End-to-End Distance Probability Distributions of Dilute Poly(ethylene oxide) in Aqueous Solution

Abstract

We introduce a powerful, widely applicable approach to characterizing polymer conformational distributions, specifically the end-to-end distance distributions, P(R ee ), accessed through double electron−electron resonance (DEER) spectroscopy in conjunction with molecular dynamics (MD) simulations. The technique is demonstrated on one of the most widely used synthetic, disordered, water-soluble polymers: poly(ethylene oxide) (PEO). Despite its widespread importance, no systematic experimental characterization of PEO's R ee conformational landscape exists. The evaluation of P(R ee ) is particularly important for short polymers or (bio)polymers with sequence complexities that deviate from simple polymer physics scaling laws valid for long chains. In this study, we characterize the R ee landscape by measuring P(R ee ) for low molecular weight (MW: 0.22−2.6 kDa) dilute PEO chains. We use DEER with end-conjugated spin probes to resolve R ee populations from ∼2−9 nm and compare them with full distributions from MD. The P( R ee )'s from DEER and MD show remarkably good agreement, particularly at longer chain lengths where populations in the DEER-unresolvable range (<1.5 nm) are low. Both the P(R ee ) and the root-mean-square R ̃ee indicate that aqueous PEO is a semiflexible polymer in a good solvent, with the latter scaling linearly with molecular weight up to its persistence length (l p ∼ 0.48 nm), and rapidly transitioning to excluded volume scaling above l p . The R ̃ee scaling is quantitatively consistent with that from experimental scattering data on high MW (>10 kDa) PEO and the P(R ee )'s crossover to the theoretical distribution for an excluded volume chain.

Quantifying Polypeptoid Conformational Landscapes through Integrated Experiment and Simulation

“…Thus, the scaling exponents computed from simulations and DEER are consistent. However, the mean end-to-end distances from simulations are systematically smaller, consistent with the previous work comparing mean distances from DEER and simulation for poly­(ethylene oxide) . This is partly due to the challenges in resolving the region below 20 Å for DEER.…”

“…This peak suggests that the spin labels on both ends have a slight tendency to aggregate with each other (Figure S39), as was previously observed in simulations of end-labeled polyethylene oxide. 39 Recalculating the P(R ee ) by removing the contribution from these shortdistance conformations, which are not captured by DEER, further improves the agreement between DEER and simulation (Figures S40 and S41).…”

“…However, the mean end-to-end distances from simulations are systematically smaller, consistent with the previous work comparing mean distances from DEER and simulation for poly(ethylene oxide). 39 This is partly due to the challenges in resolving the region below 20 Å for DEER. Computing the mean of the portion above the lower accessible limit for DEER (20 Å) for both the DEER-resolved and simulated distributions reduces the discrepancy (Figure S41).…”

“…In recent years, its ability to detail the full probability distribution over accessible distance ranges has garnered significant interest. The application of DEER to characterize disordered biological and synthetic polymeric systems through this distance distribution is emerging, − and methodological developments are continually improving the accurate resolution of the shape as well as the width of broad distributions. − Recent work on aqueous solutions of polyethylene oxide, a canonical disordered, synthetic polymer, demonstrates consistency between the broad distance distributions determined by DEER and simulation, suggesting that DEER is well positioned to characterize the conformational landscape of disordered macromolecules. Single-molecule Förster resonance energy transfer (FRET) also probes conformational distributions, but DEER requires fewer assumptions , and captures far more molecules, resulting in more accurate distance distributions.…”

Molecularly Informed Field Theories from Bottom-up Coarse-Graining

“…Specifically, we use the second-generation General Amber Force Field (GAFF2) 73,74 for PEO and the 4-site, Optimal Point Charge (OPC) 75 water model, for which we earlier found remarkably good agreement with experimental PEO conformations and temperature−composition−density behavior (see the SI). 76 To parametrize field models, we collect reference AA MD trajectories for both neat water and neat PEO chains (20mers) at 25 °C and 1 atm and for mixtures at temperatures spanning 25−600 °C using small-scale (n w = 10000 and n p = 20) AA simulations for 50mers at 0.20 polymer weight fraction. To remain faithful to the experimental PEO cloud-point measurement protocol, we equilibrate the mixtures at 25 °C and 1 atm (NPT), then fix the volume from the NPT equilibration at 25 °C during the production runs at elevated temperatures and, presumably, pressures, that is, NVT; 72 further details of the AA simulations are provided in the SI.…”