Theory for weakly polydisperse cytoskeleton filaments

The ability of actins and tubulins to change dynamically from alterations in the number density of actins/tubulin, number density and type of binding agents, and electrolyte concentration is crucial for eukaryotic cells to regulate their cytoskeleton conformations in different cellular compartments. Conventional approaches on biopolymers solution break down for cytoskeleton filaments because they entail several approximations to treat their polyelectrolyte and mechanical properties. In this article, we introduce a novel density functional theory for polydisperse, semiflexible cytoskeleton filaments. The approach accounts for the equilibrium polymerization kinetics, length, and orientation filament distributions, as well as the electrostatic interaction between filaments and the electrolyte. This is essential for cytoskeleton polymerization in different cell compartments generating filaments of different lengths, sometimes long enough to become semiflexible. We characterized the thermodynamics properties of actin filaments in electrolyte aqueous solutions. We calculated the free energy, pressure, chemical potential, and second virial coefficient for each filament conformation. We also calculated the phase diagram of actin filaments solution and compared it with available experimental data.

Cross Second Virial Coefficient of the H2O–CO System from a New Ab Initio Pair Potential

The cross second virial coefficient $$B_{12}$$ B 12 for the interaction between water (H2O) and carbon monoxide (CO) was obtained with low uncertainty at temperatures from 200 K to 2000 K employing a new intermolecular potential energy surface (PES) for the H2O–CO system. This PES was fitted to interaction energies determined for about 58 000 H2O–CO configurations using high-level quantum-chemical ab initio methods up to coupled cluster with single, double, and perturbative triple excitations [CCSD(T)]. The cross second virial coefficient $$B_{12}$$ B 12 was extracted from the PES using a semiclassical approach. An accurate correlation of the calculated $$B_{12}$$ B 12 values was used to determine the dilute gas cross isothermal Joule–Thomson coefficient, $$\phi _{12}=B_{12}-T(\mathrm {d}B_{12}/\mathrm {d}T)$$ ϕ 12 = B 12 - T ( d B 12 / d T ) . The predicted values for both $$B_{12}$$ B 12 and $$\phi _{12}$$ ϕ 12 agree reasonably well with the few existing experimental data and older calculated values and should be the most accurate estimates of these quantities to date.

Extended law of corresponding states: square-well oblates

The vapour-liquid coexistence collapse in the reduced temperature, Tr=T/Tc, reduced density, ρr= ρ/ρc, plane is known as a principle of corresponding states, and Noro and Frenkel have extended it for pair potentials of variable range. Here, we provide a theoretical basis supporting this extension and show that it can also be applied to short-range pair potentials where both repulsive and attractive parts can be anisotropic. We observe that the binodals of oblate hard ellipsoids for a given aspect ratio (κ=1/3) with varying short-range square-well interactions collapse into a single master curve in the Δ B*2--ρr plane, where Δ B*2= (B2(T)-B*2(Tc))/v0, B2 is the second virial coefficient, and v0 is the volume of the hard body. This finding is confirmed by both REMC simulation and second virial perturbation theory for varying square-well shells, mimicking uniform, equator, and pole attractions. Our simulation results reveal that the extended law of corresponding states is not related to the local structure of the fluid.

Bayesian analysis of static light scattering data for globular proteins

Static light scattering is a popular physical chemistry technique that enables calculation of physical attributes such as the radius of gyration and the second virial coefficient for a macromolecule (e.g., a polymer or a protein) in solution. The second virial coefficient is a physical quantity that characterizes the magnitude and sign of pairwise interactions between particles, and hence is related to aggregation propensity, a property of considerable scientific and practical interest. Estimating the second virial coefficient from experimental data is challenging due both to the degree of precision required and the complexity of the error structure involved. In contrast to conventional approaches based on heuristic ordinary least squares estimates, Bayesian inference for the second virial coefficient allows explicit modeling of error processes, incorporation of prior information, and the ability to directly test competing physical models. Here, we introduce a fully Bayesian model for static light scattering experiments on small-particle systems, with joint inference for concentration, index of refraction, oligomer size, and the second virial coefficient. We apply our proposed model to study the aggregation behavior of hen egg-white lysozyme and human γS-crystallin using in-house experimental data. Based on these observations, we also perform a simulation study on the primary drivers of uncertainty in this family of experiments, showing in particular the potential for improved monitoring and control of concentration to aid inference.

Mean-field theory of the interaction of the magnesium ion with biopolymers: the case of lysozyme

A statistical theory is presented of the magnesium ion interacting with lysozyme under conditions where the latter is positively charged. Temporarily assuming magnesium is not noncovalently bound to the protein, I solve the nonlinear Poisson–Boltzmann equation accurately and uniformly in a perturbative fashion. The resulting expression for the effective charge, which is larger than nominal owing to overshooting, is subtle and cannot be asymptotically expanded at high ionic strengths that are practical. An adhesive potential taken from earlier work together with the assumption of possibly bound magnesium is then fitted to be in accord with measurements of the second virial coefficient by Tessier et al. The resulting numbers of bound magnesium ions as a function of MgBr$$_2$$ 2 concentration are entirely reasonable compared with densitometry measurements.

Unusual Lower Critical Solution Temperature Phase Behavior of Poly(benzyl methacrylate) in a Pyrrolidinium-Based Ionic Liquid

Polymer/ionic liquid systems are being increasingly explored, yet those exhibiting lower critical solution temperature (LCST) phase behavior remain poorly understood. Poly(benzyl methacrylate) in certain ionic liquids constitute unusual LCST systems, in that the second virial coefficient (A2) in dilute solutions has recently been shown to be positive, indicative of good solvent behavior, even above phase separation temperatures, where A2 < 0 is expected. In this work, we describe the LCST phase behavior of poly(benzyl methacrylate) in 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide for three different molecular weights (32, 63, and 76 kg/mol) in concentrated solutions (5–40% by weight). Turbidimetry measurements reveal a strong concentration dependence to the phase boundaries, yet the molecular weight is shown to have no influence. The critical compositions of these systems are not accessed, and must therefore lie above 40 wt% polymer, far from the values (ca. 10%) anticipated by Flory-Huggins theory. The proximity of the experimental cloud point to the coexistence curve (binodal) and the thermo-reversibility of the phase transitions, are also confirmed at various heating and cooling rates.

Second Virial Coefficient of Low-density Lithium-7 (7Li) Gas in the Temperature Range 1 K40000 K and Beyond

The second virial coefficient B for low-dense 7Lithium (7Li) gas is calculated over a wide temperature range 1 K40000 K. In the ‘high’-T limit (600 K45000 K), the classical coefficient, Bcl, and the contribution of the first quantum-mechanical correction, Bqc, are computed from standard expressions, using a suitable binary potential. The classical coefficient, Bcl, together with the Boyle temperature, TB, are determined and their values are in good agreement with previous results. In addition, the interface between the classical and quantum regimes is systematically investigated. Furthermore, the calculation of the quantum-mechanical second virial coefficient, Bq, is evaluated using the Beth-Uhlenbeck formula in the temperature range 1 K500 K. A positive value of Bq indicates that the net interaction energy is repulsive, implying that the short-range repulsive forces dominate the long-range attractive forces. However, quite the opposite occurs for negative values of Bq, which are indicative of net attractive interaction. The general behavior of Bq is similar to the potential energy itself, such that the long-range attractive and the short-range repulsive potentials can be deduced from the measurements of Bq. Keywords: Second virial coefficient, Low-density Lithium-7 Gas, Short-range repulsive forces, Long-range attractive forces. PACS: 51.30.+i.

On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state.