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Using two approaches, small-angle neutron scattering (SANS) from bulk solutions and nanopore conductance-fluctuation analysis, we studied structural and dynamic features of poly(ethylene glycol) (PEG) water/salt solutions in the dilute and semidilute regimes. SANS measurements on PEG 3400 at the zero-average contrast yielded the single chain radius of gyration ( R g ) over 1-30 wt %. We observed a small but statistically reliable decrease in R g with increasing PEG concentration: at 30 wt % the chain contracts by a factor of 0.94. Analyzing conductance fluctuations of the α -hemolysin nanopore in the mixtures of PEG 200 with PEG 3400, we demonstrated that polymer partitioning into the nanopore is mostly due to PEG 200. Specifically, for a 1:1 wt/wt mixture the smaller polymer dominates to the extent that only about 1/25 of the nanopore volume is taken by the larger polymer. These findings advance our conceptual and quantitative understanding of nanopore polymer partitioning; they also support the main assumptions of the recent "polymers-pushing-polymers" model., Competing Interests: Notes The authors declare no competing financial interest.

Nonideal polymer mixtures of PEGs of different molecular weights partition differently into nanosize protein channels. Here, we assess the validity of the recently proposed theoretical approach of forced partitioning for three structurally different β-barrel channels: voltage-dependent anion channel from outer mitochondrial membrane VDAC, bacterial porin OmpC (outer membrane protein C), and bacterial channel-forming toxin α-hemolysin. Our interpretation is based on the idea that relatively less-penetrating polymers push the more easily penetrating ones into nanosize channels in excess of their bath concentration. Comparison of the theory with experiments is excellent for VDAC. Polymer partitioning data for the other two channels are consistent with theory if additional assumptions regarding the energy penalty of pore penetration are included. The obtained results demonstrate that the general concept of "polymers pushing polymers" is helpful in understanding and quantification of concrete examples of size-dependent forced partitioning of polymers into protein nanopores.

We present a first-principles density functional study elucidating the effects of solvent, metal ions and topology on the electronic structure and hydrogen bonding of 12 well-designed three dimensional G-quadruplex (G4-DNA) models in different environments. Our study shows that the parallel strand structures are more stable in dry environments and aqueous solutions containing K(+) ions within the tetrad of guanine but conversely, that the anti-parallel structure is more stable in solutions containing the Na(+) ions within the tetrad of guanine. The presence of metal ions within the tetrad of the guanine channel always enhances the stability of the G4-DNA models. The parallel strand structures have larger HOMO-LUMO gaps than antiparallel structures, which are in the range of 0.98 eV to 3.11 eV. Partial charge calculations show that sugar and alkali ions are positively charged whereas nucleobases, PO4 groups and water molecules are all negatively charged. Partial charges on each functional group with different signs and magnitudes contribute differently to the electrostatic interactions involving G4-DNA and favor the parallel structure. A comparative study between specific pairs of different G4-DNA models shows that the Hoogsteen OH and NH hydrogen bonds in the guanine tetrad are significantly influenced by the presence of metal ions and water molecules, collectively affecting the structure and the stability of G4-DNA.

We formulate a continuum approach to the equation of state (density dependence of osmotic pressure) of bulk DNA and encapsidated DNA, as well as review the phase diagram of DNA in the regime of densities relevant for DNA packing in bacteriophages. We derive the first integral of the equilibrium equations that connects the behavior of DNA in the bulk and in nanoscale enclosures, and we delineate the changes wrought upon the mesophase equilibria of encapsidated DNA. We show how multiphase equilibria and complicated spatial distribution of DNA density and orientation can emerge due to the curvature contribution to the DNA osmotic pressure within the capsid.

Observed in the folds of guanine-rich oligonucleotides, non-canonical G-quadruplex structures are based on G-quartets formed by hydrogen bonding and cation-coordination of guanosines. In dilute 5'-guanosine monophosphate (GMP) solutions, G-quartets form by the self-assembly of four GMP nucleotides. We use x-ray diffraction to characterize the columnar liquid-crystalline mesophases in concentrated solutions of various model G-quadruplexes. We then probe the transitions between mesophases by varying the PEG solution osmotic pressure, thus mimicking in vivo molecular crowding conditions. Using the GMP-quadruplex, built by the stacking of G-quartets with no covalent linking between them, as the baseline, we report the liquid-crystalline phase behaviors of two other related G-quadruplexes: (i) the intramolecular parallel-stranded G-quadruplex formed by the 22-mer four-repeat human telomeric sequence AG3(TTAG3)3 and (ii) the intermolecular parallel-stranded G-quadruplex formed by the TG4T oligonucleotides. Finally, we compare the mesophases of the G-quadruplexes, under PEG-induced crowding conditions, with the corresponding mesophases of the canonical duplex and triplex DNA analogues.

We analyze a model statistical description of the polypeptide chain helix-coil transition, where we take into account the specificity of its primary sequence, as quantified by the phase space volume ratio of the number of all accessible states to the number corresponding to a helical conformation. The resulting transition phase diagram is then juxtaposed with the unusual behavior of the secondary structures in Intrinsically Disordered Proteins (IDPs) and a number of similarities are observed, even if the protein folding is a more complex transition than the helix-coil transition. In fact, the deficit in bulky and hydrophobic amino acids observed in IDPs, translated into larger values of phase space volume, allows us to locate the region in parameter space of the helix-coil transition that would correspond to the secondary structure transformations that are intrinsic to conformational transitions in IDPs and that is characterized by a modified phase diagram when compared to globular proteins. Here, we argue how the nature of this modified phase diagram, obtained from a model of the helix-coil transition in a solvent, would illuminate the turned-out response of IDPs to the changes in the environment conditions that follow straightforwardly from the re-entrant (cold denaturation) branch in their folding phase diagram.

We consider how membrane fluctuations can modify the miscibility of lipid mixtures, that is to say how the phase diagram of a boundary-constrained membrane is modified when the membrane is allowed to fluctuate freely in the case of zero surface tension. In order for fluctuations to have an effect, the different lipid types must have differing Gaussian rigidities. We show, somewhat paradoxically, that fluctuation-induced interactions can be treated approximately in a mean-field type theory. Our calculations predict that, depending on the difference in bending and Gaussian rigidity of the lipids, membrane fluctuations can either favor or disfavor mixing.

The electronic structure and partial charge of doxorubicin (DOX) in three different molecular environments-isolated, solvated, and intercalated in a DNA complex-are studied by first-principles density functional methods. It is shown that the addition of solvating water molecules to DOX, together with the proximity to and interaction with DNA, has a significant impact on the electronic structure as well as on the partial charge distribution. Significant improvement in estimating the DOX-DNA interaction energy is achieved. The results are further elucidated by resolving the total density of states and surface charge density into different functional groups. It is concluded that the presence of the solvent and the details of the interaction geometry matter greatly in determining the stability of DOX complexation. Ab initio calculations on realistic models are an important step toward a more accurate description of the long-range interactions in biomolecular systems., (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

The role of base pair composition and stacking sequence in the optical properties and electronic transitions of DNA is of fundamental interest. We present and compare the optical properties of DNA oligonucleotides (AT)10, (AT)5(GC)5, and (AT-GC)5 using both ab initio methods and UV-vis molar absorbance measurements. Our data indicate a strong dependence of both the position and intensity of UV absorbance features on oligonucleotide composition and stacking sequence. The partial densities of states for each oligonucleotide indicate that the valence band edge arises from a feature associated with the PO4(3-) complex anion, and the conduction band edge arises from anti-bonding states in DNA base pairs. The results show a strong correspondence between the ab initio and experimentally determined optical properties. These results highlight the benefit of full spectral analysis of DNA, as opposed to reductive methods that consider only the 260 nm absorbance (A260) or simple purity ratios, such as A260/A230 or A260/A280, and suggest that the slope of the absorption edge onset may provide a useful metric for the degree of base pair stacking in DNA. These insights may prove useful for applications in biology, bioelectronics, and mesoscale self-assembly.

Composition-gradient multi-angle static light scattering (CG-MALS) is an emerging technique for the determination of intermolecular interactions via the second virial coefficient B22. With CG-MALS, detailed studies of the second virial coefficient can be carried out more accurately and effectively than with traditional methods. In addition, automated mixing, delivery and measurement enable high speed, continuous, fluctuation-free sample delivery and accurate results. Using CG-MALS we measure the second virial coefficient of bovine serum albumin (BSA) in aqueous solutions at various values of pH and ionic strength of a univalent salt (NaCl). The systematic variation of the second virial coefficient as a function of pH and NaCl strength reveals the net charge change and the isoelectric point of BSA under different solution conditions. The magnitude of the second virial coefficient decreases to 1.13 x 10(-5) ml*mol/g(2) near the isoelectric point of pH 4.6 and 25 mM NaCl. These results illuminate the role of fundamental long-range electrostatic and van der Waals forces in protein-protein interactions, specifically their dependence on pH and ionic strength.

A new method of finely temperature-tuning osmotic pressure allows one to identify the cholesteric → line hexatic transition of oriented or unoriented long-fragment DNA bundles in monovalent salt solutions as first order, with a small but finite volume discontinuity. This transition is similar to the osmotic pressure-induced expanded → condensed DNA transition in polyvalent salt solutions at small enough polyvalent salt concentrations. Therefore there exists a continuity of states between the two. This finding, together with the corresponding empirical equation of state, effectively relates the phase diagram of DNA solutions for monovalent salts to that for polyvalent salts and sheds some light on the complicated interactions between DNA molecules at high densities.

Long and short range molecular interactions govern molecular recognition and self-assembly of biological macromolecules. Microscopic parameters in the theories of these molecular interactions are either phenomenological or need to be calculated within a microscopic theory. We report a unified methodology for the ab initio quantum mechanical (QM) calculation that yields all the microscopic parameters, namely the partial charges as well as the frequency-dependent dielectric response function, that can then be taken as input for macroscopic theories of electrostatic, polar, and van der Waals-London dispersion intermolecular forces. We apply this methodology to obtain the electronic structure of the cyclic tripeptide RGD-4C (1FUV). This ab initio unified methodology yields the relevant parameters entering the long range interactions of biological macromolecules, providing accurate data for the partial charge distribution and the frequency-dependent dielectric response function of this peptide. These microscopic parameters determine the range and strength of the intricate intermolecular interactions between potential docking sites of the RGD-4C ligand and its integrin receptor.

Small changes in the dielectric response of a material result in substantial variations in the Hamaker coefficient of the van der Waals interactions, as demonstrated in a simplified approximate model as well as a realistic example of amorphous silica with and without an exciton peak. Variation of the dielectric response spectra at one particular frequency influences all terms in the Matsubara summation, making the total change in the Hamaker coefficient depend on the spectral changes not only at that frequency but also at the rest of the spectrum, properly weighted. The Matsubara terms most affected by the addition of a single peak are not those close to the position of the added peak, but are distributed doubly non-locally over the entire range of frequencies. A possibility of eliminating van der Waals interactions or at least drastically reducing them by spectral variation in a narrow regime of frequencies thus seems very remote., (Copyright © 2014. Published by Elsevier Inc.)

Gauging the interactions of a natively unfolded Parkinson disease-related protein, alpha-synuclein (α-syn) with membranes and its pathways between and within cells is important for understanding its pathogenesis. Here, to address these questions, we use a robust β-barrel channel, α-hemolysin, reconstituted into planar lipid bilayers. Transient, ~95% blockage of the channel current by α-syn was observed when 1), α-syn was added from the membrane side where the shorter (stem) part of the channel is exposed; and 2), the applied potential was lower on the side of α-syn addition. While the on-rate of α-syn binding to the channel strongly increased with the applied field, the off-rate displayed a turnover behavior. Statistical analysis suggests that at voltages >50 mV, a significant fraction of the α-syn molecules bound to the channel undergoes subsequent translocation. The observed on-rate varied by >100 times depending on the bilayer lipid composition. Removal of the last 25 amino acids from the highly negatively charged C-terminal of α-syn resulted in a significant decrease in the binding rates. Taken together, these results demonstrate that β-barrel channels may serve as sensitive probes of α-syn interactions with membranes as well as model systems for studies of channel-assisted protein transport., (Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

We analyze the problem of the helix-coil transition in explicit solvents analytically by using spin-based models incorporating two different mechanisms of solvent action: explicit solvent action through the formation of solvent-polymer hydrogen bonds that can compete with the intrinsic intra-polymer hydrogen bonded configurations (competing interactions) and implicit solvent action, where the solvent-polymer interactions tune biopolymer configurations by changing the activity of the solvent (non-competing interactions). The overall spin Hamiltonian is comprised of three terms: the background in vacuo Hamiltonian of the "Generalized Model of Polypeptide Chain" type and two additive terms that account for the two above mechanisms of solvent action. We show that on this level the solvent degrees of freedom can be explicitly and exactly traced over, the ensuing effective partition function combining all the solvent effects in a unified framework. In this way we are able to address helix-coil transitions for polypeptides, proteins, and DNA, with different buffers and different external constraints. Our spin-based effective Hamiltonian is applicable for treatment of such diverse phenomena as cold denaturation, effects of osmotic pressure on the cold and warm denaturation, complicated temperature dependence of the hydrophobic effect as well as providing a conceptual base for understanding the behavior of intrinsically disordered proteins and their analogues.

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.

The thermodynamics of binding reactions is usually studied in the framework of the linear van't Hoff analysis of the temperature dependence of the equilibrium constant. The logarithm of the equilibrium constant is plotted versus inverse temperature to discriminate between two terms: an enthalpic contribution that is linear in the inverse temperature, and a temperature-independent entropic contribution. When we apply this approach to a particular case-blockage of the anthrax PA(63) channel by a multicharged cyclodextrin derivative-we obtain a nearly linear behavior with a slope that is characterized by enthalpy of about 1 kcal/mol. In contrast, from blocker partitioning between the channel and the bulk, we estimate the depth of the potential well for the blocker in the channel to be at least 8 kcal/mol. To understand this apparent discrepancy, we use a simple model of particle interaction with the channel and show that this significant difference between the two estimates is due to the temperature dependence of the physical forces between the blocker and the channel. In particular, we demonstrate that if the major component of blocker-channel interaction is van der Waals interactions and/or Coulomb forces in water, the van't Hoff enthalpy of the binding reaction may be close to zero or even negative, including cases of relatively strong binding. The results are quite general and, therefore, of importance for studies of enzymatic reactions, rational drug design, small-molecule binding to proteins, protein-protein interactions, and protein folding, among others.

Most helix-coil transition theories can be characterized by three parameters: energetic, describing the (free) energy cost of forming a helical state in one repeating unit; entropic, accounting for the decrease of entropy due to formation of the helical state; and geometric, indicating how many repeating units are affected by the formation of one helical state. Depending on their effect on the helix-coil transition, solvents or cosolutes can be classified with respect to their action on these parameters. Solvent interactions that alter the entropic cost of helix formation by their osmotic action can affect both the stability (transition temperature) and the cooperativity (transition interval) of the helix-coil transition. Consistent inclusion of osmotic pressure effects in a description of helix-coil transition, for poly(L-glutamic acid) in solution with polyethylene glycol, can offer an explanation of the experimentally observed linear dependence of transition temperature on osmotic pressure as well as the concurrent changes in the cooperativity of the transition.

Relaxation of the thermal Casimir or van der Waals force (the high temperature limit of the Casimir force) for a model dielectric medium is investigated. We start with a model of interacting polarization fields with a dynamics that leads to a frequency dependent dielectric constant of the Debye form. In the static limit, the usual zero frequency Matsubara mode component of the Casimir force is recovered. We then consider the out-of-equilibrium relaxation of the van der Waals force to its equilibrium value when two initially uncorrelated dielectric bodies are brought into sudden proximity. For the interaction between dielectric slabs, it is found that the spatial dependence of the out-of-equilibrium force is the same as the equilibrium one, but it has a time dependent amplitude, or Hamaker coefficient, which increases in time to its equilibrium value. The final relaxation of the force to its equilibrium value is exponential in systems with a single or finite number of polarization field relaxation times. However, in systems, such as those described by the Havriliak-Negami dielectric constant with a broad distribution of relaxation times, we observe a much slower power law decay to the equilibrium value.

Using solution synchrotron x-ray scattering, we measure the variation of DNA-DNA d spacings in bacteriophage λ with mono-, di-, and polyvalent salt concentrations, for wild-type [48.5×10(3) base pairs (bp)] and short-genome-mutant (37.8 kbp) strains. From the decrease in d spacings with increasing salt, we deduce the relative contributions of DNA self-repulsion and bending to the energetics of packaged phage genomes. We quantify the DNA-DNA interaction energies within the intact phage by combining the measured d spacings in the capsid with measurements of osmotic pressure in DNA assemblies under the same salt conditions in bulk solution. In the commonly used Tris-Mg buffer, the DNA-DNA interaction energies inside the phage capsids are shown to be about 1kT/bp, an order of magnitude larger than the bending energies.

Understanding and manipulation of the forces assembling DNA/RNA helices have broad implications for biology, medicine, and physics. One subject of significance is the attractive force between dsDNA mediated by polycations of valence ≥ 3. Despite extensive studies, the physical origin of the "like-charge attraction" remains unsettled among competing theories. Here we show that triple-strand DNA (tsDNA), a more highly charged helix than dsDNA, is precipitated by alkaline-earth divalent cations that are unable to condense dsDNA. We further show that our observation is general by examining several cations (Mg(2+), Ba(2+), and Ca(2+)) and two distinct tsDNA constructs. Cation-condensed tsDNA forms ordered hexagonal arrays that redissolve upon adding monovalent salts. Forces between tsDNA helices, measured by osmotic stress, follow the form of hydration forces observed with condensed dsDNA. Probing a well-defined system of point-like cations and tsDNAs with more evenly spaced helical charges, the counterintuitive observation that the more highly charged tsDNA (vs. dsDNA) is condensed by cations of lower valence provides new insights into theories of polyelectrolytes and the biological and pathological roles of tsDNA. Cations and tsDNAs also hold promise as a model system for future studies of DNA-DNA interactions and electrostatic interactions in general.

We study the effect of osmotic stress, exerted by salts, on carbohydrate binding to the sugar-specific bacterial channel maltoporin. When the channel is reconstituted into planar lipid bilayers, single events of its occlusion by sugar are seen as transient interruptions in the flow of small ions. We find that, for most salts, changes in the free energy of maltoporin-sugar binding vary linearly with solution osmotic pressure. Such a change in binding with solution osmolarity indicates that for each salt a constant number of salt-excluding water molecules is released upon sugar-maltoporin association at all salt concentrations. We find that larger numbers of water molecules are released upon binding of the cyclic carbohydrate β-cyclodextrin (CD) than upon binding of the corresponding linear homologue maltoheptaose (m7). Remarkably, the extent to which salts affect the binding constants and rates depends sensitively on the type of salt; dehydration in solutions of different anions corresponds to the Hofmeister series. In sodium sulfate solutions, CD and m7 respectively release about 120 and 35 salt-excluding water molecules; in sodium chloride solutions, 35 and 15 waters. No water release is observed with sodium bromide. Finally, by adding adamantane, known to form an inclusion complex with CD, we can infer that CD not only dehydrates but also undergoes a conformational change upon binding to the channel. As a practical outcome, our results also demonstrate how osmotic stress can improve single-molecule detection of different solutes using protein-based nanopores.

Understanding the strength and specificity of interactions among biologically important macromolecules that control cellular functions requires quantitative knowledge of intermolecular forces. Controlled DNA condensation and assembly are particularly critical for biology, with separate repulsive and attractive intermolecular forces determining the extent of DNA compaction. How these forces depend on the charge of the condensing ion has not been determined, but such knowledge is fundamental for understanding the basis of DNA-DNA interactions. Here, we measure DNA force-distance curves for a homologous set of arginine peptides. All forces are well fit as the sum of two exponentials with 2.4- and 4.8-Å decay lengths. The shorter-decay-length force is always repulsive, with an amplitude that varies slightly with length or charge. The longer-decay-length force varies strongly with cation charge, changing from repulsion with Arg¹ to attraction with Arg². Force curves for a series of homologous polyamines and the heterogeneous protein protamine are quite similar, demonstrating the universality of these forces for DNA assembly. Repulsive amplitudes of the shorter-decay-length force are species-dependent but nearly independent of charge within each species. A striking observation was that the attractive force amplitudes for all samples collapse to a single curve, varying linearly with the inverse of the cation charge., (Copyright © 2010 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

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.

Motivated by measurements on stretched double-stranded DNA in the presence of multivalent cations, we develop a statistical mechanical model for the compaction of an insoluble semiflexible polymer under tension. Using a mean-field approach, we determine the order of the extended-to-compact transition and provide an interpretation for the magnitude and interval of tensions over which compaction takes place. In the simplest thermodynamic limit of an infinitely long homogeneous polymer, compaction is a first-order transition that occurs at a single value of tension. For finite length chains or for heterogeneous polymers, the transition progresses over an interval of tension. Our theory provides an interpretation for the result of single-molecule experiments in terms of microscopic parameters such as persistence length and free energy of condensation.

Beyond measurements of equilibria: An alpha-hemolysin nanopore is used as a single-molecule sensor to follow the effects of different salts on the complexation reaction of gamma-cyclodextrin and adamantane carboxylate (see picture). The kinetics underlying the dynamic equilibrium are studied to reveal qualitatively different dynamic actions of various cosolute salts.

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.

Quantum fluctuations create intermolecular forces that pervade macroscopic bodies. At molecular separations of a few nanometres or less, these interactions are the familiar van der Waals forces. However, as recognized in the theories of Casimir, Polder and Lifshitz, at larger distances and between macroscopic condensed media they reveal retardation effects associated with the finite speed of light. Although these long-range forces exist within all matter, only attractive interactions have so far been measured between material bodies. Here we show experimentally that, in accord with theoretical prediction, the sign of the force can be changed from attractive to repulsive by suitable choice of interacting materials immersed in a fluid. The measured repulsive interaction is found to be weaker than the attractive. However, in both cases the magnitude of the force increases with decreasing surface separation. Repulsive Casimir-Lifshitz forces could allow quantum levitation of objects in a fluid and lead to a new class of switchable nanoscale devices with ultra-low static friction.

Recognition of spatially varying optical properties is a necessity when studying the van der Waals-London dispersion (vdW-Ld) interactions of carbon nanotubes (CNTs) that have surfactant coatings, tubes within tubes, andor substantial core sizes. The ideal way to address these radially dependent optical properties would be to have an analytical add-a-layer solution in cylindrical coordinates similar to the one readily available for the plane-plane geometry. However, such a formulation does not exist nor does it appear trivial to be obtained exactly. The best and most pragmatic alternative for end-users is to take the optical spectra of the many components and to use a spectral mixing formulation so as to create effective solid-cylinder spectra for use in the far-limit regime. The near-limit regime at "contact" is dominated by the optical properties of the outermost layer, and thus no spectral mixing is required. Specifically we use a combination of a parallel capacitor in the axial direction and the Bruggeman effective medium in the radial direction. We then analyze the impact of using this mixing formulation upon the effective vdW-Ld spectra and the resulting Hamaker coefficients for small and large diameter single walled CNTs (SWCNTs) in both the near- and far-limit regions. We also test the spectra of a [16,0,s+7,0,s] multiwalled CNT (MWCNT) with an effective MWCNT spectrum created by mixing its [16,0,s] and [7,0,s] SWCNT components to demonstrate nonlinear coupling effects that exist between neighboring layers. Although this paper is primarily on nanotubes, the strategies, implementation, and analysis presented are applicable and likely necessary to any system where one needs to resolve spatially varying optical properties in a particular Lifshitz formulation.

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.

By combining single-molecule magnetic tweezers and osmotic stress on DNA assemblies, we separate attractive and repulsive components of the total intermolecular interaction between multivalent cation condensed DNA. Based on measurements of several different cations, we identify two invariant properties of multivalent cation-mediated DNA interactions: repulsive forces decay exponentially with a 2.3 +/- 0.1 A characteristic decay length and the attractive component of the free energy is always 2.3 +/- 0.2 times larger than the repulsive component of the free energy at force-balance equilibrium. These empirical constraints are not consistent with current theories that attribute DNA-DNA attractions to a correlated lattice of counterions. The empirical constraints are consistent with theories for Debye-Hückel interactions between helical line charges and with the order-parameter formalism for hydration forces. Each of these theories posits exponentially decaying attractions and, if we assume this form, our measurements indicate a cation-independent, 4.8 +/- 0.5 A characteristic decay length for intermolecular attractions between condensed DNA molecules.

Interactions governing protein folding, stability, recognition, and activity are mediated by hydration. Here, we use small-angle neutron scattering coupled with osmotic stress to investigate the hydration of two proteins, lysozyme and guanylate kinase (GK), in the presence of solutes. By taking advantage of the neutron contrast variation that occurs upon addition of these solutes, the number of protein-associated (solute-excluded) water molecules can be estimated from changes in both the zero-angle scattering intensity and the radius of gyration. Poly(ethylene glycol) exclusion varies with molecular weight. This sensitivity can be exploited to probe structural features such as the large internal GK cavity. For GK, small-angle neutron scattering is complemented by isothermal titration calorimetry with osmotic stress to also measure hydration changes accompanying ligand binding. These results provide a framework for studying other biomolecular systems and assemblies using neutron scattering together with osmotic stress.

Recent work has shown that pressures inside dsDNA phage capsids can be as high as many tens of atmospheres; it is this pressure that is responsible for initiation of the delivery of phage genomes to host cells. The forces driving ejection of the genome have been shown to decrease monotonically as ejection proceeds, and hence to be strongly dependent on the genome length. Here we investigate the effects of ambient salts on the pressures inside phage-lambda, for the cases of mono-, di-, and tetravalent cations, and measure how the extent of ejection against a fixed osmotic pressure (mimicking the bacterial cytoplasm) varies with cation concentration. We find, for example, that the ejection fraction is halved in 30 mM Mg(2+) and is decreased by a factor of 10 upon addition of 1 mM spermine. These effects are calculated from a simple model of genome packaging, using DNA-DNA repulsion energies as determined independently from x-ray diffraction measurements on bulk DNA solutions. By comparing the measured ejection fractions with values implied from the bulk DNA solution data, we predict that the bending energy makes the d-spacings inside the capsid larger than those for bulk DNA at the same osmotic pressure.

Lipid suspensions in aqueous solutions most often form multilamellar vesicles of uniformly spaced bilayers. Interlamellar spacing is determined by the balance of attractive van der Waals (charge fluctuation) and repulsive forces. This balance of forces, as well as membrane elasticity, can be probed by applied osmotic stress. We describe how osmotic stress can be imposed on multilamellar lipid samples to study lipid interactions.

We propose a model for the liquid-liquid (L(alpha)-->L(alpha(') )) phase transition observed in osmotic pressure measurements of certain charged lamellae-forming amphiphiles. The model free energy combines mean-field electrostatic and phenomenological nonelectrostatic interactions, while the number of dissociated counterions is treated as a variable degree of freedom that is determined self-consistently. The model, therefore, joins two well-known theories: the Poisson-Boltzmann theory for ionic solutions between charged lamellae and the Langmuir-Frumkin-Davies adsorption isotherm modified to account for charged adsorbing species. Minimizing the appropriate free energy for each interlamellar spacing, we find the ionic density profiles and the resulting osmotic pressure. While in the simple Poisson-Boltzmann theory the osmotic pressure isotherms are always smooth, we observe a discontinuous liquid-liquid phase transition when the Poisson-Boltzmann theory is self-consistently augmented by the Langmuir-Frumkin-Davies adsorption. This phase transition depends on the area per amphiphilic head group, as well as on nonelectrostatic interactions of the counterions with the lamellae and interactions between counterion-bound and counterion-dissociated surfactants. Coupling the lateral phase transition in the bilayer plane with electrostatic interactions in the bulk, our results offer a qualitative explanation for the existence of the L(alpha)-->L(alpha(') ) phase transition of didodecyldimethylammonium bromide (DDABr), but the transition's apparent absence for the chloride and the iodide homologs. More quantitative comparisons with experiment require better understanding of the microscopic basis of the phenomenological model parameters.

The simplest, single-component biological membrane challenges accepted models of macromolecular interactions: lipid lamellar phases swell when immersed in monovalent salt solutions. Moreover, typical of a Hofmeister series, Br salts swell multilayers more than Cl salts, offering an excellent opportunity to investigate long-standing questions of ionic specificity. In accord with earlier measurements of liposome mobilities in electric fields, we find an added electrostatic repulsion of membranes due to anion binding, with a much stronger Br binding compared with Cl. However, contrary to the expectation that electrostatic repulsion should vanish in high salinity, swelling of lipid multilayers is monotonic with increasing salt concentration for both Br and Cl salts. The apparent contradiction is resolved by recognizing that although the electrostatic repulsion is progressively screened by increasing salt concentration, so is the van der Waals (vdW) attraction. Negligible in low salt, weakening of vdW forces becomes significant by the time electrostatic forces vanish. The result is a smooth monotonic swelling curve with no apparent distinction between low and high salt concentration regimes. Furthermore, when compared with theoretical predictions, measured vdW forces decay much too slowly with added salt. However, by accounting for the recently measured salt deficit near lipid bilayers, the expected scaling with Debye screening length is recovered. The combination of ion-specific binding and nonspecific ionic screening of low-frequency fluctuations explains salt effects on lipid membrane interactions and, by extension, explains specific (Hofmeister) effects at macromolecular interfaces between low and high dielectric.

Critical to biological processes such as membrane fusion and secretion, ion-lipid interactions at the membrane-water interface still raise many unanswered questions. Using reconstituted phosphatidylcholine membranes, we confirm here that multilamellar vesicles swell in salt solutions, a direct indication that salt modifies the interactions between neighboring membranes. By varying sample histories, and by comparing with data from ion carrier-containing bilayers, we eliminate the possibility that swelling is an equilibration artifact. Although both attractive and repulsive forces could be modified by salt, we show experimentally that swelling is driven primarily by weakening of the van der Waals attraction. To isolate the effect of salt on van der Waals interactions, we focus on high salt concentrations at which any possible electrostatic interactions are screened. By analysis of X-ray diffraction data, we show that salt does not alter membrane structure or bending rigidity, eliminating the possibility that repulsive fluctuation forces change with salt. By measuring changes in interbilayer separation with applied osmotic stress, we have determined, using the standard paradigm for bilayer interactions, that 1 M concentrations of KBr or KCl decrease the van der Waals strength by 50%. By weakening van der Waals attractions, salt increases energy barriers to membrane contact, possibly affecting cellular communication and biological signaling.

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.

Expected from theory and simulations, depletion of ions at fuzzy biomembrane interfaces has long eluded experiments. Here, we show how salt exclusion can be accurately measured by surprisingly simple yet accurate benchtop measurements. Multilamellar aggregates of common phospholipids sink in low salt but float in salt solutions that are much less dense than the lipid itself. By manipulating bath and lipid densities, using heavy water and varied lipid chain length, we obtain accurate exclusion curves over a wide range of KCl and KBr concentrations. While maintaining a constant width at low salt, the exclusion layer decreases in high salt, following the Debye screening length. Consistent with interfacial accumulation of polarizable ions, bromide salts are less excluded than chloride, with an attraction of approximately 2kBT per Br- ion. So far neglected in theoretical descriptions, the competition between salt exclusion and binding is critical to understanding membrane interactions and specific ionic effects.

The distance dependence for the preferential exclusion of several salts and neutral solutes from hydroxypropyl cellulose (HPC) has been measured via the effect of these small molecules on the thermodynamic forces between HPC polymers in ordered arrays. The concentration of salts and neutral solutes decreases exponentially as the spacing between apposing nonpolar HPC surfaces decreases. For all solutes, the spatial decay lengths of this exclusion are remarkably similar to those observed between many macromolecules at close spacings where intermolecular forces have been ascribed to the energetics of water structuring. Exclusion magnitudes depend strongly on the nature and size of the particular salt or solute; for the three potassium salts studied, exclusion follows the anionic Hofmeister series. The change in the number of excess waters associated with HPC polymers is independent of solute concentration suggesting that the dominating interactions are between solutes and the hydrated polymer. These findings further confirm the importance of solvation interactions and reveal an unexpected unity of Hofmeister effects, preferential hydration, and hydration forces.

Using microcalorimetry, we follow changes in the association free energy of beta-cyclodextrin (CD) with the hydrophobic part of adamantane carboxylate (AD) due to added salt or polar (net-neutral) solutes that are excluded from the molecular interacting surfaces. Changes in binding constants with solution osmotic pressure (water activity) translate into changes in the preferential hydration upon complex formation. We find that these changes correspond to a release of 15-25 solute-excluding waters upon CD/AD association. Reflecting the preferential interaction of solute with reactants versus products, we find that changes in hydration depend on the type of solute used. All solutes used here result in a large change in the enthalpy of the CD-AD binding reaction. In one class of solutes, the corresponding entropy change is much smaller, while in the other class, the entropy change almost fully compensates the solute-specific enthalpy. For many of the solutes, the number of waters released correlates well with their effect on air-water surface tensions. We corroborate these results using vapor pressure osmometry to probe individually the hydration of reactants and products of association, and we discuss the possible interactions and forces between cosolute and hydrophobic surfaces responsible for different kinds of solute exclusion.

We propose and test a pair potential that is accurate at all relevant distances and simple enough for use in large-scale computer simulations. A combination of the Rydberg potential from spectroscopy and the London inverse-sixth-power energy, the proposed form fits spectroscopically determined potentials better than the Morse, Varnshi, and Hulburt-Hirschfelder potentials and much better than the Lennard-Jones and harmonic potentials. At long distances, it goes smoothly to the London force appropriate for gases and preserves van der Waals's "continuity of the gas and liquid states," which is routinely violated by coefficients assigned to the Lennard-Jones 6-12 form., ((c) 2004 American Institute of Physics.)

Driven by conditions set by smaller solutes, proteins fold and unfold. Experimentally, these conditions are stated as intensive variables--pH and other chemical potentials--as though small solutes were infinite resources that come at an externally varied free energy cost. Computationally, the finite spaces of simulation allow only fixed numbers of these solutes. By combining the analytic Gibbs adsorption isotherm with the computational Monte Carlo sampling of polymer configurations, we have been able to overcome an inherent limitation of computer simulation. The idea is to compute analytically the free energy changes wrought by solutes on each particular configuration. Then numerical computation is needed only to sample the set of configurations as efficiently as when no bathing solute is present. For illustration, the procedure is applied to an idealized two-dimensional heteropolymer to yield lessons about the effect of cosolutes on protein stability., (Copyright 2004 Wiley-Liss, Inc.)

We formulate and evaluate the van der Waals part of the free energy due to a dielectric profile that varies continuously throughout the space between two interacting bodies. Not considering the work needed to create the inhomogeneous dielectric profile, focusing only on that part of the free energy affected by the inhomogeneity, we compare the ensuing interaction free energy with that of the original Lifshitz formulation with its step function changes at material boundaries and uniform dielectric medium. Rather than the monotonically varying attraction between like bodies given by the original formulation, the inhomogeneous continuous dielectric function leads to attractions as well as repulsions. The Lifshitz result emerges naturally in the limit of separations much larger than the thickness of the interfaces.

Using x-ray diffraction and NMR spectroscopy, we present structural and material properties of phosphatidylserine (PS) bilayers that may account for the well documented implications of PS headgroups in cell activity. At 30 degrees C, the 18-carbon monounsaturated DOPS in the fluid state has a cross-sectional area of 65.3 A(2) which is remarkably smaller than the area 72.5 A(2) of the DOPC analog, despite the extra electrostatic repulsion expected for charged PS headgroups. Similarly, at 20 degrees C, the 14-carbon disaturated DMPS in the gel phase has an area of 40.8 A(2) vs. 48.1 A(2) for DMPC. This condensation of area suggests an extra attractive interaction, perhaps hydrogen bonding, between PS headgroups. Unlike zwitterionic lipids, stacks of PS bilayers swell indefinitely as water is added. Data obtained for osmotic pressure versus interbilayer water spacing for fluid phase DOPS are well fit by electrostatic interactions calculated for the Gouy-Chapman regime. It is shown that the electrostatic interactions completely dominate the fluctuational pressure. Nevertheless, the x-ray data definitively exhibit the effects of fluctuations in fluid phase DOPS. From our measurements of fluctuations, we obtain the product of the bilayer bending modulus K(C) and the smectic compression modulus B. At the same interbilayer separation, the interbilayer fluctuations are smaller in DOPS than for DOPC, showing that B and/or K(C) are larger. Complementing the x-ray data, (31)P-chemical shift anisotropy measured by NMR suggest that the DOPS headgroups are less sensitive to osmotic pressure than DOPC headgroups, which is consistent with a larger K(C) in DOPS. Quadrupolar splittings for D(2)O decay less rapidly with increasing water content for DOPS than for DOPC, indicating greater perturbation of interlamellar water and suggesting a greater interlamellar hydration force in DOPS. Our comparisons between bilayers of PS and PC lipids with the same chains and the same temperature enable us to focus on the effects of these headgroups on bilayer properties.

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., (Copyright 2004 American Institute of Physics)