Polymers pushing Polymers: Polymer Mixtures in Thermodynamic Equilibrium with a Pore.

We investigate polymer partitioning from polymer mixtures into nanometer size cavities by formulating an equation of state for a binary polymer mixture assuming that only one (smaller) of the two polymer components can penetrate the cavity. Deriving the partitioning equilibrium equations and solving them numerically allows us to introduce the concept of "polymers-pushing-polymers" for the action of non-penetrating polymers on the partitioning of the penetrating polymers. Polymer partitioning into a pore even within a very simple model of a binary polymer mixture is shown to depend in a complicated way on the composition of the polymer mixture and/or the pore-penetration penalty. This can lead to enhanced as well as diminished partitioning, due to two separate energy scales that we analyse in detail.

Optically anisotropic infinite cylinder above an optically anisotropic half space: Dispersion interaction of a single-walled carbon nanotube with a substrate.

A complete form of the van der Waals dispersion interaction between an infinitely long anisotropic semiconducting/insulating thin cylinder and an anisotropic half space is derived for all separations between the cylinder and the half space. The derivation proceeds from the theory of dispersion interactions between two anisotropic infinite half spaces as formulated in Phys. Rev. A 71, 042102 (2005). The approach is valid in the retarded as well as nonretarded regimes of the interaction and is coupled with the recently evaluated ab initio dielectric response functions of various semiconducting/insulating single wall carbon nanotubes, enables the authors to evaluate the strength of the van der Waals dispersion interaction for all orientation angles and separations between a thin cylindrical nanotube and the half space. The possibility of repulsive and/or nonmonotonic dispersion interactions is examined in detail.

A phenomenological one-parameter equation of state for osmotic pressures of PEG and other neutral flexible polymers in good solvents.

We present a phenomenological one-parameter scaling equation of state that accurately represents osmotic pressures of neutral flexible polymers in good solvents from the dilute through the semidilute regime. The equation comprises a sum of scaled van't Hoff and des Cloizeaux terms including a fitted parameter alpha, the "crossover index", which encapsulates all chemical specificity and determines the relevant prefactors. Strikingly different values of alpha are found for the two very different systems poly(ethyleneglycol)/water (PEG) and poly(alpha-methylstyrene)/toluene (PAMS). Alpha-dependent rescaling collapses both data sets to a simple one-parameter scaling function. The fact that the anomalous system PEG/water and the canonical system PAMS/toluene can both be described by the same equation of state attests to the robustness of the polymer-scaling concepts introduced by de Gennes.

Packing nanomechanics of viral genomes.

We investigate the osmotic equilibrium between a bulk polyethylene glycol (PEG) solution and DNA tightly packed in a spherical capsid. We base our analysis on the equations of thermodynamic equilibrium in terms of osmotic pressure. The equality between external osmotic pressure of PEG and osmotic pressure of tightly packed DNA gives us the DNA encapsidation curves. In this way we directly connect the wealth of existing osmotic pressure data for DNA in the bulk with the DNA encapsidation curves within small viral capsids. Specific calculations are made for a monovalent salt, Na(+) -DNA and a divalent salt, Mn(2+) -DNA that have quite different DNA encapsidation behaviors. The main conclusion of our work is that bending energy of DNA is of minor importance regarding the encapsidated DNA length, but has a non-negligible influence on the density distribution of DNA within the capsid.

Nonadditivity in van der Waals interactions within multilayers.

Working at the macroscopic continuum level, we investigate effective van der Waals interactions between two layers within a multilayer assembly. By comparing the pair interactions between two layers with effective pair interactions within an assembly we assess the significant consequences of nonadditivity of van der Waals interactions. This allows us to evaluate the best numerical estimate to date for the Hamaker coefficient of van der Waals interactions in lipid-water multilamellar systems.

van der Waals interactions across stratified media.

Working at the Lifshitz level, we investigate the van der Waals interactions across a series of layers with a periodic motif. We derive the complete form of the van der Waals interaction as an explicit function of the number of periodic layers. We then compare our result with an approximation based on an anisotropic-continuum representation of the stratified medium. Satisfactory agreement between discrete-layer and continuum models is reached only for thicknesses of ten or more layers.

Osmotic properties of DNA: critical evaluation of counterion condensation theory.

The osmotic coefficient of B-DNA in water may, in dilute solutions, deviate by as much as 100% from predictions based on a simple line-charge "counterion condensation" theory. In contrast, a cell model description of the ionic atmosphere near a cylindrical polyelectrolyte predicts osmotic properties that are in surprisingly good harmony with all available experimental findings over a wide range of DNA concentrations. We argue that the neglect of molecular features, such as finite radius, makes line-charge condensation theory inapplicable at all but impractically low polyelectrolyte concentrations.

The entropically favored osmotic "compression" of sickle cell hemoglobin gels.

Contrary to the accurate, hard-sphere depiction of monomeric hemoglobin in solution, sickle cell hemoglobin (HbS) polymerization/gelation requires attention to molecular interactions. From the temperature dependence of the osmotic compressibility of HbS gels, we were able to extract the entropy increase for concentrating HbS in this phase. Normalized per mole of water removed, the entropy increase from gel compression DeltaS(gel) is four times the previously measured DeltaS(trans), for the transition from monomeric HbS solution to HbS gel. The positive entropy change cannot emerge from the assembly of hard spheres but can indicate remodeling of HbS fibers driven by release of ordered water. The fourfold difference in DeltaS(gel) and DeltaS(trans) suggests that the act of initial fiber/gel formation from monomeric solution differs from the process of further polymerization due to tighter packing within the gel phase.

Intracellular osmotic action.

Water often acts as a critical reactant in cellular reactions. Its role can be detected by modulating water activity with osmotic agents. We describe the principles behind this 'osmotic stress' strategy, and survey the ubiquity of water effects on molecular structures that have aqueous, solute-excluding regions. These effects are seen with single-functioning molecules such as membrane channels and solution enzymes, as well as in the molecular assembly of actin, the organization of DNA and the specificity of protein/DNA interactions.

Positive cooperativity without domains or subunits in a monomeric membrane channel.

The monomeric VDAC channel shows an accelerated pH titration of its transport properties with a Hill coefficient of about 2. This manifests itself as a sharp peak in conductance noise as well as a fast change in channel selectivity with pH. On the basis of the known structure of this channel, we propose that this cooperativity arises from a mechanically linked mobile pair of ionizable groups. Concerted movement of these groups between two states changes the distance from nearby electrostatic charge to influence the pK of the groups. This model of pH-dependent motion produces positive cooperative behavior that fits the observations without need for subunits or identifiable domains within the protein. The mathematical formalism has never required such domains, but these are generally considered an essential part of cooperative behavior in proteins. The present proposal reduces the size of a cooperative unit to a minimum, extending the limits of what is perceived to be possible. Together with large-scale conformational transitions, these subtle cooperative structural changes may allow proteins to adapt, with high sensitivity, to changes in their environment. They might also be relatively easy to engineer into a protein.

Osmotic stress, crowding, preferential hydration, and binding: A comparison of perspectives.

There has been much confusion recently about the relative merits of different approaches, osmotic stress, preferential interaction, and crowding, to describe the indirect effect of solutes on macromolecular conformations and reactions. To strengthen all interpretations of measurements and to forestall further unnecessary conceptual or linguistic confusion, we show here how the different perspectives all can be reconciled. Our approach is through the Gibbs-Duhem relation, the universal constraint on the number of ways it is possible to change the temperature, pressure, and chemical potentials of the several components in any thermodynamically defined system. From this general Gibbs-Duhem equation, it is possible to see the equivalence of the different perspectives and even to show the precise identity of the more specialized equations that the different approaches use.

Membrane surface-charge titration probed by gramicidin A channel conductance.

We manipulate lipid bilayer surface charge and gauge its influence on gramicidin A channel conductance by two strategies: titration of the lipid charge through bulk solution pH and dilution of a charged lipid by neutral. Using diphytanoyl phosphatidylserine (PS) bilayers with CsCl aqueous solutions, we show that the effects of lipid charge titration on channel conductance are masked 1) by conductance saturation with Cs+ ions in the neutral pH range and 2) by increased proton concentration when the bathing solution pH is less than 3. A smeared charge model permits us to separate different contributions to the channel conductance and to introduce a new method for "bilayer pKa" determination. We use the Gouy-Chapman expression for the charged surface potential to obtain equilibria of protons and cations with lipid charges. To calculate cation concentration at the channel mouth, we compare different models for the ion distribution, exact and linearized forms of the planar Poisson-Boltzmann equation, as well as the construction of a "Gibbs dividing surface" between salt bath and charged membrane. All approximations yield the intrinsic pKain of PS lipid in 0.1 M CsCl to be in the range 2.5-3.0. By diluting PS surface charge at a fixed pH with admixed neutral diphytanoyl phosphatidylcholine (PC), we obtain a conductance decrease in magnitude greater than expected from the electrostatic model. This observation is in accord with the different conductance saturation values for PS and PC lipids reported earlier (, Biochim. Biophys. Acta. 552:369-378) and verified in the present work for solvent-free membranes. In addition to electrostatic effects of surface charge, gramicidin A channel conductance is also influenced by lipid-dependent structural factors.

DNA--DNA interactions.

The forces that govern DNA double helix organization are being finally systematically measured. The non-specific longer-range interactions--such as electrostatic interactions, hydration, and fluctuation forces--that treat DNA as a featureless rod are reasonably well recognized. Recently, specific interactions--such as those controlled by condensing agents or those consequent to helical structure-are beginning to be recognized, quantified and tested.

Lipid packing stress and polypeptide aggregation: alamethicin channel probed by proton titration of lipid charge.

Lipid membranes are not passive, neutral scaffolds to hold membrane proteins. In order to examine the influence of lipid packing energetics on ion channel expression, we study the relative probabilities of alamethicin channel formation in dioleoylphosphatidylserine (DOPS) bilayers as a function of pH. The rationale for this strategy is our earlier finding that the higher-conductance states, corresponding to larger polypeptide aggregates, are more likely to occur in the presence of lipids prone to hexagonal HII-phase formation (specifically DOPE), than in the presence of lamellar L alpha-forming lipids (DOPC). In low ionic strength NaCl solutions at neutral pH, the open channel in DOPS membranes spends most of its time in states of lower conductance and resembles alamethicin channels in DOPC; at lower pH, where the lipid polar groups are neutralized, the channel probability distribution resembles that in DOPE. X-Ray diffraction studies on DOPS show a progressive decrease in the intrinsic curvature of the constituent monolayers as well as a decreased probability of HII-phase formation when the charged lipid fraction is increased. We explore how proton titration of DOPS affects lipid packing energetics, and how these energetics couple titration to channel formation.

Raman spectral evidence for hydration forces between collagen triple helices.

Hydration forces are thought to result from the energetic cost of water rearrangement near macromolecular surfaces. Raman spectra, collected on the same collagen samples on which these forces were measured, reveal a continuous change in water hydrogen-bonding structure as a function of separation between collagen triple helices. The varying spectral parameters track the force-distance curve. The energetic cost of water "restructuring," estimated from the spectra, is consistent with the measured energy of intermolecular interaction. These correlations support the idea that the change in water structure underlies the exponentially varying forces seen in this system at least over the 13-18-A range of interaxial separations.

On a possible microscopic mechanism underlying the vapor pressure paradox.

We investigate the free energy and the profile of the displacement field in a stack of sterically interacting smectic multilayers bounded by surfaces under tension. We show that this tension can lead to a significant change in the multilayer free energy. It creates an additional long-range attraction (a pseudo-Casimir attraction) of the van der Waals type and leads to a perturbation in the spatial profile of the displacement field fluctuations. This perturbation can extend to macroscopic distances into the multilayer, away from the perturbing surfaces. The lowering of the free energy of the layers varies explicitly as an inverse power of the thickness of the stack, but also depends implicitly on the bare interactions between the smectic layers. One may regard this lowered energy as being due to a kind of mechanical van der Waals force. We investigate in detail the characteristics and magnitude of the free energy as well as the fluctuations in the displacement field for some typical situations of underlying interlamellar interactions.

Solvent hydrogen-bond network in protein self-assembly: solvation of collagen triple helices in nonaqueous solvents.

Forces between type I collagen triple helices are studied in solvents of varying hydrogen-bonding ability. The swelling of collagen fibers in reconstituted films is controlled by the concentration of soluble polymers that are excluded from the fibers and that compete osmotically with collagen for available solvent. The interaxial spacing between the triple helices as a function of the polymer concentration is measured by x-ray diffraction. Exponential-like changes in the spacing with increasing osmotic stress, qualitatively similar to the forces previously found in aqueous solution, are also seen in formamide and ethylene glycol. These are solvents that, like water, are capable of forming three-dimensional hydrogen-bond networks. In solvents that either cannot form a network or have a greatly impaired ability to form a hydrogen-bonded network, strikingly different behavior is observed. A hard-wall repulsion is seen with collagen solvated by ethanol, 2-propanol, and N,N-dimethylformamide. The spacing between helices hardly changes with increasing polymer concentration until the stress exceeds some threshold where removal of the solvent becomes energetically favorable. No solvation of collagen is observed in dimethoxyethane. In solvents with an intermediate ability to form hydrogen-bonded networks, methanol, 2-methoxyethanol, or N-methylformamide, the change in spacing with polymer concentration is intermediate between exponential-like and hard-wall. These results provide direct evidence that the exponential repulsion observed between collagen helices at 0-8-A surface separations in water is due to the energetic cost associated with perturbing the hydrogen-bonded network of solvent molecules between the collagen surfaces.

Bond orientational order, molecular motion, and free energy of high-density DNA mesophases.

By equilibrating condensed DNA arrays against reservoirs of known osmotic stress and examining them with several structural probes, it has been possible to achieve a detailed thermodynamic and structural characterization of the change between two distinct regions on the liquid-crystalline phase diagram: (i) a higher density hexagonally packed region with long-range bond orientational order in the plane perpendicular to the average molecular direction and (ii) a lower density cholesteric region with fluid-like positional order. X-ray scattering on highly ordered DNA arrays at high density and with the helical axis oriented parallel to the incoming beam showed a sixfold azimuthal modulation of the first-order diffraction peak that reflects the macroscopic bond-orientational order. Transition to the less-dense cholesteric phase through osmotically controlled swelling shows the loss of this bond orientational order, which had been expected from the change in optical birefringence patterns and which is consistent with a rapid onset of molecular positional disorder. This change in order was previously inferred from intermolecular force measurements and is now confirmed by 31P NMR. Controlled reversible swelling and compaction under osmotic stress, spanning a range of densities between approximately 120 mg/ml to approximately 600 mg/ml, allow measurement of the free-energy changes throughout each phase and at the phase transition, essential information for theories of liquid-crystalline states.

Watching molecules crowd: DNA double helices under osmotic stress.

Simultaneous measurements on the packing and energetics of high-density liquid crystalline DNA phases show that the crowding of long DNA polyelectrolytes at ever increasing concentrations is accomplished through straightening of the random coils that the double helix assumes in dilute solution. X-ray scattering by ordered phases reveals that the local straightening of the molecules is also accompanied by their progressive immobilization and confinement within the molecular 'cages' created by neighboring molecules. These effects can be clearly observed through the measured energies of DNA packing under osmotic stress and through the changes in structural and dynamic characteristics of X-ray scattering from DNA in ordered arrays at different concentrations. The character of the confinement of large DNA motions for a wide range of DNA concentrations is dominated by the soft potentials of direct interaction. We do not see the power-law variation of energy vs. volume expected from space-filling fluctuations of molecules that enjoy no interaction except the hard clash of steric repulsion. Rather, in highly concentrated DNA mesophases we see a crowding of molecules through electrostatic or hydration repulsion that confines their movements and positions. This view is based on directly measured packing energies as well as on concurrently measured structural parameters while the DNA double helices are condensed under an externally applied osmotic pressure.

Watching small molecules move: interrogating ionic channels using neutral solutes.

Whether they are small enough to wriggle through the current-carrying part of an ionic channel or big enough to be kept outside and thus able to exert an osmotic stress on the channel space, polymers interact with channels in several instructive ways. The osmotic stress of excluded polymers allows one to measure the number of water molecules that come out of the channel in transitions between various "open" to "closed" states. The loss of osmotic activity, due to the partial or completely unrestricted admission of small polymers becomes a measure of the transfer probabilities of polymers from solution to small cavities; it provides an opportunity to study polymer conformation in a perfectly sieved preparation. Current fluctuations due to the partial blockage by a transient polymer are converted into estimates of times of passage and diffusion constants of polymers in channels. These estimates show how a channel whose functional states last for milliseconds is able to average over the interactions with polymers, interactions that last only microseconds. One sees clearly that in this averaging, the macromolecular channel is large enough to react like a macroscopic object to the chemical potentials of the species that modulate its activity.