A hard sphere model for single-file water transport across biological membranes.

We use Gürsey's statistical mechanics of a one-dimensional fluid to find a formula for the ratio in the transport of hard spheres across a membrane through a narrow channel that can accommodate molecular movement only in single file. is the membrane permeability for osmotic flow and the permeability for exchange across the membrane in the absence of osmotic flow. The deviation of the ratio from unity indicates the degree of cooperative transport relative to ordinary diffusion of independent molecules.

The physical basis of osmosis.

Osmosis is an important force in all living organisms, yet the molecular basis of osmosis is widely misunderstood as arising from diffusion of water across a membrane separating solutions of differing osmolarities, and hence different water concentrations. In 1923, Peter Debye proposed a physical model for a semipermeable membrane emphasizing the repulsive forces between solute molecules and membrane that prevent the solute from entering the membrane. His work was hardly noticed at the time and slipped out of view.

Editorial on Special Issue "New Era in the Volume Phase Transition of Gels".

The Special Issue of gels titled "Advancements in Gel Science" has been published from MDPI in 2019 [...

On the thermodynamic stability of bubbles, immiscible droplets, and cavities.

Nanobubbles filled with air or a variety of pure gases are observed to persist in bulk water for weeks and months. Nanoemulsions consisting of oil droplets in water are also remarkably stable against coagulation, with lifetimes up to weeks even if not coated with surfactants. The inverse system of nanodroplets of water in oil is also accessible for study and application.

Construction of a Universal Gel Model with Volume Phase Transition.

The physical principle underlying the familiar condensation transition from vapor to liquid is the competition between the energetic tendency to condense owing to attractive forces among molecules of the fluid and the entropic tendency to disperse toward the maximum volume available as limited only by the walls of the container. Van der Waals incorporated this principle into his equation of state and was thus able to explain the discontinuous nature of condensation as the result of instability of intermediate states. The volume phase transition of gels, also discontinuous in its sharpest manifestation, can be understood similarly, as a competition between net free energy attraction of polymer segments and purely entropic dissolution into a maximum allowed volume.

Universal McMillan-Mayer van der Waals Langevin Gel.

We present a theory for a universal gel based on a McMillan-Mayer treatment of a solute-solvent fluid as a generalization of the universal van der Waals equation of state for a pure liquid/vapor system. The elastic resilience of the networked gel is modeled by a universal Langevin function. This combination of van der Waals interactions and nonlinear Langevin elasticity produces an abrupt onset of large-amplitude density fluctuations deep in the interior of the gel at a critical temperature.

Condensation of Counterions Gives Rise to Contraction Transitions in a One-Dimensional Polyelectrolyte Gel.

The equilibrium volume of a polyelectrolyte gel results from a balance between the tendency to swell caused by outbound polymer/counterion diffusion along with Coulomb interactions on the one hand; and, on the other, the elastic resilience of the cross-linked polymer network. Direct Coulomb forces contribute both to non-ideality of the equilibrated Donnan osmotic pressure, but also to stretching of the network. To isolate the effect of polyelectrolyte expansion, we have analyzed a "one-dimensional" version of a gel, a linear chain of charged beads connected by Hooke's law springs.

A bead-spring chain as a one-dimensional polyelectrolyte gel.

The physical principles underlying expansion of a single-chain polyelectrolyte coil caused by Coulomb repulsions among its ionized groups, and the expansion of a cross-linked polyelectrolyte gel, are probably the same. In this paper, we analyze a "one-dimensional" version of a gel, namely, a linear chain of charged beads connected by Hooke's law springs. In the Debye-Hückel range of relatively weak Coulomb strength, where counterion condensation does not occur, the springs are realistically stretched on a nanolength scale by the repulsive interactions among the beads, if we use a spring constant normalized by the inverse square of the solvent Bjerrum length.

Predicting Salt Permeability Coefficients in Highly Swollen, Highly Charged Ion Exchange Membranes.

This study presents a framework for predicting salt permeability coefficients in ion exchange membranes in contact with an aqueous salt solution. The model, based on the solution-diffusion mechanism, was tested using experimental salt permeability data for a series of commercial ion exchange membranes. Equilibrium salt partition coefficients were calculated using a thermodynamic framework (i.

An ionic-chemical-mechanical model for muscle contraction.

The dynamic process underlying muscle contraction is the parallel sliding of thin actin filaments along an immobile thick myosin fiber powered by oar-like movements of protruding myosin cross bridges (myosin heads). The free energy for functioning of the myosin nanomotor comes from the hydrolysis of ATP bound to the myosin heads. The unit step of translational movement is based on a mechanical-chemical cycle involving ATP binding to myosin, hydrolysis of the bound ATP with ultimate release of the hydrolysis products, stress-generating conformational changes in the myosin cross bridge, and relief of built-up stress in the myosin power stroke.

Partitioning of mobile ions between ion exchange polymers and aqueous salt solutions: importance of counter-ion condensation.

Equilibrium partitioning of ions between a membrane and a contiguous external solution strongly influences transport properties of polymeric membranes used for water purification and energy generation applications. This study presents a theoretical framework to quantitatively predict ion sorption from aqueous electrolytes (e.g.

The energy of naturally curved elastic rods with an application to the stretching and contraction of a free helical spring as a model for DNA.

We give a contemporary and direct derivation of a classical, but insufficiently familiar, result in the theory of linear elasticity-a representation for the energy of a stressed elastic rod with central axis that intrinsically takes the shape of a general space curve. We show that the geometric torsion of the space curve, while playing a crucial role in the bending energy, is physically unrelated to the elastic twist. We prove that the twist energy vanishes in the lowest-energy states of a rod subject to constraints that do not restrict the twist.

The response of DNA length and twist to changes in ionic strength.

We examine twist-stretch coupling of unconstrained DNA using polyelectrolyte theory as applied to a line-charge model along with published data on the ionic-strength dependence of the twist angle. We conclude that twist-stretch coupling is negative: environmental changes that stretch free DNA, unconstrained by externally applied pulling or twisting forces, are accompanied by unwinding of the double helix. We also analyze a helical model and conclude that the observed unwinding of the DNA helix when ionic strength is decreased is driven by radial swelling of the helix.

Lamellar cationic lipid-DNA complexes from lipids with a strong preference for planar geometry: A Minimal Electrostatic Model.

We formulate and analyze a minimal model, based on condensation theory, of the lamellar cationic lipid (CL)-DNA complex of alternately charged lipid bilayers and DNA monolayers in a salt solution. Each lipid bilayer, composed by a random mixture of cationic and neutral lipids, is assumed to be a rigid uniformly charged plane. Each DNA monolayer, located between two lipid bilayers, is formed by the same number of parallel DNAs with a uniform separation distance.

Excess counterion condensation on polyelectrolyte kinks and branch points and the interaction of skewed charged lines.

We have developed explicit formulas for the excess number of counterions condensed on kinked and intersecting charged lines caused by the more intense electric field in the neighborhood of the kink or intersection. As expected, the number of additionally bound counterions is greater for more pronounced kinks, and also increases with the number of lines that intersect at a common point. We have also analyzed the electrostatic interaction potential as a function of distance between two charged lines in skewed orientation.

Theoretical assessment of the oligolysine model for ionic interactions in protein-DNA complexes.

The observed salt dependence of charged ligand binding to polyelectrolytes, such as proteins to DNA or antithrombin to heparin, is often interpreted by means of the "oligolysine model." We review this model as derived entirely within the framework of the counterion condensation theory of polyelectrolytes with no introduction of outside assumptions. We update its comparison with experimental data on the structurally simple systems for which it was originally intended.

The interaction between a charged wall and its counterions: a condensation theory.

We use the theory of counterion condensation to calculate the potential of mean force between a charged planar wall and an oppositely charged ion of unsigned valence Z. We find two solutions to this problem, an outer potential when the Z-ion is relatively far from the wall and an inner one when it is relatively close. There is a discontinuous upward jump from one to the other branch, as the Z-ion approaches the wall.

On the apparent saturation of the dipole induced in a rodlike polyion at high electric fields.

It has been inferred from electric birefringence and electric dichroism data that the field-induced dipole moment on charged rodlike particles saturates at higher field strengths. We give theoretical justification for this interpretation of the data. We calculate the threshold field marking the onset of saturation and compare the result with measured values.

Counterion condensation on charged spheres, cylinders, and planes.

We use the framework of counterion condensation theory, in which deviations from linear electrostatics are ascribed to charge renormalization caused by collapse of counterions from the ion atmosphere, to explore the possibility of condensation on charged spheres, cylinders, and planes immersed in dilute solutions of simple salt. In the limit of zero concentration of salt, we obtain Zimm-Le Bret behavior: a sphere condenses none of its counterions regardless of surface charge density, a cylinder with charge density above a threshold value condenses a fraction of its counterions, and a plane of any charge density condenses all of its counterions. The response in dilute but nonzero salt concentrations is different.

The persistence length of DNA is reached from the persistence length of its null isomer through an internal electrostatic stretching force.

To understand better the effect of electrostatics on the rigidity of the DNA double helix, we define DNA*, the null isomer of DNA, as the hypothetical structure that would result from DNA if its phosphate groups were not ionized. For the purposes of theoretical analysis, we model DNA* as identical to ordinary DNA but supplemented by a longitudinal compression force equal in magnitude but oppositely directed to the stretching (tension) force on DNA caused by phosphate-phosphate repulsions. The null isomer DNA* then becomes an elastically buckled form of fully ionized DNA.

The contribution of transient counterion imbalances to DNA bending fluctuations.

A two-sided model for DNA is employed to analyze fluctuations of the spatial distribution of condensed counterions and the effect of these fluctuations on transient bending. We analyze two classes of fluctuations. In the first, the number of condensed counterions on one side of the DNA remains at its average value, while on the other side, counterions are lost to bulk solution or gained from it.

Positively charged surfaces increase the flexibility of DNA.

Many proteins "bind" DNA through positively charged amino acids on their surfaces. However, to overcome significant energetic and topological obstacles, proteins that bend or package DNA might also modulate the stiffness that is generated by repulsions between phosphates within DNA. Much previous work describes how ions change the flexibility of DNA in solution, but when considering macromolecules such as chromatin in which the DNA contacts the nucleosome core each turn of the double helix, it may be more appropriate to assess the flexibility of DNA on charged surfaces.

Is a small number of charge neutralizations sufficient to bend nucleosome core DNA onto its superhelical ramp?

X-ray diffraction structures of the nucleosome core particle along with a variety of experiments are consistent with the idea that an important source of the free energy holding DNA to the superhelical ramp on the histone octamer surface is obtained from a relatively small amount of electrostatic neutralization of the DNA phosphate charge by positively charged histone groups, especially arginine residues. Here we present a theoretical analysis of a simple model that emphasizes the competition between the high degree of bending of the stiff DNA molecule required for its tight curvature on the histone octamer and the neutralization of the DNA phosphate charge by basic histone residues. Our calculation accounts for the strong influence of condensed counterions on the electrostatic interactions.

Comments on selected aspects of nucleic acid electrostatics.

Recent experimental, theoretical, and computational developments in the field of nucleic acid electrostatics have brought interesting concepts to the fore. The phosphate charge on the double helix apparently influences its structure. When the charge is neutralized asymmetrically, the resulting force imbalance drives bending toward the neutralized side.