Interaction of Lysozyme with a Dendritic Polyelectrolyte: Quantitative Analysis of the Free Energy of Binding and Comparison to Molecular Dynamics Simulations

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.

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.

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.

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).

Interaction of Linear Polyelectrolytes with Proteins: Role of Specific Charge-Charge Interaction and Ionic Strength

We present a thermodynamic study of the interaction of synthetic, linear polyelectrolytes with bovine serum albumin (BSA). All polyelectrolytes are based on poly(allyl glycidyl ether) which has been modified by polymer-analogous reaction with anionic (-SO₃Na), cationic (-NH₃Cl or -NHMe₂Cl) or zwitterionic groups (-NMe₂(CH₂)₃SO₃). While the anionic polymer shows a very weak interaction, the zwitterionic polymer exhibits no interaction with BSA (pI = 4.7) under the applied pH = 7.4, ionic strength (I = 23–80 mM) and temperature conditions (T = 20–37 °C). A strong binding, however, was observed for the polycations bearing primary amino or tertiary dimethyl amino groups, which could be analysed in detail by isothermal titration calorimetry (ITC). The analysis was done using an expression which describes the free energy of binding, ΔG_b, as the function of the two decisive variables, temperature, T, and salt concentration, c_s. The underlying model splits ΔG_b into a term related to counterion release and a term related to water release. While the number of released counter ions is similar for both systems, the release of bound water is more important for the primary amine compared to the tertiary N,N-dimethyl amine presenting polymer. This finding is further traced back to a closer contact of the polymers’ protonated primary amino groups in the complex with oppositely charged moieties of BSA as compared to the bulkier protonated tertiary amine groups. We thus present an investigation that quantifies both driving forces for electrostatic binding, namely counterion release and change of hydration, which contribute to a deeper understanding with direct impact on future advancements in the biomedical field.

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.

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.

Nanotherapeutic Modulation of Human Neural Cells and Glioblastoma in Organoids and Monocultures

Inflammatory processes in the brain are orchestrated by microglia and astrocytes in response to activators such as pathogen-associated molecular patterns, danger-associated molecular patterns and some nanostructures. Microglia are the primary immune responders in the brain and initiate responses amplified by astrocytes through intercellular signaling. Intercellular communication between neural cells can be studied in cerebral organoids, co-cultures or in vivo. We used human cerebral organoids and glioblastoma co-cultures to study glia modulation by dendritic polyglycerol sulfate (dPGS). dPGS is an extensively studied nanostructure with inherent anti-inflammatory properties. Under inflammatory conditions, lipocalin-2 levels in astrocytes are markedly increased and indirectly enhanced by soluble factors released from hyperactive microglia. dPGS is an effective anti-inflammatory modulator of these markers. Our results show that dPGS can enter neural cells in cerebral organoids and glial cells in monocultures in a time-dependent manner. dPGS markedly reduces lipocalin-2 abundance in the neural cells. Glioblastoma tumoroids of astrocytic origin respond to activated microglia with enhanced invasiveness, whereas conditioned media from dPGS-treated microglia reduce tumoroid invasiveness. Considering that many nanostructures have only been tested in cancer cells and rodent models, experiments in human 3D cerebral organoids and co-cultures are complementary in vitro models to evaluate nanotherapeutics in the pre-clinical setting. Thoroughly characterized organoids and standardized procedures for their preparation are prerequisites to gain information of translational value in nanomedicine. This study provides data for a well-characterized dendrimer (dPGS) that modulates the activation state of human microglia implicated in brain tumor invasiveness.

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.

Facile Evaluation of Nanoparticle-Protein Interaction Based on Charge Neutralization with Pulsed Streaming Potential Measurement

Exploration of simple and universal methods to quantitatively measure nanoparticle (NP)-protein interaction is of great importance. In this work, pulsed streaming potential (SP) measurement has been used to evaluate the interaction between NPs and proteins within microchannels. Graphene oxide (GO) and SiO₂ NPs were selected to represent two kinds of NPs. Lysozyme and common blood proteins, including albumin V, γ-globulins, and fibrinogen, were used as model proteins. The linear relationship between the initial adsorption rate (S = dE_r/dt) and the concentration of proteins was observed. Combined with the Hill equation, the microscopic dissociation constant (K_D) and the Hill coefficient (n) between NPs and proteins were calculated based on the relationship between S and the concentration of each protein. The concentration of free proteins which have not interacted with the NPs in the NPs-protein mixture could also be measured. The influence of pH, conductivity, and ionic strengths of the incubation buffer on the interaction between GO and lysozyme was evaluated based on the constant K_D. The interaction intensity between NPs and proteins was defined as charge neutralization efficiency Q_C, which could be calculated from the value of S. It takes only 150 s to get the whole set of data under the optimized experiment parameters. The measurement solely depends on the surface charge, no intrinsic fluorescence is required for either the NPs or the proteins, and no labeling or immobilization process is involved as well.