200 kJ/mol. The time constant of aggregation evaluated from the calculated free energy barrier was about 28 μs at the concentration in our previous study.

Micelle Formation in Alkyl Sulfate Surfactants Using Dissipative Particle Dynamics

We use dissipative particle dynamics (DPD) to study micelle formation in alkyl sulfate surfactants, with alkyl chain lengths ranging from 6 to 12 carbon atoms. We extend our recent DPD force field [ J. Chem. Phys. 2017 , 147 , 094503 ] to include a charged sulfate chemical group and aqueous sodium ions. With this model, we achieve good agreement with the experimentally reported critical micelle concentrations (CMCs) and can match the trend in mean aggregation numbers versus alkyl chain length. We determine the CMC by fitting a charged pseudophase model to the dependence of the free surfactant on the total surfactant concentration above the CMC and compare it with a direct operational definition of the CMC as the point at which half of the surfactant is classed as micellar and half as monomers and submicellar aggregates. We find that the latter provides the best agreement with experimental results. Finally, with the same model, we are able to observe the sphere-to-rod morphological transition for sodium dodecyl sulfate (SDS) micelles and determine that it corresponds to SDS concentrations in the region of 300-500 mM.

Extracting Aggregation Free Energies of Mixed Clusters from Simulations of Small Systems: Application to Ionic Surfactant Micelles

Micelle cluster distributions from molecular dynamics simulations of a solvent-free coarse-grained model of sodium octyl sulfate (SOS) were analyzed using an improved method to extract equilibrium association constants from small-system simulations containing one or two micelle clusters at equilibrium with free surfactants and counterions. The statistical-thermodynamic and mathematical foundations of this partition-enabled analysis of cluster histograms (PEACH) approach are presented. A dramatic reduction in computational time for analysis was achieved through a strategy similar to the selector variable method to circumvent the need for exhaustive enumeration of the possible partitions of surfactants and counterions into clusters. Using statistics from a set of small-system (up to 60 SOS molecules) simulations as input, equilibrium association constants for micelle clusters were obtained as a function of both number of surfactants and number of associated counterions through a global fitting procedure. The resulting free energies were able to accurately predict micelle size and charge distributions in a large (560 molecule) system. The evolution of micelle size and charge with SOS concentration as predicted by the PEACH-derived free energies and by a phenomenological four-parameter model fit, along with the sensitivity of these predictions to variations in cluster definitions, are analyzed and discussed.

Theoretical approaches for dynamical ordering of biomolecular systems

BACKGROUND

Living systems are characterized by the dynamic assembly and disassembly of biomolecules. The dynamical ordering mechanism of these biomolecules has been investigated both experimentally and theoretically. The main theoretical approaches include quantum mechanical (QM) calculation, all-atom (AA) modeling, and coarse-grained (CG) modeling. The selected approach depends on the size of the target system (which differs among electrons, atoms, molecules, and molecular assemblies). These hierarchal approaches can be combined with molecular dynamics (MD) simulation and/or integral equation theories for liquids, which cover all size hierarchies.

SCOPE OF REVIEW

We review the framework of quantum mechanical/molecular mechanical (QM/MM) calculations, AA MD simulations, CG modeling, and integral equation theories. Applications of these methods to the dynamical ordering of biomolecular systems are also exemplified.

MAJOR CONCLUSIONS

The QM/MM calculation enables the study of chemical reactions. The AA MD simulation, which omits the QM calculation, can follow longer time-scale phenomena. By reducing the number of degrees of freedom and the computational cost, CG modeling can follow much longer time-scale phenomena than AA modeling. Integral equation theories for liquids elucidate the liquid structure, for example, whether the liquid follows a radial distribution function.

GENERAL SIGNIFICANCE

These theoretical approaches can analyze the dynamic behaviors of biomolecular systems. They also provide useful tools for exploring the dynamic ordering systems of biomolecules, such as self-assembly. This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato.