Excluded Volume Model Research Articles

The effect of Ficoll 70 on thermally-induced and chemically-induced conformational transitions of an RTX protein is quantitatively accounted for by a unified excluded volume model.

A unified excluded volume model based upon the effective hard particle approximation is developed and used to quantitatively model previously published experimental measurements of the effect of adding high concentrations of an "inert" polymer, Ficoll 70, on conformational transitions of the toxin protein RCL that are induced by addition of calcium at constant temperature or by increasing temperature in the absence and presence of high calcium concentrations. The best-fit of this model, which accounts quantitatively for all of the published data to within experimental precision, yields an estimate of the volume of solution excluded to Ficoll by each of four identified conformational states of RCL: H - the most compact conformation adopted in the limits of high calcium concentration and low temperature, H* - the conformation adopted in the limits of high calcium concentration and high temperature, A - the conformation adopted in the limits of low (or no) calcium at low temperature, and A* - the conformation adopted in the limits of low calcium and high temperature. Ficoll exclusion volumes increase in the order H < H* < A < A*. These results are discussed in the context of the physiological functions of the RTX proteins, which are involved in the secretion process and the calcium-induced folding of bacterial virulence factors.

Modeling contractility kit-mediated cytoskeletal network assembly.

The proper function of the cytoskeleton enables mechanoresponsiveness, the ability of cells to sense and respond to mechanical cues. Myosin II, cortexillin I and IQGAP proteins preassemble in the cytoplasm of Dictyostelium cells into contractility kits (CKs). These CKs are thought to play a pivotal role in the regulation and delivery of contractile proteins to sites of mechanical stress. The IQGAPs complementarily regulate the mechanoresponsiveness of cortexillin I-myosin II elements within CKs. Whereas cells that have only IQGAP2 are highly mechanoresponsive, those that have only IQGAP1 are not. Moreover, double mutants lacking both IQGAPs are also mechanoresponsive, suggesting that IQGAP1 serves as an inhibitor of cortexillin I and myosin II, and part of the role of IQGAP2 is to alleviate IQGAP1's inhibition. To investigate the mechanism of CK self-assembly and the possible molecular means for IQGAP regulation, we developed in SpringSaLaD a coarse-grained excluded-volume molecular model in which all protein polymers are represented by nm-sized spheres connected by spring-like links. The model is parameterized using experimentally measured values acquired through fluorescence cross-correlation spectroscopy (FCCS) and fluorescence correlation spectroscopy (FCS), which describe the interaction affinities and diffusion coefficients for individual molecular components. Simulations of the model provided cluster diffusion coefficients, distributions of cluster sizes, cluster component distributions, and IQGAP ratios in the clusters. Simulations of wild-type and null-mutant conditions revealed that the temporal order of assembly of these kits is dominated by myosin II dimer formation and that IQGAP proteins mediate cluster growth. Additionally, our simulations predicted, and FCCS experiments confirmed, the existence of CKs that incorporate both IQGAP1 and IQGAP2. This molecular model serves to describe the formation of CKs and how their assembly enables and regulates mechanoresponsiveness.

Aqueous biphasic systems based on ethyl lactate: Molecular interactions and modelling

Aqueous biphasic systems (ABS) based on ethyl lactate are novel green solvent systems that are biorenewable and biodegradable with the potential to replace currently used hazardous organic solvents. Models to correlate and predict binodal curves of these systems are crucial for the design of separation processes but are currently nonexistent. Here, we report the development of two empirical models based on Merchuk’s equation and the Effective Excluded Volume model for ABS composed of ethyl lactate, water and a salt (K3PO4, K2HPO4, K2CO3, Na3C6H5O7, Na2C4H4O6, Na2C4H4O4, K2S2O3, Na2S2O3 and (NH4)2S2O3). Additionally, the use of Artificial Neural Networks (ANN) as a tool to predict binodal curves was explored. An ANN composed of tansig transfer function and five neurons was built using three inputs: mole fraction of salt, molar Gibbs energy of hydration of the salt cation and anion. Furthermore, Fourier-transform infrared-attenuated total reflection spectroscopy was used to reveal the molecular interactions which were used to explain binodal data.

Simulación de la percolación eléctrica de nanotubos de carbono a través de una matriz de polimetilmetacrilato: análisis bidimensional y tridimensional usando el efecto de la tortuosidad de los nanoaditivos

The present work aims to study the simulation of the electrical percolation of carbon nanotubes (CNTs) in polymethylmethacrylate matrix (PMMA). In order to do this, simulations were employed in two-dimensional and three-dimensional analyses through a program developed by the Monte Carlo method, supported by the excluded volume model in order to analyze the geometric tortuosity in the polymeric matrix. The percolation threshold was analyzed by different aspect ratios, volumetric fractions and conductive load geometries. In the simulations, a decrease in the percolation threshold was observed when the aspect ratio increased and the particles became more tortuous, being these characteristics the parameters to evaluate both two-dimensional and three-dimensional systems. The results show percolation threshold values of 0.625% vol and aspect ratio of 1000 for two-dimensional analyses and, 0.08% vol and aspect ratio of 250 for three-dimensional analyses, being the adequacy to the main models for electrical percolation with tortuosity effect of the nanocarriers proposed by literature.

Mass and Radius Relations of Quarkyonic Stars Using an Excluded-volume Model

Abstract Inspired by the excluded-volume model for isospin symmetric quarkyonic matter of Jeong et al., we construct an excluded-volume model for a charge-neutral quarkyonic phase whose hadronic sector contains only neutrons. We refer to this model as quarkyonic neutron matter. We compute the equation of state for this model and solve the Tolman–Oppenhermer–Volkoff equations to obtain mass and radius relations relevant for neutron stars. The most straightforward extension of the model for symmetric quarkyonic matter of Jeong et al. to quarkyonic neutron matter does not satisfy the mass–radius constraints from neutron star measurements. However, we show that by incorporating appropriate nuclear interactions in the excluded-volume model, one can produce mass–radius relations that lie within the constraints obtained from gravitational waves of binary neutron star mergers and maximum-mass measurements of neutron stars.

Modulation of electrophoresis, electroosmosis and diffusion for electrical transport of proteins through a solid-state nanopore.

Nanopore probing of molecular level transport of proteins is strongly influenced by electrolyte type, concentration, and solution pH. As a result, electrolyte chemistry and applied voltage are critical for protein transport and impact, for example, capture rate (CR), transport mechanism (i.e., electrophoresis, electroosmosis or diffusion), and 3D conformation (e.g., chaotropic vs. kosmotropic effects). In this study, we explored these using 0.5–4 M LiCl and KCl electrolytes with holo-human serum transferrin (hSTf) protein as the model protein in both low (±50 mV) and high (±400 mV) electric field regimes. Unlike in KCl, where events were purely electrophoretic, the transport in LiCl transitioned from electrophoretic to electroosmotic with decreasing salt concentration while intermediate concentrations (i.e., 2 M and 2.5 M) were influenced by diffusion. Segregating diffusion-limited capture rate (Rdiff) into electrophoretic (Rdiff,EP) and electroosmotic (Rdiff,EO) components provided an approach to calculate the zeta-potential of hSTf (ζhSTf) with the aid of CR and zeta potential of the nanopore surface (ζpore) with (ζpore–ζhSTf) governing the transport mechanism. Scrutinization of the conventional excluded volume model revealed its shortcomings in capturing surface contributions and a new model was then developed to fit the translocation characteristics of proteins.

Excluded-volume model for quarkyonic matter. II. Three-flavor shell-like distribution of baryons in phase space

We extend the excluded-volume model of isospin symmetric two-flavor dense quarkyonic matter [Phys. Rev. C 101, 035201 (2020)] including strange particles and address its implications for neutron stars. The effective sizes of baryons are defined from the diverging hard-core potentials in the short interdistance regime. Around the hard-core density, the repulsive core between baryons at short distances leads to a saturation in the number density of baryons and generates perturbative quarks from the lower phase space, which leads to the shell-like distribution of baryons by the Pauli exclusion principle. The strange-quark Fermi sea always appears at high densities but the $\Lambda$ hyperon shell only appears when the effective size of the $\Lambda$ hyperon is smaller than the effective size of nucleons. We find that the pressure of strange quarkyonic matter can be large enough to support neutron stars with two times solar mass and can have a large sound speed, $c_s^2 \simeq 0.7$. The fraction of the baryon number carried by perturbative quarks is about 30% at the inner core of most massive neutron stars.

3-Flavor Extension of the Excluded Volume Model for the Hard-core Repulsion

3-Flavor Extension of the Excluded Volume Model for the Hard-core Repulsion

Finite-temperature quarkyonic matter with an excluded volume model

We introduce a theoretical framework to analyze the thermal properties of a recently proposed “excluded volume” model of quarkyonic matter. This entails proposing finite temperature distribution functions and entropy functionals constrained by internal theoretical consistency. We use the formalism developed here to analyze the effect of temperature on the quark onset as a function of baryon density. We find that the baryon density at which the quarkyonic phase emerges decreases only slightly with temperature, an effect produced by large Nc. We furthermore find that a finite temperature increases the density of quarks produced. The framework presented here can be used to compute the equation of state of hot and dense quarkyonic matter which is of relevance to neutron star mergers.

Bose-Einstein condensation phenomenology in systems with repulsive interactions

The role of repulsive interactions in statistical systems of Bose particles is investigated. Three different phenomenological frameworks are considered: a mean-field model, an excluded volume model, and a model with a medium-dependent effective mass. All three models are tuned to yield similar equations of state, with only minor deviations from the ideal Bose gas at small chemical potentials. Our analysis indicates, however, that these models lead to qualitatively different results for the Bose-Einstein condensation phenomenon. We discuss the different aspects of this phenomenon, namely, an onset of the Bose-Einstein condensation, particle number fluctuations, and a behavior of the Bose condensate. The obtained results can be helpful for interpreting the lattice QCD data at small temperature and large isospin chemical potential and the data on multiple pion production in high-energy nuclear collisions.

Excluded-volume model for quarkyonic matter: Three-flavor baryon-quark mixture

The single-flavor excluded-volume model based on the effective size of baryons reproduces the hard-soft density evolution of the equation of state (EoS) required by the recent studies of GW170817. This phenomenological model basically realizes the concept of quarkyonic matter which is introduced from large-${N}_{c}$ gauge theory for dense matter. Enhanced nucleon interactions and dynamically generated quark degrees of freedom can reproduce the hard-soft evolution of the EoS. In this paper, we extend the excluded-volume model to a three-flavor system by considering electromagnetic charge and possible weak equilibrium in order to obtain a proper description for the hard-soft behavior of the EoS inferred from the gravitational waves observations.

Dynamically generated momentum space shell structure of quarkyonic matter via an excluded volume model

The phase space structure of zero temperature Quarkyonic Matter is a Fermi sphere of Quark Matter, surrounded by a shell of Nucleonic Matter. We construct a quasi particle model of Quarkyonic Matter based on the constituent quark model, where the quark and nucleon masses are related by m_Q = m_N/N_c, and N_c is the number of quark colors. The region of occupied states is for quarks k_Q < k_F/N_c, and for nucleons k_F < k_N < k_F + \Delta. We first consider the general problem of Quarkyonic Matter with hard core nucleon interactions. We then specialize to a quasi-particle model where the hard core nucleon interactions are accounted for by an excluded volume. In this model, we show that the nucleonic shell forms past some critical density related to the hard core size, and for large densities becomes a thin shell. We explore the basic features of such a model, and argue this model has the semi-quantitative behaviour needed to describe neutron stars.

Analytic structure of thermodynamic systems with repulsive interactions

Thermodynamic properties of systems with repulsive interactions, are considered in the grand canonical ensemble. The analytic structure of the excluded-volume model in the complex plane of the system chemical potential (fugacity) is elaborated, based on the fact that the pressure function can be given in terms of the Lambert W-function. Even though the excluded volume model has no phase transitions at real values of the chemical potential, it does exhibit a branch cut singularity in the complex plane, thus limiting the convergence range of the Taylor expansion in the chemical potential. Close similarities to analytic properties of the other models with repulsive interactions, such as a cluster expansion model, the mean-field model, and the ideal Fermi gas model, are pointed out. As an example, repulsive baryonic interactions in a hadron gas, with a focus on the fugacity/virial and Taylor expansion methods used in lattice QCD, are presented. The asymptotic behavior of the Fourier expansion coefficients in these various models suggests that the singular part of net baryonic density can to leading order be universally expressed in terms of polylogarithms.

Hydrodynamic interactions dominate the structure of active swimmers' pair distribution functions.

Microswimmers often exhibit surprising patterns due to the nonequilibrium nature of their dynamics. Collectively, suspensions of microswimmers appear as a liquid whose properties set it apart from its passive counterpart. To understand the impact of hydrodynamic interactions on the basic statistical features of a microswimmer's liquid, we investigate its structure by means of the pair distribution function. We perform particle-based simulations of microswimmers that include steric effects, shape anisotropy, and hydrodynamic interactions. We find that hydrodynamic interactions considerably alter the orientation-dependent pair distribution function compared to purely excluded-volume models like active Brownian particles and generally decrease the structure of the liquid. Depletion regions are dominant at lower filling fractions, while at larger filling fraction, the microswimmer liquid develops a stronger first shell of neighbors in specific directions, while losing structure at larger distances. Our work is a first step toward a statistico-mechanical treatment of the structure of microswimmer suspensions.

Molecular Crowding Tunes Material States of Ribonucleoprotein Condensates.

Ribonucleoprotein (RNP) granules are membraneless liquid condensates that dynamically form, dissolve, and mature into a gel-like state in response to a changing cellular environment. RNP condensation is largely governed by promiscuous attractive inter-chain interactions mediated by low-complexity domains (LCDs). Using an archetypal disordered RNP, fused in sarcoma (FUS), here we study how molecular crowding impacts the RNP liquid condensation. We observe that the liquid–liquid coexistence boundary of FUS is lowered by polymer crowders, consistent with an excluded volume model. With increasing bulk crowder concentration, the RNP partition increases and the diffusion rate decreases in the condensed phase. Furthermore, we show that RNP condensates undergo substantial hardening wherein protein-dense droplets transition from viscous fluid to viscoelastic gel-like states in a crowder concentration-dependent manner. Utilizing two distinct LCDs that broadly represent commonly occurring sequence motifs driving RNP phase transitions, we reveal that the impact of crowding is largely independent of LCD charge and sequence patterns. These results are consistent with a thermodynamic model of crowder-mediated depletion interaction, which suggests that inter-RNP attraction is enhanced by molecular crowding. The depletion force is likely to play a key role in tuning the physical properties of RNP condensates within the crowded cellular space.

Theoretical framework for percolation threshold, tortuosity and transport properties of porous materials containing 3D non-spherical pores

Understanding the effects of porous network characteristics including the percolation and tortuosity on transport properties of porous materials is of great importance for the design and optimization of such materials, e.g., for superior resistance to degradation due to the transfer of corrosive fluids. Meanwhile, the percolation and tortuosity of porous networks are strongly affected by the geometrical shape of pores. In this work, we devise a generic theoretical framework for the accurate predictions of the percolation threshold and tortuosity of porous networks and a variety of transport properties of two-phase porous materials composed of three-dimensional (3D) interpenetrating non-spherical pores randomly distributed in a homogeneous solid matrix. Our framework contains three major components: (1) a coupled scheme of Monte Carlo simulations and a rigorous excluded-volume percolation model for determining of the percolation threshold of porous networks; (2) a continuum percolation-based tortuosity model (CPTM) for deriving the geometrical tortuosity of porous networks near the percolation threshold and above; and (3) a continuum percolation-based generalized effective medium theory (CP-GEMT) for predicting various effective transport properties including the effective diffusivity, permeability, electrical and thermal conductivity of porous materials over the entire range of porosities. The theoretical framework yields accurate predictions of the percolation threshold, tortuosity and various effective transport properties, which are verified and validated using extensive experimental, numerical and analytical data for a wide spectrum of different porous materials reported in literature. Our framework is readily applicable to other non-spherical percolating networks composed of interpenetrating discrete objects like cracks, particles, interfaces, capsules and tunneling networks though 3D spherocylindrical porous networks are used as an introductory example in this work. Finally, we utilize the framework to explore the influences of the pore geometrical configurations on the tortuosity and effective diffusivity of porous materials. The results shed light on the intrinsic and complex interplay of components, structures and transport properties in porous materials, which in turn can provide novel insights for understanding degradation of porous materials in practical applications.

Comparison of the thermal stabilization of proteins by oligosaccharides and monosaccharide mixtures: Measurement and analysis in the context of excluded volume theory

The thermal stability of apo α–lactalbumin (α–LA) and lysozyme was measured in the presence of mixtures of glucose, fructose, and galactose. Mixtures of these monosaccharides in the appropriate stoichiometric ratio were found to have a greater stabilizing effect on each of the two proteins than equal weight/volume concentrations of di- tri- and tetrasaccharides with identical subunit composition (sucrose, trehalose, raffinose, and stachyose). The excluded volume model for the effect of a single saccharide on the stability of a protein previously proposed by Beg et al. [Biochemistry 54 (2015) 3594] was extended to treat the case of saccharide mixtures. The extended model predicts quantitatively the stabilizing effect of all monosaccharide mixtures on α–LA and lysozyme reported here, as well as previously published results obtained for ribonuclease A [Biophys. Chem. 138 (2008) 120] to within experimental uncertainty.

Ab Initio Simulations of Water Dynamics in Aqueous TMAO Solutions: Temperature and Concentration Effects.

We use ab initio molecular dynamics simulation to study the effect of hydrophobic groups on the dynamics of water molecules in aqueous solutions of trimethylamine N-oxide (TMAO). We show that hydrophobic groups induce a moderate (<2-fold) slowdown of water reorientation and hydrogen-bond dynamics in dilute solutions, but that this slowdown rapidly increases with solute concentration. In addition, the slowdown factor is found to vary very little with temperature, thus suggesting an entropic origin. All of these results are in quantitative agreement with prior classical molecular dynamics simulations and with the previously suggested excluded-volume model. The hydrophilic TMAO headgroup is found to affect water dynamics more strongly than the hydrophobic moiety, and the magnitude of this slowdown is very sensitive to the strength of the water-solute hydrogen-bond.

Interfacial Hydration Dynamics in Cationic Micelles Using 2D-IR and NMR.

Using the thiocyanate anion as a vibrational probe chromophore in conjunction with infrared and NMR spectroscopy, we find that SCN- strongly associates with the cationic head group of dodecyltrimethylammonium bromide (DTAB) micelles, both in normal-phase and reverse micelles. In competition with chloride and iodide ions, we find no evidence for displacement of thiocyanate, in accord with the chaotropicity of the Hofmeister ordering, while lending support to a direct interaction picture of its origin. Ultrafast 2D-IR spectroscopy of the SCN- probe in a range of DTAB micelle sizes (w0 = 4 to w0 = 12) shows little if any size dependence on the time scale for spectral diffusion, which is found to be ∼3.5 times slower than in bulk water (both D2O and H2O). Normal-phase micelles studied with 2D-IR exhibit essentially the same spectral dynamics as do reverse micelles, indicating a lack of sensitivity to interfacial curvature. Combined with 1H NMR chemical shift perturbations, we conclude that the SCN- ions tightly associate with the head groups and are partially buried. The 3-4-fold slowdown in spectral diffusion is consistent with the excluded volume model for interfacial perturbation to hydrogen bond reorientation dynamics. On the basis of these observations and comparisons to previous studies of zwitterionic interfaces probed with phosphate transitions, we conclude that the SCN- spectral dynamics in both reverse- and normal-phase micelles is largely dominated by hydration contributions, and offers a promising probe of interfacial hydration at cationic interfaces. Addition of competitive anions alters neither the IR spectra nor the ultrafast dynamics, indicating that SCN- is robustly associated with the head groups.

The pH Dependence of Saccharides' Influence on Thermal Denaturation of Two Model Proteins Supports an Excluded Volume Model for Stabilization Generalized to Allow for Intramolecular Electrostatic Interactions

The reversible thermal denaturation of apo α-lactalbumin (α-LA) and lysozyme was measured in the absence and presence of multiple concentrations of each of seven saccharides (glucose, galactose, fructose, sucrose, trehalose, raffinose, and stachyose) at multiple pH values. It was observed that with increasing pH, the absolute stability of α-LA decreased, whereas the stabilizing effect per mole of all saccharides increased, and that the absolute stability of lysozyme increased, whereas the stabilizing effect per mole of all saccharides decreased. All of the data may be accounted for quantitatively by straightforward electrostatic generalization of a previously introduced coarse-grained model for stabilization of proteins by sugars.