Effective protein-protein interaction from structure factor data of a lysozyme solution.

We report the determination of an effective protein-protein central potential for a lysozyme solution, obtained from the direct inversion of the total structure factor of the system, as extracted from small angle neutron scattering. The inversion scheme rests on a hypernetted-chain relationship between the effective potential and the structural functions, and is preliminarily tested for the case of a Lennard-Jones interaction. The characteristics of our potential are discussed in comparison with current models of effective interactions in complex fluids. The phase behavior predictions are also investigated.

Effective interactions in lysozyme aqueous solutions: a small-angle neutron scattering and computer simulation study.

We report protein-protein structure factors of aqueous lysozyme solutions at different pH and ionic strengths, as determined by small-angle neutron scattering experiments. The observed upturn of the structure factor at small wavevectors, as the pH increases, marks a crossover between two different regimes, one dominated by repulsive forces, and another one where attractive interactions become prominent, with the ensuing development of enhanced density fluctuations. In order to rationalize such experimental outcome from a microscopic viewpoint, we have carried out extensive simulations of different coarse-grained models. We have first studied a model in which macromolecules are described as soft spheres interacting through an attractive r(-6) potential, plus embedded pH-dependent discrete charges; we show that the uprise undergone by the structure factor is qualitatively predicted. We have then studied a Derjaguin-Landau-Verwey-Overbeek (DLVO) model, in which only central interactions are advocated; we demonstrate that this model leads to a protein-rich/protein-poor coexistence curve that agrees quite well with the experimental counterpart; experimental correlations are instead reproduced only at low pH and ionic strengths. We have finally investigated a third, "mixed" model in which the central attractive term of the DLVO potential is imported within the distributed-charge approach; it turns out that the different balance of interactions, with a much shorter-range attractive contribution, leads in this latter case to an improved agreement with the experimental crossover. We discuss the relationship between experimental correlations, phase coexistence, and features of effective interactions, as well as possible paths toward a quantitative prediction of structural properties of real lysozyme solutions.

Molecular dynamics of an embedded-charge model of lysozyme aqueous solutions.

The onset of liquid-vapor separation in an interaction site model of a lysozyme aqueous solution is investigated by means of molecular dynamics (MD). Calculations are performed for a soft-core version of a potential early introduced by Carlsson et al. (J. Phys. Chem. B 2001, 105, 9040; 2001, 105, 12189.) whose liquid-vapor coexistence was studied by Rosch and Errington (J. Phys. Chem. B 2007, 111, 12591.); our modified model preserves the tailoring onto the experimental lysozyme solution properties embodied by those descriptions. We first show that the structural results obtained by Carlsson et al. at ambient conditions are quite well reproduced by our approach. Then, we cool the system along an isochoric path by monitoring the structural and dynamical properties at various temperatures. We thus show that a fluid-fluid separation takes place at a temperature 15% below the presumed binodal; in particular, we observe that density inhomogeneities develop rather early in the MD run and evolve over tens of nanoseconds into two dense aggregates that eventually merge, after approximately 100 ns more, into a single liquid phase separated from a vapor region by a well-defined planar interface. The densities of the two coexisting fluids are compatible with previous determinations of the binodal line. The connections of this work to the overall scenario of phase stability investigations in protein solutions, as well as possible developments based on the use of more refined models, are discussed.

Virial coefficients and demixing of athermal nonadditive mixtures.

We compute the fourth virial coefficient of a binary nonadditive, hard-sphere mixture over a wide range of deviations from diameter additivity and size ratios. Hinging on this knowledge, we build up a y expansion (Barboy, B.; Gelbart, W. N. J. Chem. Phys. 1979, 71, 3053) in order to trace the fluid-fluid coexistence lines, which we then compare with the available Gibbs-ensemble Monte Carlo data and with the estimates obtained through two refined integral-equation theories of the fluid state. We find that in a regime of moderately negative nonadditivity and largely asymmetric diameters, relevant to the modeling of sterically and electrostatically stabilized colloidal mixtures, the fluid-fluid critical point is unstable with respect to crystallization.

Thermodynamic stability of fluid-fluid phase separation in binary athermal mixtures: the role of nonadditivity.

We studied the thermodynamic stability of fluid-fluid phase separation in binary nonadditive mixtures of hard-spheres for moderate size ratios. We are interested in elucidating the role played by small amounts of nonadditivity in determining the stability of fluid-fluid phase separation with respect to the fluid-solid phase transition. The demixing curves are built in the framework of the modified-hypernetted chain and of the Rogers-Young integral equation theories through the calculation of the Gibbs free energy. We also evaluated fluid-fluid phase equilibria within a first-order thermodynamic perturbation theory applied to an effective one-component potential obtained by integrating out the degrees of freedom of the small spheres. A qualitative agreement emerges between the two different approaches. We also addressed the determination of the freezing line by applying the first-order thermodynamic perturbation theory to the effective interaction between large spheres. Our results suggest that for intermediate size ratios a modest amount of nonadditivity, smaller than earlier thought, can be sufficient to drive the fluid-fluid critical point into the thermodinamically stable region of the phase diagram. These findings could be significant for rare-gas mixtures in extreme pressure and temperature conditions, where nonadditivity is expected to be rather small.

Replica Ornstein-Zernike self-consistent theory for mixtures in random pores.

We present a self-consistent integral equation theory for a binary liquid in equilibrium with a disordered medium, based on the formalism of the replica Ornstein-Zernike (ROZ) equations. Specifically, we derive direct formulas for the chemical potentials and the zero-separation theorems (the latter provide a connection between the chemical potentials and the fluid cavity distribution functions). Next we solve a modified-Verlet closure to ROZ equations, which has built-in parameters that can be adjusted to satisfy the zero-separation theorems. The degree of thermodynamic consistency of the theory is also kept under control. We model the binary fluid in random pores as a symmetrical binary mixture of nonadditive hard spheres in a disordered hard-sphere matrix and consider two different values of the nonadditivity parameter and of the quenched matrix packing fraction, at different mixture concentrations. We compare the theoretical structural properties as obtained through the present approach with Percus-Yevick and Martinov-Sarkisov integral equation theories, and assess both structural and thermodynamic properties by performing canonical standard and biased grand canonical Monte Carlo simulations. Our theory appears superior to the other integral equation schemes here examined and provides reliable estimates of the chemical potentials. This feature should be useful in studying the fluid phase behavior of model adsorbates in random pores in general.

Atomistic versus two-body central potential models of C(60): a comparative molecular dynamics study.

We report on an extensive molecular dynamics investigation of two models of C60. The first model is based on an effective pair, central potential obtained by integrating the interaction between two carbon atoms over the fullerene cages [L.A. Girifalco, J. Phys. Chem. 96, 858 (1992)]. The second model explicitly takes into account the discrete, "atomistic" structure of the C60 molecules; we study two different parametrizations of the carbon-carbon interaction, one identical to that employed in the Girifalco approach, the other borrowed from previous studies on graphite [A. Cheng and M.L. Klein, J. Phys. Chem. 95, 6750 (1991)]. We consider a temperature range spanning from 300 to 1900 K, and pressures up to 200 kbar. Results for the lattice spacing and several thermodynamic quantities, as well as for the radial distribution functions, are reported and compared among each other and with experimental data. The central pair model yields only semiquantitative predictions at typical ambient densities, whereas pressures are generally overestimated. Atomistic simulations reproduce to an overall quantitative level of accuracy the experimental C60 properties. A comparison is also made of the central versus the atomistic potential predictions, when using the same potential parameters in the carbon-carbon interaction. We discuss applications of the adopted modelizations to fullerene systems of current interest, as well as different strategies to optimize the values of the potential parameters.

Theoretical description of phase coexistence in model C60.

We have investigated the phase diagram of a pair interaction model of C60 fullerene [L. A. Girifalco, J. Phys. Chem. 96, 858 (1992)], in the framework provided by two integral equation theories of the liquid state, namely, the modified hypernetted chain (MHNC) implemented under a global thermodynamic consistency constraint, and the self-consistent Ornstein-Zernike approximation (SCOZA), and by a perturbation theory (PT) with various degrees of refinement, for the free energy of the solid phase. We present an extended assessment of such theories as set against a recent Monte Carlo study of the same model [D. Costa, G. Pellicane, C. Caccamo, and M. C. Abramo, J. Chem. Phys. 118, 304 (2003)]. We have compared the theoretical predictions with the corresponding simulation results for several thermodynamic properties such as the free energy, the pressure, and the internal energy. Then we have determined the phase diagram of the model, by using either the SCOZA, the MHNC, or the PT predictions for one of the coexisting phases, and the simulation data for the other phase, in order to separately ascertain the accuracy of each theory. It turns out that the overall appearance of the phase portrait is reproduced fairly well by all theories, with remarkable accuracy as for the melting line and the solid-vapor equilibrium. All theories show a more or less pronounced discrepancy with the simulated fluid-solid coexistence pressure, above the triple point. The MHNC and SCOZA results for the liquid-vapor coexistence, as well as for the corresponding critical points, are quite accurate; the SCOZA tends to underestimate the density corresponding to the freezing line. All results are discussed in terms of the basic assumptions underlying each theory. We have then selected the MHNC for the fluid and the first-order PT for the solid phase, as the most accurate tools to investigate the phase behavior of the model in terms of purely theoretical approaches. It emerges that the use of different procedures to characterize the fluid and the solid phases provides a semiquantitative reproduction of the thermodynamic properties of the C60 model at issue. The overall results appear as a robust benchmark for further theoretical investigations on higher order C(n>60) fullerenes, as well as on other fullerene-related materials, whose description can be based on a modelization similar to that adopted in this work.

Simple fluids with complex phase behavior.

We find that a system of particles interacting through a simple isotropic potential with a softened core is able to exhibit a rich phase behavior including: a liquid-liquid transition in the supercooled phase, as has been suggested for water, a gas-liquid-liquid triple point, a freezing line with anomalous reentrant behavior. The essential ingredient leading to these features resides in the presence of two effective radii in the repulsive core. The potential investigated appears appropriate for a class of spherical polymeric micelles recently investigated.

Thermodynamically self-consistent theories of fluids interacting through short-range forces.

The self-consistent Ornstein-Zernike approximation (SCOZA), the generalized mean spherical approximation (GMSA), the modified hypernetted chain (MHNC) approximation, and the hierarchical reference theory (HRT) are applied to the determination of thermodynamic and structural properties, and the phase diagram of the hard-core Yukawa fluid (HCYF). We investigate different Yukawa-tail screening lengths lambda, ranging from lambda=1.8 (a value appropriate to approximate the shape of the Lennard-Jones potential) to lambda=9 (suitable for a simple one-body modelization of complex fluids like colloidal suspensions and globular protein solutions). The comparison of the results obtained with computer simulation data shows that at relatively low lambda's all the theories are fairly accurate in the prediction of thermodynamic and structural properties; as far as the phase diagram is concerned, the SCOZA and HRT are able to predict the binodal line and the critical parameters in a quantitative manner. At lambda=4 some discrepancies begin to emerge in the performances of the different theoretical approaches: the MHNC remains, on the whole, reasonably accurate in predicting the energy and the contact value of the radial distribution function; the SCOZA predicts well the equation of state up to the highest lambda values investigated. The GMSA and the MHNC underestimate and overestimate, respectively, the liquid coexisting density, while the SCOZA and HRT yield liquid branches that fall between the two former theoretical predictions, although both appear to overestimate the critical temperature somewhat. At higher lambda's the GMSA and MHNC binodals further worsen, while the SCOZA appears to remain usefully predictive. In general, the predictions of all the theories tend to slightly worsen at low temperatures and high density. The determination of the freezing line, performed by means of a one-phase "freezing criterion" (due to other authors) is not particularly satisfactory within either the SCOZA or the MHNC; the GMSA prediction for the freezing line at lambda=7 and 9 is instead able to follow in a qualitative manner the pattern of the solid-vapor coexistence line as determined through computer simulation studies. The necessity of further assessments of the freezing predictions is also discussed. Finally, versions of the GMSA, SCOZA, and HRT that can be expected to be more accurate for interactions with extremely short-ranged attractions are identified.