The use of Flory-Huggins theory in interpreting partitioning of solutes between organic liquids and water.

Solute partitioning data for dilute solutions have almost invariably been interpreted by equating experimental values of -RT in Kx (wherein Kx is the mole fraction partition coefficient) to delta mu infinity, the standard Gibbs energy change for solute transfer from one solvent to another. Recently, it has been alleged that this relation is insufficiently general. Instead, the statistical mechanical Flory-Huggins (FH) theory has been recommended for use, because it is designed to account for disparities in molecular size between solute and solvent. Our examination of the thermodynamics of partitioning shows that: (1) The customary interpretation is not only entirely correct (providing only that the solute is dilute), but is model-independent. (2) The dilute limit of the FH theory is seen to agree entirely with the usual interpretation of -RT in Kx, once certain misnomers are cleared away. (3) The use of FH theory being urged upon us in fact serves only to extract from delta mu infinity (the latter quite correctly determined as -RT in Kx) the contact part of delta mu infinity in order to obtain information on hydrophobic interactions. Some caveats are cited concerning such use of the FH statistical mechanical model.     

Study on the molecular models commonly used in the simulation of dilute polymeric solutions in flow

Three molecular models, commonly used in the simulation of polymeric solutions and melts were employed to describe the rheological behaviour of dilute, elastic and constant viscosity solution formed by bead-and-bond chain molecules immersed into a soft-sphere solvent. The intermolecular interactions for the three models were calculated by the Lennard-Jones potential. The differences amongst the models proceeded from the intramolecular restrictions: the simplest one is a Freely-Joined-Chain (FJC) model with harmonic bond potentials, in the second model bonds are restricted by a finite extensible non-linear elastic (FENE) potential plus a repulsive WCA potential, and the third model is conformed by the United Atom (UA) approach which includes bond, flexion and torsion potentials. Both Couette and Poiseuille flows were simulated using Non-Equilibrium Molecular Dynamics. Deformation displayed by the three chain models; defined in terms of their radius of gyration was calculated and according to results it was found that for Couette flow, the three chains exhibit similar response to deformation. In Poiseulle flow, the FJC and FENE models behave similarly but the UA model presents a larger resistance to deformation. For both flow regimes, the forces involved to deform the chains were estimated in terms of the first normal stress differences. From these estimations it was found that the UA model depicted the stiffest chain, followed by the FENE model, and last the FJC model.     

Temperature dependence of the solubility of non-polar gases in water

An explanation is provided for the experimentally observed temperature dependence of the solubility and the solubility minimum of non-polar gases in water. The influence of solute size and solute-water attractive interactions on the solubility minimum temperature is investigated. The transfer of a non-polar solute from the ideal gas into water is divided into two steps: formation of a cavity in water with the size and shape of the solute and insertion of the solute in this cavity which is equivalent to 'turning on' solute-water attractive interactions. This two step process divides the excess chemical potential of the non-polar solute in water into repulsive and attractive contributions, respectively. The reversible work for cavity formation is modeled using an information theory model of hydrophobic hydration. Attractive contributions are calculated by modeling the water structure in the vicinity of non-polar solutes. These models make a direct connection between microscopic quantities and macroscopic observables. Moreover, they provide an understanding of the peculiar temperature dependences of the hydration thermodynamics from properties of pure water; specifically, bulk water density and the water oxygen-oxygen radial distribution function.     

Analytical ultracentrifugation in a Gibbsian perspective

The analytical ultracentrifuge has come into new intensive use following complete instrumental redesign and the use of advanced computer technologies for the analysis and interpretation of experimental results. Major attention is now devoted to the evaluation of interactions between similar and dissimilar biological macromolecules in dilute and concentrated systems. Electrostatically charged biological solute systems additionally comprise low molecular weight charged and non-charged cosolvents. Solvent/cosolvent interactions, insufficiently considered in most current analytical ultracentrifugation analyses, may quantitatively affect solute/solute interactions. For comprehensive analysis the Svedberg derivation considering a buoyant molar mass (1 - rho0 partial specific volume)M2 and valid at vanishing solute concentration for strictly two component systems only, should be replaced, following classical thermodynamic analysis, by the ratio (delta rho/delta c2)(mu)/d pi/dc2 of the density increment at constant chemical potential of diffusible cosolvents, to the derivative of the osmotic pressure with solute concentration. Disregard of the solvent/cosolvent and solute/cosolvent interactions should be avoided.     

Partition and permeation of dextran in polyacrylamide gel.

Partition of sized FITC-dextrans in polyacrylamide gel showed a relationship between Kav and solute radius as predicted by the theory of Ogston, which is based solely on geometry of the spaces. Permeability data for the same dextrans were fit to several theories, including those based on geometry and those based on hydrodynamic interactions, and the gel structure predicted by the partition and permeability data were compared. The Brinkman effective-medium model (based on hydrodynamic interactions and requiring a measure of the hydraulic conductivity of the matrix) gave the best fit of permeability data with the values for fiber radius (rf) and void volume of the gel (epsilon) that were obtained from the partition data. The models based on geometry and the hydrodynamic screening model of Cukier, using the rf and epsilon from partition data, all predicted higher rates of permeation than observed experimentally, while the effective-medium model with added term for steric interaction predicted lower permeation than that observed. The size of cylindrical pores appropriate for the partition data predicted higher rates of permeation than observed. These relative results were unaffected by the method of estimating void volume of the gel. In sum, it appears that one can use data on partition of solute, combined with measurement of hydraulic conductivity, to predict solute permeation in polyacrylamide gel.     

Solvent-induced free energy landscape and solute-solvent dynamic coupling in a multielement solute

Molecular dynamics simulations using a simple multielement model solute with internal degrees of freedom and accounting for solvent-induced interactions to all orders in explicit water are reported. The potential energy landscape of the solute is flat in vacuo. However, the sole untruncated solvent-induced interactions between apolar (hydrophobic) and charged elements generate a rich landscape of potential of mean force exhibiting typical features of protein landscapes. Despite the simplicity of our solute, the depth of minima in this landscape is not far in size from free energies that stabilize protein conformations. Dynamical coupling between configurational switching of the system and hydration reconfiguration is also elicited. Switching is seen to occur on a time scale two orders of magnitude longer than that of the reconfiguration time of the solute taken alone, or that of the unperturbed solvent. Qualitatively, these results are unaffected by a different choice of the water-water interaction potential. They show that already at an elementary level, solvent-induced interactions alone, when fully accounted for, can be responsible for configurational and dynamical features essential to protein folding and function.     

Scaling behaviour of different polymer models in dissipative particle dynamics of unentangled melts

We present a dissipative particle dynamics (DPD) study of scaling behaviour for three polymer models. The scaling behaviour is explored for the conformational and dynamic properties of unentangled polymer melts. DPD employs a bead–spring model together with an aggressive coarse-graining to represent polymers at the mesoscale. The first model studied utilises a simple soft repulsion potential for the bead–bead interactions together with a harmonic spring potential to connect beads into a polymer chain. The second model differs from the first model by replacing the harmonic spring with a finitely extensible nonlinear elastic spring. The third model uses realistic coarse-grain potentials for the bead–bead, spring and bending interactions based on the iterative Boltzmann inversion procedure and it corresponds to a mesoscopic model of polyethylene. We systematically vary the chain length and spring constant (in the case of the first and second models), and simulate the conformational properties such as the end-to-end distance or radius of gyration, and dynamic properties such as the centre-of-mass self-diffusion coefficient or viscosity. The scaling of the conformational and dynamic properties with chain length (scaling laws) is compared with the Rouse theory, which is considered as a standard theory for unentangled polymer melts. The comparison shows that simulated scaling laws typically agree with the Rouse scaling laws for the DPD polymer models with more than 10 DPD beads. For the shorter DPD polymers, deviations from the Rouse theory exist and become significant for the dynamic properties, especially for the viscosity of the polymer melts.     

Monte Carlo Simulation Study of Adsorption Characteristics in Slit-Like Micropores Under Supercritical Conditions

Abstract

Adsorption characteristics of a solute diluted in supercritical fluids has been investigated by using the Monte Carlo simulation techniques. The Lennard-Jones potential function is used for describing interactions for a model system of CO₂ + benzene in slit-like micropores with infinite graphitic carbon walls. A modified μVT ensemble method with particle exchange proposed by Cracknell, Nicholson and Quirke (1993) is found to be much superior to the conventional μVT ensemble method especially for dense mixtures in a pore. Adsorption isotherms of CO₂ and benzene, in equilibrium with a dilute benzene mixture in CO₂ (mole fraction of benzene = 0.001), are computed by varying pressure, temperature, the benzene–surface interaction potential, and the slitwidth. Adsorption isotherm curve of CO₂ increases with an increase in pressure while that of benzene shows a maximum at a pressure far below the critical pressure of CO₂ and then it decreases with increasing pressure. The decrease in benzene adsorption with increasing pressure is attributable to both the enhanced solubility in supercritical CO₂ and the competitive adsorption of CO₂. The isotherm curves of each component at two temperatures, 313.2 K and 323.2 K, show to cross at a pressure near the critical pressure due to the “density effect” on the chemical potentials of a solute at supercritical fluid conditions. When the interaction between a solute and a surface increases, the adsorption isotherm increases. Narrowing the slitwidth results in the increase in the adsorption of solute since the external potential from two walls becomes deeper.     

Vapor pressure osmometry studies of osmolyte-protein interactions: implications for the action of osmoprotectants in vivo and for the interpretation of "osmotic stress" experiments in vitro

To interpret or to predict the responses of biopolymer processes in vivo and in vitro to changes in solute concentration and to coupled changes in water activity (osmotic stress), a quantitative understanding of the thermodynamic consequences of interactions of solutes and water with biopolymer surfaces is required. To this end, we report isoosmolal preferential interaction coefficients (Gamma(mu1) determined by vapor pressure osmometry (VPO) over a wide range of concentrations for interactions between native bovine serum albumin (BSA) and six small solutes. These include Escherichia coli cytoplasmic osmolytes [potassium glutamate (K(+)Glu(-)), trehalose], E. coli osmoprotectants (proline, glycine betaine), and also glycerol and trimethylamine N-oxide (TMAO). For all six solutes, Gamma(mu1) and the corresponding dialysis preferential interaction coefficient Gamma(mu1),(mu3) (both calculated from the VPO data) are negative; Gamma(mu1), (mu3) is proportional to bulk solute molality (m(bulk)3) at least up to 1 m (molal). Negative values of Gamma(mu1),(mu3) indicate preferential exclusion of these solutes from a BSA solution at dialysis equilibrium and correspond to local concentrations of these solutes in the vicinity of BSA which are lower than their bulk concentrations. Of the solutes investigated, betaine is the most excluded (Gamma(mu1),(mu3)/m(bulk)3 = -49 +/- 1 m(-1)); glycerol is the least excluded (Gamma(mu1),(mu3)/m(bulk)3 = -10 +/- 1 m(-1)). Between these extremes, the magnitude of Gamma(mu1),(mu3)/m(bulk)3 decreases in the order glycine betaine > proline >TMAO > trehalose approximately K(+)Glu(-) > glycerol. The order of exclusion of E. coli osmolytes from BSA surface correlates with their effectiveness as osmoprotectants, which increase the growth rate of E. coli at high external osmolality. For the most excluded solute (betaine), Gamma(mu1),(mu3) provides a minimum estimate of the hydration of native BSA of approximately 2.8 x 10(3) H(2)O/BSA, which corresponds to slightly less than a monolayer (estimated to be approximately 3.2 x 10(3) H(2)O). Consequently, of the solutes investigated here, only betaine might be suitable for use in osmotic stress experiments in vitro as a direct probe to quantify changes in hydration of protein surface in biopolymer processes. More generally, however, our results and analysis lead to the proposal that any of these solutes can be used to quantify changes in water-accessible surface area (ASA) in biopolymer processes once preferential interactions of the solute with biopolymer surface are properly taken into account.     

Phospholipid interactions in model membrane systems. II. Theory.

We describe statistical thermodynamic theory for the lateral interactions among phospholipid head groups in monolayers and bilayers. Extensive monolayer experiments show that at low surface densities, PC head groups have strong lateral repulsions which increase considerably with temperature, whereas PE interactions are much weaker and have no significant temperature dependence (see the preceding paper). In previous work, we showed that the second virial coefficients for these interactions can be explained by: (a) steric repulsions among the head groups, and (b) a tilting of the P-N+ dipole of PC so that the N+ end enters the oil phase, to an extent that increases with temperature. It was also predicted that PE interactions should be weaker and less temperature dependent because the N+ terminal of the PE head-group is hydrophilic, hence, it is tilted into the water phase, so dipolar contributions among PE's are negligible due to the high dielectric constant of water. In the present work, we broaden the theory to treat phospholipid interactions up to higher lateral surface densities. We generalize the Hill interfacial virial expansion to account for dipoles and to include the third virial term. We show that to account for the large third virial coefficients for both PC and PE requires that the short range lateral attractions among the head groups also be taken into account. In addition, the third virial coefficient includes fluctuating head group dipoles, computed by Monte Carlo integration assuming pairwise additivity of the instantaneous pair potentials. We find that because the dipole fluctuations are correlated, the average triplet interactions do not equal the sum of the average dipole pair potentials. This is important for predicting, the magnitude and the independence of temperature of the third virial coefficients for PC. The consistency of the theory with data of both the second and the third virial coefficients extends the applicability of the head-group model to semiconcentrated monolayers, in agreement with the surface potential data in the foregoing paper.     

The electrostatic contribution to DNA base-stacking interactions.

Base-stacking and phosphate-phosphate interactions in B-DNA are studied using the finite difference Poisson-Boltzmann equation. Interaction energies and dielectric constants are calculated and compared to the predictions of simple dielectric models. No extant simple dielectric model adequately describes phosphate-phosphate interactions. Electrostatic effects contribute negligibly to the sequence and conformational dependence of base-stacking interactions. Electrostatic base-stacking interactions can be adequately modeled using the Hingerty screening function. The repulsive and dispersive Lennard-Jones interactions dominate the dependence of the stacking interactions on roll, tilt, twist, and propellor. The Lennard-Jones stacking energy in ideal B-DNA is found to be essentially independent of sequence.     

Solute concentration effect on osmotic reflection coefficient

A theory for the effect of concentration on osmotic reflection coefficient, correct to first order, was developed at the molecular level by considering the effect of solute-solute interactions on solute concentration and the fluid stress tensor within a solvent-filled pore. The solvent was modeled as a continuous fluid and potential energies between solute molecules and the pore wall were assumed to be pairwise additive. Although the theory is more general, calculations are presented only for excluded volume effects (hard-sphere for solute, hard-wall for pore). The relationship between the first-order concentration effect and the infinite dilution value of reflection coefficient appears to be geometry independent. The theory is discussed in light of experimental studies of osmotic flow that have recently appeared in the literature.     

Failure of imprinting at Igf-2: two models of mutation-selection balance.

The failure of maternal imprinting at the insulin-like growth factor II (Igf-2) locus predisposes individuals to several clinical conditions, including Wilms tumor. Having two functional Igf-2 genes, therefore, is selectively disadvantageous, and the condition is probably maintained in human populations by recurrent mutation. We propose two models that predict the expected frequency of functionally diploid individuals in a large population, in terms of a mutation rate, mu, and the selection coefficient against functionally diploid individuals, s. In the first model a mutant Igf-2 allele that cannot be imprinted arises from the standard, imprintable allele at a rate mu. Our second model hypothesizes a second modifier locus at which a recessive allele arises at rate mu. Mothers who are homozygous for this recessive modifier allele fail to imprint their eggs. Both models predict the expected frequency of affecteds to be 2 mu/s(1 + mu), approximately twice that predicted by the standard one-locus model of a recessive allele in mutation-selection balance. This frequency suggests that < or = 25% of the cases of Wilms tumor are due to the failure to imprint the maternal Igf-2 gene.     

Physiologically structured models – from versatile technique to ecological theory

A ubiquitous feature of natural communities is the variation in size that can be observed between organisms, a variation that to a substantial degree is intraspecific. Size variation within species by necessity implies that ecological interactions vary both in intensity and type over the life cycle of an individual. Physiologically structured population models (PSPMs) constitute a modelling approach especially designed to analyse these size‐dependent interactions as they explicitly link individual level processes such as consumption and growth to population dynamics. We discuss two cases where PSPMs have been used to analyse the dynamics of size‐structured populations. In the first case, a model of a size‐structured consumer population feeding on a non‐structured prey was successful in predicting both qualitative (mechanisms) and quantitative (individual growth, survival, cycle amplitude) aspects of the population dynamics of a planktivorous fish population. We conclude that single generation cycles as a result of intercohort competition is a general outcome of size‐structured consumer–resource interactions. In the second case, involving both cohort competition and cannibalism, we show that PSPMs may predict double asymptotic growth trajectories with individuals ending up as giants. These growth trajectories, which have also been observed in field data, could not be predicted from individual level information, but are emergent properties of the population feedback on individual processes. In contrast to the size‐structured consumer–resource model, the dynamics in this case cannot be reduced to simpler lumped stage‐based models, but can only be analysed within the domain of PSPMs. Parameter values used in PSPMs adhere to the individual level and are derived independently from the system at focus, whereas model predictions involve both population level processes and individual level processes under conditions of population feedback. This leads to an increased ability to test model predictions but also to a larger set of variables that is predicted at both the individual and population level. The results turn out to be relatively robust to specific model assumptions and thus render a higher degree of generality than purely individual‐based models. At the same time, PSPMs offer a much higher degree of realism, precision and testing ability than lumped stage‐based or non‐structured models. The results of our analyses so far suggest that also in more complex species configurations only a limited set of mechanisms determines the dynamics of PSPMs. We therefore conclude that there is a high potential for developing an individual‐based, size‐dependent community theory using PSPMs.     

Partitioning and diffusion of large molecules in fibrous structures

This paper consists of three parts. In the first part we present diffusion and partition coefficients of proteins in agarose that were measured with gel permeation chromatography. In the second part we present a partition model which includes the effects of solute concentration and of cosolutes. In the third part we modify and extend Ogston’s diffusion equation to account for the effects of solute and fiber flexibility, solute concentration and cosolutes. We find good agreement between the proposed models and data from the literature.     

Brownian dynamics simulation of probe diffusion in DNA: effects of probe size, charge and DNA concentration

We have used Brownian dynamics simulation to study probe diffusion in solutions of short chain DNA using our previously developed simulation algorithm. We have examined the effect of probe size, charge, and DNA concentration on the probe diffusion coefficient, with the aim of gaining insight into the diffusion of proteins in a concentrated DNA environment. In these simulations, DNA was modeled as a worm-like chain of hydrodynamically equivalent spherical frictional elements while probe particles were modeled as spheres of given charge and hydrodynamic radius. The simulations allowed for both short range Lennard-Jones interactions and long ranged electrostatic interactions between charged particles. For uncharged systems, we find that the effects of probe size and DNA concentration on the probe diffusion coefficient are consistent with excluded volume models and we interpret our results in terms of both empirical scaling laws and the predictions of scaled particle theory. For charged systems, we observe that the effects of probe size and charge are most pronounced for the smallest probes and interpret the results in terms of the probe charge density. For an ionic strength of 0.1 M we find that, below a critical probe surface charge density, the probe diffusion coefficient is largely independent of probe charge and only weakly dependent on the DNA charge. These effects are discussed in terms of the interactions between the probe and the DNA matrix and are interpreted in terms of both the underlying physics of transport in concentrated solutions and the assumptions of the simulation model.     

Solute excluded-volume effects on the stability of globular proteins: A statistical thermodynamic theory

A statistical thermodynamic theory is developed to investigate the effects of solute excluded volume on the stability of globular proteins. Proteins are modeled as two states in chemical equilibrium: the denatured state is modeled as a flexible chain of tangent hard spheres (pearl-necklace chain) while the native state is modeled as a single hard sphere. Study of model proteins bovine pancreatic trypsin inhibitor and lysozyme in a McMillan-Mayer model solution of hard spheres indicates that the excluded volume of solutes has three distinct types of effects on protein stability: (1) small-size solutes strongly denature proteins, (2) medium-size solutes stabilize proteins at low solute concentrations and destabilize them at high concentrations, and (3) large-size solutes stabilize native-state proteins across the whole liquid region. The study also finds that increasing the chain length of hard-chain polymer solutes has an effect on protein stability that is similar to increasing the diameter of spherical solutes. This work qualitatively explains why stabilizers tend to be large size molecules such as sugars, polymers, polynols, nonionic, and anionic surfactants while denaturants tend to be small size molecules such as alcohols, glycols, amides, formamides, ureas, and guanidium salts. Quantitative comparison between theoretical predictions and experimental results for folding free energy changes shows that the excluded-volume effect is at least as important as the binding and/or electrostatic effects on solute-assisted protein-denaturation processes. Our theory may also be able to explain the effect of excluded volume on the Φ condensation of DNA. © 1996 John Wiley & Sons, Inc.     

Optimal Testing for Serial Correlation in a Large Number of Small Samples

In recent years, there has been an increased awareness of the potential one-sided nature of many testing problems in applied sciences. Usually, these testing problems can be reduced, either by conditioning on sufficient statistics or by invariant techniques. COX and SOLOMON (1988) considered testing the serial correlation coefficient of a stationary first order autoregressive process and concentrated on four independent samples, with each of size three. We outline a general method for testing the serial correlation coefficient, using locally best invariant, point optimal invariant and locally most mean powerful invariant test procedures. The first procedure optimizes power near the null hypothesis, the second optimizes it at a pre-determined point away from the null while the third optimizes the average curvature of the power hypersurface in the neighbourhood of the null hypothesis.     

Sedimentation equilibrium in macromolecular solutions of arbitrary concentration. I. Self-associating proteins

Relations describing sedimentation equilibrium in solutions of self-associating macromolecules at arbitrary concentration are presented. These relations are obtained by using scaled-particle theory to calculate the thermodynamic activity of each species present at a given radial distance. The results are expected to be valid for solutions of globular proteins under conditions such that interactions between individual solute molecules may be approximated by a hard-particle potential. Sedimentation equilibria in solutions containing either a nonassociating solute or a solute that self-associates according to several different schemes are simulated using the derived relations. The results of these simulations are presented in terms of the dependence of apparent weight-average molecular weight upon solute concentration. Simple empirical relations are presented for estimating the true weight-average molecular weight from the apparent weight-average molecular weight, without reference to any particular self-association scheme. The weight-average molecular weight estimated in this fashion is within a few percent of the true weight-average molecular weight at all experimentally realizable solute concentrations ( < 400 g/L).     

Geometric and potential driving formation and evolution of biomolecular surfaces

This paper presents new geometrical flow equations for the theoretical modeling of biomolecular surfaces in the context of multiscale implicit solvent models. To account for the local variations near the biomolecular surfaces due to interactions between solvent molecules, and between solvent and solute molecules, we propose potential driven geometric flows, which balance the intrinsic geometric forces that would occur for a surface separating two homogeneous materials with the potential forces induced by the atomic interactions. Stochastic geometric flows are introduced to account for the random fluctuation and dissipation in density and pressure near the solvent–solute interface. Physical properties, such as free energy minimization (area decreasing) and incompressibility (volume preserving), are realized by some of our geometric flow equations. The proposed approach for geometric and potential forces driving the formation and evolution of biological surfaces is illustrated by extensive numerical experiments and compared with established minimal molecular surfaces and molecular surfaces. Local modification of biomolecular surfaces is demonstrated with potential driven geometric flows. High order geometric flows are also considered and tested in the present work for surface generation. Biomolecular surfaces generated by these approaches are typically free of geometric singularities. As the speed of surface generation is crucial to implicit solvent model based molecular dynamics, four numerical algorithms, a semi-implicit scheme, a Crank–Nicolson scheme, and two alternating direction implicit (ADI) schemes, are constructed and tested. Being either stable or conditionally stable but admitting a large critical time step size, these schemes overcome the stability constraint of the earlier forward Euler scheme. Aided with the Thomas algorithm, one of the ADI schemes is found to be very efficient as it balances the speed and accuracy.