Strong stretching theory of polydisperse curved polymer brushes.

We investigate the effect of polydispersity on the properties of curved linear brushes in good solvent and for molten brushes. To this end, we extend the strong stretching theory for polydisperse brushes to curved geometries and investigate the polymer chain end profiles, bending moduli and other properties for experimentally relevant polymer chain length distributions of the Schulz-Zimm type. We also investigate the properties of end exclusion zones that may appear in convex geometries under certain conditions and show that their position in the brush can be engineered by careful selection of the polymer length distribution. Finally, we propose a method to engineer chain end profiles by engineering the polymer length distribution.

Polyelectrolyte Brushes with Protein-Like Nanocolloids.

Electrostatic interaction of ampholytic nanocolloidal particles (NPs), which mimic globular proteins, with polyelectrolyte brushes is analyzed within mean-field Poisson-Boltzmann approximation. In accordance with experimental findings, the theory predicts that an electrostatic driving force for the particle uptake by the brush may emerge when the net charge of the particle in the buffer and the charge of the brush are of the same sign. The origin of this driving force is change in the ionization state of weak cationic and anionic groups on the NP surface provoked by interaction with the brush. In experimental systems, the ionic interactions are complemented by excluded-volume, hydrophobic, and other types of interactions that all together control NP uptake by or expulsion from the brush. Here, we focus on the NP-brush ionic interactions. It is demonstrated that deviation between the buffer pH and the NP isoelectric point, considered usually as the key control parameter, does not uniquely determine the insertion free energy patterns. The latter depends also on the proportion of cationic and anionic groups in the NPs and their specific ionization constants as well as on salt concentration in the buffer. The analysis of the free energy landscape proves that a local minimum in the free energy inside the brush appears, provided the NP charge reversal occurs upon insertion into the brush. This minimum corresponds either to a thermodynamically stable or to a metastable state, depending on the pH offset from the IEP and salt concentration, and is separated from the bulk of the solution by a free energy barrier. The latter, being fairly independent of salt concentration in height, may strongly impede the NP absorption kinetically even when it is thermodynamically favorable. Hence, change reversal is a necessary but insufficient condition for the uptake of the NPs by similarly charged polyelectrolyte brushes.

Surface-Immobilized Interpolyelectrolyte Complexes Formed by Polyelectrolyte Brushes.

A scaling theory of interaction and complex formation between planar polyelectrolyte (PE) brush and oppositely charged mobile linear PEs is developed. Counterion release is found to be the main driving force for the complexation. An interpolyelectrolyte coacervate complex (IPEC) between the brush and oppositely charged mobile PEs is formed at moderate grafting density and low salt concentration. At higher grafting density mobile chains penetrate the brush, but the brush structure is controlled by the balance between entropic elasticity and nonelectrostatic short-range interactions, as happens in a neutral brush. An increase in salt concentration beyond the theoretically predicted threshold leads to the release of the guest polyions from the brush. For brushes with moderate grafting density, complexation with oppositely charged guest polyions is predicted to trigger lateral microphase separation and formation of the finite-size surface IPEC clusters. Power law dependencies for the cluster dimensions on the brush grafting density, PE length, and salt concentration are provided.

Interaction of Polyanionic and Polycationic Brushes with Globular Proteins and Protein-like Nanocolloids.

A large number of experimental studies have demonstrated that globular proteins can be absorbed from the solution by both polycationic and polyanionic brushes when the net charge of protein globules is of the same or of the opposite sign with respect to that of brush-forming polyelectrolyte chains. Here, we overview the results of experimental studies on interactions between globular proteins and polycationic or polyanionic brushes, and present a self-consistent field theoretical model that allows us to account for the asymmetry of interactions of protein-like nanocolloid particles comprising weak (pH-sensitive) cationic and anionic groups with a positively or negatively charged polyelectrolyte brush. The position-dependent insertion free energy and the net charge of the particle are calculated. The theoretical model predicts that if the numbers of cationic and anionic ionizable groups of the protein are approximately equal, then the interaction patterns for both cationic and anionic brushes at equal offset on the "wrong side" from the isoelectric point (IEP), i.e., when the particle and the brush charge are of the same sign, are similar. An essential asymmetry in interactions of particles with polycationic and polyanionic brushes is predicted when fractions of cationic and anionic groups differ significantly. That is, at a pH above IEP, the anionic brush better absorbs negatively charged particles with a larger fraction of ionizable cationic groups and vice versa.

Cylindrical brushes with ionized side chains: Scaling theory revisited.

We revisit the classic scaling model of a cylindrical polyelectrolyte (PE) brush focusing on molecular brushes with stiff backbones and dispersions of polymer-decorated nanorods. Based on the blob representation we demonstrate that similarly to the case of planar PE brushes, separation of intra- and intermolecular repulsions between charges leads to novel scaling regimes for cylindrical PE brushes in salt-added solution and a sharper decrease in its thickness versus salt concentration dependence. These theoretical predictions may inspire further comprehensive experimental research and computer simulations of synthetic and biopolyelectrolyte cylindrical brushes.

Polyelectrolyte Cylindrical Brushes in Hairy Gels.

We considered dispersions of cylindrical polyelectrolyte (PE) brushes with stiff backbones, and polymer-decorated nanorods with tunable solubility of the brush-forming PE chains that affected thermodynamic stability of the dispersions. We focused on thermo-induced and deionization-induced conformational transition that provokes loss of aggregative dispersion stability of nanorods decorated with weakly ionized polyions. A comparison between theoretical predictions and experiments enabled rationalization and semi-quantitative interpretation of the experimental results.

Polyelectrolyte Brush Interacting with Ampholytic Nanoparticles as Coarse-Grained Models of Globular Proteins: Poisson-Boltzmann Theory.

The self-consistent field Poisson-Boltzmann framework is applied to analyze equilibrium partitioning of ampholytic nanoparticles (NPs) between buffer solution and polyelectrolyte (PE) polyanionic brush. We demonstrate that depending on pH and salt concentration in the buffer solution, interactions between ionizable (acidic and basic) groups on the NP surface and electrostatic field created by PE brush may either lead to the spontaneous uptake of NPs or create an electrostatic potential barrier, preventing the penetration of NPs inside PE brush. The capability of PE brush to absorb or repel NPs is determined by the shape of the insertion free energy that is calculated as a function of NP distance from the grafting surface. It is demonstrated that, at a pH value below or slightly above the isoelectric point (IEP), the electrostatic free energy of the particle is negative inside the brush and absorption is thermodynamically favorable. In the latter case, the insertion free energy exhibits a local maximum (potential barrier) at the entrance to the brush. An increase in pH leads to the shallowing of the free energy minimum inside the brush and a concomitant increase in the free energy maximum, which may result in kinetic hindering of NP uptake. Upon further increase in pH the insertion free energy becomes positive, making NP absorption thermodynamically unfavorable. An increase in salt concentration diminishes the depth of the free energy minimum inside the brush and eventually leads to its disappearance. Hence, in accordance with existing experimental data our theory predicts that an increase in salt concentration suppresses absorption of NPs (protein globules) by PE brush in the vicinity of IEP. The interplay between electrostatic driving force for NP absorption and osmotic repelling force (proportional to NP volume) indicates that for large NPs with relatively small number of ionizable groups osmotic repulsion overcomes electrostatic attraction preventing thereby absorption of NPs by PE brush.

Structure and Dynamics of Hybrid Colloid-Polyelectrolyte Coacervates.

We develop a scaling theory for the structure and dynamics of "hybrid" complex coacervates formed from linear polyelectrolytes (PEs) and oppositely charged spherical colloids, such as globular proteins, solid nanoparticles, or spherical micelles of ionic surfactants. At low concentrations, in stoichiometric solutions, PEs adsorb at the colloids to form electrically neutral finite-size complexes. These clusters attract each other through bridging between the adsorbed PE layers. Above a threshold concentration, macroscopic phase separation sets in. The coacervate internal structure is defined by (i) the adsorption strength and (ii) the ratio of the resulting shell thickness to the colloid radius, H/R. A scaling diagram of different coacervate regimes is constructed in terms of the colloid charge and its radius for Θ and athermal solvents. For high charges of the colloids, the shell is thick, H ≫ R, and most of the volume of the coacervate is occupied by PEs, which determine its osmotic and rheological properties. The average density of hybrid coacervates exceeds that of their PE-PE counterparts and increases with nanoparticle charge, Q. At the same time, their osmotic moduli remain equal, and the surface tension of hybrid coacervates is lower, which is a consequence of the shell's inhomogeneous density decreasing with the distance from the colloid surface. When charge correlations are weak, hybrid coacervates remain liquid and follow Rouse/reptation dynamics with a Q-dependent viscosity, η Rouse ∼ Q 4/5 and η rep ∼ Q 28/15 for a Θ solvent. For an athermal solvent, these exponents are equal to 0.89 and 2.68, respectively. The diffusion coefficients of colloids are predicted to be strongly decreasing functions of their radius and charge. Our results on how Q affects the threshold coacervation concentration and colloidal dynamics in condensed phases are consistent with experimental observations for in vitro and in vivo studies of coacervation between supercationic green fluorescent proteins (GFPs) and RNA.

Selective Colloid Transport across Planar Polymer Brushes.

Polymer brushes are attractive as surface coatings for a wide range of applications, from fundamental research to everyday life, and also play important roles in biological systems. How colloids (e.g., functional nanoparticles, proteins, viruses) bind and move across polymer brushes is an important yet under-studied problem. A mean-field theoretical approach is presented to analyze the binding and transport of colloids in planar polymer brushes. The theory explicitly considers the effect of solvent strength on brush conformation and of colloid-polymer affinity on colloid binding and transport. The position-dependent free energy of the colloid insertion into the polymer brush which controls the rate of colloid transport across the brush is derived. It is shown how the properties of the brush can be adjusted for brushes to be highly selective, effectively serving as tuneable gates with respect to colloid size and affinity to the brush-forming polymer. The most important parameter regime simultaneously allowing for high brush permeability and selectivity corresponds to a condition when the repulsive and attractive contributions to the colloid insertion free energy nearly cancel. This theory should be useful to design sensing and purification devices with enhanced selectivity and to better understand mechanisms underpinning the functions of biological polymer brushes.

Bovine Serum Albumin Interaction with Polyanionic and Polycationic Brushes: The Case Theoretical Study.

We apply a coarse-grained self-consistent field Poisson-Boltzmann framework to study interaction between Bovine Serum Albumin (BSA) and a planar polyelectropyte brush. Both cases of negatively (polyanionic) and positively (polycationic) charged brushes are considered. Our theoretical model accounts for (1) re-ionization free energy of the amino acid residues upon protein insertion into the brush; (2) osmotic force repelling the protein globule from the brush; (3) hydrophobic interactions between non-polar areas on the globule surface and the brush-forming chains. We demonstrate that calculated position-dependent insertion free energy exhibits different patterns, corresponding to either thermodynamically favourable BSA absorption in the brush or thermodynamically or kinetically hindered absorption (expulsion) depending on the pH and ionic strength of the solution. The theory predicts that due to the re-ionization of BSA within the brush, a polyanionic brush can efficiently absorb BSA over a wider pH range on the "wrong side" of the isoelectric point (IEP) compared to a polycationic brush. The results of our theoretical analysis correlate with available experimental data and thus validate the developed model for prediction of the interaction patterns for various globular proteins with polyelectrolyte brushes.

Hybrid Molecules Consisting of Lysine Dendrons with Several Hydrophobic Tails: A SCF Study of Self-Assembling.

In this article, we used the numerical self-consistent field method of Scheutjens-Fleer to study the micellization of hybrid molecules consisting of one polylysine dendron with charged end groups and several linear hydrophobic tails attached to its root. The main attention was paid to spherical micelles and the determination of the range of parameters at which they can appear. A relationship has been established between the size and internal structure of the resulting spherical micelles and the length and number of hydrophobic tails, as well as the number of dendron generations. It is shown that the splitting of the same number of hydrophobic monomers from one long tail into several short tails leads to a decrease in the aggregation number and, accordingly, the number of terminal charges in micelles. At the same time, it was shown that the surface area per dendron does not depend on the number of hydrophobic monomers or tails in the hybrid molecule. The relationship between the structure of hybrid molecules and the electrostatic properties of the resulting micelles has also been studied. It is found that the charge distribution in the corona depends on the number of dendron generations G in the hybrid molecule. For a small number of generations (up to G=3), a standard double electric layer is observed. For a larger number of generations (G=4), the charges of dendrons in the corona are divided into two populations: in the first population, the charges are in the spherical layer near the boundary between the micelle core and shell, and in the second population, the charges are near the periphery of the spherical shell. As a result, a part of the counterions is localized in the wide region between them. These results are of potential interest for the use of spherical dendromicelles as nanocontainers for drug delivery.

Implicit-Solvent Coarse-Grained Simulations of Linear-Dendritic Block Copolymer Micelles.

The design of nanoassemblies can be conveniently achieved by tuning the strength of the hydrophobic interactions of block copolymers in selective solvents. These block copolymer micelles form supramolecular aggregates, which have attracted great attention in the area of drug delivery and imaging in biomedicine due to their easy-to-tune properties and straightforward large-scale production. In the present work, we have investigated the micellization process of linear-dendritic block copolymers in order to elucidate the effect of branching on the micellar properties. We focus on block copolymers formed by linear hydrophobic blocks attached to either dendritic neutral or charged hydrophilic blocks. We have implemented a simple protocol for determining the equilibrium micellar size, which permits the study of linear-dendritic block copolymers in a wide range of block morphologies in an efficient and parallelizable manner. We have explored the impact of different topological and charge properties of the hydrophilic blocks on the equilibrium micellar properties and compared them to predictions from self-consistent field theory and scaling theory. We have found that, at higher degrees of branching in the corona and for short polymer chains, excluded volume interactions strongly influence the micellar aggregation as well as their effective charge.

A Polyelectrolyte Colloidal Brush Based on Cellulose: Perspectives for Future Applications.

This feature article is devoted to the evaluation of different techniques for producing colloidal polyelectrolyte brushes (CPEBs) based on cellulose nanofibers modified with grafted polyacrylates. The paper also reviews the potential applications of these CPEBs in designing electrode materials and as reinforcing additives. Additionally, we discuss our own perspectives on investigating composites with CPEBs. Herein, polyacrylic acid (PAA) was grafted onto the surface of cellulose nanofibers (CNFs) employing a "grafting from" approach. The effect of the PAA shell on the morphological structure of a composite with polypyrrole (PPy) was investigated. The performance of as-obtained CNF-PAA/PPy as organic electrode material for supercapacitors was examined. Furthermore, this research highlights the ability of CNF-PAA filler to act as an additional crosslinker forming a physical sub-network due to the hydrogen bond interaction inside chemically crosslinked polyacrylamide (PAAm) hydrogels. The enhancement of the mechanical properties of the material with a concomitant decrease in its swelling ratio compared to a pristine PAAm hydrogel was observed. The findings were compared with the recent theoretical foundation pertaining to other similar materials.

Hairy Gels: A Computational Study.

We present results of MD and MC simulations of the equilibrium properties of swelling gels with comb-like or bottlebrush subchains and compare them to scaling-theory predictions. In accordance with theory, the simulation results demonstrate that swelling coefficient of the gel increases as a function of the polymerization degree of the main chains and exhibits a very weak maximum (or is virtually constant) as a function of the polymerization degree and grafting density of side chains. The bulk osmotic modulus passes through a shallow minimum as the polymerization degree of the side chains increases. This minimum is attributed to the onset of overlap of side chains belonging to different bottlebrush strands in the swollen gel.

Theoretical advances in molecular bottlebrushes and comblike (co)polymers: solutions, gels, and self-assembly.

We present an overview of state-of-the-art theory of (i) conformational properties of molecular bottlebrushes in solution, (ii) self-assembly of di- and triblock copolymers comprising comb-shaped and bottlebrush blocks in solutions and melts, and (iii) cross-linked and self-assembled gels with bottlebrush subchains. We demonstrate how theoretical models enable quantitative prediction and interpretation of experimental results and provide rational guidance for design of new materials with physical properties tunable by architecture of constituent bottlebrush blocks.

Colloidal particles interacting with a polymer brush: a self-consistent field theory.

The interaction of colloidal particles with a planar polymer brush immersed in a solvent of variable thermodynamic quality is studied by a numerical self-consistent field method combined with analytical mean-field theory. The effect of embedded particle on the distribution of polymer density in the brush is analyzed and the particle insertion free energy profiles are calculated for variable size and shape of the particles and sets of polymer-particle and polymer-solvent interaction parameters. In particular, both cases of repulsive and attractive interactions between particles and brush-forming chains are considered. It is demonstrated that for large particles the insertion free energy is dominated by repulsive (osmotic) contribution and is approximately proportional to the particle volume in accordance with earlier theoretical predictions [Halperin et al., Macromolecules, 2011, 44, 3622]. For the particles of smaller size or/and large shape asymmetry the adsorption or depletion of a polymer from the particle surface essentially contributes to the insertion free energy balance. As a result, depending on the set of polymer-solvent and polymer-particle interaction parameters and brush grafting density the insertion free energy profile may exhibit complex patterns, i.e., from a pure repulsive effective potential barrier to an attractive well. The results of our study allow for predicting equilibrium partitioning and controlling diffusive transport of (bio)nanocolloids across (bio)polymer brushes of arbitrary geometry including polymer-modified membranes or nanopores.

Bottlebrush polymer gels: architectural control over swelling and osmotic bulk modulus.

Swelling behaviour and bulk moduli of polymer gels comprising of crosslinked bottlebrush subchains enable fine tuning by varying polymerization degrees of the main and side chains of the bottlebrush strands as well as their grafting densities. By using scaling approach we predict power law dependences of structural and elastic properties of swollen bottlebrush gels on the set of relevant architectural parameters and construct phase diagrams consisting of regions corresponding to different power law asymptotics for these dependences. In particular, our theory predict that bulk elastic modulus of the gel exhibits non-monotonous dependence on the degree of polymerization of side chains of the bottlebrush strands.

Polygenic Profile of Elite Strength Athletes.

ABSTRACT: Moreland, E, Borisov, OV, Semenova, EA, Larin, AK, Andryushchenko, ON, Andryushchenko, LB, Generozov, EV, Williams, AG, and Ahmetov, II. Polygenic profile of elite strength athletes. J Strength Cond Res 36(9): 2509-2514, 2022-Strength is a heritable trait with unknown polygenic nature. So far, more than 200 DNA polymorphisms associated with strength/power phenotypes have been identified majorly involving nonathletic populations. The aim of the present study was to investigate individually and in combination the association of 217 DNA polymorphisms previously identified as markers for strength/power phenotypes with elite strength athlete status. A case-control study involved 83 Russian professional strength athletes (53 weightlifters, 30 powerlifters), 209 Russian and 503 European controls. Genotyping was conducted using micro-array analysis. Twenty-eight DNA polymorphisms (located near or in ABHD17C , ACTG1 , ADCY3 , ADPGK , ANGPT2 , ARPP21 , BCDIN3D , CRTAC1 , DHODH , GBE1 , IGF1 , IL6 , ITPR1 , KIF1B , LRPPRC , MMS22L , MTHFR , NPIPB6 , PHACTR1 , PLEKHB1 , PPARG , PPARGC1A , R3HDM1 , RASGRF1 , RMC1 , SLC39A8 , TFAP2D , ZKSCAN5 genes) were identified to have an association with strength athlete status. Next, to assess the combined impact of all 28 DNA polymorphisms, all athletes were classified according to the number of "strength" alleles they possessed. All highly elite strength athletes were carriers of at least 22 (up to 34) "strength" alleles, whereas 27.8% of Russian controls had less than 22 "strength" alleles ( p < 0.0001). The proportion of subjects with a high (≥26) number of "strength" alleles was significantly greater in highly elite strength athletes (84.8%) compared with less successful strength athletes (64.9%; odd ratio [OR] = 3.0, p = 0.042), Russian (26.3%; OR = 15.6, p < 0.0001) or European (37.8%; OR = 6.4, p < 0.0001) controls. This is the first study to demonstrate that the likelihood of becoming an elite strength athlete depends on the carriage of a high number of strength-related alleles.

The BDNF-Increasing Allele is Associated With Increased Proportion of Fast-Twitch Muscle Fibers, Handgrip Strength, and Power Athlete Status.

ABSTRACT: Guilherme, JPLF, Semenova, EA, Borisov, OV, Kostryukova, ES, Vepkhvadze, TF, Lysenko, EA, Andryushchenko, ON, Andryushchenko, LB, Lednev, EM, Larin, AK, Bondareva, EA, Generozov, EV, and Ahmetov, II. The BDNF-increasing allele is associated with increased proportion of fast-twitch muscle fibers, handgrip strength, and power athlete status. J Strength Cond Res 36(7): 1884-1889, 2022-The brain-derived neurotrophic factor (BDNF) is involved in neurogenesis and formation of regenerated myofibers following injury or damage. A recent study suggested that the BDNF overexpression increases the proportion of fast-twitch muscle fibers, while the BDNF deletion promotes a fast-to-slow transition. The purpose of this study was to evaluate the association between the BDNF gene rs10501089 polymorphism (associated with blood BDNF levels), muscle fiber composition, and power athlete status. Muscle fiber composition was determined in 164 physically active individuals (113 men, 51 women). BDNF genotype and allele frequencies were compared between 508 Russian power athletes, 178 endurance athletes, and 190 controls. We found that carriers of the minor A-allele (the BDNF-increasing allele) had significantly higher percentage of fast-twitch muscle fibers than individuals homozygous for the G-allele (males: 64.3 [7.8] vs. 50.3 [15.8]%, p = 0.0015; all subjects: 64.1 ± 7.9 vs. 49.6 ± 14.7%, p = 0.0002). Furthermore, the A-allele was associated (p = 0.036) with greater handgrip strength in a sub-group of physically active subjects (n = 83) and over-represented in power athletes compared with controls (7.7 vs. 2.4%, p = 0.0001). The presence of the A-allele (i.e., AA+AG genotypes) rather than GG genotype increased the odds ratio of being a power athlete compared with controls (odds ratio [OR]: 3.43, p = 0.00071) or endurance athletes (OR: 2.36, p = 0.0081). In conclusion, the rs10501089 A-allele is associated with increased proportion of fast-twitch muscle fibers and greater handgrip strength, and these may explain, in part, the association between the AA/AG genotypes and power athlete status.

Genomic predictors of testosterone levels are associated with muscle fiber size and strength.

PURPOSE: Circulating testosterone levels are a heritable trait with anabolic properties in various tissues, including skeletal muscle. So far, hundreds of single nucleotide polymorphisms (SNPs) associated with testosterone levels have been identified in nonathletic populations. The aim of the present study was to test the association of 822 testosterone-increasing SNPs with muscle-related traits (muscle fiber size, fat-free mass and handgrip strength) and to validate the identified SNPs in independent cohorts of strength and power athletes. METHODS: One hundred and forty-eight physically active individuals (47 females, 101 males) were assessed for cross-sectional area (CSA) of fast-twitch muscle fibers. Significant SNPs were further assessed for fat-free mass and handgrip strength in > 354,000 participants from the UK Biobank cohort. The validation cohorts included Russian elite athletes. RESULTS: From an initial panel of 822 SNPs, we identified five testosterone-increasing alleles (DOCK3 rs77031559 G, ESR1 rs190930099 G, GLIS3 rs34706136 TG, GRAMD1B rs850294 T, TRAIP rs62260729 C) nominally associated (P < 0.05) with CSA of fast-twitch muscle fibers, fat-free mass and handgrip strength. Based on these five SNPs, the number of testosterone-increasing alleles was positively associated with testosterone levels in male athletes (P = 0.048) and greater strength performance in weightlifters (P = 0.017). Moreover, the proportion of participants with ≥ 2 testosterone-increasing alleles was higher in power athletes compared to controls (68.9 vs. 55.6%; P = 0.012). CONCLUSION: Testosterone-related SNPs are associated with muscle fiber size, fat-free mass and strength, which combined can partially contribute to a greater predisposition to strength/power sports.