A coarse-grained model for polyethylene glycol polymer

Approaches and Perspective of Coarse-Grained Modeling and Simulation for Polymer-Nanoparticle Hybrid Systems

Molecular modeling and simulations have emerged as effective and indispensable tools to characterize polymeric systems. They provide fundamental and essential insights to design a product of the required properties and to improve the understanding of a phenomenon at the molecular level for a particular system. The polymer-nanoparticle hybrids are materials with outstanding properties and correspondingly large applications whose study has benefited from this new paradigm. However, despite the significant expansion of modern day computational powers, investigation of the long time and large length scale phenomenon in polymeric and polymer-nanoparticle systems is still a challenging task to complete through all-atom molecular dynamics (AA-MD) simulations. To circumvent this problem, a variety of coarse-grained (CG) models have been proposed, ranging from the generic CG models for qualitative properties predictions to more realistic chemically specific CG models for quantitative properties predictions. These CG models have already delivered some success stories in the study of several spatial and temporal evolutions of many processes. Some of these studies were beyond the feasibility of traditional atomistic resolution models due to either the size or the time constraints. This review captures the different types of popular CG approaches that are utilized in the investigation of the microscopic behavior of polymer-nanoparticle hybrid systems. The rationale of this article is to furnish an overview of the popular CG approaches and their applications, to review several important and most recent developments, and to delineate the perspectives on future directions in the field.

Bottom-up Coarse-Graining: Principles and Perspectives

Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

Effectiveness of coarse graining degree and speedup on the dynamic properties of homopolymer

Evaluation of effective coarse graining (CG) degree and reasonable speedup relative to all-atomistic (AA) model was conducted to provide a basis for building appropriate larger-scale model. The reproducibility of atomistic conformation and temperature transferability both act as the analysis criteria to resolve the maximum acceptable CG degree. Taking short- and long time spans into account simultaneously in the estimation of computational speedup, a dynamic scaling factor is accessible in fitting mean squared displacement ratio of CG to AA as an exponential function. Computing loss in parallel running is an indispensable component in acceleration, which was also added in the evaluation. Subsequently, a quantified prediction of CG speedup arises as a multiplication of dynamic scaling factor, computing loss, time step, and the square of reduction in the number of degrees of freedom. Polyethylene oxide was adopted as a reference system to execute the direct Boltzmann inversion and iterative Boltzmann inversion. Bonded and non-bonded potentials were calculated in CG models with 1~4 monomers per bead. The effective CG degree was determined as two at the most with a speedup of four orders magnitude over AA in this study. Determination of effectiveness CG degree and the corresponding speedup prediction provide available tools in larger spatiotemporal-scale calculations.

Molecular Simulations of PEGylated Biomolecules, Liposomes, and Nanoparticles for Drug Delivery Applications

Since the first polyethylene glycol (PEG)ylated protein was approved by the FDA in 1990, PEGylation has been successfully applied to develop drug delivery systems through experiments, but these experimental results are not always easy to interpret at the atomic level because of the limited resolution of experimental techniques. To determine the optimal size, structure, and density of PEG for drug delivery, the structure and dynamics of PEGylated drug carriers need to be understood close to the atomic scale, as can be done using molecular dynamics simulations, assuming that these simulations can be validated by successful comparisons to experiments. Starting with the development of all-atom and coarse-grained PEG models in 1990s, PEGylated drug carriers have been widely simulated. In particular, recent advances in computer performance and simulation methodologies have allowed for molecular simulations of large complexes of PEGylated drug carriers interacting with other molecules such as anticancer drugs, plasma proteins, membranes, and receptors, which makes it possible to interpret experimental observations at a nearly atomistic resolution, as well as help in the rational design of drug delivery systems for applications in nanomedicine. Here, simulation studies on the following PEGylated drug topics will be reviewed: proteins and peptides, liposomes, and nanoparticles such as dendrimers and carbon nanotubes.

Martini Coarse-Grained Model for Clay-Polymer Nanocomposites

We have developed a coarse-grained (CG) model of a polymer-clay system consisting of organically modified montmorillonite (oMMT) nanoclay as the nanoparticle in accordance with the MARTINI force field. We have used mechanical properties and cleavage free energy of the clay particle to respectively parameterize bonded and nonbonded interaction parameters for an oMMT clay particle, where intergallery Na⁺ ions are replaced by tetramethylammonium (TMA) ions. The mechanical properties were determined from the slope of the stress-strain curve and cleavage free energy was determined by allowing for full surface reconstruction corresponding to a slow equilibrium cleavage process. Individual dispersive and polar contributions to oMMT cleavage energy were used for determination of appropriate MARTINI bead types for the CG oMMT sheet. The self-consistency of the developed MARTINIFF parameters for the TMA-montmorillonite-polymer system was verified by comparing estimates for select structural, thermodynamic, and dynamic properties obtained in all-atomistic simulations with that obtained in CG simulations. We have determined the influence of clay particles on properties of three polymer melts (polyethylene, polypropylene, and polystyrene) at two temperatures to establish transferability of the developed parameters. We have also shown that the effect of clay-polymer interactions on structure-property relationships in the polymer-clay nanocomposite system is well captured by Rosenfeld's excess entropy scaling.

Machine-Learning Enabled New Insights into the Coil-to-Globule Transition of Thermosensitive Polymers Using a Coarse-Grained Model

We present a computational framework that integrates coarse-grained (CG) molecular dynamics (MD) simulations and a data-driven machine-learning (ML) method to gain insights into the conformations of polymers in solutions. We employ this framework to study conformational transition of a model thermosensitive polymer, poly( N-isopropylacrylamide) (PNIPAM). Here, we have developed the first of its kind, a temperature-independent CG model of PNIPAM that can accurately predict its experimental lower critical solution temperature (LCST) while retaining the tacticity in the presence of an explicit water model. The CG model was extensively validated by performing CG MD simulations with different initial conformations, varying the radius of gyration of chain, the chain length, and the angle between the adjacent monomers of the initial configuration of PNIPAM (total simulation time = 90 μs). Moreover, for the first time, we utilize the nonmetric multidimensional scaling (NMDS) method, a data-driven ML approach, to gain further insights into the mechanisms and pathways of this coil-to-globule transition by analyzing CG MD simulation trajectories. NMDS analysis provides entirely new insights and shows multiple metastable states of PNIPAM during its coil-to-globule transition above the LCST.

Multiscale approach for the construction of equilibrated all-atom models of a poly(ethylene glycol)-based hydrogel

A multiscale modeling approach is presented for the efficient construction of an equilibrated all-atom model of a cross-linked poly(ethylene glycol) (PEG)-based hydrogel using the all-atom polymer consistent force field (PCFF). The final equilibrated all-atom model was built with a systematic simulation toolset consisting of three consecutive parts: (1) building a global cross-linked PEG-chain network at experimentally determined cross-link density using an on-lattice Monte Carlo method based on the bond fluctuation model, (2) recovering the local molecular structure of the network by transitioning from the lattice model to an off-lattice coarse-grained (CG) model parameterized from PCFF, followed by equilibration using high performance molecular dynamics methods, and (3) recovering the atomistic structure of the network by reverse mapping from the equilibrated CG structure, hydrating the structure with explicitly represented water, followed by final equilibration using PCFF parameterization. The developed three-stage modeling approach has application to a wide range of other complex macromolecular hydrogel systems, including the integration of peptide, protein, and/or drug molecules as side-chains within the hydrogel network for the incorporation of bioactivity for tissue engineering, regenerative medicine, and drug delivery applications.