General methods for free-volume theory

Colloidal gelation with non-sticky particles

Colloidal gels are widely applied in industry due to their rheological character-no flow takes place below the yield stress. Such property enables gels to maintain uniform distribution in practical formulations; otherwise, solid components may quickly sediment without the support of gel matrix. Compared with pure gels of sticky colloids, therefore, the composites of gel and non-sticky inclusions are more commonly encountered in reality. Through numerical simulations, we investigate the gelation process in such binary composites. We find that the non-sticky particles not only confine gelation in the form of an effective volume fraction, but also introduce another lengthscale that competes with the size of growing clusters in gel. The ratio of two key lengthscales in general controls the two effects. Using different gel models, we verify such a scenario within a wide range of parameter space, suggesting a potential universality in all classes of colloidal composites.

A cavity formation energy formula for hard spheres in simple electrolyte solutions

A formula for cavity formation energy of a hard sphere in restricted primitive electrolyte solutions is derived based on the integral equation theory. Specifically, the contact values of radial distribution functions between the hard sphere and the ionic species, determined analytically from the first-order mean spherical approximation theory, are used to evaluate the cavity formation energy. In the large solute-size limit, the scaling relation of the cavity formation energy further leads to an analytical expression for the surface tension of the electrolyte solution near a curved interface. Our theory is applied to hard spheres immersed in restricted primitive electrolyte solutions, where the good agreement of the cavity formation energy with the hyper-netted chain theory demonstrates the accuracy of our theory.

A New Method to Determine Antioxidant Activities of Biofilms Using a pH Indicator (Resazurin) Model System

Biopolymeric films were prepared with gelatin, plasticizer, and three different types of antioxidants (ascorbic acid, phytic acid, and BHA) corresponding to different mechanisms in activity. The antioxidant activity of films was monitored for 14 storage days upon color changes using a pH indicator (resazurin). The instant antioxidant activity of films was measured by a DPPH free radical test. The system using resazurin was composed of an agar, an emulsifier, and soybean oil to simulate a highly oxidative oil-based food system (AES-R). Gelatin-based films (GBF) containing phytic acid showed higher tensile strength and energy to break than all other samples due to the increased intermolecular interactions between phytic acid and gelatin molecules. The oxygen barrier properties of GBF films containing ascorbic acid and phytic acid increased due to the increased polarity, while GBF films containing BHA showed increased oxygen permeability compared to the control. According to "a-value" (redness) of the AES-R system tested with films, films incorporating BHA showed the most retardation of lipid oxidation in the system. This retardation corresponds to 59.8% antioxidation activity at 14 days, compared with the control. Phytic acid-based films did not show antioxidant activity, whereas ascorbic acid-based GBFs accelerated the oxidation process due to its prooxidant activity. The comparison between the DPPH free radical test and the control showed that the ascorbic acid and BHA-based GBFs showed highly effective free radical scavenging behavior (71.7% and 41.7%, respectively). This novel method using a pH indicator system can potentially determine the antioxidation activity of biopolymer films and film-based samples in a food system.

Mechanical properties of sunflower oil under pressure

This article presents the results of research on the influence of high pressure on the mechanical properties of sunflower oil. The pressure value was changed by the stepwise method to obtain thermodynamic equilibrium. Dependencies of changes in the volume and compressibility of sunflower oil on pressure were investigated. A discontinuous (step) change was observed indicating the appearance of the first order phase transformation. The phase transition for sunflower oil was observed in the pressure range from 450 to 500 MPa after about 170 h. Most likely, then, there was a change to the double crystal phase. The time after which this transformation took place was the longest of all times that the authors have observed so far for the study.

Influence of solvent quality on depletion potentials in colloid-polymer mixtures

As first explained by the classic Asakura-Oosawa (AO) model, effective attractive forces between colloidal particles induced by depletion of nonadsorbing polymers can drive demixing of colloid-polymer mixtures into colloid-rich and colloid-poor phases, with practical relevance for purification of water, stability of foods and pharmaceuticals, and macromolecular crowding in biological cells. By idealizing polymer coils as effective penetrable spheres, the AO model qualitatively captures the influence of polymer depletion on thermodynamic phase behavior of colloidal suspensions. In previous work, we extended the AO model to incorporate aspherical polymer conformations and showed that fluctuating shapes of random-walk coils can significantly modify depletion potentials [W. K. Lim and A. R. Denton, Soft Matter 12, 2247 (2016); J. Chem. Phys. 144, 024904 (2016)]. We further demonstrated that the shapes of polymers in crowded environments sensitively depend on solvent quality [W. J. Davis and A. R. Denton, J. Chem. Phys. 149, 124901 (2018)]. Here, we apply Monte Carlo simulation to analyze the influence of solvent quality on depletion potentials in mixtures of hard-sphere colloids and nonadsorbing polymer coils, modeled as ellipsoids whose principal radii fluctuate according to random-walk statistics. We consider both self-avoiding and non-self-avoiding random walks, corresponding to polymers in good and theta solvents, respectively. Our simulation results demonstrate that depletion of polymers of equal molecular weight induces much stronger attraction between colloids in good solvents than in theta solvents and confirm that depletion interactions are significantly influenced by aspherical polymer conformations.

Liquid-liquid phase separation in an inhomogeneous ternary colloid-polymer mixture

Suspended colloids are often considered as models for molecules, which are sufficiently big so that they can be observed directly in (light) microscopes and for which the effective interaction among each other can be tailored. The Asakura-Oosawa model of ideal colloid-polymer mixtures captures the idea of tuning the interaction between the colloids via a potential, which possesses a range set by the size of the polymers and an attractive strength characterized by the (reservoir) number density of the polymers, which plays the role of an inverse temperature. The celebrated Asakura-Oosawa depletion potential allows one to recreate the bulk phase diagram of a simple fluid by employing a colloid-polymer mixture. This has been verified in theory, by computer simulations, and via experiments. Here, we study the phase behavior of a confined colloid-polymer mixture with two polymer species. The sizes and densities are chosen such that the resulting bulk phase diagram exhibits a second stable critical point within the framework of the classical density functional theory. Our results suggest that a suitably tuned colloid-polymer mixture can be an interesting model system to study fluids with two critical points.

Phase stability of colloidal mixtures of spheres and rods

We determined the phase boundaries of aqueous mixtures containing colloidal rod-like fd-viruses and polystyrene spheres using diffusing-wave spectroscopy and compared the results with free volume theory predictions. Excluded volume interactions in mixtures of colloidal rods and spheres lead to mediated depletion interactions. The strength and range of this attractive interaction depend on the concentrations of the particles, the length L and diameter D of the rods, and the radius R of the spheres. At strong enough attraction, this depletion interaction leads to phase separation. We experimentally determined the rod and sphere concentrations where these phase transitions occur by systematically varying the size ratios L/R and D/R and the aspect ratio L/D. This was done by using spheres with different radii and modifying the effective diameter of the rods through either the ionic strength of the buffer or anchoring a polymeric brush to the surface of the rods. The observed phase transitions were from a binary fluid to a colloidal gas/liquid phase coexistence that occurred already at very low concentrations due to the depletion efficiency of highly anisotropic rods. The experimentally measured phase transitions were compared to phase boundaries obtained using free volume theory (FVT), a well established theory for calculating the phase behavior of colloidal particles mixed with depletants. We find good correspondence between the experimental phase transitions and the theoretical FVT model where the excluded volume of the rod-like depletants was explicitly accounted for in both the reservoir and the system.

Scattering from colloidal cubic silica shells: Part II, static structure factors and osmotic equation of state

HYPOTHESIS

The shape of colloidal particles affects the structure of colloidal dispersions. The effect of the cube shape on the thermodynamics of colloidal cube dispersions has not yet been studied experimentally. Static light scattering measurements on colloidal cubic silica shells at finite concentrations allows us to measure the structure factor of colloidal cube fluids and to test theoretical predictions for the equation of state of hard convex superballs.

EXPERIMENTS

Hollow silica nanocubes of varying concentrations in N,N,-dimethylformamide were studied with static light scattering. The structure factor was extracted from the scattering curves using experimental form factors. From this experimental structure factor, the specific density of the particles, and the osmotic compressibility were obtained. This osmotic compressibility was then compared to a theoretical equation of state of hard superballs.

FINDINGS

The first experimental structure factors of a stable cube fluid are presented. The osmotic compressibility of the cube fluid can be described by the equation of state of a hard superball fluid, showing that silica cubes in N,N,-dimethylformamide with LiCl effectively interact as hard particles.

Calculation of Second Virial Coefficients of Atomistic Proteins Using Fast Fourier Transform

The second virial coefficient, B₂, measures a protein solution's deviation from ideal behavior. It is widely used to predict or explain solubility, crystallization condition, aggregation propensity, and critical temperature for liquid-liquid phase separation. B₂ is determined by the interaction energy between two protein molecules and, specifically, by the integration of the Mayer f-function in the relative configurational space (translation and rotation) of the two molecules. Simple theoretical models, such as one attributed to Derjaguin, Landau, Verwey, and Overbeek (DLVO), can fit the dependence of B₂ on salt concentrations. However, model parameters derived often are physically unrealistic and hardly transferable from protein to protein. Previous B₂ calculations incorporating atomistic details were done with limited sampling in the configurational space, due to enormous computational cost. Our FMAP method, based on fast Fourier transform, can considerably accelerate such calculations, and here we adapt it to calculate B₂ values for proteins represented at the atomic level in implicit solvent. After tuning of a single parameter in the energy function, FMAPB2 predicts well the B₂ values for lysozyme and other proteins over wide ranges of solvent conditions (salt concentration, pH, and temperature). The method is available as a web server at http://pipe.rcc.fsu.edu/fmapb2 .

Influence of solvent quality on conformations of crowded polymers

The structure and function of polymers in confined environments, e.g., biopolymers in the cytoplasm of a cell, are strongly affected by macromolecular crowding. To explore the influence of solvent quality on conformations of crowded polymers, we model polymers as penetrable ellipsoids, whose shape fluctuations are governed by the statistics of self-avoiding walks, appropriate for a polymer in a good solvent. Within this coarse-grained model, we perform Monte Carlo simulations of mixtures of polymers and hard-nanosphere crowders, including trial changes in polymer size and shape. Penetration of polymers by crowders is incorporated via a free energy cost predicted by polymer field theory. To analyze the impact of crowding on polymer conformations in different solvents, we compute the average polymer shape distributions, radius of gyration, volume, and asphericity over ranges of the polymer-to-crowder size ratio and crowder volume fraction. The simulation results are accurately predicted by a free-volume theory of polymer crowding. Comparison of results for polymers in good and theta solvents indicates that excluded-volume interactions between polymer segments significantly affect crowding, especially in the limit of crowders much smaller than polymers. Our approach may help to motivate future experimental studies of polymers in crowded environments, with possible relevance for drug delivery and gene therapy.

Phase behaviour of colloidal superballs mixed with non-adsorbing polymers

Inspired by experimental work on colloidal cuboid-polymer dispersions (Rossi et al., Soft Matter, 7, 4139 (2011)) we have theoretically studied the phase behaviour of such mixtures. To that end, free volume theory (FVT) was applied to predict the phase behaviour of mixtures of superballs and non-adsorbing polymer chains in a common solvent. Closed expressions for the thermodynamic properties of a suspension of hard colloidal superballs have been derived, accounting for fluid (F), face-centred cubic (FCC) and simple cubic (SC) phase states. Even though the considered solid phases are approximate, the hard superballs phase diagram semi-quantitatively matches with more evolved methods. The theory developed for the cuboid-polymer mixture reveals a rich phase behaviour, which includes not only isostructural F₁-F₂ coexistence, but also SC₁-SC₂ coexistence, several triple coexistences, and even a quadruple-phase coexistence region (F₁-F₂-SC-FCC). The model proposed offers a tool to asses the stability of cuboid-polymer mixtures in terms of the colloid-to-polymer size ratio.

Protein Composition Determines the Effect of Crowding on the Properties of Disordered Proteins

Unlike dilute experimental conditions under which biological molecules are typically characterized, the cell interior is crowded by macromolecules, which affects both the thermodynamics and kinetics of in vivo processes. Although the excluded-volume effects of macromolecular crowding are expected to cause compaction of unfolded and disordered proteins, the extent of this effect is uncertain. We use a coarse-grained model to represent proteins with varying sequence content and directly observe changes in chain dimensions in the presence of purely repulsive spherical crowders. We find that the extent of crowding-induced compaction is dependent not only on crowder size and concentration, but also on the properties of the protein itself. In fact, we observe a nonmonotonic trend between the dimensions of the polypeptide chain in bulk and the degree of compaction: the most extended chains experience up to 24% compaction, the most compact chains show virtually no change, and intermediate chains compress by up to 40% in size at a 40% crowder volume fraction. Free-volume theory combined with an impenetrable ellipsoidal representation of the chains predicts the crowding effects only for collapsed protein chains. An additional scaling factor, which can be easily computed from protein-crowder potential of mean force, corrects for the penetrability of extended chains and is sufficient to capture the observed nonmonotonic trend in compaction.

Structural relaxation and diffusion in a model colloid-polymer mixture: dynamical density functional theory and simulation

Within the Asakura-Oosawa model, we study structural relaxation in mixtures of colloids and polymers subject to Brownian motion in the overdamped limit. We obtain the time evolution of the self and distinct parts of the van Hove distribution function G(r,t) by means of dynamical density functional theory (DDFT) using an accurate free-energy functional based on Rosenfeld's fundamental measure theory. In order to remove unphysical interactions within the self part, we extend the recently proposed quenched functional framework (Stopper et al 2015 J. Chem. Phys. 143 181105) toward mixtures. In addition, we obtain results for the long-time self diffusion coefficients of colloids and polymers from dynamic Monte Carlo simulations, which we incorporate into the DDFT. From the resulting DDFT equations we calculate G(r, t), which we find to agree very well with our simulations. In particular, we examine the influence of polymers which are slow relative to the colloids-a scenario for which both DDFT and simulation show a significant peak forming at r  =  0 in the colloid-colloid distribution function, akin to experimental findings involving gelation of colloidal suspensions. Moreover, we observe that, in the presence of slow polymers, the long-time self diffusivity of the colloids displays a maximum at an intermediate colloid packing fraction. This behavior is captured by a simple semi-empirical formula, which provides an excellent description of the data.

Using depletion to control colloidal crystal assemblies of hard cuboctahedra

Depletion interactions arise from entropic forces, and their ability to induce aggregation and even ordering of colloidal particles through self-assembly is well established, especially for spherical colloids. We vary the size and concentration of penetrable hard sphere depletants in a system of cuboctahedra, and we show how depletion changes the preferential facet alignment of the colloids and thereby selects different crystal structures. Moreover, we explain the cuboctahedra phase behavior using perturbative free energy calculations. We find that cuboctahedra can form a stable simple cubic phase, and, remarkably, that the stability of this phase can be rationalized only by considering the effects of both the colloid and depletant entropy. We corroborate our results by analyzing how the depletant concentration and size affect the emergent directional entropic forces and hence the effective particle shape. We propose the use of depletants as a means of easily changing the effective shape of self-assembling anisotropic colloids.

Influence of polymer shape on depletion potentials and crowding in colloid-polymer mixtures

Depletion-induced interactions between colloids in colloid-polymer mixtures depend in range and strength on size, shape, and concentration of depletants. Crowding by colloids in turn affects shapes of polymer coils, such as biopolymers in biological cells. By simulating hard-sphere colloids and random-walk polymers, modeled as fluctuating ellipsoids, we compute depletion-induced potentials and polymer shape distributions. Comparing results with exact density-functional theory calculations, molecular simulations, and experiments, we show that polymer shape fluctuations play an important role in depletion and crowding phenomena.

Entropic forces stabilize diverse emergent structures in colloidal membranes

The depletion interaction mediated by non-adsorbing polymers promotes condensation and assembly of repulsive colloidal particles into diverse higher-order structures and materials. One example, with particularly rich emergent behaviors, is the formation of two-dimensional colloidal membranes from a suspension of filamentous fd viruses, which act as rods with effective repulsive interactions, and dextran, which acts as a condensing, depletion-inducing agent. Colloidal membranes exhibit chiral twist even when the constituent virus mixture lacks macroscopic chirality, change from a circular shape to a striking starfish shape upon changing the chirality of constituent rods, and partially coalesce via domain walls through which the viruses twist by 180°. We formulate an entropically-motivated theory that can quantitatively explain these experimental structures and measurements, both previously published and newly performed, over a wide range of experimental conditions. Our results elucidate how entropy alone, manifested through the viruses as Frank elastic energy and through the depletants as an effective surface tension, drives the formation and behavior of these diverse structures. Our generalizable principles propose the existence of analogous effects in molecular membranes and can be exploited in the design of reconfigurable colloidal structures.

Scaled-particle theory analysis of cylindrical cavities in solution

The solvation of hard spherocylindrical solutes is analyzed within the context of scaled-particle theory, which takes the view that the free energy of solvating an empty cavitylike solute is equal to the pressure-volume work required to inflate a solute from nothing to the desired size and shape within the solvent. Based on our analysis, an end cap approximation is proposed to predict the solvation free energy as a function of the spherocylinder length from knowledge regarding only the solvent density in contact with a spherical solute. The framework developed is applied to extend Reiss's classic implementation of scaled-particle theory and a previously developed revised scaled-particle theory to spherocylindrical solutes. To test the theoretical descriptions developed, molecular simulations of the solvation of infinitely long cylindrical solutes are performed. In hard-sphere solvents classic scaled-particle theory is shown to provide a reasonably accurate description of the solvent contact correlation and resulting solvation free energy per unit length of cylinders, while the revised scaled-particle theory fitted to measured values of the contact correlation provides a quantitative free energy. Applied to the Lennard-Jones solvent at a state-point along the liquid-vapor coexistence curve, however, classic scaled-particle theory fails to correctly capture the dependence of the contact correlation. Revised scaled-particle theory, on the other hand, provides a quantitative description of cylinder solvation in the Lennard-Jones solvent with a fitted interfacial free energy in good agreement with that determined for purely spherical solutes. The breakdown of classical scaled-particle theory does not result from the failure of the end cap approximation, however, but is indicative of neglected higher-order curvature dependences on the solvation free energy.

An FFT-based method for modeling protein folding and binding under crowding: benchmarking on ellipsoidal and all-atom crowders

It is now well recognized that macromolecular crowding can exert significant effects on protein folding and binding stability. In order to calculate such effects in direct simulations of proteins mixed with bystander macromolecules, the latter (referred to as crowders) are usually modeled as spheres and the proteins represented at a coarse-grained level. Our recently developed postprocessing approach allows the proteins to be represented at the all-atom level but, for computational efficiency, has only been implemented for spherical crowders. Modeling crowder molecules in cellular environments and in vitro experiments as spheres may distort their effects on protein stability. Here we present a new method that is capable for treating aspherical crowders. The idea, borrowed from protein-protein docking, is to calculate the excess chemical potential of the proteins in crowded solution by fast Fourier transform (FFT). As the first application, we studied the effects of ellipsoidal crowders on the folding and binding free energies of all-atom proteins, and found, in agreement with previous direct simulations with coarse-grained protein models, that the aspherical crowders exert greater stabilization effects than spherical crowders of the same volume. Moreover, as demonstrated here, the FFT-based method has the important property that its computational cost does not increase strongly even when the level of details in representing the crowders is increased all the way to all-atom, thus significantly accelerating realistic modeling of protein folding and binding in cell-like environments.

Folding free energy surfaces of three small proteins under crowding: validation of the postprocessing method by direct simulation

We have developed a 'postprocessing' method for modeling biochemical processes such as protein folding under crowded conditions (Qin and Zhou 2009 Biophys. J. 97 12-19). In contrast to the direct simulation approach, in which the protein undergoing folding is simulated along with crowders, the postprocessing method requires only the folding simulation without crowders. The influence of the crowders is then obtained by taking conformations from the crowder-free simulation and calculating the free energies of transferring to the crowders. This postprocessing yields the folding free energy surface of the protein under crowding. Here the postprocessing results for the folding of three small proteins under 'repulsive' crowding are validated by those obtained previously by the direct simulation approach (Mittal and Best 2010 Biophys. J. 98 315-20). This validation confirms the accuracy of the postprocessing approach and highlights its distinct advantages in modeling biochemical processes under cell-like crowded conditions, such as enabling an atomistic representation of the test proteins.

Simulation and Modeling of Crowding Effects on the Thermodynamic and Kinetic Properties of Proteins with Atomic Details

Recent experimental studies of protein folding and binding under crowded solutions suggest that crowding agents exert subtle influences on the thermodynamic and kinetic properties of the proteins. While some of the crowding effects can be understood qualitatively from simple models of the proteins, quantitative rationalization of these effects requires an atomistic representation of the protein molecules in modeling their interactions with crowders. A computational approach, known as postprocessing, has opened the door for atomistic modeling of crowding effects. This review summarizes the applications of the postprocessing approach for studying crowding effects on the thermodynamics and kinetics of protein folding, conformational transition, and binding. The integration of atomistic modeling with experiments in crowded solutions promises new insight into biochemical processes in cellular environments.

Crowding of polymer coils and demixing in nanoparticle-polymer mixtures

The Asakura-Oosawa-Vrij (AOV) model of colloid-polymer mixtures idealises nonadsorbing polymers as effective spheres that are fixed in size and impenetrable to hard particles. Real polymer coils, however, are intrinsically polydisperse in size (radius of gyration) and may be penetrated by smaller particles. Crowding by nanoparticles can affect the size distribution of polymer coils, thereby modifying effective depletion interactions and thermodynamic stability. To analyse the influence of crowding on polymer conformations and demixing phase behaviour, we adapt the AOV model to mixtures of nanoparticles and ideal, penetrable polymer coils that can vary in size. We perform Gibbs ensemble Monte Carlo simulations, including trial nanoparticle-polymer overlaps and variations in the radius of gyration. Results are compared with predictions of free-volume theory. Simulation and theory consistently predict that ideal polymers are compressed by nanoparticles, and that compressibility and penetrability stabilise nanoparticle-polymer mixtures.

Structure of colloidal sphere-plate mixtures

In addition to containing spherical pigment particles, coatings usually contain plate-like clay particles. It is thought that these improve the opacity of the paint film by providing an efficient spacing of the pigment particles. This observation is counterintuitive, as suspensions of particles of different shapes and sizes tend to phase separate on increase of concentration. In order to clarify this matter a model colloidal system is studied here, with a sphere-plate diameter ratio similar to that found in paints. For dilute suspensions, small angle neutron scattering revealed that the addition of plates leads to enhanced density fluctuations of the spheres, in agreement with new theoretical predictions. On increasing the total colloid concentration the plates and spheres phase separate due to the disparity in their shape. This is in agreement with previous theoretical and experimental work on colloidal sphere-plate mixtures, where one particle acts as a depleting agent. The fact that no large scale phase separation is observed in coatings is ascribed to dynamic arrest in intimately mixed, or possibly micro-phase separated structures, at elevated concentration.

Tensorial density functional theory for non-spherical hard-body fluids

In a recent publication (Hansen-Goos and Mecke 2009 Phys. Rev. Lett. 102 018302) we constructed a free energy functional for the inhomogeneous hard-body fluid, which reduces to Rosenfeld's fundamental measure theory (Rosenfeld 1989 Phys. Rev. Lett. 63 980) when applied to hard spheres. The new functional is able to yield the isotropic-nematic transition for the hard-spherocylinder fluid in contrast to Rosenfeld's fundamental measure theory for non-spherical particles (Rosenfeld 1994 Phys. Rev. E 50 R3318). The description of inhomogeneous isotropic fluids is also improved when compared with data from Monte Carlo simulations for hard spherocylinders in contact with a planar hard wall. However, the new functional for the inhomogeneous fluid in general does not comply with the exact second order virial expansion. We introduced the ζ correction in order to minimize the deviation from Onsager's exact result in the isotropic bulk fluid. In this article we give a detailed account of the construction of the new functional. An extension of the ζ correction makes the latter better suited for non-isotropic particle distributions. The extended ζ correction is shown to improve the description of the isotropic-nematic bulk phase diagram while it has little effect on the results for the isotropic but inhomogeneous hard-spherocylinder fluid. We argue that the gain from using higher order tensorial weighted densities in the theory is likely to be inferior to the associated increase in complexity.

Effects of macromolecular crowding on protein conformational changes

Many protein functions can be directly linked to conformational changes. Inside cells, the equilibria and transition rates between different conformations may be affected by macromolecular crowding. We have recently developed a new approach for modeling crowding effects, which enables an atomistic representation of “test” proteins. Here this approach is applied to study how crowding affects the equilibria and transition rates between open and closed conformations of seven proteins: yeast protein disulfide isomerase (yPDI), adenylate kinase (AdK), orotidine phosphate decarboxylase (ODCase), Trp repressor (TrpR), hemoglobin, DNA β-glucosyltransferase, and Ap₄A hydrolase. For each protein, molecular dynamics simulations of the open and closed states are separately run. Representative open and closed conformations are then used to calculate the crowding-induced changes in chemical potential for the two states. The difference in chemical-potential change between the two states finally predicts the effects of crowding on the population ratio of the two states. Crowding is found to reduce the open population to various extents. In the presence of crowders with a 15 Å radius and occupying 35% of volume, the open-to-closed population ratios of yPDI, AdK, ODCase and TrpR are reduced by 79%, 78%, 62% and 55%, respectively. The reductions for the remaining three proteins are 20–44%. As expected, the four proteins experiencing the stronger crowding effects are those with larger conformational changes between open and closed states (e.g., as measured by the change in radius of gyration). Larger proteins also tend to experience stronger crowding effects than smaller ones [e.g., comparing yPDI (480 residues) and TrpR (98 residues)]. The potentials of mean force along the open-closed reaction coordinate of apo and ligand-bound ODCase are altered by crowding, suggesting that transition rates are also affected. These quantitative results and qualitative trends will serve as valuable guides for expected crowding effects on protein conformation changes inside cells.

The biophysical properties of proteins inside cells can be expected to be quite different from those typically measured by in vitro experiments in dilute solutions. In particular, intracellular macromolecular crowding may significantly affect the equilibria and transition rates between different conformations of a protein, and hence its functions. What are the trends and magnitudes of such crowding effects? We address this question here by applying a recently developed approach for modeling crowding. Seven proteins, each with structures for both an open state and a closed state, are studied. Crowding exerts significant effects on the open-closed equilibria of four proteins and more modest effects on the remaining three. Potentials of mean force along the open-closed reaction coordinate, and hence transition rates, are similarly affected. The extent of conformational changes is the main determinant for the magnitudes of crowding effects, but the protein size also plays an important role. The effects of crowding become stronger as the protein size increases. Conformational transitions of the ribosome, an extremely large complex, during translation are predicted to experience particularly strong effects of intracellular crowding. We conclude that deduction of intracellular behaviors from in vitro experiments requires explicit consideration of crowding effects.

Generalized fundamental measure theory for atomistic modeling of macromolecular crowding

Macromolecular crowding inside cells affects the thermodynamic and kinetic properties of proteins. The scaled particle theory (SPT) has played an important role toward establishing a qualitative picture for the effects of crowding. However, SPT-based modeling lacks molecular details. Molecular dynamics simulations overcome this limitation, but at great computational cost. Here, we present a theoretical method for modeling crowding at the atomic level. The method makes it possible to achieve exhaustive conformational sampling in modeling crowding effects and to tackle challenges posed by large protein oligomers and by complex mixtures of crowders.

Fundamental measure theory for hard-sphere mixtures: a review

Hard-sphere systems are one of the fundamental model systems of statistical physics and represent an important reference system for molecular or colloidal systems with soft repulsive or attractive interactions in addition to hard-core repulsion at short distances. Density functional theory for classical systems, as one of the core theoretical approaches of statistical physics of fluids and solids, has to be able to treat such an important system successfully and accurately. Fundamental measure theory is up to date the most successful and most accurate density functional theory for hard-sphere mixtures. Since its introduction fundamental measure theory has been applied to many problems, tested against computer simulations, and further developed in many respects. The literature on fundamental measure theory is already large and is growing fast. This review aims to provide a starting point for readers new to fundamental measure theory and an overview of important developments.

Phase behaviour of a dispersion of charge-stabilised colloidal spheres with added non-adsorbing interacting polymer chains

We present a theory for the phase behaviour of mixtures of charge-stabilised colloidal spheres plus interacting polymer chains in good and theta -solvents within the framework of free-volume theory. We use simple but accurate combination rules for the depletion thickness around a colloidal particle and for the osmotic pressure up to the semi-dilute concentration regime. Hence, we obtain expressions for the free energy for mixtures of charged colloidal particles and non-adsorbing interacting polymers. From that, we calculate the phase behaviour, and discuss its topology in dependence on the competition between the charge-induced repulsion and the polymer-induced attraction. The homogeneous mixture of colloids and polymers becomes more stabilised against demixing when increasing the electrostatic repulsion. This charge-induced stabilisation is strongest for small polymer-to-colloid size ratios and is more pronounced for charged colloids mixed with polymers in a good solvent than for polymers in a theta -solvent. For the weakly charged regime we find that the phase diagram becomes salt-concentration-independent in the protein limit for charged colloids plus polymers in a theta -solvent. The liquid window, i.e., the concentration regimes where a colloidal liquid exists, is narrowed down upon increasing the charge-induced repulsion. Also this effect is more pronounced when charged colloids are mixed with polymer chains in a good solvent. In summary, we demonstrate that the solvent quality significantly influences the phase behaviour of mixtures of charged colloids plus non-adsorbing polymers if the range of the screened electrostatic repulsion becomes of the order of the range of the depletion-induced attraction.