arXiv subjects

Walter G. Chapman

Publications and source records attributed to Walter G. Chapman.

18 recordsLinked to original sources

arXiv2025

The Protein Force Field Plays a Crucial Role in Obtaining Accurate Macromolecular Ensembles of IDPs

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.

physics.bio-ph↗

arXiv2024

Quantifying the Errors Introduced by Continuum Scattering Models on the Inferred Structural Properties of Proteins

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.

physics.chem-ph↗

arXiv2024

Theory and modeling of molecular modes in the NMR relaxation of fluids

Traditional theories of the NMR autocorrelation function for intramolecular dipole pairs assume single-exponential decay, yet the calculated autocorrelation of realistic systems display 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 autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational 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 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 Pad{é}-Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory.

physics.chem-ph↗

arXiv2022

Effect of Nano-Confinement on NMR Relaxation of Heptane in Kerogen from MD Simulations and Measurements

Kerogen-rich shale reservoirs will play a key role during the energy transition, yet the effects of nano-confinement on the NMR relaxation of hydrocarbons in kerogen are poorly understood. We use atomistic MD simulations to investigate the effects of nano-confinement on the $^1$H NMR relaxation times $T_1$ and $T_2$ of heptane in kerogen. In the case of $T_1$, we discover the important role of confinement in reducing $T_1$ by $\sim$3 orders of magnitude from bulk heptane, in agreement with measurements of heptane dissolved in kerogen from the Kimmeridge Shale, without any models or free parameters. In the case of $T_2$, we discover that confinement breaks spatial isotropy and gives rise to residual dipolar coupling which reduces $T_2$ by $\sim$5 orders of magnitude from bulk heptane. We use the simulated $T_2$ to calibrate the surface relaxivity and thence predict the pore-size distribution of the organic nano-pores in kerogen, without additional experimental data.

physics.chem-ph↗

arXiv2022

Hydration free energies of polypeptides from popular implicit solvent models versus all-atom simulation results based on molecular quasichemical theory

The hydration free energy of a macromolecule is the central property of interest for understanding its distribution over conformations and its state of aggregation. Calculating the hydration free energy of a macromolecule in all-atom simulations has long remained a challenge, necessitating the use of models wherein the effect of the solvent is captured without explicit account of solvent degrees of freedom. This situation has changed with developments in the molecular quasi-chemical theory (QCT), an approach that enables calculation of the hydration free energy of macromolecules within all-atom simulations at the same resolution as is possible for small molecule solutes. The theory also provides a rigorous and physically transparent framework to conceptualize and model interactions in molecular solutions, and thus provides a convenient framework to investigate the assumptions in implicit-solvent models. In this study, we compare the results using molecular QCT versus predictions from EEF1, ABSINTH, and GB/SA implicit-solvent models for poly-glycine and poly-alanine solutes covering a range of chain lengths and conformations. Among the three models, GB/SA does best in capturing the broad trends in hydration free energy. We trace the deficiencies of the group-additive EEF1 and ABSINTH models to their under-appreciation of the cooperativity of hydration between solute groups; seen in this light, the better performance of GB/SA can be attributed to its treatment of the collective properties of hydration, albeit within a continuum dielectric framework. We highlight the importance of validating the individual physical components that enter implicit solvent models for protein solution thermodynamics.

cond-mat.soft↗

arXiv2021

Molecular dynamics simulations of $^1$H NMR relaxation in Gd$^{3+}$--aqua

Atomistic molecular dynamics simulations are used to investigate $^1$H NMR $T_1$ relaxation of water from paramagnetic Gd$^{3+}$ ions in solution at 25$^{\circ}$C. Simulations of the $T_1$ relaxivity dispersion function $r_1$ computed from the Gd$^{3+}$--$^1$H dipole--dipole autocorrelation function agree within $\simeq 8$\% of measurements in the range $f_0 \simeq $ 5 $\leftrightarrow$ 500 MHz, without any adjustable parameters in the interpretation of the simulations, and without any relaxation models. The simulation results are discussed in the context of the Solomon-Bloembergen-Morgan inner-sphere relaxation model, and the Hwang-Freed outer-sphere relaxation model. Below $f_0 \lesssim $ 5 MHz, the simulation overestimates $r_1$ compared to measurements, which is used to estimate the zero-field electron-spin relaxation time. The simulations show potential for predicting $r_1$ at high frequencies in chelated Gd$^{3+}$ contrast-agents used for clinical MRI.

physics.chem-ph↗

arXiv2020

$^1$H-NMR Dipole-Dipole Relaxation in Fluids: Relaxation of Individual $^1$H-$^1$H Pairs versus Relaxation of Molecular Modes

The intra-molecular $^1$H-NMR dipole-dipole relaxation of molecular fluids has traditionally been interpreted within the Bloembergen-Purcell-Pound (BPP) theory of NMR intra-molecular relaxation. The BPP theory draws upon Debye's theory for describing the rotational diffusion of the $^1$H-$^1$H pair and predicts a mono-exponential decay of the $^1$H-$^1$H dipole-dipole autocorrelation function between distinct spin pairs. Using molecular dynamics (MD) simulations, we show that for both $n$-heptane and water this is not the case. In particular, the autocorrelation function of individual $^1$H-$^1$H intra-molecular pairs itself evinces a rich stretched-exponential behavior, implying a distribution in rotational correlation times. However for the high-symmetry molecule neopentane, the individual $^1$H-$^1$H intra-molecular pairs do conform to the BPP description, suggesting an important role of molecular symmetry in aiding agreement with the BPP model. The inter-molecular autocorrelation functions for $n$-heptane, water, and neopentane also do not admit a mono-exponential behavior of individual $^1$H-$^1$H inter-molecular pairs at distinct initial separations. We suggest expanding the auto-correlation function in terms of molecular modes, where the molecular modes do have an exponential relaxation behavior. With care, the resulting Fredholm integral equation of the first kind can be inverted to recover the probability distribution of the molecular modes. The advantages and limitations of this approach are noted.

physics.chem-ph↗

arXiv2020

Elucidating the $^1$H NMR relaxation mechanism in polydisperse polymers and bitumen using measurements, MD simulations, and models

The mechanism behind the $^1$H NMR frequency dependence of $T_1$ and the viscosity dependence of $T_2$ for polydisperse polymers and bitumen remains elusive. We elucidate the matter through NMR relaxation measurements of polydisperse polymers over an extended range of frequencies ($f_0 = 0.01 \leftrightarrow$ 400 MHz) and viscosities ($η= 385 \leftrightarrow 102,000$ cP) using $T_{1}$ and $T_2$ in static fields, $T_{1}$ field-cycling relaxometry, and $T_{1ρ}$ in the rotating frame. We account for the anomalous behavior of the log-mean relaxation times $T_{1LM} \propto f_0$ and $T_{2LM} \propto (η/T)^{-1/2}$ with a phenomenological model of $^1$H-$^1$H dipole-dipole relaxation which includes a distribution in molecular correlation times and internal motions of the non-rigid polymer branches. We show that the model also accounts for the anomalous $T_{1LM}$ and $T_{2LM}$ in previously reported bitumen measurements. We find that molecular dynamics (MD) simulations of the $T_{1} \propto f_0$ dispersion and $T_2$ of similar polymers simulated over a range of viscosities ($η= 1 \leftrightarrow 1,000$ cP) are in good agreement with measurements and the model. The $T_{1} \propto f_0$ dispersion at high viscosities agrees with previously reported MD simulations of heptane confined in a polymer matrix, which suggests a common NMR relaxation mechanism between viscous polydisperse fluids and fluids under confinement, without the need to invoke paramagnetism.

physics.chem-ph↗

arXiv2020

Molecular Dynamics Simulations of NMR Relaxation and Diffusion of Heptane Confined in a Polymer Matrix

The mechanism behind the NMR surface relaxation and the large $T_1$/$T_2$ ratio of light hydrocarbons confined in the nano-pores of kerogen remains poorly understood, and consequently has engendered much debate. Towards bringing a molecular-scale resolution to this problem, we present molecular dynamics (MD) simulations of $^1$H NMR relaxation and diffusion of heptane in a polymer matrix, where the high-viscosity polymer is a model for kerogen and bitumen that provides an organic "surface" for heptane. We calculate the autocorrelation function $G(t)$ for $^1$H-$^1$H dipole-dipole interactions of heptane in the polymer matrix and use this to generate the NMR frequency ($f_0$) dependence of $T_1$ and $T_2$ relaxation times as a function of $ϕ_{C7}$. We find that increasing molecular confinement increases the correlation time of the heptane molecule, which decreases the surface relaxation times for heptane in the polymer matrix. For weak confinement ($ϕ_{C7} > 50$ vol%), we find that $T_{1S}/T_{2S} \simeq 1$. Under strong confinement ($ϕ_{C7} \lesssim $ 50 vol%), we find that the ratio $T_{1S}/T_{2S} \gtrsim 4$ increases with decreasing $ϕ_{C7}$, and that the dispersion relation $T_{1S} \propto f_0$ is consistent with previously reported measurements of polymers and bitumen. Such frequency dependence in bitumen has been previously attributed to paramagnetism, but our studies suggests that $^1$H-$^1$H dipole-dipole interactions enhanced by organic nano-pore confinement dominates the NMR response in saturated organic-rich shales, without the need to invoke paramagnetism.

physics.chem-ph↗

arXiv2018

NMR Spin-Rotation Relaxation and Diffusion of Methane

The translational-diffusion coefficient $D_T$ and the spin-rotation contribution to the $^1$H NMR relaxation time $T_{1J}$ for methane (CH$_4$) are investigated using MD (molecular dynamics) simulations, over a wide range of densities $ρ$ and temperatures $T$, spanning the liquid, supercritical, and gas phases. The simulated $D_T$ agree well with measurements, without any adjustable parameters in the interpretation of the simulations. A minimization technique is developed to compute the angular-velocity for non-rigid spherical molecules, which is used to simulate the autocorrelation function $G_{\!J}(t)$ for spin-rotation interactions. With increasing $D_T$ (i.e. decreasing $ρ$), $G_{\!J}(t)$ shows increasing deviations from the single-exponential decay predicted by the Langevin theory for hard spheres, and the deviations are quantified using inverse Laplace transforms of $G_{\!J}(t)$. $T_{1J}$ is derived from $G_{\!J}(t)$ using the kinetic model "km" for gases ($T_{1J}^{km}$), and the diffusion model "dm" for liquids ($T_{1J}^{dm}$). $T_{1J}^{km}$ shows better agreement with $T_1$ measurements at higher $D_T$, while $T_{1J}^{dm}$ shows better agreement with $T_1$ measurements at lower $D_T$. $T_{1J}^{km}$ is shown to dominate over the MD simulated $^1$H-$^1$H dipole-dipole relaxation $T_{1RT}$ at high $D_T$, while the opposite is found at low $D_T$. At high $D_T$, the simulated spin-rotation correlation-time $τ_J$ agrees with the kinetic collision time $τ_K$ for gases, from which a new relation $1/T_{1J}^{km} \propto D_T$ is inferred, without any adjustable parameters.

physics.chem-ph↗

arXiv2018

Role of Internal Motions and Molecular Geometry on the NMR Relaxation of Hydrocarbons

The role of internal motions and molecular geometry on $^1$H NMR relaxation times $T_{1,2}$ in hydrocarbons is investigated using MD (molecular dynamics) simulations of the autocorrelation functions for in{\it tra}molecular $G_R(t)$ and in{\it ter}molecular $G_T(t)$ $^1$H-$^1$H dipole-dipole interactions arising from rotational ($R$) and translational ($T$) diffusion, respectively. We show that molecules with increased molecular symmetry such as neopentane, benzene, and isooctane show better agreement with traditional hard-sphere models than their corresponding straight-chain $n$-alkane, and furthermore that spherically-symmetric neopentane agrees well with the Stokes-Einstein theory. The influence of internal motions on the dynamics and $T_{1,2}$ relaxation of $n$-alkanes are investigated by simulating rigid $n$-alkanes and comparing with flexible (i.e. non-rigid) $n$-alkanes. Internal motions cause the rotational and translational correlation-times $τ_{R,T}$ to get significantly shorter and the relaxation times $T_{1,2}$ to get significantly longer, especially for longer-chain $n$-alkanes. Site-by-site simulations of $^1$H's along the chains indicate significant variations in $τ_{R,T}$ and $T_{1,2}$ across the chain, especially for longer-chain $n$-alkanes. The extent of the stretched (i.e. multi-exponential) decay in the autocorrelation functions $G_{R,T}(t)$ are quantified using inverse Laplace transforms, for both rigid and flexible molecules, and on a site-by-site bases. Comparison of $T_{1,2}$ measurements with the site-by-site simulations indicate that cross-relaxation (partially) averages-out the variations in $τ_{R,T}$ and $T_{1,2}$ across the chain of long-chain $n$-alkanes. This work also has implications on the role of nano-pore confinement on the NMR relaxation of fluids in the organic-matter pores of kerogen and bitumen.

physics.chem-ph↗

arXiv2017

Quasichemical theory and the description of associating fluids relative to a reference: Multiple bonding of a single site solute

We derive an expression for the chemical potential of an associating solute in a solvent relative to the value in a reference fluid using the quasichemical organization of the potential distribution theorem. The fraction of times the solute is not associated with the solvent, the monomer fraction, is expressed in terms of (a) the statistics of occupancy of the solvent around the solute in the reference fluid and (b) the Widom factors that arise because of turning on solute-solvent association. Assuming pair-additivity, we expand the Widom factor into a product of Mayer f-functions and the resulting expression is rearranged to reveal a form of the monomer fraction that is analogous to that used within the statistical associating fluid theory (SAFT). The present formulation avoids all graph-theoretic arguments and provides a fresh, more intuitive, perspective on Wertheim's theory and SAFT. Importantly, multi-body effects are transparently incorporated into the very foundations of the theory. We illustrate the generality of the present approach by considering examples of multiple solvent association to a colloid solute with bonding domains that range from a small patch on the sphere, a Janus particle, and a solute whose entire surface is available for association.

cond-mat.soft↗

arXiv2017

Mini-grand canonical ensemble: chemical potential in the solvation shell

Quantifying the statistics of occupancy of solvent molecules in the vicinity of solutes is central to our understanding of solvation phenomena. Number fluctuations in small `solvation shells' around solutes cannot be described within the macroscopic grand canonical framework using a single chemical potential that represents the solvent `bath'. In this communication, we hypothesize that molecular-sized observation volumes such as solvation shells are best described by coupling the solvation shell with a mixture of particle baths each with its own chemical potential. We confirm our hypotheses by studying the enhanced fluctuations in the occupancy statistics of hard sphere solvent particles around a distinguished hard sphere solute particle. Connections with established theories of solvation are also discussed.

cond-mat.stat-mech↗

arXiv2017

Electrostatic and induction effects in the solubility of water in alkanes

Experiments show that at 298~K and 1 atm pressure the transfer free energy, $μ^{\rm ex}$, of water from its vapor to liquid normal alkanes $C_nH_{2n+2}$ ($n=5\ldots12$) is negative. Earlier it was found that with the united-atom TraPPe model for alkanes and the SPC/E model for water, one had to artificially enhance the attractive alkane-water cross interaction to capture this behavior. Here we revisit the calculation of $μ^{\rm ex}$ using the polarizable AMOEBA and the non-polarizable Charmm General (CGenFF) forcefields. We test both the AMOEBA03 and AMOEBA14 water models; the former has been validated with the AMOEBA alkane model while the latter is a revision of AMOEBA03 to better describe liquid water. We calculate $μ^{\rm ex}$ using the test particle method. With CGenFF, $μ^{\rm ex}$ is positive and the error relative to experiments is about 1.5 $k_{\rm B}T$. With AMOEBA, $μ^{\rm ex}$ is negative and deviations relative to experiments are between 0.25 $k_{\rm B}T$ (AMOEBA14) and 0.5 $k_{\rm B}T$ (AMOEBA03). Quantum chemical calculations in a continuum solvent suggest that zero point effects may account for some of the deviation. Forcefield limitations notwithstanding, electrostatic and induction effects, commonly ignored in considerations of water-alkane interactions, appear to be decisive in the solubility of water in alkanes.

physics.chem-ph↗

arXiv2017

Thermodynamics of mixtures of patchy and spherical colloids of different sizes: a multi-body association theory with complete reference fluid information

We present a theory to predict the structure and thermodynamics of mixtures of colloids of different diameters, building on our earlier work [J. Chem. Phys. 145, 074904 (2016)] that considered mixtures with all particles constrained to have the same size. The patchy, solvent particles have short-range directional interactions, while the solute particles have short-range isotropic interactions. The hard-sphere mixture without any association site forms the reference fluid. An important ingredient within the multi-body association theory is the description of clustering of the reference solvent around the reference solute. Here we account for the physical, multi-body clusters of the reference solvent around the reference solute in terms of occupancy statistics in a defined observation volume. These occupancy probabilities are obtained from enhanced sampling simulations, but we also present statistical mechanical models to estimate these probabilities with limited simulation data. Relative to an approach that describes only up to three-body correlations in the reference, incorporating the complete reference information better predicts the bonding state and thermodynamics of the physical solute for a wide range of system conditions. Importantly, analysis of the residual chemical potential of the infinitely dilute solute from molecular simulation and theory shows that whereas the chemical potential is somewhat insensitive to the description of the structure of the reference fluid the energetic and entropic contributions are not, with the results from the complete reference approach being in better agreement with particle simulations.

cond-mat.soft↗

arXiv2016

Stabilized density gradient theory algorithm for modeling interfacial properties of pure and mixed systems

Density gradient theory (DGT) allows fast and accurate determination of surface tension and density profile through a phase interface. Several algorithms have been developed to apply this theory in practical calculations. While the conventional algorithm requires a reference substance of the system, a modified "stabilized density gradient theory" (SDGT) algorithm is introduced in our work to solve DGT equations for multiphase pure and mixed systems. This algorithm makes it possible to calculate interfacial properties accurately at any domain size larger than the interface thickness without choosing a reference substance or assuming the functional form of the density profile. As part of DGT inputs, the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) was employed for the first time with the SDGT algorithm. PC-SAFT has excellent performance in predicting liquid phase properties as well as phase behaviors. The SDGT algorithm with the PC-SAFT EoS was tested and compared with experimental data for several systems. Numerical stability analyses were also included in each calculation to verify the reliability of this approach for future applications.

physics.chem-ph↗

arXiv2016

Structure and thermodynamics of a mixture of patchy and spherical colloids: a multi-body association theory with complete reference fluid information

A mixture of solvent particles with short-range, directional interactions and solute particles with short-range, isotropic interactions that can bond multiple times is of fundamental interest in understanding liquids and colloidal mixtures. Because of multi-body correlations predicting the structure and thermodynamics of such systems remains a challenge. Earlier Marshall and Chapman developed a theory wherein association effects due to interactions multiply the partition function for clustering of particles in a reference hard-sphere system. The multi-body effects are incorporated in the clustering process, which in their work was obtained in the absence of the bulk medium. The bulk solvent effects were then modeled approximately within a second order perturbation approach. However, their approach is inadequate at high densities and for large association strengths. Based on the idea that the clustering of solvent in a defined coordination volume around the solute is related to occupancy statistics in that defined coordination volume, we develop an approach to incorporate the complete information about hard-sphere clustering in a bulk solvent at the density of interest. The occupancy probabilities are obtained from enhanced sampling simulations but we also develop a concise parametric form to model these probabilities using the quasichemical theory of solutions. We show that incorporating the complete reference information results in an approach that can predict the bonding state and thermodynamics of the colloidal solute for a wide range of system conditions.

cond-mat.soft↗

arXiv2016

Incorporating multi-body effects in SAFT by improving the description of the reference system. I. Mean activity correction for cluster integrals in the reference system

A system of patchy colloidal particles interacting with a solute that can associate multiple times in any direction is a useful model for patchy colloidal mixtures. Despite the simplicity of the interaction, because of the presence of multi-body correlations predicting the thermodynamics of such systems remains a challenge. Earlier Marshall and Chapman developed a multi-body formulation for such systems wherein the cluster partition function for the hard-sphere solvent molecules in a defined inner-shell (or coordination volume) of the hard-sphere solute is used as the reference within the statistical association fluid theory formalism. The multi-body contribution to these partition functions are obtained by ignoring the bulk solvent, thus limiting the applicability of the theory to low system densities. Deriving inspiration from the quasichemical theory of solutions where these partition functions occur in the guise of equilibrium constants for cluster formation, we develop a way to account for the multi-body correlations including the effect of the bulk solvent. We obtain the free energy to evacuate the inner-shell, the chemistry contribution within quasichemical theory, from simulations of the hard-sphere reference. This chemistry contribution reflects association in the reference in the presence of the bulk medium. The gas-phase partition functions are then augmented by a mean activity factor that is adjusted to reproduce the chemistry contribution. We show that the updated partition function provides a revised reference that better captures the distribution of solvent around the solute up to high system densities. Using this updated reference, we find that theory better describes both the bonding state and the excess chemical potential of the colloid in the physical system.

cond-mat.soft↗