Model analysis of surfactant–polymer interaction as cooperative ligand binding to linear lattice

Cooperative kinetics of ligand binding to linear polymers

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Cooperative kinetic equation for large ligands binding to long polymers.

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Cooperativity in general affects binding and release rates.

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Appropriate counting of the available binding sites for a ligand to a linear polymer.

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Positive cooperativity increases polymer coverage by the ligand.

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Large ligand size reduces cooperativity effects.

Ligands change the chemical and mechanical properties of polymers. In particular, single strand binding protein (SSB) non-specifically bounds to single-stranded DNA (ssDNA), modifying the ssDNA stiffness and the DNA replication rate, as recently measured with single-molecule techniques. SSB is a large ligand presenting cooperativity in some of its binding modes. We aim to develop an accurate kinetic model for the cooperative binding kinetics of large ligands. Cooperativity accounts for the changes in the affinity of a ligand to the polymer due to the presence of another bound ligand. Large ligands, attaching to several binding sites, require a detailed counting of the available binding possibilities. This counting has been done by McGhee and von Hippel to obtain the equilibrium state of the ligands-polymer complex. The same procedure allows to obtain the kinetic equations for the cooperative binding of ligands to long polymers, for all ligand sizes. Here, we also derive approximate cooperative kinetic equations in the large ligand limit, at the leading and next-to-leading orders. We found cooperativity is negligible at the leading-order, and appears at the next-to-leading order. Positive cooperativity (increased affinity) can be originated by increased binding affinity or by decreased release affinity, implying different kinetics. Nevertheless, the equilibrium state is independent of the origin of cooperativity and only depends on the overall increase in affinity. Next-to-leading approximation is found to be accurate, particularly for small cooperativity. These results allow to understand and characterize relevant ligand binding processes, as the binding kinetics of SSB to ssDNA, which has been reported to affect the DNA replication rate for several SSB-polymerase pairs.

Stimuli-Induced Nonequilibrium Phase Transitions in Polyelectrolyte-Surfactant Complex Coacervates

Polyelectrolyte-surfactant complexes (PESCs) are important soft colloids with applications in the fields of personal care, cosmetics, pharmaceutics, and much more. If their phase diagrams have long been studied under pseudoequilibrium conditions, and often inside the micellar or vesicular regions, understanding the effect of nonequilibrium conditions, applied at phase boundaries, on the structure of PESCs generates an increasing interest. In this work we cross the micelle-vesicle and micelle-fiber phase boundaries in an isocompositional surfactant-polyelectrolyte aqueous system through a continuous and rapid variation of pH. We employ two microbial glycolipid biosurfactants in the presence of polyamines, both systems being characterized by their responsiveness to pH. We show that complex coacervates (Co) are always formed in the micellar region of both glycolipids' phase diagram and that their phase behavior drives the PESC stability and structure. However, for glycolipid forming single-wall vesicles, we observe an isostructural and isodimensional transition between complex coacervates and a multilamellar walls vesicle (MLWV) phase. For the fiber-forming glycolipid, on the contrary, the complex coacervate disassembles into free polyelectrolyte coexisting with the equilibrium fiber phase. Last but not least, this work also demonstrates the use of microbial glycolipid biosurfactants in the development of sustainable PESCs.

Impact of the bulk aggregation on the adsorption of oppositely charged polyelectrolyte-surfactant mixtures onto solid surfaces

The understanding of the deposition of oppositely charged polyelectrolytes-surfactant mixtures onto solid surfaces presents a high interest in current days due to the recognized impact of the obtained layers on different industrial sectors and the performance of several consumer products (e.g. formulations of shampoos and hair conditioners). This results from the broad range of structures and properties that can present the mixed layers, which in most of the cases mirror the association process occurring between the polyelectrolyte chains and the oppositely charged surfactants in the bulk. Therefore, the understanding of the adsorption processes and characteristics of the adsorbed layers can be only attained from a careful examination of the self-assembly processes occurring in the solution. This review aims to contribute to the understanding of the interaction of polyelectrolyte-surfactant mixtures with solid surfaces, which is probably one of the most underexplored aspects of these type of systems. For this purpose, a comprehensive discussion on the correlations between the aggregates formed in the solutions and the deposition of the obtained complexes upon such association onto solid surfaces will be presented. This makes it necessary to take a closer look to the most important forces driving such processes.

Noncooperative thermodynamics and kinetic models of ligand binding to polymers: Connecting McGhee-von Hippel model with the Tonks gas model

Ligand binding to polymers modifies the physical and chemical properties of the polymers, leading to physical, chemical, and biological implications. McGhee and von Hippel obtained the equilibrium coverage as a function of the ligand affinity, through the computation of the possible binding sites for the ligand. Here, we complete this theory deriving the kinetic model for the ligand-binding dynamics and the associated equilibrium chemical potential, which turns out to be of the Tonks gas model type. At low coverage, the Tonks chemical potential becomes the Fermi chemical potential and even the ideal gas chemical potential. We also discuss kinetic models associated with these chemical potentials. These results clarify the kinetic models of ligand binding, their relations with the chemical potentials, and their range of validity. Our results highlight the inaccuracy of ideal and simplified kinetic approaches for medium and high coverages.

Counterion Condensation, the Gibbs Equation, and Surfactant Binding: An Integrated Description of the Behavior of Polyelectrolytes and Their Mixtures with Surfactants at the Air-Water Interface

By applying the Gibbs equation to the bulk binding isotherms and surface composition of the air-water (A-W) interface in polyelectrolyte-surfactant (PE-S) systems, we show that their surface behavior can be explained semiquantitatively in terms of four concentration regions, which we label as A, B, C, and D. In the lowest-concentration range A, there are no bound PE-S complexes in the bulk but there may be adsorption of PE-S complexes at the surface. When significant adsorption occurs in this region, the surface tension (ST) drops with increasing concentration like a simple surfactant solution. Region B extends from the onset of bulk PE-S binding to the end of cooperative binding, in which the slow variation of surfactant activity with cooperative binding means that the ST changes relatively little, although adsorption may be significant. This leads to an approximate plateau, which may be at high or low ST. Region C starts where the binding in the bulk complex loses its cooperativity leading to a rapid change of surfactant activity with the total concentration. This, combined with significant adsorption, often leads to a sharp drop in ST. Region D is where precipitation and redissolution of the bulk PE-S complex occur. ST peaks may arise in region D because of loss of the solution complex that matches the value of the preferred surface stoichiometry, which seems to have a well-defined value for each system. The analysis is applied to the experimental systems, sodium polystyrene sulfonate-alkyltrimethylammonium bromides and poly(diallyldimethyl chloride)-sodium alkyl sulfates, with and without the added electrolyte, and includes data from bulk binding isotherms, phase diagrams, aggregation behavior, and direct measurements of the surface excess and stoichiometry of the surface. The successful fits of the Gibbs equation to the data confirm that the surfaces in these systems are largely equilibrated.

Polymer-surfactant systems in bulk and at fluid interfaces

The interest of polymer-surfactant systems has undergone a spectacular development in the last thirty years due to their complex behavior and their importance in different industrial sectors. The importance can be mainly associated with the rich phase behavior of these mixtures that confers a wide range of physico-chemical properties to the complexes formed by polymers and surfactants, both in bulk and at the interfaces. This latter aspect is especially relevant because of the use of their mixture for the stabilization of dispersed systems such as foams and emulsions, with an increasing interest in several fields such as cosmetic, food science or fabrication of controlled drug delivery structures. This review presents a comprehensive analysis of different aspects related to the phase behavior of these mixtures and their intriguing behavior after adsorption at the liquid/air interface. A discussion of some physical properties of the bulk is also included. The discussion clearly points out that much more work is needed for obtaining the necessary insights for designing polymer-surfactant mixtures for specific applications.

Co-assembly in chitosan-surfactant mixtures: thermodynamics, structures, interfacial properties and applications

In this review, different aspects characterizing chitosan-surfactant mixtures are summarized and compared. Chitosan is a bioderived cationic polysaccharide that finds wide-ranged applications in various field, e.g., medical or food industry, in which synergistic effects with surfactant can play a fundamental role. In particular, the behavior of chitosan interacting with strong and weak anionic, nonionic as well as cationic surfactants is reviewed. We put a focus on oppositely charged systems, as they exhibit the most interesting features. In that context, we discuss the thermodynamic description of the interaction and in particular the structural changes as they occur as a function of the mixed systems and external parameters. Moreover, peculiar properties of chitosan coated phospholipid vesicles are summarized. Finally, their co-assembly at interfaces is briefly reviewed. Despite the behavior of the mentioned systems might strongly differ, resulting in a high variety of properties, few general rules can be pointed out which improve the understanding of such complex systems.

Universal binding behavior for ionic alkyl surfactants with oppositely charged polyelectrolytes

Oppositely charged polyelectrolyte-surfactant mixtures are ubiquitous in biology and the basis of numerous consumer healthcare products. Despite their broad use, however, a rational approach to their formulation remains challenging because of the complicated association mechanisms. Through compilation and analysis of literature reports and our own research, we have developed a semiempirical correlation of the binding strength of surfactants to polyelectrolytes in salt-free mixtures as a function of the polyion linear charge density and the surfactant hydrophobicity. We have found that the cooperative binding strength increases as the square of the polyelectrolyte's linear charge density and in proportion to the surfactant's hydrophobicity, such that a quantitative relationship holds across a broad range of polyelectrolytes. Deviations from the correlation reveal the role of system-specific interactions not considered in the analysis. This engineering relationship aids in the rational design of oppositely charged polyelectrolyte-surfactant formulations for consumer products and biomedicines by enabling the prediction of binding strengths in polyelectrolyte-surfactant mixtures based on mesoscale parameters determined from the chemical composition.

Phase behavior and molecular thermodynamics of coacervation in oppositely charged polyelectrolyte/surfactant systems: a cationic polymer JR 400 and anionic surfactant SDS mixture

Coacervation in mixtures of polyelectrolytes and surfactants with opposite charge is common in nature and is also technologically important to consumer health care products. To understand the complexation behavior of these systems better, we combine multiple experimental techniques to systematically study the polymer/surfactant binding interactions and the phase behavior of anionic sodium dodecyl sulfate (SDS) surfactant in cationic JR 400 polymer aqueous solutions. The phase-behavior study resolves a discrepancy in the literature by identifying a metastable phase between the differing redissolution phase boundaries reported in the literature for the surfactant-rich regime. Isothermal titration calorimetry analyzed within the framework of the simple Satake-Yang model identifies binding parameters for the surfactant-lean phase, whereas a calculation for polymer-bound micelles coexisting with free micelles is analyzed in the surfactant-rich redissolution regime. This analysis provides a preliminary understanding of the interactions governing the observed phase behavior. The resulting thermodynamic properties, including binding constants and the molar Gibbs free energies, enthalpies, and entropies, identify the relative importance of both hydrophobic and electrostatic interactions and provide a first approximation for the corresponding microstructures in the different phases. Our study also addresses the stability and metastability of oppositely charged polyelectrolytes and surfactant mixtures.

Calculating transcription factor binding maps for chromatin

Current high-throughput experiments already generate enough data for retrieving the DNA sequence-dependent binding affinities of transcription factors (TF) and other chromosomal proteins throughout the complete genome. However, the reverse task of calculating binding maps in a chromatin context for a given set of concentrations and TF affinities appears to be even more challenging and computationally demanding. The problem can be addressed by considering the DNA sequence as a one-dimensional lattice with units of one or more base pairs. To calculate protein occupancies in chromatin, one needs to consider the competition of TF and histone octamers for binding sites as well as the partial unwrapping of nucleosomal DNA. Here, we consider five different classes of algorithms to compute binding maps that include the binary variable, combinatorial, sequence generating function, transfer matrix and dynamic programming approaches. The calculation time of the binary variable algorithm scales exponentially with DNA length, which limits its use to the analysis of very small genomic regions. For regulatory regions with many overlapping binding sites, potentially applicable algorithms reduce either to the transfer matrix or dynamic programming approach. In addition to the recently proposed transfer matrix formalism for TF access to the nucleosomal organized DNA, we develop here a dynamic programming algorithm that accounts for this feature. In the absence of nucleosomes, dynamic programming outperforms the transfer matrix approach, but the latter is faster when nucleosome unwrapping has to be considered. Strategies are discussed that could further facilitate calculations to allow computing genome-wide TF binding maps.

Statistical-mechanical lattice models for protein-DNA binding in chromatin

Statistical-mechanical lattice models for protein-DNA binding are well established as a method to describe complex ligand binding equilibria measured in vitro with purified DNA and protein components. Recently, a new field of applications has opened up for this approach since it has become possible to experimentally quantify genome-wide protein occupancies in relation to the DNA sequence. In particular, the organization of the eukaryotic genome by histone proteins into a nucleoprotein complex termed chromatin has been recognized as a key parameter that controls the access of transcription factors to the DNA sequence. New approaches have to be developed to derive statistical-mechanical lattice descriptions of chromatin-associated protein-DNA interactions. Here, we present the theoretical framework for lattice models of histone-DNA interactions in chromatin and investigate the (competitive) DNA binding of other chromosomal proteins and transcription factors. The results have a number of applications for quantitative models for the regulation of gene expression.

Condensed DNA: condensing the concepts

DNA is stored in vivo in a highly compact, so-called condensed phase, where gene regulatory processes are governed by the intricate interplay between different states of DNA compaction. These systems often have surprising properties, which one would not predict from classical concepts of dilute solutions. The mechanistic details of DNA packing are essential for its functioning, as revealed by the recent developments coming from biochemistry, electrostatics, statistical mechanics, and molecular and cell biology. Different aspects of condensed DNA behavior are linked to each other, but the links are often hidden in the bulk of experimental and theoretical details. Here we try to condense some of these concepts and provide interconnections between the different fields. After a brief description of main experimental features of DNA condensation inside viruses, bacteria, eukaryotes and the test tube, main theoretical approaches for the description of these systems are presented. We end up with an extended discussion of the role of DNA condensation in the context of gene regulation and mention potential applications of DNA condensation in gene therapy and biotechnology.

Calorimetric Determination of Surfactant/Polyelectrolyte Binding Isotherms

Mixing of oppositely charged surfactants and polyelectrolytes in aqueous solutions leads to cooperative surfactant adsorption onto the polyelectrolyte chains. Experimental determination of surfactant/polyelectrolyte binding isotherms is usually done using custom-built surfactant-ion-specific electrodes. As an alternative, we present an indirect isotherm approximation method that uses conventional isothermal titration calorimetry (ITC). The calorimetric data is fitted to the two-binding-state Satake-Yang adsorption model, which quantifies the extent of binding in terms of the binding constant (Ku) and the cooperativity parameter (u). This approach is investigated using two surfactant/polyelectrolyte mixtures: sodium perfluorooctanoate (FC7) and N,N,N-trimethylammonium derivatized hydroxyethyl cellulose (UCARE Polymer JR-400), whose binding behavior follows the Satake-Yang model, and dodecyltrimethylammonium bromide (DTAB) and poly(styrenesulfonate) (NaPSS), whose behavior deviates dramatically from the Satake-Yang model. These studies demonstrate that, in order to apply the indirect ITC method of binding isotherm determination, the surfactant/polyelectrolyte adsorption process must have no more than two dominant binding states. Thus, the technique works well for the FC7/JR-400 mixture. It fails in the case of the DTAB/NaPSS adsorption, but its mode of failure offers insight into the multiple-binding-state adsorption mechanism.

Dynamics of adsorption of an oppositely charged polymer-surfactant mixture at the air-water interface: poly(dimethyldiallylammonium chloride) and sodium dodecyl sulfate

The dynamic adsorption behavior of mixtures of the cationic polymer poly(dimethyldiallylammonium chloride) [poly(dmdaac)] and the anionic surfactant sodium dodecyl sulfate (SDS) has been studied at the expanding liquid surface of an overflowing cylinder. A combination of ellipsometry and external reflection Fourier transform infrared spectroscopy was used to measure the adsorbed amounts of poly(dmdaac) and SDS as a function of the bulk surfactant concentration for various polymer concentrations in the range 0-0.2 g dm-3. Laser Doppler velocimetry was used to determine the surface age, which was approximately 1 s for solutions where the polymer adsorbed. The interfacial behavior is rationalized in terms of competition between surface activity and mass transport to the expanding surface. At low surfactant concentrations, adsorption of both poly(dmdaac) and SDS is enhanced as a result of the formation in solution of polymer-surfactant complexes that are more surface active than either component alone. The rate of adsorption of these complexes is diffusion-controlled, and their interfacial composition remains constant at three dmdaac units per SDS molecule over a 5-fold change in the surfactant concentration. For the higher polymer concentrations studied, the complexes saturate the air-water interface: the adsorbed amount is independent of the polymer concentration and remains constant also over a factor of 5 in the surfactant concentration. Once the number of bound surfactant molecules per dmdaac monomer exceeds 0.3, the complexes begin to form large aggregates, which are not surface active due to their slower mass transport. The adsorbed amount decreases rapidly on approach to the equivalence point (one SDS molecule per dmdaac monomer), and when it is reached, only a very small amount of material remains at the interface. At still higher surfactant concentrations, the free SDS adsorbs but there is no adsorbed poly(dmdaac). The dynamic adsorption data are compared with equilibrium measurements of the same system by Staples et al. (Langmuir 2002, 18, 5147), which show very different surface compositions and no significant change in surface coverage at the equivalence point.