Poly(ethylene glycol)s in Semidilute Regime: Radius of Gyration in the Bulk and Partitioning into a Nanopore.

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 (Rg) over 1-30 wt %. We observed a small but statistically reliable decrease in Rg 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.

Implication of the solvent effect, metal ions and topology in the electronic structure and hydrogen bonding of human telomeric G-quadruplex DNA.

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.

Size-dependent forced PEG partitioning into channels: VDAC, OmpC, and α-hemolysin.

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 ß-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.

X-ray characterization of mesophases of human telomeric G-quadruplexes and other DNA analogues.

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.

DNA Equation of State: In Vitro vs In Viro.

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.

Solvent effects in the helix-coil transition model can explain the unusual biophysics of intrinsically disordered proteins.

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.

Fluctuation mediated interactions due to rigidity mismatch and their effect on miscibility of lipid mixtures in multicomponent membranes.

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.

Electronic structure and partial charge distribution of Doxorubicin in different molecular environments.

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.

Optical properties and electronic transitions of DNA oligonucleotides as a function of composition and stacking sequence.

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.

Determination of the second virial coefficient of bovine serum albumin under varying pH and ionic strength by composition-gradient multi-angle static light scattering.

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.

Continuity of states between the cholesteric → line hexatic transition and the condensation transition in DNA solutions.

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.

Unified description of solvent effects in the helix-coil transition.

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.

Electronic structure, dielectric response, and surface charge distribution of RGD (1FUV) peptide.

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.

Alpha-synuclein lipid-dependent membrane binding and translocation through the α-hemolysin channel.

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 ß-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 ß-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.

Dielectric response variation and the strength of van der Waals interactions.

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.

Kinetics and thermodynamics of binding reactions as exemplified by anthrax toxin channel blockage with a cationic cyclodextrin derivative.

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.

Osmotic Pressure Induced Coupling between Cooperativity and Stability of a Helix-Coil Transition.

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.

Out-of-equilibrium relaxation of the thermal Casimir effect in a model polarizable material.

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.

Salt-dependent DNA-DNA spacings in intact bacteriophage λ reflect relative importance of DNA self-repulsion and bending energies.

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.

Divalent counterion-induced condensation of triple-strand DNA.

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.