Single-ion conductors are attractive electrolyte materials because of their inherent safety and ease of processing. Most ions in a sodium-neutralized PEO sulfonated-isophthalate ionomer electrolyte exist as one dimensional chains, restricted in dimensionality by the steric hindrance of the attached polymer. Because the ions are slow to reconfigure, atomistic MD simulations of this material are unable to adequately sample equilibrium ion structures. We apply a novel coarse-graining scheme using a generalized-YBG procedure in which the polymer backbone is completely removed and implicitly represented by the effective potentials of the remaining ions. The ion-only coarse-grained simulation allows for substantial sampling of equilibrium aggregate configurations. We extend the wormlike micelle theory to model ion chain equilibrium. Our aggregates are random walks which become more positively charged with increasing size. Defects occur on the string-like structure in the form of “dust” and “knots,” which form due to cation coordination with open sites along the string. The presence of these defects suggest that cation hopping along open third-coordination sites could be an important mechanism of charge transport using ion aggregates.
Low resolution coarse-grained (CG) models enable highly efficient simulations of complex systems. The interactions in CG models are often iteratively refined over multiple simulations until they reproduce the one-dimensional (1-D) distribution functions, e.g., radial distribution functions (rdfs), of an all-atom (AA) model. In contrast, the multiscale coarse-graining (MS-CG) method employs a generalized Yvon-Born-Green (g-YBG) relation to determine CG potentials directly (i.e., without iteration) from the correlations observed for the AA model. However, MS-CG models do not necessarily reproduce the 1-D distribution functions of the AA model. Consequently, recent studies have incorporated the g-YBG equation into iterative methods for more accurately reproducing AA rdfs. In this work, we consider a theoretical framework for an iterative g-YBG method. We numerically demonstrate that the method robustly determines accurate models for both hexane and also a more complex molecule, 3-hexylthiophene. By examining the MS-CG and iterative g-YBG models for several distinct CG representations of both molecules, we investigate the approximations of the MS-CG method and their sensitivity to the CG mapping. More generally, we explicitly demonstrate that CG models often reproduce 1-D distribution functions of AA models at the expense of distorting the cross-correlations between the corresponding degrees of freedom. In particular, CG models that accurately reproduce intramolecular 1-D distribution functions may still provide a poor description of the molecular conformations sampled by the AA model. We demonstrate a simple and predictive analysis for determining CG mappings that promote an accurate description of these molecular conformations.
Coarse-grained (CG) models enable highly efficient simulations of complex processes that cannot be effectively studied with more detailed models. CG models are often parameterized using either force- or structure-motivated approaches. The present work investigates parallels between these seemingly divergent approaches by examining the relative entropy and multiscale coarse-graining (MS-CG) methods. We demonstrate that both approaches can be expressed in terms of an information function that discriminates between the ensembles generated by atomistic and CG models. While it is well known that the relative entropy approach minimizes the average of this information function, the present work demonstrates that the MS-CG method minimizes the average of its gradient squared. We generalize previous results by establishing conditions for the uniqueness of structure-based potentials and identify similarities with corresponding conditions for the uniqueness of MS-CG potentials. We analyze the mapping entropy and extend the MS-CG and generalized-Yvon-Born-Green formalisms for more complex potentials. Finally, we present numerical calculations that highlight similarities and differences between structure- and force-based approaches. We demonstrate that both methods obtain identical results, not only for a complete basis set, but also for an incomplete harmonic basis set in Cartesian coordinates. However, the two methods differ when the incomplete basis set includes higher order polynomials of Cartesian coordinates or is expressed as functions of curvilinear coordinates.
Coarse-grained (CG) models often employ pair potentials that are parametrized to reproduce radial distribution functions (rdfs) determined for an atomistic model. This implies that the CG model must reproduce the corresponding atomistic mean forces. These mean forces include not only a direct contribution from the corresponding interaction but also correlated contributions from the surrounding environment. The many-body correlations that influence this second contribution present significant challenges for accurately reproducing atomistic distribution functions. This work presents a detailed investigation of these many-body correlations and their significance for determining CG potentials while using liquid heptane as a model system. We employ a transparent geometric framework for directly determining CG potentials that has been previously developed within the context of the multiscale coarse-graining and generalized Yvon-Born-Green methods. In this framework, a metric tensor quantifies the relevant many-body correlations and precisely decomposes atomistic mean forces into contributions from specific interactions, which then determine the CG force field. Numerical investigations reveal that this metric tensor reflects both the CG representation and also subtle correlations between molecular geometry and intermolecular packing, but can be largely interpreted in terms of generic considerations. Our calculations demonstrate that contributions from correlated interactions can significantly impact the pair mean force and, thus, also the CG force field. Finally, an eigenvector analysis investigates the importance of these interactions for reproducing atomistic distribution functions.
Nucleic acid-based aptamers possess many useful features that make them a promising alternative to antibodies and other affinity reagents, including well-established chemical synthesis, reversible folding, thermal stability and low cost. However, the selection process typically used to generate aptamers (SELEX) often requires significant resources and can fail to yield aptamers with sufficient affinity and specificity. A number of seminal theoretical models and numerical simulations have been reported in the literature offering insights into experimental factors that govern the effectiveness of the selection process. Though useful, these previous models have not considered the full spectrum of experimental factors or the potential impact of tuning these parameters at each round over the course of a multi-round selection process. We have developed an improved mathematical model to address this important question, and report that both target concentration and the degree of non-specific background binding are critical determinants of SELEX efficiency. Although smaller target concentrations should theoretically offer superior selection outcome, we show that the level of background binding dramatically affect the target concentration that will yield maximum enrichment at each round of selection. Thus, our model enables experimentalists to determine appropriate target concentrations as a means for protocol optimization. Finally, we perform a comparative analysis of two different selection methods over multiple rounds of selection, and show that methods with inherently lower background binding offer dramatic advantages in selection efficiency.
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