Persistence length of dendronized polymers: the self-consistent field theory.

We present numerical results for the thermodynamic rigidity and induced persistence length of dendronized polymers with systematically varied topology of their grafts obtained by the Scheutjens-Fleer self-consistent field method. The results were compared to predictions of an analytical mean-field theory. The two approaches have marked different predictions. In particular, the analytical theory predicts that the induced persistence length and the effective segment aspect ratio of dendronized polymers are increasing functions of the degree of branching of their side chains, whereas numerical calculations provide evidence of the opposite dependences. This discrepancy is argued to be due to the ability of side chains to repartition from the compressed to the dilated regions of a curved bottle brush, which is accounted for by the numerical, but not by the analytical method. The difference is most crucial in the light of the expected ability of dendronized polymers to have a liquid crystalline ordering in semi-dilute solutions.

Dendron brushes and dendronized polymers: a theoretical outlook.

Dendron brushes are molecular structures built up of treelike macromolecules, with multiple generations of branches, grafted with a root segment to a surface (particle) or to a backbone chain (dendronized polymer) with a sufficiently high grafting density so that the dendrons interact laterally. Recent advances in the theory of dendron brushes are highlighted and complemented by insights from numerical self-consistent field modelling. Our focus is on controversial issues, which are still under debate, such as, the strain distribution in individual dendrons and the appearance of distinct populations with a different extent of stretching for dendrons in planar brushes. We anticipate that dendritic brushes (i) show a strong resistance against bending, which may manifest in a high apparent persistence length of dendronized polymers, and (ii) have an unusually large beneficial effect on the colloidal stability due to the sharp steric repulsive interaction observed when these surface layers are pushed towards the overlap.

Effect of Block Copolymer Architecture on Morphology of Self-Assembled Aggregates in Solution.

We predict how equilibrium morphology of self-assembled aggregates in dilute solution could be tuned by replacing a linear AB diblock copolymer by a heteroarm star-like or cyclic block copolymer. We demonstrate that in selective solvent AB miktoarm stars or diblock copolymers with cyclic associating block may give rise to cylindrical assemblies or vesicles, while linear diblock copolymers with same composition form only spherical micelles. The theoretical predictions are in line with experimental observations.

Persistence Length of Dendritic Molecular Brushes.

On the basis of mean-field theory, we predict that molecular brushes with dendritic side chains ("dendronized polymers") may exhibit the behavior of semirigid polymers capable of lyotropic odering. The apparent persistence length of these molecular brushes is governed by the interactions between dendritic grafts and may significantly exceed the characteristic brush thickness. Compared to bottle-brushes with linear grafts, manifestation of the induced rigidity in molecular brushes with dendritic branches is expected at smaller degrees of polymerization of the grafts. Under good solvent conditions, the induced rigidity depends solely on the number of side chain monomers per unit length of backbone and the second virial coeffcient of monomer-monomer interactions, irrespective of graft topology.

Poisson-Boltzmann theory of pH-sensitive (annealing) polyelectrolyte brush.

We present a self-consistent field analytical theory of a polymer brush formed by weakly charged pH-sensitive (annealing) polyelectrolytes tethered to a solid-liquid interface and immersed in buffer solution of low molecular weight salt. We use the Poisson-Boltzmann framework, applied by us previously to polyelectrolyte (PE) brushes with quenched charge (Zhulina, E. B.; Borisov, O. V. J. Chem. Phys. 1997, 107, 5952). This approach allows for detailed analysis of the internal structure of annealing PE brush in terms of polymer density distribution, profiles of electrostatic potential and of local degree of chain ionization as a function of buffer ionic strength and pH without any assumptions on mobile ion distribution imposed in earlier scaling-type models. The presented analytical theory recovers all major asymptotic dependences for average brush properties predicted earlier. In particular, a nonmonotonic dependence of brush thickness on ionic strength and grafting density is confirmed and specified with accuracy of numerical coefficients including crossover regions. Moreover, the theory predicts qualitatively new effects, such as, e.g., disproportionation of tethered polyions into weakly charged concentrated proximal and strongly charged sparse distal brush domains at low salt and moderate grating densities. The presented results allow us to quantify responsive features of annealing PE brushes whose large-scale and local conformational properties can be manipulated by external stimuli.

Monte carlo simulations of tau proteins: effect of phosphorylation.

We perform Monte Carlo simulations of tau proteins bound to a cylinder that mimics a microtubule (MT), and then study them in solution. Tau protein binds to a highly anionic MT surface to stabilize the cylindrical structure of MT. The negatively charged tail domain floats away from the anionic MT surface while positively charged tau segments localize near the MT surface. Monte Carlo simulations demonstrate that, in 3RS tau isoform (which has three imperfect repeats (R) short (S) isoform), amino acids are more condensed near a highly charged interface compared to 4RL isoform (which has four imperfect repeats (R) long (L) isoform). In 4RL isoform, amino acids in tail domain stay mostly apart from the MT surface. In the bulk solution, dephosphorylated taus are separated due to Coulomb repulsion between similarly charged isoforms. Moderate phosphorylation of 3RS isoform decreases average intermolecular distance between dephosphorylated and phosphorylated taus and lead to their overlap. Further phosphorylation does not change noticeably the intermolecular distances.

Atomic force microscopy of polymer brushes: colloidal versus sharp tips.

Force versus distance profiles acquired by atomic force microscopy probe the structure and interactions of polymer brushes. An interpretation utilizing the Derjaguin approximation and assuming local compression of the brush is justified when colloidal probes are utilized. The assumptions underlying this approach are not satisfied for sharp tips, and deviations from this model were reported for experiments and simulations. The sharp-tip force law proposed assumes that the free energy penalty of insertion into the brush is due to the osmotic pressure of the unperturbed brush. This static force law is in semiquantitative agreement with the simulation results of Murat and Grest (Murat, M.; Grest, G. S. Macromolecules 1996, 29, 8282).

How the projection domains of NF-L and alpha-internexin determine the conformations of NF-M and NF-H in neurofilaments.

Making use of a numerical self-consistent field method and polymer brush concepts, we model the solvated corona of neurofilaments (NF) composed of projection domains (unstructured tails) of constituent proteins. Projections are modeled with amino acid resolution. We focus on the importance of the two shortest ones (alpha-internexin and NF-L) in regulating the conformations of the two longer ones (NF-M and NF-H) in an isolated NF. We take the wild-type NF with no alpha-internexin as the reference, for which the phosphorylation-induced translocation of M- and H-tails has been examined previously. We demonstrate that a subbrush of L-tails creates an electrostatic potential profile with an approximately parabolic shape. An experimentally relevant (2:1) ratio of L- to alpha-projections reduces the charge density of the L subbrush and shifts the translocation transition of the H-tails to slightly higher degrees of phosphorylation. Replacing all L-tails by alpha-projections destroys the substructure of the NF corona and this alters the NF response to the phosphorylation of long tails.

The polymer brush model of neurofilament projections: effect of protein composition.

Applying self-consistent field theory, we consider a coarse-grained model for the polymerlike projections of neurofilament (NF) proteins that form a brush structure around neurofilaments. We focus on effects of molecular composition, which is the relative occurrence of NF-H, NF-M, and NF-L proteins, on the organization of NF projection domains. We consider NF brushes with selectively truncated projections, and with a varied ratio L:H:M of constituent tails. Our conclusion is that the NF brush structure is remarkably tolerant with respect to the variation in M and H chains. Results compare favorably with experimental data on model animals, provided that due attention is paid on the level of phosphorylation of the KSP repeats.

Effect of the ionic strength and pH on the equilibrium structure of a neurofilament brush.

Using the numerical model of Scheutjens and Fleer, we investigated, on a self-consistent field level, the equilibrium structure of the neurofilament brush formed by projection domains of the constituent NF-H, NF-M, and NF-L proteins. The phosphorylation of such a brush is a major regulatory process that triggers the relocation of the H tails from the NF core to the brush periphery. We explore how the pH and the ionic strength affect the rearrangements in the NF brush structure upon phosphorylation. We demonstrate that the translocation of H tails in an individual NF occurs as a sharp cooperative transition below and up to the physiological salt concentration. Regularities of this process are reminiscent of the collapse-to-stretching transition in a cylindrical polyelectrolyte brush in a poor solvent. The effect of pH at physiological ionic strength is noticeable only in the acidic range and is more pronounced for a dephosphorylated NF.

A self-consistent field analysis of the neurofilament brush with amino-acid resolution.

Using the numerical model of Scheutjens and Fleer we investigated, on a self-consistent field level, the equilibrium structure of the neurofilament brush formed by the projection domains of NF-H, NF-M, and NF-L proteins. Although the actual amino-acid sequences in the projection domains are coarse-grained, the different (realistic) solubilities of amino-acid residues and the specific distribution of its intrinsic charges inside the arms of the NF proteins are taken explicitly into account. We collect strong evidence that the electrostatic interactions are a dominant force that controls the NF brush structure. There exists a remarkable spatial separation of the H, M, and L tails. In a dephosphorylated NF we found confined and flowerlike conformations for the H and M projection domains, respectively. We demonstrate that the ionization of KSP repeats in NF proteins triggers a conformational transition in the H tail that leads to the expulsion of its terminal (KEP) domain to the periphery of the NF brush. We argue that the phosphorylation of the NF proteins in axons can both increase the interfilament distance and stabilize cross bridges between neurofilaments.

Hybridization at a surface: the role of spacers in DNA microarrays.

Flexible spacer chains are utilized to enhance the hybridization of terminally anchored oligonucleotide probes of DNA microarrays. A polymer physics approach identifies an underlying mechanism and yields guidelines for the optimal spacer length in terms of the effect on the equilibrium state. For low grafting densities, the dominant effect arises because of the decimation in the number of accessible chain configurations due to the impenetrable surface. Opposing trends are found for long targets and for short targets. At higher grafting densities, different brush regimes introduce an extra hybridization penalty. A novel brush regime is obtained for long neutral spacers and short targets at intermediate ionic strength where the chain stretching is due to the electrostatic interactions between the probes.

Wetting phase diagrams of a polyacid brush with a triple point.

The (pre)wetting behavior of an annealed polyelectrolyte (PE) brush by an electrolyte solution that is strongly segregated from an apolar phase is analyzed. In this complex interface, there are interactions on various length scales. There are short-range interactions with the (uncharged) surface, and there are interactions on the length scale of the brush height. Using either the ionic strength or the water-surface interaction strength as the control parameters, it is possible to approach and induce a wetting transition in this system. The first-order wetting transition, promoted by favorable short-range substrate interactions with the surface, is in competition with the wetting transition controlled by the detachment of the fluid interface from the periphery of the PE brush. The electric double layer on top of the PE brush contributes with a repulsive forces to the disjoining pressure that tends to thicken the wetting film, and therefore, the transition in all cases is first order. Various phase portraits of the wetting phase diagram are envisioned. One of these features the crossing of two prewetting lines. At the crossing point three surface states coexist. This triple point is analyzed in some detail with the help of a molecular-level self-consistent field model.

Curved polymer and polyelectrolyte brushes beyond the Daoud-Cotton model.

We revise the classical Daoud-Cotton (DC) model to describe conformations of polymer and polyelectrolyte chains end-grafted to convex spherical and cylindrical surfaces. In the framework of the DC model, local stretching of chains in the brush does not depend on the degree of polymerization of grafted chains, and the polymer density profile follows a single-exponent power law. This model, however, does not correspond to a minimum in free energy of the curved brush. The nonlocal (NL) approximation exploited in the present paper implies the minimization of the overall free energy of the brush and predicts that the polymer density profile does not follow a single-exponent power law. In the limit of large surface curvature the NL approximation provides the same scaling laws for brush thickness and free energy as the local DC model. Numerical prefactors are however different. Extra extension of chains in the brush interior region leads to larger equilibrium brush thickness and lower free energy per chain. A significant difference between outcomes of the two models is found for brushes formed by ionic polymers, particularly for weakly dissociating (p H-sensitive) polyelectrolytes at low solution salinity.

Brush effects on DNA chips: thermodynamics, kinetics, and design guidelines.

In biology experiments, oligonucleotide microarrays are contacted with a solution of long nucleic acid targets. The hybridized probes thus carry long tails. When the surface density of the oligonucleotide probes is high enough, the progress of hybridization gives rise to a polyelectrolyte brush due to mutual crowding of the nucleic acid tails. The free-energy penalty associated with the brush modifies both the hybridization isotherms and the rate equations: the attainable hybridization is lowered significantly as is the hybridization rate. When the equilibrium hybridization fraction, x(eq), is low, the hybridization follows a Langmuir type isotherm, x(eq)/(1 - x(eq)) = c(t)K where c(t) is the target concentration and K is the equilibrium constant. K is smaller than its bulk value by a factor (n/N)(2/5) due to wall effects where n and N denote the number of bases in the probe and the target. At higher x(eq), when the brush is formed, the leading correction is x(eq)/(1 - x(eq)) = c(t)K exp - const'x(eq)(2/3) - x(B)(2/3) where x(B) corresponds to the onset of the brush regime. The denaturation rate constant in the two regimes is identical. However, the hybridization rate constant in the brush regime is lower, the leading correction being exp -const' x(2/3) - x(B)(2/3).

Reentrant morphological transitions in copolymer micelles with pH-sensitive corona.

In contrast to self-assembled aggregates of conventional ionic (including polymeric) surfactants the equilibrium micelles of diblock copolymer with a pH-sensitive polyelectrolyte block can exhibit two inverse sequences of morphological transitions triggered by an increase in solution salinity. The direct sequence of the sphere-cylinder-lamella transitions is similar to that for the copolymer with a strongly dissociating ionic block and occurs at a high salt concentration in solution. The abnormal reversed sequence of the lamella-cylinder-sphere transitions is predicted to occur at relatively low ionic strength in solution. The origin of the reentrant transitions is coupling between aggregation and ionization in copolymer micelles.

Sensitivity, specificity, and the hybridization isotherms of DNA chips.

Competitive hybridization, at the surface and in the bulk, lowers the sensitivity of DNA chips. Competitive surface hybridization occurs when different targets can hybridize with the same probe. Competitive bulk hybridization takes place when the targets can hybridize with free complementary chains in the solution. The effects of competitive hybridization on the thermodynamically attainable performance of DNA chips are quantified in terms of the hybridization isotherms of the spots. These relate the equilibrium degree of the hybridization to the bulk composition. The hybridization isotherm emerges as a Langmuir isotherm modified for electrostatic interactions within the probe layer. The sensitivity of the assay in equilibrium is directly related to the slope of the isotherm. A simpler description is possible, in terms of c(50) values specifying the bulk composition corresponding to 50% hybridization at the surface. The effects of competitive hybridization are important for the quantitative analysis of DNA chip results, especially when used to study point mutations.

Annealing polyelectrolytes at charged interfaces.

The conformation of a weakly dissociating (annealing) polyelectrolyte chain end-tethered to a similarly or oppositely charged planar surface is analyzed in the framework of scaling arguments. For a similarly charged interface an analytical model is also utilized. We demonstrate that at low salt concentration in bulk solution there is a strong coupling between the polyelectrolyte conformation and its degree of ionization. In the case of an oppositely charged (adsorbing) surface, adsorption promotes ionization of the annealing polyelectrolyte. As a result, the adsorbed layer thickness decreases as a function of surface charge density more rapidly for an annealing polyelectrolyte than for a quenched one. In the case of a similarly charged (repulsive) surface the chain ionization is suppressed, and the annealing polyelectrolyte chain is less extended than the quenched one. Moreover, an increase in surface charge density leads to non-monotonous extension of the tethered polyelectrolyte.

[The effect of external restrictions on the stability of the globular state]. / Vliianie vneshnikh ogranichenii na stabil'nost' globuliarnogo sostoianiia.

The delta Td changes of heat denaturation temperature for globule proteins were estimated, for a globule inserted into pores of a inert carrier, that limits the conformational set of the denatured chain. Based on calculations for a grated selfintercepted chain in a slit-like pore, with no interactions with the pore walls, functions of delta Td depending on the rigidity of the unfolded chain, its length and pore sizes were determined. For alpha-chymotrypsin in polyacrylamide gels the estimated delta Td was of several degrees. The possible influence of the pore form and intramolecular interactions for a denatured chain on the value of the stabilizing effect is discussed.

[Helix-globule transitions of polypeptides selectively reacting with the interface]. / Perekhody spiral'--klubok v polipeptidakh, izbiratel'no vzaimodeistvuiushchikh s poverkhnost'iu razdela faz.

An analytical theory of helix-coil transitions for polypeptides in a solution near a flat and homogeneous interface is given. The following cases were considered: a) only the helical parts are absorbtively active; b) only the coiled sections of the chain are active in adsorption. It has been shown that the binding of the polymer chain to the surface is a result of a phase transition of a second order, moreover in case a) the presence of a secondary structure abruptly increases the ability of the macromolecules to bind to the interface. This largely increases the stability of the helical structure of the chain and leads to a practically complete spiralization of the macromolecule. The profile of the conformational transitions was strictly asymmetrical which is typical for the phase transitions. In case b) the process of binding resembles the adsorbtion of the Gaussian coils. In this case the rate of spiralization of the chain decreases in the course of binding and the degradation of the secondary structure is significant even if the helical state in volume is stable. The profile of the transition remains qualitatively similar to the helix-coil transition in volume but is displaced to the region of larger equilibrium constants.