Coarse-grained models for aqueous polyethylene glycol solutions

Crowder titrations enable the quantification of driving forces for macromolecular phase separation

Macromolecular solubility is an important contributor to the driving forces for phase separation. Formally, the driving forces in a binary mixture comprising a macromolecule dissolved in a solvent can be quantified in terms of the saturation concentration, which is the threshold macromolecular concentration above which the mixture separates into coexisting dense and dilute phases. In addition, the second virial coefficient, which measures the effective strength of solvent-mediated intermolecular interactions provides direct assessments of solvent quality. The sign and magnitude of second virial coefficients will be governed by a combination of solution conditions and the nature of the macromolecule of interest. Here, we show, using a combination of theory, simulation, and in vitro experiments, that titrations of crowders, providing they are true depletants, can be used to extract the intrinsic driving forces for macromolecular phase separation. This refers to saturation concentrations in the absence of crowders and the second virial coefficients that quantify the magnitude of the incompatibility between macromolecules and the solvent. Our results show how the depletion-mediated attractions afforded by crowders can be leveraged to obtain comparative assessments of macromolecule-specific, intrinsic driving forces for phase separation.

Sequence Sensitivity in Membrane Remodeling by Polyampholyte Condensates

Intrinsically disordered peptides (IDPs) have been found to undergo liquid-liquid phase separation (LLPS) and produce complex coacervates that play numerous regulatory roles in the cell. Recent experimental studies have discovered that LLPS at or near the membrane surface helps in the biomolecular organization during signaling events and can significantly alter the membrane morphology. However, the molecular mechanism and microscopic details of such processes still remain unclear. Here we study the effect of polyampholyte and polyelectrolyte condensation on two different anionic membranes, as they represent a majority of naturally occurring IDPs. The polyampholytes are fifty-residue polymers, made of glutamate(E) and lysine(K) with different charge patterns. The polyelectrolytes are separate chains of E25 and K25. We first calibrate the MARTINI v3.0 force field and then perform long-time-scale coarse-grained molecular dynamics simulations. We find that condensates formed by all the polyampholytes get adsorbed on the membrane. However, the strong polyampholytes (i.e., blocky sequences) can remodel the membranes more prominently than the weaker ones (i.e., scrambled sequences). Condensates formed by the blocky sequences induce a significant negative curvature (∼0.1 nm-1) and local demixing of lipids, whereas those by the scrambled sequences tend to wet the membrane to a greater extent without generating significant curvature or demixing. We perform several microscopic analyses to characterize the nature of the interaction between membranes and these condensates. Our analyses of interaction energetics reveal that membrane remodeling and/or wetting are favored by enhanced interactions between polyampholytes with lipids and the counterions.

Hydrogen Bond Network Disruption by Hydration Layers in Water Solutions with Salt and Hydrogen-Bonding Polymers (PEO)

A mean field theory model describing the interaction of ion hydration layers with the network of hydrogen bonds of both water and the nonionic polymer poly(ethylene oxide) (PEO) is presented. The predictions of the model for types and statistics of hydrogen bonds, the number of water molecules bound to PEO, or their dependence on temperature are successfully verified from all-atom simulations at different NaCl and PEO concentrations. Furthermore, our simulations show that the binding of cations to PEO increases monotonically with salt concentration, in agreement with recent experimental results, through a mechanism in which the sum of the number of bound water and cations is independent of salt concentration. The model introduced is general and can describe any salt or hydrogen-bond-forming polymer.

Crowder titrations enable the quantification of driving forces for macromolecular phase separation

Macromolecular solubility is an important contributor to the driving forces for phase separation. Formally, the driving forces in a binary mixture comprising a macromolecule dissolved in a solvent can be quantified in terms of the saturation concentration, which is the threshold macromolecular concentration above which the mixture separates into coexisting dense and dilute phases. Additionally, the second virial coefficient, which measures the effective strength of solvent-mediated intermolecular interactions provides direct assessments of solvent quality. The sign and magnitude of second virial coefficients will be governed by a combination of solution conditions and the nature of the macromolecule of interest. Here, we show, using a combination of theory, simulation, and in vitro experiments, that titrations of crowders, providing they are true depletants, can be used to extract the intrinsic driving forces for macromolecular phase separation. This refers to saturation concentrations in the absence of crowders and the second virial coefficients that quantify the magnitude of the incompatibility between macromolecules and the solvent. Our results show how the depletion-mediated attractions afforded by crowders can be leveraged to obtain comparative assessments of macromolecule-specific, intrinsic driving forces for phase separation.

SIGNIFICANCE

Phase separation has emerged as a process of significant relevance to sorting macromolecules into distinct compartments, thereby enabling spatial and temporal control over cellular matter. Considerable effort is being invested into uncovering the driving forces that enable the separation of macromolecular solutions into coexisting phases. At its heart, this process is governed by the balance of macromolecule-solvent, inter-macromolecule, and solvent-solvent interactions. We show that the driving forces for phase separation, including the coefficients that measure interaction strengths between macromolecules, can be extracted by titrating the concentrations of crowders that enable macromolecules to phase separate at lower concentrations. Our work paves the way to leverage specific categories of measurements for quantitative characterizations of driving forces for phase separation.

The Martini Model in Materials Science

The Martini model, a coarse-grained force field initially developed with biomolecular simulations in mind, has found an increasing number of applications in the field of soft materials science. The model's underlying building block principle does not pose restrictions on its application beyond biomolecular systems. Here, the main applications to date of the Martini model in materials science are highlighted, and a perspective for the future developments in this field is given, particularly in light of recent developments such as the new version of the model, Martini 3.

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.

A coarse-grain force field based on quantum mechanics (CGq FF) for molecular dynamics simulation of poly(ethylene glycol)-block-poly(ε-caprolactone) (PEG-b-PCL) micelles

In order to provide the means to predict from molecular dynamics (MD) simulations the structures of copolymer-based micelles in solution, we developed coarse grain force field (CGq FF) parameters for poly(ethylene glycol) (PEG) and for poly(ε-caprolactone) (PCL). A key advance here is the use of quantum mechanics to train the parameters describing the non-bonded (NB) interactions between the CG beads. The functional forms are the same as the MARTINI CG FF so standard MD codes can be used. Our CGq FF describes well the experimentally observed properties for the polymer-air and polymer-water interfaces, indicating the accuracy of the NB interactions. The structural properties (density, radius of gyration (R_g), and end-to-end distance (h)) match both experiment and all atom (AA) simulations. We illustrate the application of this CGq FF by following the formation of a spherical micelle from 250 chains of PEG₂₃-b-PCL₉ diblock copolymer, each block with molecular weight of 1000 Daltons (10 500 beads, corresponding to 123 250 atoms), in a water box with 119 139 water beads (426 553 water molecules).

The coarse-grained models of poly(ethylene oxide) and poly(propylene oxide) homopolymers and poloxamers in big multipole water (BMW) and MARTINI frameworks

Polyethylene oxide (PEO) and poly(propylene oxide) (PPO), especially their tri-block copolymers PEO-PPO-PEO (poloxamers), have a broad range of applications in biotechnology and medical science. Understanding their specific interactions with biomembranes is the key to unveil the unique features of poloxamers either as membrane-healing or membrane pore-forming agents. Based on the coarse-graining convention of the MARTINI force field and the big multipole water (BMW) model, which has a three charged site topology and can reproduce the correct dipole moment of four-water clusters, we generated coarse-grained (CG) models with analytical and numerical potentials for PEO and PPO homopolymers and poloxamers in dilute solution. The effective bonded interaction potentials between CG beads were determined from the probability distributions of bond lengths, angles and dihedrals that are determined from atomistic simulations. The nonbonded interaction parameters were fine-tuned to reproduce the conformational properties of atomistic PEO and PPO homopolymers and poloxamers via extensive CG simulations of PEO and PPO homopolymers and poloxamers in a BMW water environment. The reported CG models provide a promising framework for a comprehensive understanding of the microstructural, conformational, and dynamic properties of poloxamers and their delicate interactions with other species in an explicit water environment.

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.

Sequence transferable coarse-grained model of amphiphilic copolymers

Polymer properties are inherently multi-scale in nature, where delicate local interaction details play a key role in describing their global conformational behavior. In this context, deriving coarse-grained (CG) multi-scale models for polymeric liquids is a non-trivial task. Further complexities arise when dealing with copolymer systems with varying microscopic sequences, especially when they are of amphiphilic nature. In this work, we derive a segment-based generic CG model for amphiphilic copolymers consisting of repeat units of hydrophobic (methylene) and hydrophilic (ethylene oxide) monomers. The system is a simulation analogue of polyacetal copolymers [S. Samanta et al., Macromolecules 49, 1858 (2016)]. The CG model is found to be transferable over a wide range of copolymer sequences and also to be consistent with existing experimental data.

Parameterization and atomistic simulations of biomimetic membranes

We have developed CHARMM force-field compatible parameters and conducted all-atom explicit-solvent MD simulations of biomimetic membranes composed of block copolymers of poly(butadiene), poly(isoprene), and poly(ethylene oxide).

Effect of Chain Length on the Partition Properties of Poly(ethylene oxide): Comparison between MARTINI Coarse-Grained and Atomistic Models

The MARTINI coarse-grained beads are parameterized to match the partition coefficients of several organic molecules in different solvents. Here, we test the method when modeling the partitioning properties of poly(ethylene oxide) between solvents of different polarities. We show that, among the existing models, the latest model developed by Lee and co-workers [ Lee , H. ; Pastor , R. W. J. Phys. Chem. B 2011 , 115 , 7830 - 7837 ] is the one that most successfully reproduces the hydration free energy of short oligomers, although it predicts highly negative solvation free energies in octanol and hexane. We develop a new CG model matching the solvation free energy of the monomer in different solvents and propose a simple method to select the Lennard-Jones parameters that reproduce the desired partition coefficients. The model correctly reproduces water/hexane partition properties for oligomers up to 10 monomers but still suffers from a transferability problem for larger molecular weight.

Simulated Permeation and Characterization of PEGylated Gold Nanoparticles in a Lipid Bilayer System

PEGylated gold nanoparticles are considered suitable nanocarriers for use in biomedical applications and targeted drug delivery systems. In our previous investigation with the alkanethiol-functionalized gold nanoparticle, we found that permeation across a protein-free phospholipid membrane resulted in damaging effects of lipid displacement and water and ion leakage. In the present study, we carry out a series of coarse-grained molecular simulations to explore permeation of lipid bilayer systems by a PEGylated gold nanoparticle, especially at the bulk-liquid-lipid interface as well as the interface between the two lipid leaflets. Initially, we examine molecular-level details of a PEGylated gold nanoparticle (constructed from cycled annealing) in water and find a distribution of ligand configurations (from mushroom to brush states) present in nanoparticles with medium to high surface coverage. We also find that the characteristic properties of the PEGylated gold nanoparticle do not change when it is placed in a salt solution. In our permeation studies, we investigate events of water and ion penetration as well as lipid translocation while varying the ligand length, nanoparticle surface coverage, and ion concentration gradient of our system. Results from our studies show the following: (1) The number of water molecules in the interior of the membrane during ligand-coated nanoparticle permeation increases with PEGn-SH surface coverage, ligand length, and permeation velocity but is not sensitive to the ion concentration gradient. (2) Lipid molecules do not leave the membrane; instead they complete trans-bilayer lipid flip-flop with longer ligands and higher surface coverages. (3) The lack of formation of stable water pores prevents ion translocation. (4) The PEGylated nanoparticle causes less damage to the membrane overall due to favorable interactions with the lipid headgroups which may explain why experimentalists observe endocytosis of PEGylated nanocarriers in vivo.

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.