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Supplemental Tables S1-2, Figures S1-2. Table S1. NanoString nCounterTM assay measurements of miRNA copy numbers/cell detected in MCF7 and MCF10A cells at 72 hrs of serum deprivation and in EVs derived from MCF7 and MCF10A cells over 72 hrs of serum deprivation. Table S2. qRT-PCR assay measurements of miRNA copy numbers/cell detected in MCF7 and MCF10A cells at 72 hrs of serum deprivation and in EVs secreted from MCF7 and MCF10A cells over 72 hrs of serum deprivation. Figure S1. Total cellular RNA concentration (top panel) and changes in miR-21 expression levels (middle panel) and changes in miR-1274a and miR-1274b expression levels (bottom panel) for MCF10A cells (open symbols) and MCF7 cells (filled symbols) as a function of time in response to serum deprivation at 0 hrs. Figure S2. Sequence alignments for miRNA pairs depicting positions that share identical nucleotides.

Gadolinium-based contrast agents are key in clinical MRI for enhancing the longitudinal NMR relativity (r1) of hydrogen nuclei (1H) in water and improving the contrast among different tissues.

Gadolinium-based contrast agents are key in clinical MRI for enhancing the longitudinal NMR relativity (

Atomistic molecular dynamics simulations are used to predict 1H NMR T1 relaxation of water from paramagnetic Gd3+ ions in solution at 25 °C. Simulations of the T1 relaxivity dispersion function r1 computed from the Gd3+–1H dipole–dipole autocorrelation function agree within ≃8% of measurements in the range f0 ≃ 5 ↔ 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 f0 ≲ 5 MHz, the simulation overestimates r1 compared to measurements, which is used to estimate the zero-field electron-spin relaxation time. The simulations show potential for predicting r1 at high frequencies in chelated Gd3+ contrast-agents used for clinical MRI.

The intramolecular ¹H NMR dipole–dipole relaxation of molecular fluids has traditionally been interpreted within the Bloembergen–Purcell–Pound (BPP) theory of NMR intramolecular relaxation. The BPP theory draws upon Debye’s theory for describing the rotational diffusion of the ¹H–¹H pair and predicts a monoexponential decay of the ¹H–¹H 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 ¹H–¹H intramolecular pairs itself evinces a rich stretched-exponential behavior, implying a distribution in rotational correlation times. However, for the high-symmetry molecule neopentane, the individual ¹H–¹H intramolecular pairs do conform to the BPP description, suggesting an important role of molecular symmetry in aiding agreement with the BPP model. The intermolecular autocorrelation functions for n-heptane, water, and neopentane also do not admit a monoexponential behavior of individual ¹H–¹H intermolecular pairs at distinct initial separations. We suggest expanding the autocorrelation function in terms of modes, provisionally termed molecular modes, that 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.

Atomistic molecular dynamics simulations are used to predict

Water molecules bind strongly to the polar calcite surface and form a surface-adsorbed layer that has properties akin to an apolar surface. This has important implications for understanding the thermodynamic driving forces underlying the adsorption of acid groups from crude oil, in particular, naphthenic acid, onto calcite. Free energy calculations show that naphthenic acid binds favorably to the water monolayer adsorbed on the calcite surface. However, to bond directly to calcite, a free energy barrier has to be overcome to expel the intervening layer of water. Further, naphthenic acids with longer alkyl chains bind with lower free energy to the calcite surface than those with shorter alkyl chains, and, for the same chain length, branching enhances adsorption. To better understand this behavior, for a specified alkyl chain length, we study adsorption at different temperatures. Consistent with experiments, we find that adsorption is enhanced at higher temperatures. Examination of the enthalpic and entropi...

The mechanism behind the

The Third Modeling Workshop focusing on bioprocess modeling was held in Kenilworth, NJ in May 2019. A summary of these Workshop proceedings is captured in this manuscript. Modeling is an active area of research within the biotechnology community, and there is a critical need to assess the current state and opportunities for continued investment to realize the full potential of models, including resource and time savings. Beyond individual presentations and topics of novel interest, a substantial portion of the Workshop was devoted toward group discussions of current states and future directions in modeling fields. All scales of modeling, from biophysical models at the molecular level and up through large scale facility and plant modeling, were considered in these discussions and are summarized in the manuscript. Model life cycle management from model development to implementation and sustainment are also considered for different stages of clinical development and commercial production. The manuscript provides a comprehensive overview of bioprocess modeling while suggesting an ideal future state with standardized approaches aligned across the industry.

Low salinity water flooding has shown great promise due to its cost-effectiveness and low environmental impact for improving and sustaining oil production. It is believed that injecting water with ionic strength lower than that of the reservoir changes the reservoir from less to more water-wet and enhances oil recovery. This alteration phenomenon is not well understood, due to complex interactions between oil, water, and rock. Here we use molecular simulations to characterize the wettability of the 10.4-face of calcite in a calcite/brine/oil system, and address how wettability is altered by changing ionic strength and salt type (NaCl vs. CaCl2). Using the test area method we calculate the superficial tension of the fluids against the solid and the surface tension between the two fluid phases. As the salinity is decreased, the wetting of calcite by brine is progressively less favored, contrary to what might be expected based on low salinity flooding. However, as salinity is decreased, forming the oil-brine interface is more favored. On balance, it is the latter effect that leads to the enhanced wetting of calcite by brine in the oil-brine-calcite system, and it is suggested as an important element in the physics underlying low-salinity flooding.

The role that van der Waals (vdW) attractive forces play in the hydration and association of atomic hydrophobic solutes such as argon (Ar) in water is reanalyzed using the local molecular field (LMF) theory of those interactions. In this problem, solute vdW attractive forces can reduce or mask hydrophobic interactions as measured by contact peak heights of the ArAr correlation function compared to reference results for purely repulsive core solutes. Nevertheless, both systems exhibit a characteristic hydrophobic inverse temperature behavior in which hydrophobic association becomes stronger with increasing temperature through a moderate temperature range. The new theoretical approximation obtained here is remarkably simple and faithful to the statistical mechanical LMF assessment of the necessary force balance. Our results extend and significantly revise approximations made in a recent application of the LMF approach to this problem and, unexpectedly, support a theory of nearly 40 years ago.

We study binary mixtures of multi-bonding single site solute particles in a solvent comprising patchy colloid particles. The particles in the mixture interact by very short-ranged attraction and hard-sphere repulsion. The attractive patch on the solute can bond with multiple solvent particles, whereas the patch on the solvent is restricted to bond only once. From a quasi-chemical analysis of association, in the hard-sphere reference we develop an accurate multi-body correlation information for the distribution of solvent particles over the patch region of the solute. We use this information within Wertheim's multi-density formalism to develop a cluster size distribution theory that is capable of capturing the physics of multi-body association for any geometry of association sites on the solute. We use this general framework to study a mixture containing Janus solutes and one- or two-patch solvent particles over a range of concentration of the solute and association strengths. We find that a mixture of two-patch solvent (with both patches of the same kind) and multi-bonding solutes with different patch geometries can have a vapor-liquid equilibrium, although the pure components themselves cannot phase separate. The liquid state occurs at very low densities, forming a so-called empty liquid. For the relative association strengths studied in this work, we observe that the vapor-liquid coexistence curve broadens as the concentration of the patchy solvent particles in the liquid phase is increased. The pressure-composition phase equilibrium curves show negative azeotropes for these mixtures. We also observe that, for these mixtures, as the size of the patch on the solute particles is decreased, the critical temperature and the critical packing fraction decreases.

The stability of foam in the presence of oil is of fundamental interest in enhanced oil recovery processes using foam for mobility control. Experimentally, it is known that lauryl betaine (LB) increases foam stability of certain anionic surfactants, and LB is referred to as a foam booster. However, the molecular basis for this effect is not well understood. Using molecular dynamics simulations, here we study a system of LB and alpha olefin sulfonate (AOS-14), an anionic surfactant that is used as a foam stabilizer. We monitor the area per molecule, a quantity that correlates with the surface shear viscosity, and the surface dilatational modulus to infer the stability of the various mixtures. We find that the influence of LB is nonmonotonic: the area per molecule and surface dilatational modulus have a minimum and maximum, respectively, around 30% LB in the monolayer. We show that this net effect has its basis in two competing effects: the favorable interaction between LB and AOS-14 that tends to shrink th...

Water molecules bind strongly to the polar calcite surface and form a surface adsorbed layer that has properties akin to an apolar surface. This has important implications for understanding the thermodynamic driving forces underlying the adsorption of acid groups from crude oil, in particular naphthenic acid, onto calcite. Free energy calculations show that naphthenic acid binds favorably to the water mono-layer adsorbed on the calcite surface. But to bond directly to the calcite, a free energy barrier has to be overcome to expel the intervening layer of water. Further, naphthenic acids with longer alkyl chains bind with lower free energy to the calcite surface than those with shorter alkyl chains, and, for the same chain length, branching also enhances adsorption. To better understand this behavior, for a specified alkyl chain length we study adsorption at different temperatures. Consistent with experiments, we find that adsorption is enhanced at higher temperatures. Examining the enthalpic and entropic contributions to adsorption shows that adsorption of naphthenic acid is entropically favored.

In honor of the 25th anniversary of the SAFT equation of state, this paper presents a brief review of successes in modeling fluid mixtures with associating, polyatomic, and polar components using the SAFT equation of state. Challenges for the association term to predict monomer and dimer fractions in comparison with spectroscopic data are described. To address these challenges and challenges in patchy colloids, extensions to the associating term are reviewed that incorporate multiple bonding at association sites and cooperative association. Approximations in these extensions are validated through comparisons with molecular simulation results. Further, application of the density functional form of the theory to form micelles is briefly reviewed.

The interfacial tension (IFT) between oil and water impacts many industrial operations. For example, in low salinity flooding, water with optimal salinity is injected into an oil reservoir, to change the oil/water interfacial tension and fluid/rock interfacial energy to mobilize trapped oil and enhance the displacement of oil. Theoretical and experimental studies have shown that different ions can enhance or inhibit the production. To develop a fundamental understanding of IFT in these systems, particularly in the context of salinity and the ion-type effect, molecular dynamics simulations were used to probe the change in IFT with the salt types and concentrations. In agreement with experimental measurements, our results show that the oil/water IFT increases with increasing salt concentration, with the increase dependent on the salt species. The results revealed that the presence of divalent anions at the interface increases the electrostatic interactions, which leads to a smaller increase in the IFT compared to other salts. Moreover, the analysis showed that the increase in IFT is due to ion depletion near the interface. The water orientations at the interface and the bulk explain why this depletion occurs.

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 $\rho$ 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 $\rho$), $G_{\!J}(t)$ 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 $\tau_J$ agrees with the kinetic collision time $\tau_K$ for gases, from which a new relation $1/T_{1J}^{km} \propto D_T$ is inferred, without any adjustable parameters.

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 $\tau_{R,T}$ 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 $\tau_{R,T}$ 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 $\tau_{R,T}$ 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.

The perturbed chain form of the polar statistical associating fluid theory (Polar PC-SAFT) was used to model lower 1-alcohol + n-alkane mixtures. The ability of the equation of state to predict accurate activity coefficients at infinite dilution was demonstrated as a function of temperature. Investigations show that the association term in SAFT plays an important role in capturing the right composition dependence of the activity coefficients in comparison with nonassociating models (UNIQUAC). Results also show that considering long-range polar interactions can significantly improve the fractions of free monomers predicted by PC-SAFT in comparison with spectroscopic data and molecular dynamic (MD) simulations carried out in this work. Furthermore, evidence of hydrogen-bonding cooperativity in 1-alcohol + n-alkane systems is discussed using spectroscopy, simulation, and theory. In general, results demonstrate the theory's predictive power, limitations of first-order perturbation theories, as well as the importance of considering long-range polar interactions for better hydrogen-bonding thermodynamics.

Extracellular vesicles (EV), including exosomes and shed vesicles, have been implicated in intercellular communication; however, their biomarker potential is less clear. Therefore, EVs derived from MCF7 and MCF10A cells were analyzed to identify unique miRNA (miR) profiles that distinguish their origin. One characteristic common to the miR profiles of MCF7 EVs and their parent cells is the high abundance of miR-21 , let-7a , miR-100 , and miR-125b , and low levels of miR-205 . A second characteristic is the high abundance of “miRNA-like” tRNA fragments, which is unique to the MCF7 EVs, and is not found in comparing the cellular profiles. In addition, correlations were examined in the MCF7 cellular expression levels of these five miRs and two tRNA-derived miRNAs, miR-720 and miR-1274b , and compared with the correlations in MCF7 EV levels. Interestingly, correlations in the cellular expression of miR-125b , miR-100 , and let-7a are mirrored in the EVs. In contrast, correlations in tRNA-derived miRNA levels are found only in the EVs. The findings suggest that EV miR clusters can be defined based on functional miR interactions related to correlated cellular expression levels or physical miR interactions, for example, aggregation due to comparable binding affinities to common targets. Implications: These results point to using high levels of tRNA-derived small RNA fragments in combination with known miR signatures of tumors to distinguish tumor-derived EVs in circulation from EVs derived from other cell sources. Such biomarkers would be unique to the EVs where high abundances of tRNA fragments are amplified with respect to their cellular levels. Mol Cancer Res; 13(5); 891–901. ©2015 AACR . This article is featured in Highlights of This Issue, [p. 807][1] [1]: /lookup/volpage/13/807?iss=5

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.

We present a theory to predict the structure and thermodynamics of mixtures of colloids of different diameters, building on our earlier work [A. Bansal et al., 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.

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.

Experiments show that at 298~K and 1 atm pressure the transfer free energy, $\mu^{\rm ex}$, 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 $\mu^{\rm ex}$ 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 $\mu^{\rm ex}$ using the test particle method. With CGenFF, $\mu^{\rm ex}$ is positive and the error relative to experiments is about 1.5 $k_{\rm B}T$. With AMOEBA, $\mu^{\rm ex}$ 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., Comment: Fixed several small typos throughout the document. Added a discussion on coarse-graining, including new figure 5. This version is being submitted to JCP

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., Revision: References 27 and 28 were updated. Formatting of last name in acknowledgement was corrected; Expressions for Larmor frequency in terms of magnetic field was included. Caption for figure 7 was corrected (table I should read table II)

Crystal polymorphs of glucose isomerase were examined to characterize the properties and to quantify the energetics of protein crystal growth. Transitions of polymorph stability were measured in poly(ethylene glycol)/NaCl solutions, and one transition point was singled out for more detailed quantitative analysis. Single crystal x-ray diffraction was used to confirm space groups and identify complementary crystal structures. Crystal polymorph stability was found to depend on the NaCl concentration, with stability transitions requiring > 1 M NaCl combined with a low concentration of PEG. Both salting-in and salting-out behavior was observed and was found to differ for the two polymorphs. For NaCl concentrations above the observed polymorph transition, the increase in solubility of the less stable polymorph together with an increase in the osmotic second virial coefficient suggests that changes in protein hydration upon addition of salt may explain the experimental trends. A combination of atomistic and continuum models was employed to dissect this behavior. Molecular dynamics simulations of the solvent environment were interpreted using quasi-chemical theory to understand changes in protein hydration as a function of NaCl concentration. The results suggest that protein surface hydration and Na+ binding may introduce steric barriers to contact formation, resulting in polymorph selection.

The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.

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., Comment: arXiv admin note: text overlap with arXiv:1601.04384

By introducing an external field to temper short-range protein water interactions, we regularize the statistical problem of calculating the hydration free energy, μ(ex), of the protein cytochrome C using the potential distribution theorem. Using this approach, we calculate the nonelectrostatic (dispersion) and electrostatic contributions to μ(ex). The nonelectrostatic contribution interpreted within an accessible surface area approach leads to a surface energy parameter that is about twice the value based on the hydration of small alkanes: at the size scale of the protein, hydrophobic hydration is more stronger relative to small alkanes. The electrostatic contribution does not obey linear response behavior. Further, depending on the choice of the protein dielectric constant, continuum dielectric calculations of the electrostatic contribution differ from the all-atom result by between 6%-12% (in a net value of about -2000 kcal/mol). We conclude by indicating potential applications of the present physically transparent approach toward illuminating the role of water, ions, and osmolytes in protein solution thermodynamics, including in protein folding and aggregation.

Cosolvent hydrophobic preferential interactions with methane in aqueous methanol solutions are evaluated on the basis of the solute excess chemical potential derived from molecular simulations using the quasi-chemical (QC) theory generalization of the potential distribution theorem (PDT). We find that the methane-methanol preferential interaction parameter derived from QC theory quantitatively captures the favorable solvation of methane in methanol solutions in terms of important local solute-solvent (water and methanol) intermolecular interactions within a defined inner shell around the solute, and nonlocal solute interactions with solvent molecules outside this inner shell. Moreover, a unique inner shell can be defined such that the preferential interaction parameter is derived exclusively from the free energy of cavity formation in the aqueous cosolvent solution without the solute, where this cavity corresponds to the specified inner shell, and the mean interaction or binding energy of the solute with solvent molecules outside this inner shell. This inner-shell definition leads to a description of solute-cosolvent preferential interactions in which the molecular details of those interactions are derived from the effect of cosolvent on cavity statistics in the aqueous cosolvent solution alone. The finding suggests that solution thermodynamic behavior beyond steric exclusion (macromolecular crowding) contribute to the molecular mechanisms by which cosolvent preferential interactions influence protein stability and activity.

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 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 opposite in sign and larger in magnitude than predicted by LMF theory. That comparison is discussed from the point of view of quasichemical 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 B2. Those B2's also show that incorporation of attractive interactions leads to more positive (repulsive) values. With attractive interactions in play, B2 can change from positive to negative values with increasing temperatures. This is consistent with the puzzling suggestions of decades ago that B2 ≈ 0 for intermediate cases of temperature or solute size. In all cases here, B2 becomes more attractive with increasing temperature.

For a model deca-alanine peptide the cavity (ideal hydrophobic) contribution to hydration favors the helix state over extended states and the paired helix bundle in the assembly of two helices. The energetic contributions of attractive protein-solvent interactions are separated into quasi-chemical components consisting of a short-range part arising from interactions with solvent in the first hydration shell and the remaining long-range part that is well described by a Gaussian. In the helix-coil transition, short-range attractive protein-solvent interactions outweigh hydrophobic hydration and favor the extended 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 favoring folding. In the pairing of two helices, the cavity contribution outweighs the 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. Overall, hydrophilic protein-solvent interactions and protein intramolecular interactions are found to play a significant role in the thermodynamics of folding and assembly in the system studied.

We study two designed and one natural zinc finger peptide each with the Cys(2)His(2) (CCHH) type of metal binding motif. In the approach we have developed, we describe the role of the protein and solvent outside the Zn(II)-CCHH metal-residue cluster by a molecular field represented by generalized harmonic restraints. The strength of the field is adjusted to reproduce the binding energy distribution of the metal with the cluster obtained in a reference all-atom simulation with empirical potentials. The quadratic field allows us to investigate analytically the protein restraints on the binding site in terms of its eigenmodes. Examining these eigenmodes suggests, consistent with experimental observations, the importance of the first histidine (H) in the CCHH cluster in metal binding. Further, the eigenvalues corresponding to these modes also indicate that the designed proteins form a tighter complex with the metal. We find that the bulk protein and solvent response tends to destabilize metal binding, emphasizing that the favorable energetics of metal-residue interaction is necessary to drive folding in this system. The representation of the bulk protein and solvent response by a local field allows us to perform Monte Carlo simulations of the metal-residue cluster using quantum-chemical approaches, here using a semiempirical Hamiltonian. For configurations sampled from this simulation, we study the free energy of replacing Zn(2+) with Fe(2+), Co(2+), and Ni(2+) using density functional theory. The calculated selectivities are in fair agreement with experimental results.

I. Introduction In the voltage-gated K+ channels, measurements of ion channel permeability show that the protein selectively allows the flow of K+ over Na+ with a fidelity of better than 1 part in 1,000 ([Latorre and Miller, 1983][1]). Recent measurements ([Lockless et al., 2007][2]) of

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, ΣSE, which theory helps identify as the solvent excluded volume, and ΣG, a larger envelope beyond which solute-solvent interactions are Gaussian. The ΣSE envelope is independent of the solvent, as expected on the basis of the insensitivity to the solvent type of the distance of closest approach between protein heavy atoms and solvent heavy atoms, but contrary to the intuition based on treating solvent constituents as spheres of some effective radii. 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 the limitation of using molecular area to assess solvation energetics. The ΣG-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 ΣG-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.

To understand the thermodynamic exclusion of Na + relative to K + from the S 2 site of the selectivity filter, the distribution P X ( ɛ ) (X = K + or Na + ) of the binding energy ( ɛ ) of the ion with the channel is analyzed using the potential distribution theorem. By expressing the excess chemical potential of the ion as a sum of mean-field 〈 ɛ 〉 and fluctuation μ ex flux,X contributions, we find that selectivity arises from a higher value of μ flux , Na + ex relative to μ flux , K + ex . To understand the role of site-site interactions on μ ex flux,X , we decompose P X ( ɛ ) into n -dependent distributions, where n is the number of ion-coordinating ligands within a distance λ from the ion. For λ comparable to typical ion-oxygen bond distances, investigations building on this multistate model reveal an inverse correlation between favorable ion-site and site-site interactions: the ion-coordination states that most influence the thermodynamics of the ion are also those for which the binding site is energetically less strained and vice versa. This correlation motivates understanding entropic effects in ion binding to the site and leads to the finding that μ ex flux,X is directly proportional to the average site-site interaction energy, a quantity that is sensitive to the chemical type of the ligand coordinating the ion. Increasing the coordination number around Na + only partially accounts for the observed magnitude of selectivity; acknowledging the chemical type of the ion-coordinating ligand is essential.

We model the hydration contribution to short-range electrostatic/dispersion protein interactions embodied in the osmotic second virial coefficient, B(2), by adopting a quasi-chemical description in which water molecules associated with the protein are identified through explicit molecular dynamics simulations. These water molecules reduce the surface complementarity of highly favorable short-range interactions, and therefore can play an important role in mediating protein-protein interactions. Here we examine this quasi-chemical view of hydration by predicting the interaction part of B(2) and comparing our results with those derived from light-scattering measurements of B(2) for staphylococcal nuclease, lysozyme, and chymotrypsinogen at 25 degrees C as a function of solution pH and ionic strength. We find that short-range protein interactions are influenced by water molecules strongly associated with a relatively small fraction of the protein surface. However, the effect of these strongly associated water molecules on the surface complementarity of short-range protein interactions is significant, and must be taken into account for an accurate description of B(2). We also observe remarkably similar hydration behavior for these proteins despite substantial differences in their three-dimensional structures and spatial charge distributions, suggesting a general characterization of protein hydration.

The excess proton in water, H + (aq), plays a fundamental role in aqueous solution chemistry. Its solution thermodynamic properties are essential to molecular descriptions of that chemistry and for validation of dynamical calculations. Within the quasichemical theory of solutions those thermodynamic properties are conditional on recognizing underlying solution structures. The quasichemical treatment identifies H 3 O + and H 2 O 5 + as natural inner-shell complexes, corresponding to the cases of n = 1, 2 water molecule ligands, respectively, of a distinguished H + ion. A quantum-mechanical treatment of the inner-shell complex with both a dielectric continuum and a classical molecular dynamics treatment of the outer-shell contribution identifies the latter case (the Zundel complex) as the more numerous species. Ab initio molecular dynamics simulations, with two different electron density functionals, suggest a preponderance of Zundel-like structures, but a symmetrical ideal Zundel cation is not observed.

The usual rate-determining step in the catalytic mechanism of the low molecular weight tyrosine phosphatases involves the hydrolysis of a phosphocysteine intermediate. To explain this hydrolysis, general base-catalyzed attack of water by the anion of a conserved aspartic acid has sometimes been invoked. However, experimental measurements of solvent deuterium kinetic isotope effects for this enzyme do not reveal a rate-limiting proton transfer accompanying dephosphorylation. Moreover, base activation of water is difficult to reconcile with the known gas-phase proton affinities and solution phase pK(a)'s of aspartic acid and water. Alternatively, hydrolysis could proceed by a direct nucleophilic attack by a water molecule. To understand the hydrolysis mechanism, we have used high-level density functional methods of quantum chemistry combined with continuum electrostatics models of the protein and the solvent. Our calculations do not support a catalytic activation of water by the aspartate. Instead, they indicate that the water oxygen directly attacks the phosphorus, with the aspartate residue acting as a H-bond acceptor. In the transition state, the water protons are still bound to the oxygen. Beyond the transition state, the barrier to proton transfer to the base is greatly diminished; the aspartate can abstract a proton only after the transition state, a result consistent with experimental solvent isotope effects for this enzyme and with established precedents for phosphomonoester hydrolysis.

The hydration of some of the alkaline earth divalent metal cations and first row transition metal cations is considered within the quasi-chemical theory of solutions. Quantum chemical calculations provide information on the chemically important interactions between the ion and its first-shell water molecules. A dielectric continuum model supplies the outer-shell contribution. The theory then provides the framework to mesh these quantities together. The agreement between the calculated and experimental quantities is good. For the transition metal cations, it is seen that the ligand field contributions play an important role in the physics of hydration. Removing these bonding contributions from the computed hydration free energy results in a linear decrease in the hydration free energy along the period. It is precisely such effects that molecular mechanics force fields have not captured. The implications and extensions of this study to metal atoms in proteins are suggested.

The K+(aq) ion is an integral component of many cellular processes, amongst which the most important, perhaps, is its role in transmitting electrical impulses along the nerve. Understanding its hydration structure and thermodynamics is crucial in dissecting its role in such processes. Here we address these questions using both the statistical mechanical quasi-chemical theory of solutions and ab initio molecular dynamics simulations. Simulations predict an interesting hydration structure for K+(aq): the population of about six (6) water molecules within the initial minimum of the observed gKO(r) at infinite dilution involves four (4) innermost molecules that the quasi-chemical theory suggests should be taken as the theoretical inner shell. The contribution of the fifth and sixth closest water molecules is observable as a distinct shoulder on the principal maximum of the gKO(r). The quasi-chemical estimate of solvation free energy for the neutral pair KOH is also in good agreement with experiments.

Be$^{2+}$(aq) hydrolysis can to lead to the formation of multi-beryllium clusters, but the thermodynamics of this process has not been resolved theoretically. We study the hydration state of an isolated Be$^{2+}$ ion using both the quasi-chemical theory of solutions and ab initio molecular dynamics. These studies confirm that Be$^{2+}$(aq) is tetra-hydrated. The quasi-chemical approach is then applied to then the deprotonation of $Be(H_2O)_4^{2+}}$ to give $BeOH(H_2O)_3{}^{+}}$. The calculated pK$_a$ of 3.8 is in good agreement with the experimentally suggested value around 3.5. The calculated energetics for the formation of BeOHBe$^{3+}$ are then obtained in fair agreement with experiments., 11 pages, 3 figures

Quasi-chemical theory and electronic structure results on inner-sphere H(H2O)n+ clusters are used to discuss the absolute hydration free energy of H+(aq). It is noted that this quantity is not thermodynamically measurable, and this leads to some relative misalignment of available tables of absolute hydration free energies of ions in water. The simplest quasi-chemical model produces a reasonable quantitative result in the range of −256 to −251 kcal/mol. The primitive concepts on which the model is based naturally identify the Zundel cation H5O2+ as the principal chemical structure contributing to this hydration free energy. The specific participation of an Eigen cation H9O4+ is not required in this model because the definition of that structure depends on outer-sphere arrangements, and a crude dielectric continuum model is here used for outer-sphere contributions.

The hydration thermodynamics of the amino acid X relative to the reference G (glycine) or the hydration thermodynamics of a small-molecule analog of the side chain of X is often used to model the contribution of X to protein stability and solution thermodynamics. We consider the reasons for successes and limitations of this approach by calculating and comparing the conditional excess free energy, enthalpy, and entropy of hydration of the isoleucine side chain in zwitterionic isoleucine, in extended penta-peptides, and in helical deca-peptides. Butane in gauche conformation serves as a small-molecule analog for the isoleucine side chain. Parsing the hydrophobic and hydrophilic contributions to hydration for the side chain shows that both of these aspects of hydration are context-sensitive. Furthermore, analyzing the solute–solvent interaction contribution to the conditional excess enthalpy of the side chain shows that what is nominally considered a property of the side chain includes entirely nonobvious contributions of the background. The context-sensitivity of hydrophobic and hydrophilic hydration and the conflation of background contributions with energetics attributed to the side chain limit the ability of a single scaling factor, such as the fractional solvent exposure of the group in the protein, to map the component energetic contributions of the model-compound data to their value in the protein. But ignoring the origin of cancellations in the underlying components the group-transfer model may appear to provide a reasonable estimate of the free energy for a given error tolerance.

The accurate calculation of the energetics of electrostatically driven binding of amino acid residues to other amino acids (salt bridges) or to synthetic molecules is critical in numerous physiological and technological processes. Commonly used continuum methods are unable to capture differences in interaction energies resulting from specific chemical changes, such as the stronger retention of basic proteins on sulfated (strong) than on carboxylated (weak) cation exchangers. The inadequacies of continuum models in describing hydration effects, specifically local solvent structure and associated polarization effects, are especially apparent in such systems. These shortcomings have been addressed by modeling the protein−cation exchanger interaction as that of methylammonium, a model for a protonated lysine residue, with the methylated analogues of the ion-exchange functionalities, namely methyl sulfate and acetate ion, respectively. A hybrid quantum-continuum treatment of the solvent is able to capture the ...