Counterion-Release Entropy Governs the Inhibition of Serum Proteins by Polyelectrolyte Drugs

Charge Regulation Triggers Condensation of Short Oligopeptides to Polyelectrolytes

Electrostatic interactions between charged macromolecules are ubiquitous in biological systems, and they are important also in materials design. Attraction between oppositely charged molecules is often interpreted as if the molecules had a fixed charge, which is not affected by their interaction. Less commonly, charge regulation is invoked to interpret such interactions, i.e., a change of the charge state in response to a change of the local environment. Although some theoretical and simulation studies suggest that charge regulation plays an important role in intermolecular interactions, experimental evidence supporting such a view is very scarce. In the current study, we used a model system, composed of a long polyanion interacting with cationic oligolysines, containing up to 8 lysine residues. We showed using both simulations and experiments that while these lysines are only weakly charged in the absence of the polyanion, they charge up and condense on the polycations if the pH is close to the pKa of the lysine side chains. We show that the lysines coexist in two distinct populations within the same solution: (1) practically nonionized and free in solution; (2) highly ionized and condensed on the polyanion. Using this model system, we demonstrate under what conditions charge regulation plays a significant role in the interactions of oppositely charged macromolecules and generalize our findings beyond the specific system used here.

Respiratory viruses interacting with cells: the importance of electrostatics

The COVID-19 pandemic has rekindled interest in the molecular mechanisms involved in the early steps of infection of cells by viruses. Compared to SARS-CoV-1 which only caused a relatively small albeit deadly outbreak, SARS-CoV-2 has led to fulminant spread and a full-scale pandemic characterized by efficient virus transmission worldwide within a very short time. Moreover, the mutations the virus acquired over the many months of virus transmission, particularly those seen in the Omicron variant, have turned out to result in an even more transmissible virus. Here, we focus on the early events of virus infection of cells. We review evidence that the first decisive step in this process is the electrostatic interaction of the spike protein with heparan sulfate chains present on the surface of target cells: Patches of cationic amino acids located on the surface of the spike protein can interact intimately with the negatively charged heparan sulfate chains, which results in the binding of the virion to the cell surface. In a second step, the specific interaction of the receptor binding domain (RBD) within the spike with the angiotensin-converting enzyme 2 (ACE2) receptor leads to the uptake of bound virions into the cell. We show that these events can be expressed as a semi-quantitative model by calculating the surface potential of different spike proteins using the Adaptive Poison-Boltzmann-Solver (APBS). This software allows visualization of the positive surface potential caused by the cationic patches, which increased markedly from the original Wuhan strain of SARS-CoV-2 to the Omicron variant. The surface potential thus enhanced leads to a much stronger binding of the Omicron variant as compared to the original wild-type virus. At the same time, data taken from the literature demonstrate that the interaction of the RBD of the spike protein with the ACE2 receptor remains constant within the limits of error. Finally, we briefly digress to other viruses and show the usefulness of these electrostatic processes and calculations for cell-virus interactions more generally.

Adsorption of Mono- and Divalent Ions onto Dendritic Polyglycerol Sulfate (dPGS) as Studied Using Isothermal Titration Calorimetry

The effective charge of highly charged polyelectrolytes is significantly lowered by a condensation of counterions. This effect is more pronounced for divalent ions. Here we present a study of the counterion condensation to dendritic polyglycerol sulfate (dPGS) that consists of a hydrophilic dendritic scaffold onto which sulfate groups are appended. The interactions between the dPGS and divalent ions (Mg²⁺ and Ca²⁺) were analyzed using isothermal titration calorimetry (ITC) and showed no ion specificity upon binding, but clear competition between the monovalent and divalent ions. Our findings, in line with the latest theoretical studies, demonstrate that a large fraction of the monovalent ions is sequentially replaced with the divalent ions.

Functionalized Fullerene for Inhibition of SARS-CoV-2 Variants

As virus outbreaks continue to pose a challenge, a nonspecific viral inhibitor can provide significant benefits, especially against respiratory viruses. Polyglycerol sulfates recently emerge as promising agents that mediate interactions between cells and viruses through electrostatics, leading to virus inhibition. Similarly, hydrophobic C₆₀ fullerene can prevent virus infection via interactions with hydrophobic cavities of surface proteins. Here, two strategies are combined to inhibit infection of SARS-CoV-2 variants in vitro. Effective inhibitory concentrations in the millimolar range highlight the significance of bare fullerene's hydrophobic moiety and electrostatic interactions of polysulfates with surface proteins of SARS-CoV-2. Furthermore, microscale thermophoresis measurements support that fullerene linear polyglycerol sulfates interact with the SARS-CoV-2 virus via its spike protein, and highlight importance of electrostatic interactions within it. All-atom molecular dynamics simulations reveal that the fullerene binding site is situated close to the receptor binding domain, within 4 nm of polyglycerol sulfate binding sites, feasibly allowing both portions of the material to interact simultaneously.

Sulfated Hyperbranched and Linear Polyglycerols Modulate HMGB1 and Morphological Plasticity in Neural Cells

The objective of this study was to establish if polyglycerols with sulfate or sialic acid functional groups interact with high mobility group box 1 (HMGB1), and if so, which polyglycerol could prevent loss of morphological plasticity in excitatory neurons in the hippocampus. Considering that HMGB1 binds to heparan sulfate and that heparan sulfate has structural similarities with dendritic polyglycerol sulfates (dPGS), we performed the experiments to show if polyglycerols can mimic heparin functions by addressing the following questions: (1) do dendritic and linear polyglycerols interact with the alarmin molecule HMGB1? (2) Does dPGS interaction with HMGB1 influence the redox status of HMGB1? (3) Can dPGS prevent the loss of dendritic spines in organotypic cultures challenged with lipopolysaccharide (LPS)? LPS plays a critical role in infections with Gram-negative bacteria and is commonly used to test candidate therapeutic agents for inflammation and endotoxemia. Pathologically high LPS concentrations and other stressful stimuli cause HMGB1 release and post-translational modifications. We hypothesized that (i) electrostatic interactions of hyperbranched and linear polysulfated polyglycerols with HMGB1 will likely involve sites similar to those of heparan sulfate. (ii) dPGS can normalize HMGB1 compartmentalization in microglia exposed to LPS and prevent dendritic spine loss in the excitatory hippocampal neurons. We performed immunocytochemistry and biochemical analyses combined with confocal microscopy to determine cellular and extracellular locations of HMGB1 and morphological plasticity. Our results suggest that dPGS interacts with HMGB1 similarly to heparan sulfate. Hyperbranched dPGS and linear sulfated polymers prevent dendritic spine loss in hippocampal excitatory neurons. MS/MS analyses reveal that dPGS-HMGB1 interactions result in fully oxidized HMGB1 at critical cysteine residues (Cys23, Cys45, and Cys106). Triply oxidized HMGB1 leads to the loss of its pro-inflammatory action and could participate in dPGS-mediated spine loss prevention. LPG-Sia exposure to HMGB1 results in the oxidation of Cys23 and Cys106 but does not normalize spine density.

Specific Ion and Electric Field Controlled Diverse Ion Distribution and Electroosmotic Transport in a Polyelectrolyte Brush Grafted Nanochannel

Controlling ion distribution inside a charged nanochannel is central to using such channels in diverse applications. Here, we show the possibility of using a charged polyelectrolyte (PE) brush-grafted nanochannel for triggering diverse nanoscopic ion distribution and nanofluidic electroosmotic transport by controlling the valence and size of the counterions (that screen the charges of the PE brushes) and the strength of an externally applied axial electric field. We atomistically simulate separate cases of fully charged polyacrylic acid (PAA) brush functionalized nanochannels with Na⁺, Cs⁺, Ca²⁺, Ba²⁺, and Y³⁺ counterions screening the PE charges. Four key findings emerge from our simulations. First, we find that the counterions with a greater valence and a smaller size prefer to remain localized inside the brush layer. Second, for the case where there is an added chloride salt with the same cation (as the screening counterions), there are more coions (Cl^- ions) in the brush-free bulk than counterions (for counterions Na⁺, Ca²⁺, Ba²⁺, Y³⁺): this is a manifestation of the overscreening (OS) of the PE brush layer. Contrastingly, the number of Cs⁺ ions remain higher than the Cl^- ions inside the brush-free bulk, ensuring that there is no OS effect for this case. Third, large applied electric field enables a few Na⁺, Cs⁺, and Ba²⁺ counterions to leave the brush layer and to go to the bulk: this makes the OS of the PE brush layer disappear for the cases of PE brushes being screened by the Na⁺ and Ba²⁺ ions. On the other hand, no such electric-field-mediated disappearance of OS is observed for the cases of Ca²⁺ and Y³⁺ screening counterions; we attribute this to the firm attachment of these counterions to the negatively charged monomers. Free energy associated with a counterion binding to a PE chain corroborates this diversity in the counterion-specific response to the applied electric field. Finally, we demonstrate that such diverse ion distributions, along with specific electric-field-strength-dependent ion properties, lead to (1) electroosmotic (EOS) transport in nanochannels grafted with PAA brushes screened with Cs⁺ ions to be always counterion dominated, (2) EOS transport in nanochannels grafted with PAA brushes screened with Ca²⁺ and Y³⁺ ions to be always coion-dominated, and (3) EOS transport in nanochannels grafted with PAA brushes screened with Na⁺ and Ba²⁺ ions to be coion dominated for smaller electric fields and counterion dominated for larger electric fields.

Polyelectrolytes for Enzyme Immobilization and the Regulation of Their Properties

In this review, we considered aspects related to the application of polyelectrolytes, primarily synthetic polyanions and polycations, to immobilize enzymes and regulate their properties. We mainly focused on the description of works in which polyelectrolytes were used to create complex and unusual systems (self-regulated enzyme-polyelectrolyte complexes, artificial chaperones, polyelectrolyte brushes, layer-by-layer immobilization and others). These works represent the field of "smart polymers", whilst the trivial use of charged polymers as carriers for adsorption or covalent immobilization of proteins is beyond the scope of this short review. In addition, we have included a section on the molecular modeling of interactions between proteins and polyelectrolytes, as modeling the binding of proteins with a strictly defined, and already known, spatial structure, to disordered polymeric molecules has its own unique characteristics.

Binding of Proteins to Copolymers of Varying Charges and Hydrophobicity: A Molecular Mechanism and Computational Strategies

Because of their ability to selectively bind to a target protein, copolymer nanoparticles (NPs) containing a selected combination of hydrophobic and charged groups have been frequently reported as potent antibody-like analogues. However, due to the intrinsic disorder of the copolymer NP in terms of its random monomer sequence and the cross-linked copolymer matrix, the copolymer NP is indeed strikingly different from a well-folded protein antibody and the complexation between the copolymer NP and a target protein is likely not due to a lock-key type of interaction but possibly due to a novel and unexplored molecular mechanism. Here, we study a key biomarker protein, vimentin, interacting with a set of random copolymer chains using implicit-water explicit-ion coarse-grained (CG) molecular dynamics (MD) simulations along with biolayer interferometry (BLI) analysis. Due to the charge and hydrophobicity anisotropy on the vimentin dimer (VD) surface, a set of bound copolymers are found inhomogenously adsorbed on the VD, with energetic heterogeneity for different binding sites and cooperative effect in the adsorption. Increasing the charge or hydrophobicity of the copolymer may have different consequences on the adsorption. In this study, we found that with more copolymer charges, the protein coverage increases for copolymers of low hydrophobicity and decreases of high hydrophobicity, which is explained by the distribution and size of various functional patches on the VD in loading those copolymers. Employing a coverage-dependent Langmuir model, we propose a simulation protocol to address the full profile of the copolymer binding free energy through the fit to the simulated binding isotherm. The obtained results correlate well with those from the BLI experiment, indicating the significance of this method for the rational design of the copolymer NP with engineered protein binding affinity.

Interaction of Heparin with Proteins: Hydration Effects

We present a thermodynamic investigation of the interaction of heparin with lysozyme in the presence of potassium glutamate (KGlu). The binding constant K_b is measured by isothermal titration calorimetry (ITC) in a temperature range from 288 to 310 K for concentrations of KGlu between 25 and 175 mM. The free energy of binding ΔG_b derived from K_b is strongly decreasing with increasing concentration of KGlu, whereas the dependence of ΔG_b on temperature T is found to be small. The decrease of ΔG_b can be explained in terms of counterion release: Binding of lysozyme to the strong polyelectrolyte heparin liberates approximately three of the condensed counterions of heparin, thus increasing the entropy of the system. The dependence of ΔG_b on T, on the other hand, is traced back to a change of hydration of the protein and the polyelectrolyte upon complex formation. This dependence is quantitatively described by the parameter Δw that depends on T and vanishes at a characteristic temperature T₀. A comparison of the complex formation in the presence of KGlu with the one in the presence of NaCl demonstrates that the parameters related to hydration are changed considerably. The characteristic temperature T₀ in the presence of KGlu solutions is considerably smaller than that in the presence of NaCl solutions. The change of specific heat Δc_p is found to become more negative with increasing salt concentration: This finding agrees with the model-free analysis by the generalized van't Hoff equation. The entire analysis reveals a small but important change of the free energy of binding by hydration. It shows that these ion-specific Hofmeister effects can be modeled quantitatively in terms of a characteristic temperature T₀ and a parameter describing the dependence of Δc_p on salt concentration.

Polyethylenimine-DNA Nanoparticles under Endosomal Acidification and Implication to Gene Delivery

Non-viral gene delivery using polyethylenimine (PEI) has shown tremendous promise as a therapeutic technique. Through the formation of nanoparticles (NPs), PEIs protect genetic material such as DNA from degradation. Escape of the NPs from endosomes and lysosomes is facilitated by PEI's buffering capacity over a wide range of pH. However, little is known about the effects of endosomal acidification on the morphology of the NPs. In this work, large-scale coarse-grained simulations performed to mimic endosomal acidification reveal that NPs undergo a resizing process that is highly dependent on the N/P ratio (ratio of PEI nitrogen to DNA phosphate) at which they are prepared. With a low N/P ratio, NPs further aggregate after endosomal acidification, whereas with a high N/P ratio they dissociate. The mechanisms behind such NP resizing and its consequences on endosomal escape and nuclear trafficking are discussed. Based on the findings, suggestions are made on the PEI architecture that may enhance NP dissociation driven by endosomal acidification.

Affinity of disordered protein complexes is modulated by entropy-energy reinforcement

Intrinsically disordered proteins (IDPs), which are very common and essential to many biological activities, sometimes function via interaction with another IDP and form a fuzzy complex, which can be highly stable. It is unclear what the biophysical forces are that govern their thermodynamics and specificity, which are essential for de novo fuzzy complex design. Here, we explored the fuzzy complex formed between ProTα and H1, which are oppositely charged IDPs, by swapping the charges between them, generating variants that have either greater polyampholytic or polyelectrolytic nature as well as different charge patterns. Charge swapping and shuffling dramatically change the affinity of the fuzzy complex, which is contributed to by both enthalpy and entropy, where the latter is dominated by counterion release.

The association between two intrinsically disordered proteins (IDPs) may produce a fuzzy complex characterized by a high binding affinity, similar to that found in the ultrastable complexes formed between two well-structured proteins. Here, using coarse-grained simulations, we quantified the biophysical forces driving the formation of such fuzzy complexes. We found that the high-affinity complex formed between the highly and oppositely charged H1 and ProTα proteins is sensitive to electrostatic interactions. We investigated 52 variants of the complex by swapping charges between the two oppositely charged proteins to produce sequences whose negatively or positively charged residue content was more homogeneous or heterogenous (i.e., polyelectrolytic or polyampholytic, having higher or lower absolute net charges, respectively) than the wild type. We also changed the distributions of oppositely charged residues within each participating sequence to produce variants in which the charges were segregated or well mixed. Both types of changes significantly affect binding affinity in fuzzy complexes, which is governed by both enthalpy and entropy. The formation of H1–ProTa is supported by an increase in configurational entropy and by entropy due to counterion release. The latter can be twice as large as the former, illustrating the dominance of counterion entropy in modulating the binding thermodynamics. Complexes formed between proteins with greater absolute net charges are more stable, both enthalpically and entropically, indicating that enthalpy and entropy have a mutually reinforcing effect. The sensitivity of the thermodynamics of the complex to net charge and the charge pattern within each of the binding constituents may provide a means to achieve binding specificity between IDPs.

Development of the Sequential Binding Model and Application for Anticooperative Protein Adsorption onto Charged Dendrimers

The Langmuir binding model provides one of the simplest and elegant methods for characterizing an adsorption process. Despite its wide-ranging applications, enormous effort has been spent to further integrate complexity onto the standard Langmuir isotherm to incorporate a wide breadth of binding kinetics with the heterogeneity and cooperative effect among ligands and receptors. Here, we use statistical mechanics as a convenient theoretical framework to depict several adsorption processes on a Langmuir-like description. With regard to the system with a two-component mixture of macromolecular binders, we have derived the two-group sequential binding isotherm as an important extension of the original sequential model with more applications, including systems of non-identical binders. Via comparison of the Langmuir equilibrium with the Boltzmann equilibrium, for the first time the binding free energy defined in the Langmuir-like models can be meaningfully compared with simulations. In a practical example of the adsorption between the lysozyme protein and charged dendrimer, we have demonstrated how the calorimetry data of this system could be interpreted by the binding models described above, with an accurate description of the adsorption process, including the cooperative effect and dendrimer heterogeneity. Using the computer simulation as a benchmark, we also reveal and discuss the strengths and limitations of the proposed binding models. The entire analysis serves as a starting point for extending the standard Langmuir model to access more complicated binding processes.

Denaturation of proteins: electrostatic effects vs. hydration

The unfolding transition of proteins in aqueous solution containing various salts or uncharged solutes is a classical subject of biophysics. In many cases, this transition is a well-defined two-stage equilibrium process which can be described by a free energy of transition ΔG_u and a transition temperature T_m. For a long time, it has been known that solutes can change T_m profoundly. Here we present a phenomenological model that describes the change of T_m with the solute concentration c_s in terms of two effects: (i) the change of the number of correlated counterions Δn_ci and (ii) the change of hydration expressed through the parameter Δw and its dependence on temperature expressed through the parameter dΔc_p/dc_s. Proteins always carry charges and Δn_ci describes the uptake or release of counterions during the transition. Likewise, the parameter Δw measures the uptake or release of water during the transition. The transition takes place in a reservoir with a given salt concentration c_s that defines also the activity of water. The parameter Δn_ci is a measure for the gain or loss of free energy because of the release or uptake of ions and is related to purely entropic effects that scale with ln c_s. Δw describes the effect on ΔG_u through the loss or uptake of water molecules and contains enthalpic as well as entropic effects that scale with c_s. It is related to the enthalpy of transition ΔH_u through a Maxwell relation: the dependence of ΔH_u on c_s is proportional to the dependence of Δw on temperature. While ionic effects embodied in Δn_ci are independent of the kind of salt, the hydration effects described through Δw are directly related to Hofmeister effects of the various salt ions. A comparison with literature data underscores the general validity of the model.

A phenomenological approach to the unfolding transition of proteins is given. The model treats quantitatively the effect of electrostatics as well as of hydration (Hofmeister effects).

Dendritic polyelectrolytes with monovalent and divalent counterions: the charge regulation effect and counterion release

The charge regulation and the release of counterions are extremely important and substantial in determining the charge state of polyelectrolytes and the interaction between polyelectrolytes and proteins. Going beyond monovalent to multivalent cations, it is well-known that the effects of ions are qualitatively different. Therefore, the well-accepted descriptions of the charge regulation and the counterion release based on monovalent ions do not immediately apply to systems with multivalent ions. Here, we study the key structural and electrostatic features of charged dendrimers at hand of the pharmaceutically important dendritic polyglycerol sulfate (dPGS) macromolecule equilibrated with monovalent and divalent salts by molecular dynamics (MD) simulations. Following a simple but accurate scheme to determine its effective radius, the counterion condensed layer of the dPGS is determined with high accuracy and we observe the sequential replacement of condensed monovalent cations (MCs) to divalent cations (DCs) rendering a smaller dPGS effective charge versus the DC concentration. We resolve and track the release of counterions on the dPGS along its binding pathway with the plasma protein Human Serum Albumin (HSA). We find that the release of MCs remains favorable for the complexation leading to a considerable amount of release entropy as the driving force for complexation. The release of DCs only occurs above a certain DC concentration with a comparably smaller number of released ions than MCs. Its contribution to the binding free energy is small indicating a subtle cancellation between the entropy gain in releasing DCs and the enthalpy penalty from dissociating DCs from the dendrimer.

Polysulfates Block SARS-CoV-2 Uptake through Electrostatic Interactions*

Here we report that negatively charged polysulfates can bind to the spike protein of SARS‐CoV‐2 via electrostatic interactions. Using a plaque reduction assay, we compare inhibition of SARS‐CoV‐2 by heparin, pentosan sulfate, linear polyglycerol sulfate (LPGS) and hyperbranched polyglycerol sulfate (HPGS). Highly sulfated LPGS is the optimal inhibitor, with an IC₅₀ of 67 μg mL⁻¹ (approx. 1.6 μm). This synthetic polysulfate exhibits more than 60‐fold higher virus inhibitory activity than heparin (IC₅₀: 4084 μg mL⁻¹), along with much lower anticoagulant activity. Furthermore, in molecular dynamics simulations, we verified that LPGS can bind more strongly to the spike protein than heparin, and that LPGS can interact even more with the spike protein of the new N501Y and E484K variants. Our study demonstrates that the entry of SARS‐CoV‐2 into host cells can be blocked via electrostatic interactions, therefore LPGS can serve as a blueprint for the design of novel viral inhibitors of SARS‐CoV‐2.

Interaction of Polyelectrolytes with Proteins: Quantifying the Role of Water

A theoretical model is presented for the free energy ΔGb of complex formation between a highly charged polyelectrolyte and a protein. The model introduced here comprises both the effect of released counterions and the uptake or release of water molecules during complex formation. The resulting expression for ΔGb is hence capable of describing the dependence of ΔGb on temperature as well as on the concentration of salt in the system: An increase of the salt concentration in the solution increases the activity of the ions and counterion release becomes less effective for binding. On the other hand, an increased salt concentration leads to the decrease of the activity of water in bulk. Hence, release of water molecules during complex formation will be more advantageous and lead to an increase of the magnitude of ΔGb and the binding constant. It is furthermore demonstrated that the release or uptake of water molecules is the origin of the marked enthalpy-entropy cancellation observed during complex formation of polyelectrolytes with proteins. The comparison with experimental data on complex formation between a synthetic (sulfated dendritic polyglycerol) and natural polyelectrolytes (DNA; heparin) with proteins shows full agreement with theory.

Biomolecular interactions of ultrasmall metallic nanoparticles and nanoclusters

The use of nanoparticles (NPs) in biomedicine has made a gradual transition from proof-of-concept to clinical applications, with several NP types meeting regulatory approval or undergoing clinical trials. A new type of metallic nanostructures called ultrasmall nanoparticles (usNPs) and nanoclusters (NCs), while retaining essential properties of the larger (classical) NPs, have features common to bioactive proteins. This combination expands the potential use of usNPs and NCs to areas of diagnosis and therapy traditionally reserved for small-molecule medicine. Their distinctive physicochemical properties can lead to unique in vivo behaviors, including improved renal clearance and tumor distribution. Both the beneficial and potentially deleterious outcomes (cytotoxicity, inflammation) can, in principle, be controlled through a judicious choice of the nanocore shape and size, as well as the chemical ligands attached to the surface. At present, the ability to control the behavior of usNPs is limited, partly because advances are still needed in nanoengineering and chemical synthesis to manufacture and characterize ultrasmall nanostructures and partly because our understanding of their interactions in biological environments is incomplete. This review addresses the second limitation. We review experimental and computational methods currently available to understand molecular mechanisms, with particular attention to usNP-protein complexation, and highlight areas where further progress is needed. We discuss approaches that we find most promising to provide relevant molecular-level insight for designing usNPs with specific behaviors and pave the way to translational applications.

Insights into Interactions between Interleukin-6 and Dendritic Polyglycerols

Interleukin-6 (IL-6) is involved in physiological and pathological processes. Different pharmacological agents have been developed to block IL-6 deleterious effects and to recover homeostatic IL-6 signaling. One of the proposed nanostructures in pre-clinical investigations which reduced IL-6 concentrations is polyglycerol dendrimer, a nano-structure with multiple sulfate groups. The aim of the present study was to uncover the type of binding between critical positions in the human IL-6 structure available for binding dPGS and compare it with heparin sulfate binding. We studied these interactions by performing docking simulations of dPGS and heparins with human IL-6 using AutoDock Vina. These molecular docking analyses indicate that the two ligands have comparable affinities for the positively charged positions on the surface of IL-6. All-atom molecular dynamics simulations (MD) employing Gromacs were used to explore the binding sites and binding strengths. Results suggest two major binding sites and show that the strengths of binding are similar for heparin and dPGS (−5.5–6.4 kcal/ mol). dPGS or its analogs could be used in the therapeutic intervention in sepsis and inflammatory disorders to reduce unbound IL-6 in the plasma or tissues and its binding to the receptors. We propose that analogs of dPGS could specifically block IL-6 binding in the desired signaling mode and would be valuable new probes to establish optimized therapeutic intervention in inflammation.

Understanding the Interaction of Polyelectrolyte Architectures with Proteins and Biosystems

The counterions neutralizing the charges on polyelectrolytes such as DNA or heparin may dissociate in water and greatly influence the interaction of such polyelectrolytes with biomolecules, particularly proteins. In this Review we give an overview of studies on the interaction of proteins with polyelectrolytes and how this knowledge can be used for medical applications. Counterion release was identified as the main driving force for the binding of proteins to polyelectrolytes: Patches of positive charge become multivalent counterions of the polyelectrolyte and lead to the release of counterions from the polyelectrolyte and a concomitant increase in entropy. This is shown from investigations on the interaction of proteins with natural and synthetic polyelectrolytes. Special emphasis is paid to sulfated dendritic polyglycerols (dPGS). The Review demonstrates that we are moving to a better understanding of charge-charge interactions in systems of biological relevance. Research along these lines will aid and promote the design of synthetic polyelectrolytes for medical applications.

Overcharging of polyelectrolyte complexes: an entropic phenomenon

Overcharging in complex coacervation, in which a polyelectrolyte complex coacervate (PEC) initially containing equal moles of the cationic and anionic monomers absorbs a large excess of one type of polyelectrolyte species, is predicted using a recently developed thermodynamic model describing complexation through a combination of reversible ion binding on the chains and long-range electrostatic correlations. We show that overcharging is favored roughly equally by the translational entropy of released counterions and the binding entropy of polyelectrolytes in the polyelectrolyte complex, thus helping resolve competing explanations for overcharging in the literature. We find that the extent of overcharging is non-monotonic in the concentration of added salt and increases with both strength of ion-pairing between polyions and chain hydrophobicity. The predicted extent of overcharging of the PEC is directly compared with that of multilayers made of poly(diallyldimethylammonium), PDADMA, and poly(styrene-sulfonate), PSS, overcompensated by the polycation in two different salts: KBr and NaCl. Accounting for the specificity of salt ion interactions with the polyelectrolytes, we find good qualitative agreement between theory and experiment.

Probing the protein corona around charged macromolecules: interpretation of isothermal titration calorimetry by binding models and computer simulations

Isothermal titration calorimetry (ITC) is a widely used tool to experimentally probe the heat signal of the formation of the protein corona around macromolecules or nanoparticles. If an appropriate binding model is applied to the ITC data, the heat of binding and the binding stoichiometry as well as the binding affinity per protein can be quantified and interpreted. However, the binding of the protein to the macromolecule is governed by complex microscopic interactions. In particular, due to the steric and electrostatic protein–protein interactions within the corona as well as cooperative, charge renormalization effects of the total complex, the application of standard (e.g., Langmuir) binding models is questionable and the development of more appropriate binding models is very challenging. Here, we discuss recent developments in the interpretation of the Langmuir model applied to ITC data of protein corona formation, exemplified for the well-defined case of lysozyme coating highly charged dendritic polyglycerol sulfate (dPGS), and demonstrate that meaningful data can be extracted from the fits if properly analyzed. As we show, this is particular useful for the interpretation of ITC data by molecular computer simulations where binding affinities can be calculated but it is often not clear how to consistently compare them with the ITC data. Moreover, we discuss the connection of Langmuir models to continuum binding models (where no discrete binding sites have to be assumed) and their possible extensions toward the inclusion of leading order cooperative electrostatic effects.

Counterion Exchange in Peptide-Complexed Core-Shell Microgels

The complexation of polyvalent macroions with oppositely charged polyelectrolyte microgels can lead to core-shell structures. The shell is believed to be highly deswollen with a high concentration of counter-macroions. The core is believed to be relatively free of macroions but under a uniform compressive stress due to the deswollen shell. We use cryo-scanning electron microscopy (SEM) with X-ray microanalysis to confirm this understanding. We study poly(acrylic acid) (PAA) microgels which form a core-shell structure when complexed with a small cationic antimicrobial peptide (L5). We follow the spatial distribution of polymer, water, Na counterions, and peptide based on the characteristic X-ray intensities of C, O, Na, and N, respectively. Frozen-hydrated microgel suspensions include buffers of known composition from which calibration curves can be generated and used to quantify both the microgel water and sodium concentrations, the latter with a minimum quantifiable concentration less than 0.048 M. We find that as-synthesized PAA microgels are enriched in Na relative to the surrounding buffer as anticipated from established ideas of counterion shielding of electrostatic charge. The shell in L5-complexed microgels is depleted in Na and enriched in peptide and contains relatively little water. Our measurements furthermore show that shell/core interface is diffuse over a length scale of a few micrometers. Within the limits of detection, the core Na concentration is the same as that in as-synthesized microgels, and the core is free of peptide. The core has a slightly lower water concentration than as-synthesized controls, consistent with the hypothesis that the core is under compression from the shell.

Protein-Polyelectrolyte Complexes and Micellar Assemblies

In this review, we highlight the recent progress in our understanding of the structure, properties and applications of protein-polyelectrolyte complexes in both bulk and micellar assemblies. Protein-polyelectrolyte complexes form the basis of the genetic code, enable facile protein purification, and have emerged as enterprising candidates for simulating protocellular environments and as efficient enzymatic bioreactors. Such complexes undergo self-assembly in bulk due to a combined influence of electrostatic interactions and entropy gains from counterion release. Diversifying the self-assembly by incorporation of block polyelectrolytes has further enabled fabrication of protein-polyelectrolyte complex micelles that are multifunctional carriers for therapeutic targeted delivery of proteins such as enzymes and antibodies. We discuss research efforts focused on the structure, properties and applications of protein-polyelectrolyte complexes in both bulk and micellar assemblies, along with the influences of amphoteric nature of proteins accompanying patchy distribution of charges leading to unique phenomena including multiple complexation windows and complexation on the wrong side of the isoelectric point.

Interaction of Proteins with Polyelectrolytes: Comparison of Theory to Experiment

We discuss recent investigations of the interaction of polyelectrolytes with proteins. In particular, we review our recent studies on the interaction of simple proteins such as human serum albumin (HSA) and lysozyme with linear polyelectrolytes, charged dendrimers, charged networks, and polyelectrolyte brushes. In all cases discussed here, we combined experimental work with molecular dynamics (MD) simulations and mean-field theories. In particular, isothermal titration calorimetry (ITC) has been employed to obtain the respective binding constants K_b and the Gibbs free energy of binding. MD simulations with explicit counterions but implicit water demonstrate that counterion release is the main driving force for the binding of proteins to strongly charged polyelectrolytes: patches of positive charges located on the surface of the protein become multivalent counterions of the polyelectrolyte, thereby releasing a number of counterions condensed on the polyelectrolyte. The binding Gibbs free energy due to counterion release is predicted to scale with the logarithm of the salt concentration in the system, which is verified by both simulations and experiment. In several cases, namely, for the interaction of proteins with linear polyelectrolytes and highly charged hydrophilic dendrimers, the binding constant could be calculated from simulations to very good approximation. This finding demonstrated that in these cases explicit hydration effects do not contribute to the Gibbs free energy of binding. The Gibbs free energy can also be used to predict the kinetics of protein uptake by microgels for a given system by applying dynamic density functional theory. The entire discussion demonstrates that the direct comparison of theory with experiments can lead to a full understanding of the interaction of proteins with charged polymers. Possible implications for applications, such as drug design, are discussed.

Protein Interaction with Charged Macromolecules: From Model Polymers to Unfolded Proteins and Post-Translational Modifications

Interaction of proteins with charged macromolecules is involved in many processes in cells. Firstly, there are many naturally occurred charged polymers such as DNA and RNA, polyphosphates, sulfated glycosaminoglycans, etc., as well as pronouncedly charged proteins such as histones or actin. Electrostatic interactions are also important for "generic" proteins, which are not generally considered as polyanions or polycations. Finally, protein behavior can be altered due to post-translational modifications such as phosphorylation, sulfation, and glycation, which change a local charge of the protein region. Herein we review molecular modeling for the investigation of such interactions, from model polyanions and polycations to unfolded proteins. We will show that electrostatic interactions are ubiquitous, and molecular dynamics simulations provide an outstanding opportunity to look inside binding and reveal the contribution of electrostatic interactions. Since a molecular dynamics simulation is only a model, we will comprehensively consider its relationship with the experimental data.

Protein⁻Polyelectrolyte Interaction: Thermodynamic Analysis Based on the Titration Method †

This review discussed the mechanisms including theories and binding stages concerning the protein⁻polyelectrolyte (PE) interaction, as well as the applications for both complexation and coacervation states of protein⁻PE pairs. In particular, this review focused on the applications of titration techniques, that is, turbidimetric titration and isothermal titration calorimetry (ITC), in understanding the protein⁻PE binding process. To be specific, by providing thermodynamic information such as pHc, pHφ, binding constant, entropy, and enthalpy change, titration techniques could shed light on the binding affinity, binding stoichiometry, and driving force of the protein⁻PE interaction, which significantly guide the applications by utilization of these interactions. Recent reports concerning interactions between proteins and different types of polyelectrolytes, that is, linear polyelectrolytes and polyelectrolyte modified nanoparticles, are summarized with their binding differences systematically discussed and compared based on the two major titration techniques. We believe this short review could provide valuable insight in the understanding of the structure⁻property relationship and the design of applied biomedical PE-based systems with optimal performance.

Thermodynamics of the Binding of Lysozyme to a Dendritic Polyelectrolyte: Electrostatics Versus Hydration

The interaction between dendritic polyglycerol sulfate (dPGS) of the second generation and lysozyme was studied by isothermal titration calorimetry (ITC) at different temperatures and salt concentrations. Analysis by ITC showed that 2-3 lysozyme molecules were bound to each dPGS. The resulting binding constant K _b and the Gibbs free energy ΔG ^o decreased markedly with increasing salt concentration but were nearly independent of temperature. The salt dependence of K _b led to the conclusion that ca. 3 counterions bound to dPGS were released upon complex formation. The gain in entropy ΔG _ci by this counterion-release scales logarithmically with salt concentration and is the main driving force for binding. The temperature dependence of ΔG ^o was analyzed by the nonlinear van't Hoff plot, taking into account a finite heat capacity change ΔC _p,vH. This evaluation led to the binding enthalpy ΔH _vH and the binding entropy ΔS _vH. Both quantities varied strongly with temperature and even changed sign, but they compensated each other throughout the entire range of temperature. Coarse-grained computer simulations with explicit salt and implicit water were used to obtain the binding free energies that agreed with ITC results. Thus, electrostatic factors were the driving forces for binding whereas all hydration contributions leading to the strongly varying ΔH _vH and ΔS _vH canceled out. The calorimetric enthalpy ΔH _ITC measured directly by ITC differed largely from ΔH _vH. ITC measurements done in two buffer systems with different ionization enthalpies revealed that binding was linked to buffer ionization and a partial protonation of the protein.

Charge and hydration structure of dendritic polyelectrolytes: molecular simulations of polyglycerol sulphate

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 renormalization effects, we address the challenges of how to obtain a well-defined effective charge and surface potential of dPGS for practical applications. We compare implicit- and explicit-solvent approaches in our all-atom simulations with the coarse-grained simulations from our previous work. We find consistent values for the effective electrostatic size (i.e., the location of the effective charge of a Debye-Hückel sphere) within all the approaches, deviating at most by the size of a water molecule. Finally, the excess chemical potential of water insertion into dPGS and its thermodynamic signature are presented and rationalized.