Selection for Replicases in Protocells

PMCID: PMC3649988This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Equilibrium model for supramolecular copolymerizations

The coassembly of different building blocks into supramolecular copolymers provides a promising avenue to control their properties and to thereby expand the potential of supramolecular polymers in applications. However, contrary to covalent copolymerization which nowadays can be well controlled, the control over sequence, polymer length, and morphology in supramolecular copolymers is to date less developed, and their structures are more determined by the delicate balance in binding free energies between the distinct building blocks than by kinetics. Consequently, to rationalize the structures of supramolecular copolymers, a thorough understanding of their thermodynamic behavior is needed. Though this is well established for single-component assemblies and over the past years several models have been proposed for specific copolymerization cases, a generally applicable model for supramolecular cooperative copolymers is still lacking. Here, we provide a generalization of our earlier mass-balance models for supramolecular copolymerizations that encompasses all our earlier models. In this model, the binding free energies of each pair of monomer types in each aggregate type can be set independently. We provide scripts to solve the model numerically for any (co)polymerization of one or two types of monomer into an arbitrary number of distinct aggregate types. We illustrate the applicability of the model on data from literature as well as on new experimental data of triarylamine triamide-based copolymers in three distinct solvents. We show that apart from common properties such as the degree of polymerization and length distributions, our approach also allows us to investigate properties such as the copolymer microstructure, that is, the internal ordering of monomers within the copolymers. Moreover, we show that in some cases, also intriguing analytical approximations can be derived from the mass balances

Computation of accommodation coefficients and the use of velocity correlation profiles in molecular dynamics simulations

For understanding the behavior of a gas close to a channel wall it is important to model the gas-wall interactions as detailed as possible. When using molecular dynamics simulations these interactions can be modeled explicitly, but the computations are time consuming. Replacing the explicit wall with a wall model reduces the computational time but the same characteristics should still remain. Elaborate wall models, such as the Maxwell-Yamamoto model or the Cercignani-Lampis model need a phenomenological parameter (the accommodation coefficient) for the description of the gas-wall interaction as an input. Therefore, computing these accommodation coefficients in a reliable way is very important. In this paper, two systems (platinum walls with either argon or xenon gas confined between them) are investigated and are used for comparison of the accommodation coefficients for the wall models and the explicit molecular dynamics simulations. Velocity correlations between incoming and outgoing particles colliding with the wall have been used to compare explicit simulations and wall models even further. Furthermore, based on these velocity correlations, a method to compute the accommodation coefficients is presented, and these newly computed accommodation coefficients are used to show improved correlation behavior for the wall models

Multivalency in a dendritic host-guest system

\u3cp\u3eMultivalency is an important instrument in the supramolecular chemistry toolkit for the creation of strong specific interactions. In this paper we investigate the multivalency effect in a dendritic host-guest system using molecular dynamics simulations. Specifically, we consider urea-adamantyl decorated poly(propyleneimine) dendrimers that together with compatible mono-, bi-, and tetravalent ureidoacetic acid guests can form dynamic patchy nanoparticles. First, we simulate the self-assembly of these particles into macromolecular nanostructures, showing guest-controlled reduction of dendrimer aggregation. Subsequently, we systematically study guest concentration dependent multivalent binding. At low guest concentrations multivalency of the guests clearly increases relative binding as tethered headgroups bind more often than free guests' headgroups. We find that despite an abundance of binding sites, most of the tethered headgroups bind in close proximity, irrespective of the spacer length; nevertheless, longer spacers do increase binding. At high guest concentrations the dendrimer becomes saturated with bound headgroups, independent of guest valency. However, in direct competition the tetravalent guests prevail over the monovalent ones. This demonstrates the benefit of multivalency at high as well as low concentrations.\u3c/p\u3

Velocity correlations and accommodation coefficients for gas-wall interactions in nanochannels

\u3cp\u3eIn order to understand the behavior of a gas close to a channel wall, it is important to model the gas-wall interactions correctly. When using Molecular Dynamics (MD) simulations these interactions are modeled explicitly, but the computations are time consuming. Replacing the explicit wall with an appropriate wall model reduces the computational time, but should still remain the same characteristics. In this paper the focus lies with an argon gas confined between two platinum walls at different temperature. Several wall models are investigated for their feasibility as a replacement of the MD simulations and are mainly compared using the velocity correlations between impinging and reflecting particles. Moreover, a new method to compute the accommodation coefficient using the velocity correlations is demonstrated.\u3c/p\u3

Comparison of molecular dynamics and kinetic modeling of gas-surface interactions

The interaction of a dilute monatomic gas with a solid surface is studied byMolecular Dynamics (MD) simulations and by numerical solutions of a recently proposed kinetic model. Following previous investigations, the heat transport between parallel walls and Couette flow have been adopted as test problems. The distribution functions of re-emitted atoms and the accommodation coefficients obtained from the two techniques are compared in different flow conditions. It is shown that the kinetic model predictions are close to MD results

Molecular dynamics study of lipid based vesicle fission

Together with vesicle fusion and budding, vesicle fission plays an important role in intracellular traffic. Vesicle fission is known to take place in different ways, either or not instigated by proteins. However, as at a molecular level the dynamics of the cell membrane and the working mechanisms of proteins cannot be readily asserted experimentally, many different hypotheses exist to predict and explain these processes. Therefore, we use coarse grained molecular dynamics simulations to elucidate the fission mechanism of vesicles, where we focus on possible mechanisms in the absence of proteins. Two distinct routes are considered that are both based on an asymmetry of the lipid distribution in the membrane. I n the first mechanism, the two types of lipids are equally distributed over both leaflets of the membrane. However, phase separation of the lipids within both leaflets results in domains which form buds that can split off. I n the second mechanism, the asymmetry consists either of a difference in composition between the two monolayers of the membrane or of a difference between the vesicle interior and exterior. This difference in composition yields a spontaneous curvature of the membrane, reshaping the vesicle into a dumbbell which can split. Both pathways are studied using molecular dynamics simulations of the same coarse grained lipid model that has been used before to study spontaneous bilayer and vesicle formation [1], vesicle fusion [2], and vesicle deformations [3]. Using these simulations, the specific conditions to obtain complete fission are investigated for both pathways

An equilibrium model for chiral amplification in supramolecular polymers

We describe a model that rationalizes amplification of chirality in cooperative supramolecular copolymerization. The model extends nucleation-elongation based equilibrium models for growth of supramolecular homopolymers to the case of two monomer and aggregate types. Using the principle of mass-balance for the two monomer types, we derive a set of two nonlinear equations, describing the thermodynamic equilibrium state of the system. These equations can be solved by numerical methods, but also analytical approximations are derived. The equilibrium model allows two-sided growth of the aggregates and can be applied to symmetric supramolecular copolymerizations, corresponding to the situation in which the monomers are enantiomerically related, as well as to the more general case of nonsymmetric supramolecular copolymerizations. In detail, so-called majority-rules phenomena in supramolecular systems with isodesmic as well as cooperative growth are analyzed. Comparison of model predictions with experimental data shows that the model gives a very good description of both titration and melting curves. When the system shows cooperative growth, the model leads to a phase diagram in which the presence of the various aggregate types is given as a function of composition and temperature