Structural and thermodynamic properties of the model solution containing charged oligomers and the equivalent number of counterions were studied by means of the canonical Monte Carlo simulation technique. The oligomers are represented as (flexible) freely jointed chains or as a linear (rigid) array of charged hard spheres. In accordance with the primitive model of electrolyte solutions, the counterions are modeled as charged hard spheres and the solvent as dielectric continuum. Significant differences in the pair distribution functions, obtained for the rigid (rod-like) and flexible model are found but the differences in thermodynamic properties, such as, enthalpy of dilution and excess chemical potential, are less significant. The results are discussed in light of the experimental data an aqueous polyelectrolyte solutions. The simulations suggest that deviations from the fully extended (rod-like) conformation yield slightly stronger binding of counterions. On the other hand, the flexibility of polyions, even when coupled with the ion-size effects, cannot be blamed for qualitative differences between the theoretical results and experimental data for enthalpy of dilution.
Similarly-charged polymers in solution, known as polyelectrolytes, are known to form aggregated structures in the presence of oppositely charged counterions. Understanding the dependence of the equilibrium phases and the dynamics of the process of aggregation on parameters such as backbone flexibility and charge density of such polymers is crucial for insights into various biological processes which involve biological polyelectrolytes such as protein, DNA etc., Here, we use large-scale coarse-grained molecular dynamics simulations to obtain the phase diagram of the aggregated structures of fle…
We present the results of extensive computer simulations performed on solutions of monodisperse charged rod-like polyelectrolytes in the presence of trivalent counterions. To overcome energy barriers we used a combination of parallel tempering and hybrid Monte Carlo techniques. Our results show that for small values of the electrostatic interaction the solution mostly consists of dispersed single rods. The potential of mean force between the polyelectrolyte monomers yields an attractive interaction at short distances. For a range of larger values of the Bjerrum length, we find finite size poly…
Bending rigidity of a charged membrane or a charged polyelectrolyte screened by monovalent counterions is known to be enhanced by electrostatic effects. We show that in the case of screening by multivalent counterions the electrostatic effects reduce the bending rigidity. This inversion of the sign of the electrostatic contribution is related to the formation of two-dimensional strongly correlated liquids (SCL) of counterions at the charged surface due to strong lateral repulsion between them. When a membrane or a polyelectrolyte is bent, SCL is compressed on one side and stretched on the othe…
Using extensive Molecular Dynamics simulations we study the behavior of polyelectrolytes with hydrophobic side chains, which are known to form cylindrical micelles in aqueous solution. We investigate the stability of such bundles with respect to hydrophobicity, the strength of the electrostatic interaction, and the bundle size. We show that for the parameter range relevant for sulfonated poly-para-phenylenes (PPP) one finds a stable finite bundle size. In a more generic model we also show the influence of the length of the precursor oligomer on the stability of the bundles. We also point out t…
Interplay of Coulomb interaction energy, free ion entropy, and conformational elasticity is a fascinating aspect in polyelectrolytes (PEs). We develop a theory for complexation of two oppositely charged PEs, a process known to be the precursor to the formation of complex coacervates in PE solutions, to explore the underlying thermodynamics of complex formation, at low salts. Explicit calculation of the free energy of complexation and its components indicates that the entropy of free counterions and salt ions and the Coulomb enthalpy of bound ion-pairs dictate the equilibrium of PE complexation…
The charge of a polyelectrolyte (PE) controls myriads of phenomena in biology, biotechnology, and materials science, but still remains elusive from an understanding. Considering the adsorption of counterions on an isolated PE chain, an analytical expression for the effective charge - valid for all chain flexibility, for variable salt, in good solvents at all conditions, in poor solvents in the expanded (coil) state away from the critical point, and for gels, brushes and other PE systems in their expanded state - is derived. Phase boundaries and the critical point for the I-st order collapse tr…
Macromolecules based on dendritic or hyperbranched polyelectrolytes have been emerging as high potential candidates for biomedical applications. Here we study the charge and solvation structure of dendritic polyglycerol sulphate (dPGS) of generations 0 to 3 in aqueous sodium chloride solution by explicit-solvent molecular dynamics computer simulations. We characterize dPGS by calculating several important properties such as relevant dPGS radii, molecular distributions, the solvent accessible surface area, and the partial molecular volume. In particular, as the dPGS exhibits high charge renorma…
The low-frequency limit of the electrical conductivity (d.c. conductivity) of differently flexible polyions in aqueous solutions has been measured over an extended polyion concentration range, covering both the dilute and semidilute (entangled and unentangled) regime, up to the concentrated regime. The data have been analyzed taking into account the different flexibility of the polymer chains according to the scaling theory of polyion solutions, in the case of flexible polyions, and according to the Manning model, in the case of rigid polyions. In both cases, the fraction f of free counterions…
Quantitative Prediction of Protein-Polyelectrolyte Binding Thermodynamics: Adsorption of Heparin-Analog Polysulfates to the SARS-CoV-2 Spike Protein RBD
Polyelectrolytes such as single and double stranded DNA and many synthetic polymers undergo two structural transitions upon increasing the concentration of multivalent salt or molecules. First, the expanded-stretched chains in low monovalent salt solutions collapse into nearly neutral compact structures when the density of multivalent salt approaches that of the monomers. With further addition of multivalent salt the chains redissolve acquiring expanded-coiled conformations. We study the redissolution transition using a two state model [F. Solis and M. Olvera de la Cruz, {\it J. Chem. Phys.} {…
By resorting to the thick-chain model we discuss how the stretching response of a polymer is influenced by the self-avoidance entailed by its finite thickness. The characterization of the force versus extension curve for a thick chain is carried out through extensive stochastic simulations. The computational results are captured by an analytic expression that is used to fit experimental stretching measurements carried out on DNA and single-stranded RNA (poly-U) in various solutions. This strategy allows us to infer the apparent diameter of two biologically-relevant polyelectrolytes, namely DNA…
Strong coupling phenomena, such as the like charged macroions attraction, opposite charged macroions repulsion, charge renormalization or charge inversion, are known to be mediated by multivalent counterions. Most theories treat the counterions as point charges, and describe the system by a single coupling parameter that measures the strength of the Coulomb interactions. In many biological systems, the counterions are highly charged and have finite sizes and can be well-described by polyelectrolytes. The shapes and orientations of these polymer counterions play a major role in the thermodynami…
We present a comprehensive study of the interaction of human serum albumin (HSA) with poly(acrylic acid) (PAA; number average degree of polymerization: 25) in aqueous solution. The interaction of HSA with PAA is studied in dilute solution as the function of the concentration of added salt (20 - 100 mM) and temperature (25 - 37$^{\circ}$C). Isothermal titration calorimetry (ITC) is used to analyze the interaction and to determine the binding constant and related thermodynamic data. It is found that only one PAA chain is bound per HSA molecule. The free energy of binding $ΔG_b$ increases with te…
We study the thermodynamic properties of a simple model for the possible mechanism of attraction between like charged rodlike polyions inside a polyelectrolyte solution. We consider two polyions in parallel planes, with $Z$ charges each, in a solution containing multivalent counterions of valence $α$. The model is solved exactly for $Z \le 13$ for a general angle $θ$ between the rods and supposing that $n$ counterions are condensed on each polyion. The free energy has two minima, one at $θ=0$ (parallel rods) and another at $θ=π/2$ (perpendicular rods). In general, in situations where an attrac…
In this study, we investigated the thermodynamic features of a system based on oppositely charged polyelectrolytes, sodium alginate, and poly(diallyldimethylammonium chloride) (PDADMAC) at different pH values. Additionally, a comparison of the effects of the thermodynamic parameters on the growth of the layers based on the same polymers is presented. For this investigation, different techniques were combined to compare results from the association in solution and co-assembled layers at the silicon surface. Dynamic light scattering (DLS) and isothermal titration calorimetry (ITC) were used for …
A brief review is presented of the scaling of complex fluids, polymers and polyelectrolytes in solution and in confined geometry, in thermodynamical, structural and rheology properties using equilibrium and nonequilibrium dissipative particle dynamics simulations. All simulations were carried out on high performance computational facilities using parallelized algorithms, solved on computers using both central and graphical processing units. The scaling approach is shown to be a unifying axis around which general trends and basic knowledge can be gained, illustrated through a series of case stu…
Electrostatic interactions between macroions largely govern the equilibrium thermodynamic and dynamical properties of charge-stabilized colloidal suspensions and polyelectrolyte solutions. Predicting the properties of such complex, multicomponent systems with accuracy sufficient to guide and interpret experiments requires realistic modeling of the interparticle interactions and collective behavior of many-particle systems. While the fundamental interactions may be simple, the sheer number of particles and the broad ranges of length and time scales confront the modeler with significant computat…
The osmotic equation of state for the athermal bond fluctuation model on the simple cubic lattice is obtained from extensive Monte Carlo simulations. For short macromolecules (chain length N=20) we study the influence of various choices for the chain stiffness on the equation of state. Three techniques are applied and compared in order to critically assess their efficiency and accuracy: the repulsive wall method, the thermodynamic integration method (which rests on the feasibility of simulations in the grand canonical ensemble), and the recently advocated sedimentation equilibrium method, whic…
Conformational flexibility of molecules involved in crystal growth and dissolution is rarely investigated in detail, and usually considered to be negligible in the formulation of mesoscopic models of crystal growth. In this work we set out to investigate the conformational isomerism of ibuprofen as it approaches and is incorporated in the morphologically dominant {100} crystal face, in a range of different solvents - water, 1-butanol, toluene, cyclohexanone, cyclohexane, acetonitrile and trichloromethane. To this end we combine extensive molecular dynamics and well-tempered metadynamics simula…
The specificity and thermal reversibility of DNA interactions have enabled the self-assembly of crystal structures, self-replicating materials and colloidal molecules. Grafting DNA onto liquid interfaces of emulsions leads to exciting new architectural possibilities due to the mobility of the DNA ligands and the patches they form between bound droplets. Here we show that the size and number of these adhesion patches (valency) can be controlled. Valence 2 leads to flexible polymers of emulsion droplets, while valence above 4 leads to rigid droplet networks. A simple thermodynamic model quantita…
Chain-like macromolecules (polymers) show characteristic adsorption properties due to their flexibility and internal degrees of freedom, when attracted to surfaces and interfaces. In this review we discuss concepts and features that are relevant to the adsorption of neutral and charged polymers at equilibrium, including the type of polymer/surface interaction, the solvent quality, the characteristics of the surface, and the polymer structure. We pay special attention to the case of charged polymers (polyelectrolytes) that have a special importance due to their water solubility. We present a su…
We analyze the structural behavior of a single polymer chain grafted to an attractive, flexible surface. Our model is composed of a coarse-grained bead-and-spring polymer and a tethered membrane. By means of extensive parallel tempering Monte Carlo simulations it is shown that the system exhibits a rich phase behavior ranging from highly ordered, compact to extended random coil structures and from desorbed to completely adsorbed or even partially embedded conformations. These findings are summarized in a pseudophase diagram indicating the predominant class of conformations as a function of the…
We develop a theory describing density profile of the semi-flexible polymers absorbed onto a planar surface. The theoretical analysis consists of two parts. As a first part, we calculate a density profile of the adsorbed polymers by developing an extension of the Bethe-Peierls approximation to the case of nonhomogeneous systems. This approach relies on the combination of the single chain adsorption theory and the lattice version of the self-consistent field theory. Semi-flexibility of a chain is described by incorporating a finite coordination number of the lattice into the consideration, in t…
The oxidative damage of DNA is a compelling issue in molecular biophysics as it plays a vital role in the epigenetic control of gene expression and is believed to be associated with mutagenesis, carcinogenesis, and ageing. To understand the microscopic structural changes in physical properties of DNA and the resulting influence on its function due to oxidative damage of its nucleotide bases, we have conducted all-atom molecular dynamic simulations of double-stranded DNA (dsDNA) with its guanine bases being oxidized. The guanine bases are more prone to oxidative damage due to the lowest value o…
The Infrared Spectrum is used as an experimental data target, to improved the TIP4P/$ε$, adding harmonic potential U(r) in all bonds and harmonic potential U(θ) in the angle formed by the hydrogens and oxygen atoms of the water molecule. The flexibility in the molecule gives the ability of the water molecules to change, around different temperatures and pressures, their structure and in the bulk liquid the distribution of the dipole moment. This distribution helps to reproduce better the experimental data that the rigid models can not describe. The rigid water models of 3 and 4 sites have limi…
