Walter G. Chapman

This work investigates the equilibrium swelling of poly(N-isopropylacrylamide) (pNIPAM)-based lyogels in multicomponent solvent systems using a Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT)-based thermodynamic framework coupled with polymer-network elasticity. Literature parameter sets for the butyl esterification system were assessed and refined, and different network models were compared within a sequential fitting strategy that links solvent, polymer-solution, and gel data. The results show that the framework can reproduce key swelling trends and supports the transfer of calibrated network parameters between related solvent descriptions. At the same time, the study highlights important limitations: quantitative fitting of lower critical solution temperature (LCST) behavior requires a temperature-dependent interaction parameter, finite-extensibility effects are negligible for the investigated systems, and the transferability of fitted interaction parameters to mixed solvents is limited. Overall, the work provides a practical framework for gel-equilibrium calculations while emphasizing the need for careful interpretation of fitted parameters.

The thermodynamic calculation of gel phase equilibria is numerically challenging because of the strong asymmetry of polymer–solvent systems and the coupling of mixing and elastic contributions. In this work, a framework for gel phase equilibria is developed using the PC-SAFT equation of state. Building on strategies for polymer–solution liquid–liquid equilibria, the method is extended to gel systems by incorporating the elastic contribution of the polymer network through a Poynting-like correction. To improve numerical stability, the framework combines a second-order Newton–Raphson scheme with homotopy-based phase-envelope tracing and alternating-tangent initialization. The method is applicable to multicomponent systems and allows continuation in composition and temperature space. Its performance is demonstrated for pNIPAM–water and pNIPAM–water–ethanol systems. The results show that continuation strategies established for conventional polymer–solution phase equilibria can be transferred consistently to gel equilibria without repeated reinitialization.

Atomistic models of water with increased dispersion interactions (e.g., OPC, TIP4P-D) have been proposed to produce extended conformational ensembles of intrinsically disordered proteins (IDPs). However, the role of the protein force field in obtaining accurate macromolecular ensembles of IDPs remains unclear. Isolating the influence of the protein and water models by comparison to an experimental measure (such as X-ray scattering) requires an atomic consideration of the hydration layer waters around a thermally fluctuating protein. To enable an atomically detailed scattering calculation around a thermally fluctuating solute, we have developed a new scattering model termed small and wide angle X-ray scattering for all molecular dynamics engines (SWAXS-AMDE). SWAXS-AMDE can handle the trajectory files from all of the popular molecular dynamics (MD) simulation softwares, thus facilitating a straightforward validation of force field improvements. SWAXS-AMDE computed scattering profiles for polyampholyte peptides show the AMBER ff19SB protein force field to play a crucial role in obtaining accurate macromolecular ensembles of both folded proteins and IDPs.

Traditional models of NMR relaxation fail to account for the complex, multi-exponential behavior of the autocorrelation function in realistic systems characterized by soft-interactions and molecules that are chemically and physically complex. Here, we describe the relative diffusion of the spin dipoles by means of a Fokker–Planck equation that includes an interaction potential of mean force to account for the response of the physical/chemical environment around the dipoles. By numerically solving the Fokker–Planck equation for the diffusion propagator, we estimate dipole–dipole NMR relaxation for like- and unlike-spin systems via its eigenmode solution. We test the model against molecular simulations of diffusing dipoles with harmonic potentials and also validate using experimental longitudinal relaxation data from real systems, including Gd(III)–aqua and Gd(III)–DO3A–butrol complexes, the latter being an important MRI contrast agent. Using this novel approach, we predict both the inner- and outer-shell contributions to the relaxivity rates with excellent accuracy at frequencies relevant to MRI. We also show that, under the appropriate assumptions, our framework naturally recovers the Bloembergen–Purcell–Pound, the Solomon–Bloembergen–Morgan, and the Hwang–Freed models. Our implementation is general and publicly available for application to a broad range of systems.

Intrinsically disordered proteins (IDPs) play a significant role in intracellular phenomena and are known to exist in an ensemble of inter-converting conformations in solution. Accurately modeling the conformations of IDPs in solution poses a challenge to traditional force fields that are tuned to predict the properties of folded proteins. There is a need for generalized atomistic force fields that can accurately predict the properties of both folded proteins and IDPs. Improvements to protein force fields for increased accuracy in secondary structure prediction and new water models with increased water-water dispersion interactions have been proposed in search of a generalized simulation method. Validating the proposed improvements against experiments poses challenges such as a lack of suitable systems to test the generalizability and choosing a property of interest to match the simulation results against experiments. In this work, we use small angle X-ray scattering (SAXS) data from peptide-based polyampholytes that mimic IDPs to test the generalizability of the AMBER protein force fields and the OPC water model. The specific improvements due to the AMBER ff19SB protein force field and the OPC water model are isolated and studied. Analysis of SAXS profiles and the conformational distribution of polyampholyte sequences show the AMBER ff19SB-OPC water combination to be a generalized model that predicts both ordered polyampholyte sequences and disordered polyampholyte sequences in good agreement with experiments. We have developed a new scattering model termed SWAXS-AMDE that accounts for the hydration layer density changes in atomic detail and is particularly useful in making one-to-one comparisons of simulated scattering profiles to experiments. SWAXS-AMDE allows for the thermal fluctuations of the solute which is particularly consequential for IDPs.

MRI is an indispensable diagnostic tool in modern medicine; however, understanding the molecular-level processes governing NMR relaxation of water in the presence of MRI contrast agents remains a challenge, hindering the molecular-guided development of more effective contrast agents. By using quantum-based polarizable force fields, the first-of-its-kind molecular dynamics (MD) simulations of Gadobutrol are reported where the ¹H NMR longitudinal relaxivity r ₁ of the aqueous phase is determined without any adjustable parameters. The MD simulations of r ₁ dispersion (i.e., frequency dependence) show good agreement with measurements at frequencies of interest in clinical MRI. Importantly, the simulations reveal key insights into the molecular level processes leading to r ₁ dispersion by decomposing the NMR dipole–dipole autocorrelation function G(t) into a discrete set of molecular modes, analogous to the eigenmodes of a quantum harmonic oscillator. The molecular modes reveal important aspects of the underlying mechanisms governing r ₁, such as its multiexponential nature and the importance of the second eigenmodal decay. By simply analyzing the MD trajectories on a parameter-free approach, the Gadobutrol simulations show that the outer-shell water contributes ∼50% of the total relaxivity r ₁ compared to the inner-shell water, in contrast to simulations of (nonchelated) gadolinium-aqua where the outer shell contributes only ∼15% of r ₁. The deviation between simulations and measurements of r ₁ below clinical MRI frequencies is used to determine the low-frequency electron-spin relaxation time for Gadobutrol, in good agreement with independent studies.

The Bloembergen, Purcell, and Pound (BPP) theory of nuclear magnetic resonance (NMR) relaxation in fluids dating back to 1948 continues to be the linchpin in interpreting NMR relaxation data in applications ranging from characterizing fluids in porous media to medical imaging (MRI). The BPP theory is founded on assuming molecules are hard spheres with ¹H-¹H dipole pairs reorienting randomly; assumptions that are severe in light of modern understanding of liquids. Nevertheless, it is intriguing to this day that the BPP theory was consistent with the original experimental data for glycerol, a hydrogen-bonding molecular fluid for which the hard-sphere-rigid-dipole assumption is inapplicable. To better understand this incongruity, atomistic molecular simulations are used to compute ¹H NMR T₁ relaxation dispersion (i.e., frequency dependence) in two contrasting cases: glycerol, and a (non hydrogen-bonding) viscosity standard. At high viscosities, simulations predict distinct functional forms of T₁ for glycerol compared to the viscosity standard, in agreement with modern measurements, yet both in contrast to BPP theory. The cause of these departures from BPP theory is elucidated, without assuming any relaxation models and without any free parameters, by decomposing the simulated T₁ response into dynamic molecular modes for both intramolecular and intermolecular interactions. The decomposition into dynamic molecular modes provides an alternative framework to understand the physics of NMR relaxation for viscous fluids.

Atomistic force fields that are tuned to describe folded proteins predict overly compact structures for intrinsically disordered proteins (IDPs). To correct this, improvements in force fields to better model IDPs are usually paired with scattering models for validation against experiments. For scattering calculations, protein configurations from all-atom simulations are used within the continuum-solvent model CRYSOL for comparison with experiments. To check this approach, we develop an equation to evaluate the radius of gyration (Rg) for any defined inner-hydration shell thickness given all-atom simulation data. Rg based on an explicit description of hydration waters compares well with the reference value of Rg obtained using Guinier analysis of the all-atom scattering model. However, these internally consistent estimates disagree with Rg from CRYSOL for the same definition of the inner-shell. CRYSOL can over-predict Rg by up to 2.5 Angstroms. We rationalize the reason for this behavior and highlight the consequences for force field design.

Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. We recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker–Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole–dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé–Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory.