Quantitative prediction of multivalent ligand–receptor binding affinities for influenza, cholera, and anthrax inhibition

Multivalency achieves strong, yet reversible binding by the simultaneous formation of multiple weak bonds. It is a key interaction principle in biology and promising for the synthesis of high-affinity inhibitors of pathogens. We present a molecular model for the binding affinity of synthetic multivalent ligands onto multivalent receptors consisting of n receptor units arranged on a regular polygon. Ligands consist of a geometrically matching rigid polygonal core to which monovalent ligand units are attached via flexible linker polymers, closely mimicking existing experimental designs. The calculated binding affinities quantitatively agree with experimental studies for cholera toxin (n = 5) and anthrax receptor (n = 7) and allow to predict optimal core size and optimal linker length. Maximal binding affinity is achieved for a core that matches the receptor size and for linkers that have an equilibrium end-to-end distance that is slightly longer than the geometric separation between ligand core and receptor sites. Linkers that are longer than optimal are greatly preferable compared to shorter linkers. The angular steric restriction between ligand unit and linker polymer is shown to be a key parameter. We construct an enhancement diagram that quantifies the multivalent binding affinity compared to monovalent ligands. We conclude that multivalent ligands against influenza viral hemagglutinin (n = 3), cholera toxin (n = 5), and anthrax receptor (n = 7) can outperform monovalent ligands only for a monovalent ligand affinity that exceeds a core-size dependent threshold value. Thus, multivalent drug design needs to balance core size, linker length, as well as monovalent ligand unit affinity

Chemically Active Wetting

Wetting of liquid droplets on passive surfaces is ubiquitous in our daily lives, and the governing physical laws are well-understood. When surfaces become active, however, the governing laws of wetting remain elusive. Here we propose chemically active wetting as a new class of active systems where the surface is active due to a binding process that is maintained away from equilibrium. We derive the corresponding non-equilibrium thermodynamic theory and show that active binding fundamentally changes the wetting behavior, leading to steady, non-equilibrium states with droplet shapes reminiscent of a pancake or a mushroom. The origin of such anomalous shapes can be explained by mapping to electrostatics, where pairs of binding sinks and sources correspond to electrostatic dipoles along the triple line. This is an example of a more general analogy, where localized chemical activity gives rise to a multipole field of the chemical potential. The underlying physics is relevant for cells, where droplet-forming proteins can bind to membranes accompanied by the turnover of biological fuels

The effect of temperature on single-polypeptide adsorption

The hydrophobic attraction (HA) is believed to be one of the main driving forces for protein folding. Understanding its temperature dependence promises a deeper understanding of protein folding. Herein, we present an approach to investigate the HA with a combined experimental and simulation approach, which is complementary to previous studies on the temperature dependence of the solvation of small hydrophobic spherical particles. We determine the temperature dependence of the free-energy change and detachment length upon desorption of single polypeptides from hydrophobic substrates in aqueous environment. Both the atomic force microscopy (AFM) based experiments and the molecular dynamics (MD) simulations show only a weak dependence of the free energy change on temperature. In fact, depending on the substrate, we find a maximum or a minimum in the temperature-dependent free energy change, meaning that the entropy increases or decreases with temperature for different substrates. These observations are in contrast to the solvation of small hydrophobic particles and can be rationalized by a compensation mechanism between the various contributions to the desorption force. On the one hand this is reminiscent of the protein folding process, where large entropic and enthalpic contributions compensate each other to result in a small free energy difference between the folded and unfolded state. On the other hand, the protein folding process shows much stronger temperature dependence, pointing to a fundamental difference between protein folding and adsorption. Nevertheless such temperature dependent single molecule desorption studies open large possibilities to study equilibrium and non-equilibrium processes dominated by the hydrophobic attraction

Theory of Wetting Dynamics with Surface Binding

Biomolecules, such as proteins and RNAs, can phase separate in the cytoplasm of cells to form biological condensates. Such condensates are liquid-like droplets that can wet biological surfaces such as membranes. Many molecules that can participate in phase separation can also reversibly bind to membrane surfaces. When a droplet wets such a surface, these molecules can diffuse both inside the droplet or in the bound state on the surface. How the interplay between surface binding and surface diffusion affects the wetting kinetics is not well understood. Here, we derive the governing equations using non-equilibrium thermodynamics by relating the diffusive fluxes and forces at the surface coupled to the bulk. We use our theory to study the spreading kinetics in the presence of surface binding and find that binding speeds up wetting by nucleating a droplet inside the surface. Our results are relevant both to artificial systems and to condensates in cells. They suggest that the wetting of droplets in living cells could be regulated by two-dimensional droplets in the surface-bound layer changing the binding affinity to biological surfaces

A simulation method for the wetting dynamics of liquid droplets on deformable membranes

Biological cells utilize membranes and liquid-like droplets, known as biomolecular condensates, to structure their interior. The interaction of droplets and membranes, despite being involved in several key biological processes, is so far little understood. Here, we present a first numerical method to simulate the continuum dynamics of droplets interacting with deformable membranes via wetting. The method combines the advantages of the phase-field method for multi-phase flow simulation and the arbitrary Lagrangian-Eulerian (ALE) method for an explicit description of the elastic surface. The model is thermodynamically consistent, coupling bulk hydrodynamics with capillary forces, as well as bending, tension, and stretching of a thin membrane. The method is validated by comparing simulations for single droplets to theoretical results of shape equations, and its capabilities are illustrated in 2D and 3D axisymmetric scenarios

Stability of a biomembrane tube covered with proteins

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Hydration effects turn a highly stretched polymer from an entropic into an energetic spring

Polyethylene glycol (PEG) is a structurally simple and nontoxic water-soluble polymer that is widely used in medical and pharmaceutical applications as molecular linker and spacer. In such applications, PEG’s elastic response against conformational deformations is key to its function. According to text-book knowledge, a polymer reacts to the stretching of its end-to-end separation by a decrease in entropy that is due to the reduction of available conformations, which is why polymers are commonly called entropic springs. By a combination of single-molecule force spectroscopy experiments with molecular dynamics simulations in explicit water, we show that entropic hydration effects almost exactly compensate the chain conformational entropy loss at high stretching. Our simulations reveal that this entropic compensation is due to the stretching-induced release of water molecules that in the relaxed state form double hydrogen bonds with PEG. As a consequence, the stretching response of PEG is predominantly of energetic, not of entropic, origin at high forces and caused by hydration effects, while PEG backbone deformations only play a minor role. These findings demonstrate the importance of hydration for the mechanics of macromolecules and constitute a case example that sheds light on the antagonistic interplay of conformational and hydration degrees of freedom

Force Response of Polypeptide Chains from Water-Explicit MD Simulations

Using molecular dynamics simulations in explicit water, the force–extension relations for the five homopeptides polyglycine, polyalanine, polyasparagine, poly(glutamic acid), and polylysine are investigated. From simulations in the low-force regime the Kuhn length is determined, from simulations in the high-force regime the equilibrium contour length and the linear and nonlinear stretching moduli, which agree well with quantum-chemical density-functional theory calculations, are determined. All these parameters vary considerably between the different polypeptides. The augmented inhomogeneous partially freely rotating chain (iPFRC) model, which accounts for side-chain interactions and restricted dihedral rotation, is demonstrated to describe the simulated force–extension relations very well. We present a quantitative comparison between published experimental single-molecule force–extension curves for different polypeptides with simulation and model predictions. The thermodynamic stretching properties of polypeptides are investigated by decomposition of the stretching free energy into energetic and entropic contributions

Size Dependence of Steric Shielding and Multivalency Effects for Globular Binding Inhibitors

Competitive binding inhibitors based on multivalent nanoparticles have shown great potential for preventing virus infections. However, general design principles of highly efficient inhibitors are lacking as the quantitative impact of factors such as virus concentration, inhibitor size, steric shielding, or multivalency effects in the inhibition process is not known. Based on two complementary experimental inhibition assays we determined size- dependent steric shielding and multivalency effects. This allowed us to adapt the Cheng–Prusoff equation for its application to multivalent systems. Our results show that the particle and volume normalized IC50 value of an inhibitor at very low virus concentration predominantly depends on its multivalent association constant, which itself exponentially increases with the inhibitor/virus contact area and ligand density. Compared to multivalency effects, the contribution of steric shielding to the IC50 values is only minor, and its impact is only noticeable if the multivalent dissociation constant is far below the virus concentration, which means if all inhibitors are bound to the virus. The dependence of the predominant effect, either steric shielding or multivalency, on the virus concentration has significant implications on the in vitro testing of competitive binding inhibitors and determines optimal inhibitor diameters for the efficient inhibition of viruses

On the relationship between peptide adsorption resistance and surface contact angle: a combined experimental and simulation single-molecule study

The force-induced desorption of single peptide chains from mixed OH/CH3-terminated self-assembled monolayers is studied in closely matched molecular dynamics simulations and atomic force microscopy experiments with the goal to gain microscopic understanding of the transition between peptide adsorption and adsorption resistance as the surface contact angle is varied. In both simulations and experiments, the surfaces become adsorption resistant against hydrophilic as well as hydrophobic peptides when their contact angle decreases below θ ≈ 50°-60°, thus confirming the so-called Berg limit established in the context of protein and cell adsorption. Entropy/enthalpy decomposition of the simulation results reveals that the key discriminator between the adsorption of different residues on a hydrophobic monolayer is of entropic nature and thus is suggested to be linked to the hydrophobic effect. By pushing a polyalanine peptide onto a polar surface, simulations reveal that the peptide adsorption resistance is caused by the strongly bound water hydration layer and characterized by the simultaneous gain of both total entropy in the system and total number of hydrogen bonds between water, peptide, and surface. This mechanistic insight into peptide adsorption resistance might help to refine design principles for anti-fouling surfaces