Sampling the kinetic pathways of a micelle fusion and fission transition

The fats of the matter: Lipids in prebiotic chemistry and in origin of life studies

The unique biophysical and biochemical properties of lipids render them crucial in most models of the origin of life (OoL). Many studies have attempted to delineate the prebiotic pathways by which lipids were formed, how micelles and vesicles were generated, and how these micelles and vesicles became selectively permeable towards the chemical precursors required to initiate and support biochemistry and inheritance. Our analysis of a number of such studies highlights the extremely narrow and limited range of conditions by which an experiment is considered to have successfully modeled a role for lipids in an OoL experiment. This is in line with a recent proposal that bias is introduced into OoL studies by the extent and the kind of human intervention. It is self-evident that OoL studies can only be performed by human intervention, and we now discuss the possibility that some assumptions and simplifications inherent in such experimental approaches do not permit determination of mechanistic insight into the roles of lipids in the OoL. With these limitations in mind, we suggest that more nuanced experimental approaches than those currently pursued may be required to elucidate the generation and function of lipids, micelles and vesicles in the OoL.

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.

Salt- and pH-Dependent Viscosity of SDS/LAPB Solutions: Experiments and a Semiempirical Thermodynamic Model

We present novel data on the composition-, pH-, and salt-dependent zero shear viscosity of the commercially important mixture of anionic sodium dodecyl sulfate (SDS) and zwitterionic lauramidopropyl betaine (LAPB). We show via proton NMR experiments that the notionally zwitterionic LAPB exhibits a large pK_a shift in the presence of SDS and can become partially cationic at formulation-relevant pH ranges of 4.5-6.0-that is, the binary system is effectively a ternary system. This has a pronounced effect on the viscosity of the system at low pH, especially if the fraction of LAPB is high. We use theoretical arguments to motivate a semiempirical but practical approach to model the viscosity of the mixtures using thermodynamic parameters such as the excess chemical potentials or activity coefficients of the surfactants. We demonstrate this using an augmented regular solution theory-based mixed micelle thermodynamic model and develop robust regression models using Bayesian approaches. We also show how the pK_a shift from NMR experiments can be used to parameterize the thermodynamic model. This framework should be extensible to other arbitrary surfactant mixtures in the future and hence will be of broad interest for the development of surfactant formulations for household, personal care, and other applications.

The SARS-CoV-2 nucleocapsid protein is dynamic, disordered, and phase separates with RNA

The SARS-CoV-2 nucleocapsid (N) protein is an abundant RNA-binding protein critical for viral genome packaging, yet the molecular details that underlie this process are poorly understood. Here we combine single-molecule spectroscopy with all-atom simulations to uncover the molecular details that contribute to N protein function. N protein contains three dynamic disordered regions that house putative transiently-helical binding motifs. The two folded domains interact minimally such that full-length N protein is a flexible and multivalent RNA-binding protein. N protein also undergoes liquid-liquid phase separation when mixed with RNA, and polymer theory predicts that the same multivalent interactions that drive phase separation also engender RNA compaction. We offer a simple symmetry-breaking model that provides a plausible route through which single-genome condensation preferentially occurs over phase separation, suggesting that phase separation offers a convenient macroscopic readout of a key nanoscopic interaction.

The SARS-CoV-2 nucleocapsid protein is dynamic, disordered, and phase separates with RNA

The SARS-CoV-2 nucleocapsid (N) protein is an abundant RNA binding protein critical for viral genome packaging, yet the molecular details that underlie this process are poorly understood. Here we combine single-molecule spectroscopy with all-atom simulations to uncover the molecular details that contribute to N protein function. N protein contains three dynamic disordered regions that house putative transiently-helical binding motifs. The two folded domains interact minimally such that full-length N protein is a flexible and multivalent RNA binding protein. N protein also undergoes liquid-liquid phase separation when mixed with RNA, and polymer theory predicts that the same multivalent interactions that drive phase separation also engender RNA compaction. We offer a simple symmetry-breaking model that provides a plausible route through which single-genome condensation preferentially occurs over phase separation, suggesting that phase separation offers a convenient macroscopic readout of a key nanoscopic interaction.

Simulation of diblock copolymer surfactants. II. Micelle kinetics

Molecular dynamics (MD) simulations are used to measure dynamical properties of a simple bead-spring model of A-B diblock copolymer molecules, and to characterize rates and mechanisms of several dynamical processes. Dynamical properties are analyzed within the context of a kinetic population model that allows for both stepwise insertion and expulsion of individual free molecules and occasional fission and fusion of micelles. Kinetic coefficients for stepwise processes and micelle fission have been extracted from MD simulations of individual micelles. Insertion of a free surfactant molecule into a preexisting micelle is shown to be a completely diffusion-controlled process for the model studied here. Estimates are given for rates of rare events that create and destroy entire micelles by competing mechanisms involving stepwise association and dissociation or fission and fusion. Both mechanisms are shown to be relevant over the range of parameters studied here, with association and dissociation dominating in systems with more soluble surfactants and fission and fusion dominating in systems with less soluble surfactants.

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.

Micelle response to changes in solvent properties

The dynamics of co-polymer systems play an important role in the preparation and stability of formulations, as well as on their capability to function in drug delivery systems. Micelle inversion can occur as a result of a change in concentration when a solvent is very volatile and evaporates, or as a result of a change in solvent quality upon addition of another solvent to the original solution, or upon changes in pH. In this work, dissipative particle dynamics (DPD) is used to examine the dynamics of micelle inversion in concentrated systems of diblock and triblock amphiphiles, where interactions between neighboring aggregates are observed. Significant differences were observed in the inversion process of different amphiphilic molecules, with a large amount of co-polymer exchange between inverting aggregates made of diblock amphiphiles, and practically no exchange of molecules between aggregates during the inversion of triblock copolymer aggregates. Fundamental mechanisms of inversion are revealed that provide information which can be used to help design micelles for targeted drug release and allow understanding of history dependant formulations.

Transformation from Globular to Cylindrical Mixed Micelles through Molecular Exchange that Induces Micelle Fusion

Transformations between different micellar morphologies in solution induced by changes in composition, salt, or temperature are well-known phenomena; however, the understanding of the associated kinetic pathways is still limited. Especially for mixed surfactant systems, the micelles can take a very wide range of structures, depending on the surfactant packing parameter and other thermodynamic conditions. Synchrotron-based small-angle X-ray scattering (SAXS) in combination with fast mixing using a stopped-flow apparatus can give direct access to the structural kinetics on a millisecond time scale. Here, this approach is used to study the formation of cylindrical micelles after mixing two solutions with globular micelles of the nonionic surfactant dodecyl maltoside (DDM) and the anionic surfactant sodium dodecyl sulfate (SDS), respectively. Two separate processes were identified: (i) a transition in micellar shell structure, interpreted as exchange of surfactant molecules resulting in mixed globular micelles, and subsequently, (ii) fusion into larger, cylindrical structures.

Molecular dynamic simulations of self-assembly of amphiphilic comb-like anionic polybenzoxazines

Fully atomistic molecular dynamic simulations were performed to address the self-assembly of amphiphilic and comb-like polybenzoxazines (iBnXz) in water, with i = 3 (trimer), i = 4 (tetramer); i = 6 (hexamer), i = 8 (octamer), and i = 10 (decamer). Spontaneous aggregation of these comb-like polybenzoxazine molecules into a single micelle occurs in the simulations. The simulations show that molecular size and concentration play important roles in micellar morphology. At an iBnXz concentration of 50 mM, the 3BnXz and 4BnXz molecules aggregate into spherical micelles, whereas the 6BnXz, 8BnXz, and 10BnXz molecules aggregate into cylindrical micelles. The micellar morphology is spherical at low concentrations, but undergoes a transition to cylindrical shape as concentration increases. The transition point depends on the molecular size-both the true size as indicated by molecular weight, as well as an additional effective size dependent on molecular flexibility.

Multi-scale times and modes of fast and slow relaxation in solutions with coexisting spherical and cylindrical micelles according to the difference Becker-Döring kinetic equations

The eigenvalues and eigenvectors of the matrix of coefficients of the linearized kinetic equations applied to aggregation in surfactant solution determine the full spectrum of characteristic times and specific modes of micellar relaxation. The dependence of these relaxation times and modes on the total surfactant concentration has been analyzed for concentrations in the vicinity and well above the second critical micelle concentration (cmc2) for systems with coexisting spherical and cylindrical micelles. The analysis has been done on the basis of a discrete form of the Becker-Döring kinetic equations employing the Smoluchowsky diffusion model for the attachment rates of surfactant monomers to surfactant aggregates with matching the rates for spherical aggregates and the rates for large cylindrical micelles. The equilibrium distribution of surfactant aggregates in solution has been modeled as having one maximum for monomers, another maximum for spherical micelles and wide slowly descending branch for cylindrical micelles. The results of computations have been compared with the analytical ones known in the limiting cases from solutions of the continuous Becker-Döring kinetic equation. They demonstrated a fair agreement even in the vicinity of the cmc2 where the analytical theory looses formally its applicability.

Fusion and fission inhibited by the same mechanism in electrostatically charged surfactant micelles

This paper revises the general idea about the role of intermicellar and intramiceller interactions in inhibiting fusion of self-assembled surfactant micelles. Fusion and fission of micelles are usually thought to be limited by different mechanisms. While fission is accepted to be controlled by surface instabilities (intramicellar interactions), fusion is commonly thought to be rate limited by the barrier to the close approach between two micelles due to the steric or Coulombic repulsions (intramicellar interactions). Here we describe the role of electrostatic repulsions in inhibiting fusion and fission kinetics in self-assembled micelles. We use stopped flow-fluorescence technique with hydrophobic pyrene to quantify fusion and fission in ionic/nonionic mixed micelles (Triton X-100/SDS). We show that the fusion and fission rates decrease with the same tendency with increasing the fraction of the ionic charges, while their ratio remains constant. Our results are interpreted to mean that, in slightly charged micelles, fusion shares the same limiting step with fission, which most likely involves surface instabilities and intramiceller interactions.

Optimizing Nucleus Size Metrics for Liquid-Solid Nucleation from Transition Paths of Near-Nanosecond Duration

We determine the mechanism for the liquid-solid phase transition in the Lennard-Jones fluid close to coexistence with aimless shooting and likelihood maximization. The reaction coordinate for this process is a product of a structural descriptor and the size of the nascent solid nucleus and is quantitatively verified with the committor probability histogram test. This study identifies the first accurate scalar reaction coordinate for the liquid-solid nucleation process in Lennard-Jonesium, which will likely extend to nucleation processes in other spherically symmetric fluids. On the basis of our results, we propose a structural correction factor for the commonly cited nucleus size reaction coordinate from classical nucleation theory that enables connection of simulation data to stochastic models of nucleation kinetics. In addition, we show that aimless shooting is able to obtain reasonable acceptance rates for transitions with highly diffusive characteristics, which has been problematic for transition path sampling methods for diffusive processes such as nucleation and macromolecular transitions.

Extracting bulk properties of self-assembling systems from small simulations

For systems that self-assemble into finite-sized objects, it is sometimes convenient to compute the thermodynamics for a small system where a single assembly can form. However, we show that in the canonical ensemble the use of small systems can lead to significant finite-size effects due to the suppression of concentration fluctuations. We introduce methods for estimating the bulk yields from simulations of small systems and for following the convergence of yields with system size, under the assumptions that the various species behave ideally.

Enzymatic transition states and dynamic motion in barrier crossing

What are the atomic motions at enzymatic catalytic sites on the timescale of chemical change? Combined experimental and computational chemistry approaches take advantage of transition-state analogs to reveal dynamic motions linked to transition-state formation. QM/MM transition path sampling from reactive complexes provides both temporal and dynamic information for barrier crossing. Fast (femtosecond to picosecond) dynamic motions provide essential links to enzymatic barrier crossing by local or promoting-mode dynamic searches through bond-vibrational space. Transition-state lifetimes are within the femtosecond timescales of bond vibrations and show no manifestations of stabilized, equilibrated complexes. The slow binding and protein conformational changes (microsecond to millisecond) also required for catalysis are temporally decoupled from the fast dynamic motions forming the transition state. According to this view of enzymatic catalysis, transition states are formed by fast, coincident dynamic excursions of catalytic site elements, while the binding of transition-state analogs is the conversion of the dynamic excursions to equilibrated states.

Principal role of the stepwise aggregation mechanism in ionic surfactant solutions near the critical micelle concentration. Molecular dynamics study

The validity of the assumption on the predominant contribution of the stepwise processes to the ionic micelle formation/destruction in the vicinity of critical micelle concentration was investigated by molecular dynamics simulation. A coarse-grained model was used to describe the surfactant/water mixture. The cluster size distribution was estimated directly from molecular dynamics simulations or obtained from a reduced set of kinetic equations. The good agreement between two approaches shows that the neglect of the terms responsible for cluster fusion/fission is fully justified and that such processes are less important than stepwise aggregation.