Measurement of electrostatic interactions in protein folding with the use of protein charge ladders

This paper describes a new method for the measurement of the role of interactions between charged groups on the energetics of protein folding. This method uses capillary electrophoresis (CE) and protein charge ladders (mixtures of protein derivatives that differ incrementally in number of charged groups) to measure, in a single set of electrophoresis experiments, the free energy of unfolding (DeltaG(D-N)) of alpha-lactalbumin (alpha-LA) as a function of net charge. These same data also yield the hydrodynamic radius, R(H), and net charge measured by CE, Z(CE), of the folded and denatured proteins. Alpha-LA unfolds to a compact denatured state under mildly alkaline conditions; a small increase in R(H) (11%, 2 A) coincides with a large increase in Z(CE) (71%, -4 charge units), relative to the folded state. The increase in Z(CE), in turn, predicts a large pH dependence of free energy of unfolding (-22 kJ/mol per unit increase in pH), due to differences in proton binding in the folded and denatured states. The free energy of unfolding correlates with the square of net charge of the members of the charge ladder. The differential dependence of DeltaG(D-N) on net charge for holo-alpha-LA, (partial differential) DeltaG(D-N)/(partial differential)Z = -0.14Z kJ/mol per unit of charge. This dependence of DeltaG(D-N) on net charge is a result of a net electrostatic repulsion among charge groups on the protein. These results, together with data from pH titrations, show that both the effects of electrostatic repulsion and differences in proton binding in the folded and denatured states can play an important role in the pH dependence of this protein; the relative magnitude of these effects varies with pH. The combination of charge ladders and CE is a rapid and efficient tool that measures the contributions of electrostatics to the energetics of protein folding, and the size and charge of proteins as they unfold. All this information is obtained from a single set of electrophoresis experiments.     

Fundamental aspects of electrostatic interactions and charge renormalization in electrolyte systems

The consistent inclusion of ion-ion correlations and molecular solvent effects in electrolyte theory can be expressed in a physical formalism, where the particles acquire a renormalized charge density and where they interact electrostatically via a generalized screened Coulomb potential. The latter usually decays for large distances r like a Yukawa function exp(-κr)/r, where 1/κ is the decay length (normally different from the Debye length), but, for smaller r, the screened Coulomb potential is a more complicated function. The resulting electrostatic theory, “Yukawa electrostatics”, differs in many important aspects from ordinary (unscreened) Coulomb electrostatics. In the present paper, we give illustrations and explanations of some important differences between Coulomb and Yukawa electrostatics. The effective “Yukawa charge” of a particle differs from the ordinary Coulombic charge. Furthermore, contributions from multipoles of all orders contribute, in general, to the leading asymptotic term in the potential for large r, which decays like exp(-κr)/r. Thus, the electrostatic potential from, for example, an electroneutral molecule with an internal charge distribution has generally the same range as the potential from an ion. Some implications of these facts are pointed out. The presentation is based on exact statistical mechanical analysis where all particles are treated on the same fundamental level, but the main focus lies on physical consequences and interpretations of the theory. The text was submitted by the author in English.     

Designing electrostatic interactions in biological systems via charge optimization or combinatorial approaches: insights and challenges with a continuum electrostatic framework

Electrostatic interactions between biological molecules are crucially influenced by their aqueous environment, with efficient and accurate models of solvent effects required for robust molecular design strategies. Continuum electrostatic models provide a reasonable balance between computational efficiency and accurate system representation. In this article, I review two specific molecular design strategies, charge optimization and combinatorial design, paying particular attention to how the continuum framework (also briefly described herein) successfully enables both theoretical insights and molecular designs and presents a challenge in design applications due to what I call “the isostericity constraint.” Efforts to work around the isostericity constraint and other challenges are discussed. Additionally, particular emphasis is placed on using such models in the rational design of particularly tight, specific, or promiscuous interactions, in keeping with the increased sophistication of current molecular design applications.     

Fragment-based quantum mechanical methods for periodic systems with Ewald summation and mean image charge convention for long-range electrostatic interactions

We describe an Ewald-summation method to incorporate long-range electrostatic interactions into fragment-based electronic structure methods for periodic systems. The present method is an extension of the particle-mesh Ewald technique for combined quantum mechanical and molecular mechanical (QM/MM) calculations, and it has been implemented into the explicit polarization (X-Pol) potential to illustrate the computational details. As in the QM/MM-Ewald method, the X-Pol-Ewald approach is a linear-scaling electrostatic method, in which the short-range electrostatic interactions are determined explicitly in real space and the long-range Ewald pair potential is incorporated into the Fock matrix as a correction. To avoid the time-consuming Fock matrix update during the self-consistent field procedure, a mean image charge (MIC) approximation is introduced, in which the running average with a user-chosen correlation time is used to represent the long-range electrostatic correction as an average effect. Test simulations on liquid water show that the present X-Pol-Ewald method takes about 25% more CPU time than the usual X-Pol method using spherical cutoff, whereas the use of the MIC approximation reduces the extra costs for long-range electrostatic interactions by 15%. The present X-Pol-Ewald method provides a general procedure for incorporating long-range electrostatic effects into fragment-based electronic structure methods for treating biomolecular and condensed-phase systems under periodic boundary conditions.     

A new technique for studying gelation in polyesters

A new method for studying polymer network formation has been devised. Crosslinking reactions are carried out in a recording viscometer, which provides accurate determination of incipient gel points and also serves as a high-speed stirrer. The molten, nonstoichiometric mixtures are reacted to completion to eliminate the inaccuracies inherent in the determination of reaction extent and this, together with the use of esterification reactions with minimal side reactions, reduces many of the problems of previous methods. The experimental results for the reactions of simple model compounds are in very close agreement with Flory's network theory. A system containing crosslinking reagents with unequally reactive groups has also been considered and the accuracy of the method enables the reactivity ratios of the different groups to be calculated.     

Toward a new approach for determination of solute's charge distribution to analyze interatomic electrostatic interactions in quantum mechanical/molecular mechanical simulations

We present an alternative approach to determine "density-dependent property"-derived charges for molecules in the condensed phase. In the case of a solution, it is essential to take into consideration the electron polarization of molecules in the active site of this system. The solute and solvent molecules in this site have to be described by a quantum mechanical technique and the others are allowed to be treated by a molecular mechanical method (QM/MM scheme). For calculations based on this scheme, using the forces and interaction energy as density-dependent property our charges from interaction energy and forces (CHIEF) approach can provide the atom-centered charges on the solute atoms. These charges reproduce well the electrostatic potentials around the solvent molecules and present properly the picture of the electron density of the QM subsystem in the solution system. Thus, the CHIEF charges can be considered as the atomic charges under the conditions of the QM/MM simulation, and then enable one to analyze electrostatic interactions between atoms in the QM and MM regions. This approach would give a view of the QM nuclei and electrons different from the conventional methods.     

Photoelectric measurements of s-BLM/nucleoli: a new technique for studying apoptosis

A new method based on photoelectric measurement for analyzing apoptosis of cell-free MCF-7 nucleoli is reported. Supported bilayer lipid membrane (s-BLM) was used to enclose nucleoli in biological environment. The s-BLM was self-assembled on the wall of a super-thin cell. During the apoptosis induced by Taxol, the photoelectric current of the self-assembled s-BLM/nucleoli was found decreasing with time, suggesting the degradation of nucleus DNA. Electron transfer along the DNA double helix and along nuclear skeleton is assumed in the interpretation. This novel photoelectric analytical method may provide a rapid and sensitive technique to evaluate apoptosis.     

Intrinsic charge ladders of a monoclonal antibody in hydroxypropylcellulose-coated capillaries

Capillary zone electrophoresis (CZE) has been used to resolve the charge heterogeneity of an intact ( approximately 150 kDa) monoclonal IgG antibody (mAb). Although this microheterogeneity can also be observed by isoelectric focusing, CZE allows the net charge of each variant to be measured as a function of pH and other solution conditions. Separation was achieved in both borate and Tris run buffers using capillaries that had been statically coated with hydroxypropylcellulose (HPC). The HPC coating makes inadvertent chromatographic retention of the mAb undetectably small and decreases electroosmotic flow (EOF) to approximately 10(-5) cm(2) V(-1) s(-1), with reasonable stability over dozens of runs under the conditions tested (pH 8.5 and 9.0 for each buffer). We also describe a novel means of measuring small, positive EOF coefficients and larger, negative net mobilities in the same run. This allows determination of accurate electrophoretic mobilities despite variations in EOF. The resolved mAb charge variants (which most likely result from deamidation or partial truncation) constitute what we call an "intrinsic" charge ladder. As with conventional charge ladders formed by deliberate modification of a homogeneous protein, net charge is obtained by extrapolating a plot of electrophoretic mobility versus (assumed) incremental charge difference. At a given pH, the mAb is more negatively charged in borate than in Tris, reflecting specific binding of the B(OH)(4)(-) anion. We also report hydrodynamic radii calculated from the slopes of these plots.     

Ultrafiltration as a technique for studying metal—humate interactions: studies with iron and copper

An ultrafiltration method was employed to study Fe(II)/Fe(III) and Cu(II) binding by Armadale Horizon fulvic acid. The results of the Fe—fulvate studies indicate the formation of “aggregates” between Fe and the fulvic acid molecule. The reduction of Fe(III) to Fe(II) by fulvic acid is also observed. Results for Cu(II)—fulvate electrode method. An algorithm developed previously for the prediction of metal ion binding by fulvic acid at different pH and salt concentration levels was tested further by comparing Cu²⁺ ion binding predictions with their measured values.     

Vibronic excitation of single molecules: a new technique for studying low-temperature dynamics.

Herein, we present vibronic excitation and detection of purely electronic zero-phonon lines (ZPL) of single molecules as a new tool for investigating dynamics at cryogenic temperatures. Applications of this technique to study crystalline and amorphous matrix materials are presented. In the crystalline environment, spectrally stable ZPLs are observed at moderate excitation powers. By contrast, investigations at higher excitation intensities reveal the opening of local degrees of freedom and spectral jumps, which we interpret as the observation of elementary steps in the melting of a crystal. We compare these results to spectral single-molecule trajectories recorded in a polymer. The way in which much more complicated spectral features can be analysed is shown. Surprisingly, pronounced spectral shifts on a previously not accessible large energy scale are observed, which are hard to reconcile with the standard two-level model system used to describe low-temperature dynamics in disordered systems.     

Effect of charge distribution on electrostatic chromophore—protein interactions in Bacteriorhodopsin

Charge distributions of a protonated and unprotonated Schiff base model compound are determined using different quantum chemical methods. After fitting the model molecule onto the protonated retinal Schiff base in Bacteriorhodopsin, electrostatic interaction energies between the model molecule and protein are calculated. Interaction energies as well as the calculated pK_1/2 values of the model molecule are shown to depend considerably on the chosen charge distribution. Electrostatic potential derived partial charges determined at different ab initio levels reveal interaction energies between the model molecule and nearby residues such as ARG-82, ASP-85, and ASP-212, which are relatively method independent. Consequently, such charge distributions also result in pK_1/2 values for the model molecule that are very similar. Larger deviations in the electrostatic interaction energies, however, are found in the case of charge distributions derived according to the Mulliken population analysis. Nevertheless, some sets of Mulliken derived partial charges predicted pK_1/2 values for the model molecule that are close to those determined with electrostatic potential derived partial charges. This agreement, however, is only achieved because the individual errors of the contributing terms are approximately compensated. The use of the extended atom model is shown to be problematic. Although potential derived charges can correctly describe electrostatic interaction energies, they fail to predict pK_1/2 values. On the basis of the present investigation a new set of partial charges for the protonated and unprotonated retinal Schiff base is proposed to be used in molecular dynamics simulations and electrostatics calculations. © 1997 by John Wiley & Sons, Inc.     

Bile salt-induced vesicle-to-micelle transition in catanionic surfactant systems: steric and electrostatic interactions

The vesicle-to-micelle transition (VMT) was realized in catanionic surfactant systems by the addition of two kinds of bile salts, sodium cholate (SC) and sodium deoxycholate (SDC). It was found that steric interaction between the bile salt and catanionic surfactant plays an important role in catanionic surfactant systems that are usually thought to be dominated by electrostatic interaction. The facial amphiphilic structure and large occupied area of the bile salt are crucial to the enlargement of the average surfactant headgroup area and result in the VMT. Moreover, bile salts can also induce a macroscopic phase transition. Freeze-fracture transmission electron microscopy, dynamic light scattering, isothermal titration calorimetry, and absorbance measurements were used to follow the VMT process.     

The role of externally-modulated electrostatic interactions in amplifying charge transport across lysine-doped peptide junctions

Many evolved biomolecular functions such as ion pumping or redox catalysis rely on controlled charge transport through the polypeptide matrix, which can be regulated by shifts in molecular protonation states and dependent supramolecular packing modes in response to environmental cues. However, the exact roles of such dynamic, non-covalent interactions in peptide charge transport have remained elusive. To tackle this challenge, here we report the modulation of charge transport in a series of lysine (Lys)-substituted hepta-glycine (Gly) peptide self-assembled monolayers (SAMs) on template-striped gold (Au^TS) bottom electrodes with eutectic gallium-indium (EGaIn) liquid metal top electrodes. We demonstrate systematic modulation of hydrogen bonding and more general electrostatic interactions by shifting the position of the charged Lys-residue and creating different protonation patterns by changing the environmental pH in the Au^TS/peptide//GaO_x/EGaIn junctions. The effective modulation is evidenced by current density–voltage (J-V) measurements combined with SAM characterization using ultraviolet photoelectron spectroscopy (UPS) and angle-resolved X-ray photoelectron spectroscopy (ARXPS), polarization modulation–infrared reflection-absorption spectroscopy (PM-IRRAS), and molecular dynamics (MD) simulations. Decreasing the hydrogen bonding inside the peptide SAMs and increasing the electrostatic interactions by environmental counterions amplifies the charge transport differently with Lys-position, which means that the sensitive electrical response of peptide SAMs can be tuned by the peptide sequence. Our results provide insights into the relationship between molecular design and in situ modulation of charge transport properties for the development of bionanoelectronics.     

Photoelectric measurements of self-assembled and supported planar lipid bilayers: a new technique for studying apoptosis

A new method based on photoelectrochemistry for analyzing apoptosis of bilayer lipid membranes (s-BLMs) containing MCF-7 nuclei is reported. The s-BLM cell responded to white light (200–800 nm). During the apoptosis induced by Taxol, the photoelectric current of the cell decreased, suggesting degradation of the nuclear DNA. Electron transfer along the DNA double helix and along the nuclear skeleton is assumed in the interpretation. This novel photoelectric analytical method may provide a rapid and sensitive technique to evaluate apoptosis.     

On the proper calculation of electrostatic interactions in solid-supported bilayer systems

Modeling systems that are not inherently isotropic, e.g., extended bilayers, using molecular simulation techniques poses a potential problem. Since these methods rely on a finite number of atoms and molecules to describe the system, periodic boundary conditions are implemented to avoid edge effects and capture long-range electrostatic interactions. Systems consisting of a solvated bilayer adsorbed on a solid surface and exposed to an air/vacuum interface occur in many experimental settings and present some unique challenges in this respect. Here, we investigated the effects of implementing different electrostatic boundary conditions on the structural and electrostatic properties of a quartz/water/vacuum interface and a similar quartz-supported hydrated lipid bilayer exposed to vacuum. Since these interfacial systems have a net polarization, implementing the standard Ewald summation with the conducting boundary condition for the electrostatic long-range interactions introduced an artificial periodicity in the out-of-plane dimension. In particular, abnormal orientational polarizations of water were observed with the conducting boundary condition. Implementing the Ewald summation technique with the planar vacuum boundary condition and calculating electrostatic properties compatible with the implemented electrostatic boundary condition removed these inconsistencies. This formulation is generally applicable to similar interfacial systems in bulk solution.     

Steric and electrostatic interactions in hexacyclic ring systems: The origin of the buttressing effect

Ring deformation in a number of 2-trichloromethyl-1,3-dioxanes could be traced in their ¹H NMR spectra from anomalies in coupling constants. No distortion occurs when the 2-substituent is a dichloromethyl or a tertiobutyl group, or when a 4-axial substituent is lacking. It was impossible to deduce the ring geometry from the vicinal coupling constants, but the nature of the ring deformation has been ascertained by NMR data (³J_exo, Δδ) and dipole moment calculations. Flexible conformations are not the origin of the observed anomalies. The rotomeric populations in 2-dichloromethyl-1,3-dioxanes has been evaluated and the origin of the buttressing effect, as caused by different substitution, has been disclosed.     

MMM1D: a method for calculating electrostatic interactions in one-dimensional periodic geometries

We present a new method to accurately calculate the electrostatic energy and forces on charges in a system with periodic boundary conditions in one of three spatial dimensions. We transform the Coulomb sum via a convergence factor into a series of fast decaying functions similar to the Lekner method. Rigorous error bounds for the energies and the forces are derived and numerically verified. The method has a computational complexity of O(N(2)), but is faster and easier to use than previously reported methods.     

Model systems for flavoenzyme activity. Control of flavin recognition via specific electrostatic interactions

[structure: see text] A model system has been used to study the interactions of dipole-containing aromatic systems with oxidized and reduced flavin. Ab initio computational and experimental studies show that dipole orientation within the host is a critical determinant for recognition and redox behavior of the flavin guest.     

Self-complementarity of oligo-2-aminopyridines: a new class of hydrogen-bonded ladders

A new class of hydrogen-bonded ladders based on hydrogen-bonded dimerization of oligo-alpha-aminopryidines has been demonstrated. Jorgensen's model can be successfully applied to this hydrogen-bonding system in nonpolar solvents. The results show the competitive enthalpy/entropy compensation relationship upon dimerization. Although increasing the number of hydrogen-bonding interactions would enhance the hydrogen-bonding stabilization enthalpy, this stabilization enthalpy per unit would be partially sacrificed to compensate for the entropy loss due to dimerization. These results clearly support the importance of preorganization in designing hydrogen-bonding guest-host molecules.