Anomalous multipole expansion: Charge regulation of patchy inhomogeneously charged spherical particles

Combined Effects of Pressure and Ionic Strength on Protein-Protein Interactions: An Empirical Approach

Proteins are exposed to hydrostatic pressure (HP) in a variety of ecosystems as well as in processing steps such as freeze-thaw, cell disruption, sterilization, and homogenization, yet pressure effects on protein-protein interactions (PPIs) remain underexplored. With the goal of contributing toward the expanded use of HP as a fundamental control parameter in protein research, processing, and engineering, small-angle X-ray scattering was used to examine the effects of HP and ionic strength on ovalbumin, a model protein. Based on an extensive data set, we develop an empirical method for scaling PPIs to a master curve by combining HP and osmotic effects. We define an effective pressure parameter that has been shown to successfully apply to other model protein data available in the literature, with deviations evident for proteins that do not follow the apparent Hofmeister series. The limitations of the empirical scaling are discussed in the context of the hypothesized underlying mechanisms.

Unusual Aspects of Charge Regulation in Flexible Weak Polyelectrolytes

This article reviews the state of the art of the studies on charge regulation (CR) effects in flexible weak polyelectrolytes (FWPE). The characteristic of FWPE is the strong coupling of ionization and conformational degrees of freedom. After introducing the necessary fundamental concepts, some unconventional aspects of the the physical chemistry of FWPE are discussed. These aspects are: (i) the extension of statistical mechanics techniques to include ionization equilibria and, in particular, the use of the recently proposed Site Binding-Rotational Isomeric State (SBRIS) model, which allows the calculation of ionization and conformational properties on the same foot; (ii) the recent progresses in the inclusion of proton equilibria in computer simulations; (iii) the possibility of mechanically induced CR in the stretching of FWPE; (iv) the non-trivial adsorption of FWPE on ionized surfaces with the same charge sign as the PE (the so-called "wrong side" of the isoelectric point); (v) the influence of macromolecular crowding on CR.

Adsorption of lysozyme into a charged confining pore

Several applications arise from the confinement of proteins on surfaces because their stability and biological activity are enhanced. It is also known that the way in which a protein adsorbs on the surface is important for its biological function since its active sites should not be obstructed. In this study, the adsorption properties of hen egg-white lysozyme, HEWL, into a negatively charged silica pore is examined by employing a coarse-grained model and constant-pH Monte Carlo simulations. The role of electrostatic interactions is taken into account via including the Debye-Hückel potentials into the Cα structure-based model. We evaluate the effects of pH, salt concentration, and pore radius on the protein preferential orientation and spatial distribution of its residues regarding the pore surface. By mapping the residues that stay closer to the pore surface, we find that the increase of pH leads to orientational changes of the adsorbed protein when the solution pH gets closer to the HEWL isoelectric point. Under these conditions, the pK_a shift of these important residues caused by the adsorption into the charged confining surface results in a HEWL charge distribution that stabilizes the adsorption in the observed protein orientation. We compare our observations to the results of the pK_a shift for HEWL available in the literature and to some experimental data.

Site Correlations, Capacitance, and Polarizability From Protein Protonation Fluctuations

We generalize the Kirkwood-Shumaker theory of protonation fluctuation for an anisotropic distribution of dissociable charges on a globular protein. The fluctuations of the total charge and the total dipole moment, in contrast to their average values, depend on the same proton occupancy correlator, thus exhibiting a similar dependence also on the solution pH. This has important consequences for the Kirkwood-Shumaker interaction and its dependence on the bathing solution conditions.

Effects of surface charge and environmental factors on the electrostatic interaction of fiber with virus-like particle: A case of coronavirus

We propose a theoretical model to elucidate intermolecular electrostatic interactions between a virus and a substrate. Our model treats the virus as a homogeneous particle having surface charge and the polymer fiber of the respirator as a charged plane. Electric potentials surrounding the virus and fiber are influenced by the surface charge distribution of the virus. We use Poisson-Boltzmann equations to calculate electric potentials. Then, Derjaguin's approximation and a linear superposition of the potential function are extended to determine the electrostatic force. In this work, we apply this model for coronavirus or SARS-CoV-2 case and numerical results quantitatively agree with prior simulation. We find that the influence of fiber's potential on the surface charge of the virus is important and is considered in interaction calculations to obtain better accuracy. The electrostatic interaction significantly decays with increasing separation distance, and this curve becomes steeper when adding more salt. Although the interaction force increases with heating, one can observe the repulsive-attractive transition when the environment is acidic.

Quantifying the Separation of Positive and Negative Areas in Electrostatic Potential for Predicting Feasibility of Ammonium Sulfate for Protein Crystallization

Ammonium sulfate (AS) and poly(ethylene glycol) (PEG) are the most popular precipitants in protein crystallization. Some proteins are preferably crystallized by AS, while some are by PEG. The electrostatic potential is related to the preference of the precipitant agents. The iso-surfaces of the electrostatic potentials for the AS-crystallized proteins display a common shape and a distinct separation between the positive and negative areas. In contrast, the PEG-crystallized proteins show unclear positive and negative separation. In this work, we propose schemes to quantitatively evaluate the separation for predicting which precipitant is favorable for crystal growth between AS or PEG. Three methods were attempted to quantify the amplitude of the separation, separation distance, dipole moment, and shape regularity. The positive and negative areas are approximated to the spherical potentials caused by point charges. The first method is a measurement of the distance between the positive and negative point charges. The second one is an assessment including the quantity of electric charge into the distance. The last one is an approach monitoring the clarity of the positive and negative separation. The average value for 25 kinds of AS-preferring proteins was higher than that for the PEG-preferring ones in all three methods. Therefore, every method can distinguish the proteins preferring AS for crystal growth from those preferring PEG. These methods require an iso-surface of the electrostatic potential depicted at a certain contouring value. The shape of the iso-surface depends on the contouring value. The dependency on contour was examined by depicting the iso-surfaces of electrostatic potential with three values at ±0.8, ±0.5, and ±0.2 kT/e. While reducing the contouring value leads to the increase in separation distance and the decrease in shape regularity, dipole moment is independent of the alteration of contouring value. While the AS-preferring proteins are distinguishable from the PEG-preferring ones in any contouring values, the iso-surface at ±0.5 kT/e seems adequate for regular use. The dipole moment assessment is feasible for the choice of potent precipitants for crystal growth in experiments.

Relative humidity in droplet and airborne transmission of disease

A large number of infectious diseases are transmitted by respiratory droplets. How long these droplets persist in the air, how far they can travel, and how long the pathogens they might carry survive are all decisive factors for the spread of droplet-borne diseases. The subject is extremely multifaceted and its aspects range across different disciplines, yet most of them have only seldom been considered in the physics community. In this review, we discuss the physical principles that govern the fate of respiratory droplets and any viruses trapped inside them, with a focus on the role of relative humidity. Importantly, low relative humidity-as encountered, for instance, indoors during winter and inside aircraft-facilitates evaporation and keeps even initially large droplets suspended in air as aerosol for extended periods of time. What is more, relative humidity affects the stability of viruses in aerosol through several physical mechanisms such as efflorescence and inactivation at the air-water interface, whose role in virus inactivation nonetheless remains poorly understood. Elucidating the role of relative humidity in the droplet spread of disease would permit us to design preventive measures that could aid in reducing the chance of transmission, particularly in indoor environment.

Charge regulation of colloidal particles in aqueous solutions

We study the charge regulation of colloidal particles inside aqueous electrolyte solutions. To stabilize a colloidal suspension against precipitation, colloidal particles are synthesized with either acidic or basic groups on their surface. On contact with water, these surface groups undergo proton transfer reactions, resulting in colloidal surface charge. The charge is determined by the condition of local chemical equilibrium between hydronium ions inside the solution and at the colloidal surface. We use a model of Baxter sticky spheres to explicitly calculate the equilibrium dissociation constants and to construct a theory which is able to quantitatively predict the effective charge of colloidal particles with either acidic or basic surface groups. The predictions of the theory for the model are found to be in excellent agreement with the results of Monte Carlo simulations. This theory is further extended to treat colloidal particles with a mixture of both acidic and basic surface groups.

Complete Charge Regulation by a Redox Enzyme Upon Single Electron Transfer

The degree by which metalloproteins partially regulate net charge (Z) upon electron transfer (ET) was recently measured for the first time using "protein charge ladders" of azurin, cytochrome c, and myoglobin [Angew. Chem. Int. Ed. 2018, 57(19), 5364-5368; Angew. Chem. 2018, 130, 5462-5466]. Here, we show that Cu, Zn superoxide dismutase (SOD1) is unique among proteins in its ability to resist changes in net charge upon single ET (e.g., ΔZ_ET(SOD1) =0.05±0.08 per electron, compared to ΔZ_ET(Cyt-c) =1.19±0.02). This total regulation of net charge by SOD1 is attributed to the protonation of the bridging histidine upon copper reduction, yielding redox centers that are isoelectric at both copper oxidation states. Charge regulation by SOD1 would prevent long range coulombic perturbations to residue pK_a 's upon ET at copper, allowing SOD1's "electrostatic loop" to attract superoxide with equal affinity (at both redox states of copper) during diffusion-limited reduction and oxidation of superoxide.

Charge Regulation of Colloidal Particles: Theory and Simulations

To explore charge regulation (CR) in physicochemical and biophysical systems, we present a model of colloidal particles with sticky adsorption sites which account for the formation of covalent bonds between the hydronium ions and the surface functional groups. Using this model and Monte Carlo simulations, we find that the standard Ninham and Parsegian (NP) theory of CR leads to results which deviate significantly from computer simulations. The problem with the NP approach is traced back to the use of a bulk equilibrium constant to account for surface chemical reactions. To resolve this difficulty we present a new theory of CR. The fundamental ingredient of the new approach is the sticky length, which is nontrivially related to the bulk equilibrium constant. The theory is found to be in excellent agreement with computer simulations, without any adjustable parameters. As an application of the theory we calculate the effective charge of colloidal particles containing carboxyl groups, as a function of pH and salt concentration.

Effects of Intrinsic Local Fields on Molecular Fluorescence and Energy Transfer: Dipole Mechanisms and Surface Potentials

A general theory is developed to identify the influence of local dipole fields on fluorescence and intermolecular electronic excitation transfer. The analysis, based on electrodynamical principles, identifies the fundamental quantum mechanisms and delivers full analytical results. The aim is to afford new physical insights, assisting the interpretation of measurements on the specific effects of local molecular dipoles on direct fluorescence and on fluorescence resonance energy transfer. Dipole field effects, which include those originating from intrinsically polar chromophores and surface field gradients, also prove to be manifest in electronic transitions of quadrupole symmetry character. The results have particular significance for fluorescence studies of cell membrane biophysics.

What Are We Missing by Not Measuring the Net Charge of Proteins?

The net electrostatic charge (Z) of a folded protein in solution represents a bird's eye view of its surface potentials-including contributions from tightly bound metal, solvent, buffer, and cosolvent ions-and remains one of its most enigmatic properties. Few tools are available to the average biochemist to rapidly and accurately measure Z at pH≠pI. Tools that have been developed more recently seem to go unnoticed. Most scientists are content with this void and estimate the net charge of a protein from its amino acid sequence, using textbook values of pK_a . Thus, Z remains unmeasured for nearly all folded proteins at pH≠pI. When marveling at all that has been learned from accurately measuring the other fundamental property of a protein-its mass-one wonders: what are we missing by not measuring the net charge of folded, solvated proteins? A few big questions immediately emerge in bioinorganic chemistry. When a single electron is transferred to a metalloprotein, does the net charge of the protein change by approximately one elementary unit of charge or does charge regulation dominate, that is, do the pK_a values of most ionizable residues (or just a few residues) adjust in response to (or in concert with) electron transfer? Would the free energy of charge regulation (ΔΔG_z ) account for most of the outer sphere reorganization energy associated with electron transfer? Or would ΔΔG_z contribute more to the redox potential? And what about metal binding itself? When an apo-metalloprotein, bearing minimal net negative charge (e.g., Z=-2.0) binds one or more metal cations, is the net charge abolished or inverted to positive? Or do metalloproteins regulate net charge when coordinating metal ions? The author's group has recently dusted off a relatively obscure tool-the "protein charge ladder"-and used it to begin to answer these basic questions.

Insights into the ZIKV NS1 Virology from Different Strains through a Fine Analysis of Physicochemical Properties

The flavivirus genus has several organisms responsible for generating various diseases in humans. Recently, especially in tropical regions, Zika virus (ZIKV) has raised great health concerns due to the high number of cases affecting the area during the last years that has been accompanied by a rise in the cases of the Guillain-Barré syndrome and fetal and neonatal microcephaly. Diagnosis is still difficult since the clinical symptoms between ZIKV and other flaviviruses (e.g., dengue and yellow fever) are highly similar. The understanding of their common physicochemical properties that are pH-dependent and biomolecular interaction features and their differences sheds light on the relation strain-virulence and might suggest alternative strategies toward differential serological diagnostics and therapeutic intervention. Due to their immunogenicity, the primary focus of this study was on the ZIKV nonstructural proteins 1 (NS1). By means of computational studies and semiquantitative theoretical analyses, we calculated the main physicochemical properties of this protein from different strains that are directly responsible for the biomolecular interactions and, therefore, can be related to the differential infectivity of the strains. We also mapped the electrostatic differences at both the sequence and structural levels for the strains from Uganda to Brazil, which could suggest possible molecular mechanisms for the increase of the virulence of ZIKV in Brazil. Exploring the interfaces used by NS1 to self-associate in some different oligomeric states and interact with membranes and the antibody, we could map the strategy used by the ZIKV during its evolutionary process. This indicates possible molecular mechanisms that can be correlated with the different immunological responses. By comparing with the known antibody structure available for the West Nile virus, we demonstrated that this antibody would have difficulties to neutralize the NS1 from the Brazilian strain. The present study also opens up perspectives to computationally design high-specificity antibodies.

Solution Structure Effects on the Properties of Electric Double Layers with Surface Charge Regulation Assessed by Density Functional Theory

The structure of electrolyte solutions in electric double layers is primarily determined by the solvent, despite the fact that it is usually neutral and not subject to Coulombic interactions. The number of solvent molecules in a typical electrolyte solution may be significantly greater that the number of ions. Hence, the charged species compete for space with a much larger number of neutral molecules, which has a strong effect on the density distributions near charged surfaces. Even for very dilute electrolyte solutions, the density profiles resemble liquidlike structure, which is entirely due to the presence of the dense solvent. Our work demonstrates that the solvent structural effect strongly couples to the surface chemistry, which governs the charge and potential. We argue that a comprehensive statistical-mechanical approach, such as classical density functional theory that explicitly includes all solution species, in combination with a surface charge regulation condition at the interface, provides an excellent approach for describing charged interfaces. It allows for revealing important physical features and includes non-Coulombic contributions such as ionic and surface solvation.