arXiv subjects

D. Asthagiri

Publications and source records attributed to D. Asthagiri.

At least 19 recordsLinked to original sources

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

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↗

arXiv2019

System size dependence of hydration shell occupancy

The free energies to evacuate the first hydration shell around a solute and a cavity defined by the first hydration shell depend on the system size. This observation interpreted within the quasichemical theory shows that both the hydrophilic and the hydrophobic contributions to hydration depend on the system size, decreasing with increasing system size. Although the net hydration free energy benefits somewhat from the balancing of hydrophilic and hydrophobic contributions, a large system still appears necessary to describe the effect of the solvent on the macromolecule.

physics.chem-ph↗

arXiv2019

Long-Range Interactions Dominate the Inverse-Temperature Dependence of Polypeptide Hydration Free Energies

Direct, all-atom calculations of the free energy of hydration of aqueous deca-alanine structures --- holistically including backbone and side-chain interactions together --- show that attractive interactions and the thermal expansion of the solvent explain the inverse temperature signatures that have been interpreted traditionally in favor of hydrophobic mechanisms for stabilizing the structure and function of soluble proteins.

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

Solvophobic and solvophilic contributions in the water-to-aqueous guanidinium chloride transfer free energy of model peptides

We study the solvation free energy of two different conformations (helix and extended) of two different peptides (deca-alanine and deca-glycine) in two different solvents (water and aqueous guanidinium chloride, GdmCl). The free energies are obtained using the quasichemical organization of the potential distribution theorem, an approach that naturally provides the repulsive (solvophobic or cavity) and attractive (solvophilic) contributions to solvation. The solvophilic contribution is further parsed into a chemistry contribution arising from solute interaction with the solvent in the first solvation shell and a long-range contribution arising from non-specific interactions between the solute and the solvent beyond the first solvation shell. The cavity contribution is obtained for two different envelopes, $Σ_{SE}$ which theory identifies as the solvent excluded volume and a larger envelope ($Σ_G$) beyond which solute-solvent interactions are Gaussian. For both envelopes, the cavity contribution in water is proportional to the surface area of the envelope. The same does not hold for GdmCl(aq), revealing limitations of using molecular area to assess solvation energetics, especially in mixed solvents. The $Σ_G$-cavity contribution predicts that GdmCl(aq) should favor the more compact state, contrary to the role of GdmCl in unfolding proteins. The chemistry contribution attenuates this effect, but still the net local (chemistry plus $Σ_G$-packing) contribution is inadequate in capturing the role of GdmCl. With the inclusion of the long-range contribution, which is dominated by van~der~Waals interaction, aqueous GdmCl favors the extended conformation over the compact conformation. Our finding emphasizes the importance of weak, but attractive, long-range dispersion interactions in protein solution thermodynamics.

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

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↗

arXiv2017

Molecular Dynamics Simulations of NMR Relaxation and Diffusion of Bulk Hydrocarbons and Water

Molecular dynamics (MD) simulations are used to investigate $^1$H nuclear magnetic resonance (NMR) relaxation and diffusion of bulk $n$-C$_5$H$_{12}$ to $n$-C$_{17}$H$_{36}$ hydrocarbons and bulk water. The MD simulations of the $^1$H NMR relaxation times $T_{1,2}$ in the fast motion regime where $T_1 = T_2$ agree with measured (de-oxygenated) $T_2$ data at ambient conditions, without any adjustable parameters in the interpretation of the simulation data. Likewise, the translational diffusion $D_T$ coefficients calculated using simulation configurations are well-correlated with measured diffusion data at ambient conditions. The agreement between the predicted and experimentally measured NMR relaxation times and diffusion coefficient also validate the forcefields used in the simulation. The molecular simulations naturally separate intramolecular from intermolecular dipole-dipole interactions helping bring new insight into the two NMR relaxation mechanisms as a function of molecular chain-length (i.e. carbon number). Comparison of the MD simulation results of the two relaxation mechanisms with traditional hard-sphere models used in interpreting NMR data reveals important limitations in the latter. With increasing chain length, there is substantial deviation in the molecular size inferred on the basis of the radius of gyration from simulation and the fitted hard-sphere radii required to rationalize the relaxation times. This deviation is characteristic of the local nature of the NMR measurement, one that is well-captured by molecular simulations.

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

Thermodynamics of the collapse transition of the all-backbone peptide Gly15

Simulations show Gly$_{15}$, a polypeptide lacking any side-chains, can collapse in water. We assess the hydration thermodynamics in this collapse by calculating the hydration free energy at each of the end points of the reaction coordinate, here the end-to-end distance ($r$) in the chain. To examine the role of the various conformations for a given $r$, we study the conditional distribution, $P(R_g | r)$, of the radius of gyration for a given value of $r$. $P(R_g|r)$ is found to vary more gently compared to the corresponding variation in the excess hydration free energy. Using this insight within a multistate generalization of the potential distribution theorem, we calculate a reasonable upper bound for the hydration free energy of the peptide for a given $r$. On this basis we find that peptide hydration greatly favors the expanded state of the chain, despite primitive hydrophobic effects favoring chain collapse. The net free energy of collapse is seen to be a delicate balance between opposing intra-peptide and hydration effects, with intra-peptide contributions favoring collapse by a small margin. The favorable intra-peptide interactions are primarily electrostatic in origin, and found to arise primarily from interaction between C=O dipoles, hydrogen bonding interaction between C=O and N-H groups, and favorable interaction between N-H dipoles.

physics.bio-ph↗

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↗

arXiv2015

Molecular theory and the effects of solute attractive forces on hydrophobic interactions

The role of solute attractive forces on hydrophobic interactions is studied by coordinated development of theory and simulation results for Ar atoms in water. We present a concise derivation of the local molecular field (LMF) theory for the effects of solute attractive forces on hydrophobic interactions, a derivation that clarifies the close relation of LMF theory to the EXP approximation applied to this problem long ago. The simulation results show that change from purely repulsive atomic solute interactions to include realistic attractive interactions \emph{diminishes} the strength of hydrophobic bonds. For the Ar-Ar rdfs considered pointwise, the numerical results for the effects of solute attractive forces on hydrophobic interactions are of opposite sign and larger in magnitude than predicted by LMF theory. That comparison is discussed from the point of view of quasi-chemical theory, and it is suggested that the first reason for this difference is the incomplete evaluation within LMF theory of the hydration energy of the Ar pair. With a recent suggestion for the system-size extrapolation of the required correlation function integrals, the Ar-Ar rdfs permit evaluation of osmotic second virial coefficients $B_2$. Those $B_2$ also show that incorporation of attractive interactions leads to more positive (repulsive) values. With attractive interactions in play, $B_2$ can change from positive to negative values with increasing temperatures. This is consistent with the historical work of Watanabe, \emph{et al.,} that $B_2 \approx 0$ for intermediate cases. In all cases here, $B_2$ becomes more attractive with increasing temperature.

physics.chem-ph↗

arXiv2015

Role of hydration and intramolecular interactions in the helix-coil transition and helix-helix assembly in a deca-alanine peptide

For a model deca-alanine peptide the cavity (ideal hydrophobic) contribution to hydration favors the helix state in the coil-to-helix transition and the paired helix bundle in the assembly of two helices. The energetic contributions of attractive protein-solvent interactions are separated into a short-range part arising from interactions with solvent in the first hydration shell and the remaining long-range part. In the helix-coil transition, short-range attractive protein-solvent interactions outweigh hydrophobic hydration and favor the unfolded coil states. Analysis of enthalpic effects shows that it is the favorable hydration of the peptide backbone that favors the unfolded state. Protein intramolecular interactions favor the helix state and are decisive in folding. In the pairing of two helices, the cavity contribution outweighs short-range attractive protein-water interactions. However, long-range, protein-solvent attractive interactions can either enhance or reverse this trend depending on the mutual orientation of the helices. In helix-helix assembly, change in enthalpy arising from change in attractive protein-solvent interactions favors disassembly. In helix pairing as well, favorable protein intramolecular interactions are found to be as important as hydration effects.

physics.bio-ph↗

arXiv2013

Conditional solvation of isoleucine in model extended and helical peptides: context dependence of hydrophobic hydration and the failure of the group-transfer model

The hydration thermodynamics of the GXG tripeptide relative to the reference GGG is often used to define the conditional hydration contribution of X. This quantity or the hydration thermodynamics of a small molecule analog of the side-chain or some combination of such estimates, have anchored the interpretation of seminal experiments on protein stability and folding. We show that such procedures to model protein hydration have significant limitations. We study the conditional hydration thermodynamics of the isoleucine side-chain in an extended pentapeptide and in helical deca-peptides, using as appropriate an extended penta-glycine or appropriate helical deca-peptides as reference. Hydration of butane in the gauche conformation provides a small molecule reference for the side-chain. We use the quasichemical theory to parse the hydration thermodynamics into chemical, packing, and long-range interaction contributions. The chemical contribution reflects the contribution of solvent clustering within the defined inner-shell of the solute; the chemical contribution of g-butane is substantially more negative than the conditional chemical contribution of isoleucine. The packing contribution gives the work required to create a cavity in the solvent, a quantity of interest in understanding hydrophobic hydration. The packing contribution for g-butane substantially overestimates the conditional packing of isoleucine. The net of such compensating contributions still disagrees with the conditional free energy of isoleucine but by a lesser magnitude. The excess enthalpy and entropy of hydration of g-butane model are also more negative than the corresponding conditional quantities for the side-chain. The conditional solvation of isoleucine in GGIGG also proves unsatisfactory in describing the conditional solvation of isoleucine in the helical peptides.

physics.bio-ph↗

arXiv2013

Examining the meaning of the peptide transfer free energy obtained from blocked (Gly)_n and cyclic-diglycine model compounds

In experiments, the free energy of transferring the peptide group from water to an osmolyte solution is obtained using the transfer free energy of (Gly)_n with the added assumption that a constant incremental change in free energy with n implies that each additional unit makes an independent contribution to the free energy. Here we test this assumption and uncover its limitations. Together with results for cyclic-diglycine, we show that, in principle, it is not possible to obtain a peptide group transfer free energy that is independent of the model system. We calculate the hydration free energy of acetyl-(Gly)_n-methyl amide (n=1..7) peptides modeled in the extended conformation in water and osmolyte solutions and find that the hydration free energy is linear in n, suggestive of independent, additive group-contributions. To probe the observed linearity further, we study the hydration of the solute bereft of water molecules in the first hydration shell. This conditioned solute arises naturally in the theoretical formulation and helps us focus on hydration effects uncluttered by the complexities of short-range solute-water interactions. We subdivide the conditioned solute into n+1 peptide groups and a methyl end group. The binding energy of each of these groups with the solvent is Gaussian distributed, but the near neighbor binding energies are themselves correlated: the (i,i+1) correlation is the strongest and tends to lower the free energy over the independent group case. We show that the observed linearity can be explained by the similarity of near neighbor correlations. Implications for group additive transfer free energy models are indicated.

physics.chem-ph↗

arXiv2011

Regularizing binding energy distributions and thermodynamics of hydration. Application to water modeled with classical and ab initio simulations

The high-energy tail of the distribution of solute-solvent interaction energies is poorly characterized for condensed systems, but this tail region is of principal interest in determining the excess free energy of the solute. We introduce external fields centered on the solute to modulate the short-range repulsive interaction between the solute and solvent. This regularizes the binding energy distribution and makes it easy to calculate the free energy of the solute with the field. Together with the work done to apply the field in the presence and absence of the solute, we calculate the excess chemical potential of the solute. We present the formal development of this idea and apply it to study liquid water.

physics.chem-ph↗