Electrostatics of hemoglobins from measurements of the electric dichroism and computer simulations

A New Model for Thermodynamic Characterization of Hemoglobin

In this paper, we formulate a thermodynamic model of hemoglobin that describes, by a physical point of view, phenomena favoring the binding of oxygen to the protein. Our study is based on theoretical methods extrapolated by experimental data. After some remarks on the non-equilibrium thermodynamic theory with internal variables, some thermodynamic functions are determined by the value of the complex dielectric constant. In previous papers, we determined the explicit expression of a dielectric constant as a function of a complex dielectric modulus and frequency. The knowledge of these functions allows a new characterization of the material and leads to the study of new phenomena that has yet to be studied. In detail, we introduce the concept of “hemoglobe”, a model that considers the hemoglobin molecule as a plane capacitor, the dielectric of which is almost entirely constituted by the quaternary structure of the protein. This model is suggested by considering a phenomenological coefficient of the non-equilibrium thermodynamic theory related to the displacement polarization current. The comparison of the capacity determined by the mean of this coefficient, and determined by geometrical considerations, gives similar results; although more thermodynamic information is derived by the capacity determined considering the aforementioned coefficient. This was applied to the normal human hemoglobin, homozygous sickle hemoglobin, and sickle cell hemoglobin C disease. Moreover, the energy of the capacitor of the three hemoglobin was determined. Through the identification of displacement currents, the introduction of this model presents new perspectives and helps to explain hemoglobin functionality through a physical point of view.

Solid-state biophotovoltaic cells containing photosystem I

The large multiprotein complex, photosystem I (PSI), which is at the heart of light-dependent reactions in photosynthesis, is integrated as the active component in a solid-state organic photovoltaic cell. These experiments demonstrate that photoactive megadalton protein complexes are compatible with solution processing of organic-semiconductor materials and operate in a dry non-natural environment that is very different from the biological membrane.

Prediction of hydrodynamic and other solution properties of rigid proteins from atomic- and residue-level models

Here we extend the ability to predict hydrodynamic coefficients and other solution properties of rigid macromolecular structures from atomic-level structures, implemented in the computer program HYDROPRO, to models with lower, residue-level resolution. Whereas in the former case there is one bead per nonhydrogen atom, the latter contains one bead per amino acid (or nucleotide) residue, thus allowing calculations when atomic resolution is not available or coarse-grained models are preferred. We parameterized the effective hydrodynamic radius of the elements in the atomic- and residue-level models using a very large set of experimental data for translational and rotational coefficients (intrinsic viscosity and radius of gyration) for >50 proteins. We also extended the calculations to very large proteins and macromolecular complexes, such as the whole 70S ribosome. We show that with proper parameterization, the two levels of resolution yield similar and rather good agreement with experimental data. The new version of HYDROPRO, in addition to considering various computational and modeling schemes, is far more efficient computationally and can be handled with the use of a graphical interface.

PHEMTO: protein pH-dependent electric moment tools

PHEMTO (protein pH-dependent electric moment tools) is released in response to the high demand in protein science community for evaluation of electrostatic characteristics in relations to molecular recognition. PHEMTO will serve protein scientists with new advanced features for analysis of protein molecular interactions: Electric/dipole moments, their pH-dependence and in silico charge mutagenesis effects on these properties as well as alternative algorithms for electric/dipole moment computation--Singular value decomposition of electrostatic potential (EP) to account for reaction field. The implementation is based on long-term experience--PHEI mean field electrostatics and PHEPS server for evaluation of global and local pH-dependent properties. However, PHEMTO is not just an update of our PHEPS server. Besides standard electrostatics, we offer new, advanced and useful features for analysis of protein molecular interactions. In addition our algorithms are very fast. Special emphasis is given to the interface--intuitive and user-friendly. The input is comprised of the atomic coordinate file in Protein Data Bank format. The advanced user is provided with a special input section for addition of non-polypeptide charges. The output covers actually full electrostatic characteristics but special emphasis is given to electric/dipole moments and their interactive visualization. PHEMTO server can be accessed at http://phemto.orgchm.bas.bg/.

A server and database for dipole moments of proteins

An Internet server at http://bip.weizmann.ac.il/dipol calculates the net charge, dipole moment and mean radius of any 3D protein structure or its constituent peptide chains, and displays the dipole vector superimposed on a ribbon backbone of the protein. The server can also display the angle between the dipole and a selected list of amino acid residues in the protein. When the net charges and dipole moments of ∼12 000 non-homologous PDB biological units (PISCES set), and their unique chains of length 50 residues or longer, were examined, the great majority of both charges and dipoles fell into a very narrow range of values, with long extended tails containing a few extreme outliers. In general, there is no obvious relation between a protein's charge or dipole moment and its structure or function, so that its electrostatic properties are highly specific to the particular protein, except that the majority of chains with very large positive charges or dipoles bind to ribosomes or interact with nucleic acids.

Metastable mesoscopic clusters in solutions of sickle-cell hemoglobin

Sickle cell hemoglobin (HbS) is a mutant, whose polymerization while in deoxy state in the venous circulation underlies the debilitating sickle cell anemia. It has been suggested that the nucleation of the HbS polymers occurs within clusters of dense liquid, existing in HbS solutions. We use dynamic light scattering with solutions of deoxy-HbS, and, for comparison, of oxy-HbS and oxy-normal adult hemoglobin, HbA. We show that solutions of all three Hb variants contain clusters of dense liquid, several hundred nanometers in size, which are metastable with respect to the Hb solutions. The clusters form within a few seconds after solution preparation and their sizes and numbers remain relatively steady for up to 3 h. The lower bound of the cluster lifetime is 15 ms. The clusters exist in broad temperature and Hb concentration ranges, and occupy 10(-5)-10(-2) of the solution volume. The results on the cluster properties can serve as test data for a potential future microscopic theory of cluster stability and kinetics. More importantly, if the clusters are a part of the nucleation mechanism of HbS polymers, the rate of HbS polymerization can be controlled by varying the cluster properties.

Multiple advantages of capillary zone electrophoresis for exploring protein conformational stability

This review summarizes the work of our laboratory to explore the use of capillary zone electrophoretic (CZE) methods for the investigation of protein conformational stability. Early CZE works on protein denaturation as well as fundamental and theoretical considerations are discussed. Instrumental aspects of the CE-based approach including general and particular CE requirements are documented. Several aspects dealing with estimation of stability of enzymes (cholinesterases and organophosphate-hydrolyzing enzymes) interacting with organophosphates profusely illustrate the multiple advantages of CZE. The discrimination of parameters controlling the "good compromise" stability/plasticity for allowing functional efficiency of these enzymes is exemplified. Thermal stability, susceptibility to high electric field, alteration of stability by bound ligands and the role of associated cations in metalloenzymes have been successfully investigated.

Dual effect of high electric field in capillary electrophoresis study of the conformational stability of Bungarus fasciatus acetylcholinesterase

The effect of high electric field in capillary zone electrophoresis (CZE) was evaluated for the study of the thermally induced unfolding of Bungarus fasciatus acetylcholinesterase. This monomer enzyme is characterised by two interdependent uncommon structural features, the asymmetrical distribution of charged residues and a relatively low thermal denaturation temperature. Both traits were presumed to interfere in the thermal unfolding of this enzyme as investigated by CZE. This paper analyses the effect of high electric field on the behaviour of the enzyme native state. It is shown that increasing the applied field causes denaturation-like transition of the enzyme at a current power which does not induce excessive Joule heating in the capillary. The susceptibility to electric field of proteins like cholinesterases, with charge distribution anisotropy, large permanent dipole moment and notable molecular flexibility associated with moderate thermal stability, was subsequently discussed.

Calculation of hydrodynamic properties of globular proteins from their atomic-level structure

The solution properties, including hydrodynamic quantities and the radius of gyration, of globular proteins are calculated from their detailed, atomic-level structure, using bead-modeling methodologies described in our previous article (, Biophys. J. 76:3044-3057). We review how this goal has been pursued by other authors in the past. Our procedure starts from a list of atomic coordinates, from which we build a primary hydrodynamic model by replacing nonhydrogen atoms with spherical elements of some fixed radius. The resulting particle, consisting of overlapping spheres, is in turn represented by a shell model treated as described in our previous work. We have applied this procedure to a set of 13 proteins. For each protein, the atomic element radius is adjusted, to fit all of the hydrodynamic properties, taking values close to 3 A, with deviations that fall within the error of experimental data. Some differences are found in the atomic element radius found for each protein, which can be explained in terms of protein hydration. A computational shortcut makes the procedure feasible, even in personal computers. All of the model-building and calculations are carried out with a HYDROPRO public-domain computer program.

Docking of 4-oxalocrotonate tautomerase substrates: implications for the catalytic mechanism

The enzyme 4-oxalocrotonate tautomerase catalyzes the ketonization of dienols, which after further processing become intermediates in the Krebs cycle. The enzyme uses a general acid-base mechanism for proton transfer: the amino-terminal proline has been shown to function as the catalytic base and Arg39 has been implicated as the catalytic acid. We report the results of molecular docking simulations of 4-oxalocrotonate tautomerase with two substrates, 2-hydroxymuconate and 5-carboxymethyl-2-hydroxymuconate. pKa calculations are also performed for the free enzyme. The predicted binding mode of 2-hydroxymuconate is in agreement with experimental data. A model for the binding mode of 5-carboxymethyl-2-hydroxymuconate is proposed which explains the lower catalytic efficiency of the enzyme toward this substrate. The pKa predictions and docking simulations support residue Arg39 as the general acid for the enzyme catalysis.

Global structure and flexibility of hairpin ribozymes with extended terminal helices

Global structure and flexibility of three different hairpin ribozyme constructs have been analyzed by measuring their electric dichroism decay in various buffers at temperatures between 2 and 30 degrees C. The hairpin ribozyme is characterized by two independently folding domains A and B that are connected through a hinge and have to interact to enable catalysis. The analyzed constructs feature extended terminal helices 1 and 4 with 27 and 25 bp, respectively, to increase the sensitivity of the molecular rotational diffusion time constants with respect to the interdomain bending angle. Constructs HP1 and HP2 cannot cleave because of a G+1A change at the 3'-side of the cleavage site; in HP1 the helices 2 and 3 that flank the hinge form a continuous double helical segment; in HP2 and HP3, a six nucleotide bulge confers flexibility to the expected bending site; HP3 is a cleavable form of HP2 with a G+1-base. For comparison, a standard RNA double helix with 72 bp was included in our analysis. The dichroism decay curves of the hairpin constructs after pulses of low electric field strengths can be fitted to single exponentials taus, whereas the curves after pulses of high field strengths require two exponentials. In all cases, time constants increase with RNA concentration, indicating intermolecular interactions. Extrapolation of the tausvalues measured in standard buffer (50 mM Tris (pH 7.5) and 12 mM MgCl2) to zero RNA concentration provide values of 112, 93, and 73 ns for HP1, HP2 and HP3, respectively, at 30 degrees C, indicating increasingly compact structures. The 72 bp RNA reference under corresponding conditions did not show a dependence of its decay time constant on the RNA concentration nor on the field strength; its time constant is 175 ns (standard buffer, 30 degrees C). The observation of two relaxation processes for the hairpin constructs at high field strengths indicates stretching to a more elongated state; the fast process with a time constant of the order of 50 ns is assigned to reversion of stretching, the slow process to overall rotation. The overall rotational time of the stretched state at 20 degrees C is close to that for a completely stretched rigid state; at 30 degrees C the experimental values are around 70 % of that expected for a completely stretched rigid state, indicating flexibility and/or residual bending. Bead models were constructed to simulate dichroism decay curves. The time constants observed for the 72 bp RNA are as expected for a rigid rod with a rise of 2.8 A per base-pair. Based on this rise per base-pair for models of a V and a Y-shape, we estimate average bending angles of 80(+/-20) degrees and 105 (+/-25) degrees, respectively, for the catalytically active hairpin ribozyme HP3. The energy required for stretching is of the order of the thermal energy.

Simulation of electrostatic and hydrodynamic properties of Serratia endonuclease

We analyze the electrostatic and hydrodynamic properties of a nuclease from the pathogenic gram-negative bacterium Serratia marcescens using finite-difference Poisson-Boltzmann methods for electrostatic calculations and a bead-model approach for diffusion coefficient calculations. Electrostatic properties are analyzed for the enzyme in monomeric and dimeric forms and also in the context of DNA binding by the nuclease. Our preliminary results show that binding of a double-stranded DNA dodecamer by nuclease causes an overall shift in the charge of the protein by approximately three units of elementary charge per monomer, resulting in a positively charged protein at physiologic pH. In these calculations, the free enzyme was found to have a negative (-1 e) charge per monomer at pH 7. The most dramatic shift in pKa involves His 89 whose pKa increases by three pH units upon DNA binding. This shift leads to a protonated residue at pH 7, in contrast to the unprotonated form in the free enzyme. DNA binding also leads to a decrease in the energetic distances between the most stable protonation states of the enzyme. Dimerization has no significant effect on the electrostatic properties of each of the monomers for both free enzyme and that bound to DNA. Results of hydrodynamic calculations are consistent with the dimeric form of the enzyme in solution. The computed translational diffusion coefficient for the dimer model of the enzyme is in very good agreement with measurements from light scattering experiments. Preliminary electrooptical calculations indicate that the dimer should possess a large dipole moment (approximately 600 Debye units) as well as substantial optical anisotropy (limiting reduced linear electric dichroism of about 0.3). Therefore, this system may serve as a good model for investigation of electric and hydrodynamic properties by relaxation electrooptical experiments.

Electrostatics and electrodynamics of bacteriorhodopsin

The stationary electric dichroism of bacteriorhodopsin is in qualitative, but not quantitative, agreement with the orientation function for disks having a permanent dipole directed perpendicular to the plane and an induced dipole in the plane. Fits of the orientation function to data measured at low field strengths demonstrate: an increase of the permanent dipole moment mu with the square of the disk radius r2, whereas the polarizability alpha increases with r4; the ionic strength dependence is small for mu and clearly stronger for alpha; the permanent dipole moment is 4x10(6) D at r = 0.5 micron. According to the risetime constants, the induced dipole does not saturate and increases to 4x10(8) D at 40 kV/cm and r = 0.5 micron. The data indicate that the permanent dipole is not of some interfacial character but is due to a real assymetry of the charge distribution. The experimental dipole moment per protein monomer is approximately 55 D, whereas calculations based on the structure of Grigorieff et al. (Grigorieff, N., T.A. Ceska, K.H. Downing, J.M. Baldwin, and R. Henderson. 1996. Electron-crystallographic refinement of the structure of bacteriorhodopsin. J. Mol. Biol. 259:393-421) provide a dipole moment of approximately 570 D. The difference is probably due to a nonsymmetric distribution of charged lipid residues. It is concluded that experimental dipole moments reflect the mu-potential at the plane of shear for rotational diffusion, in analogy to the sigma-potential used for translational diffusion. It is suggested that the permanent dipole of bacteriorhodopsin supports proton transport by attraction of protons inside and repulsion of protons outside of the cell. Dichroism rise curves at field strengths between E = 150 and 800 V/cm reveal an exponential component with time constants tau 3r in the range between 1 and 40 ms, which is not found in Brownian dynamics simulations on a disk structure using hydrodynamic and electric parameters characteristic of bacteriorhodopsin disks. The experimental data suggest that this process reflects a cooperative change of the bacteriorhodopsin structure, which is induced already at a remarkably low field strength of approximately 150 V/cm.

Acetylcholinesterase: role of the enzyme's charge distribution in steering charged ligands toward the active site

The electrostatic steering of charged ligands toward the active site of Torpedo californica acetylcholinesterase is investigated by Brownian dynamics simulations of wild type enzyme and several mutated forms, in which some normally charged residues are neutralized. The simulations reveal that the total ligand influx through a surface of 42 A radius centered in the enzyme monomer and separated from the protein surface by 1-14 A is not significantly influenced by electrostatic interactions. Electrostatic effects are visible for encounters with a surface of 32 A radius, which is partially hidden inside the protein, but mostly within the solvent. A clear accumulation of encounter events for that sphere is observed in the area directly above the entrance to the active site gorge. In this area, the encounter events are increased by 40% compared to the case of a neutral ligand. However, the differences among the encounter rates for the various mutants considered here are not pronounced, all rate constants being within +/- 10% of the average value. The enzyme charge distribution becomes more important as the charged ligand moves toward the bottom of the gorge, where the active site is located. We show that neither the enzyme's total charge, nor its dipole moment, fully account for the electrostatic steering of ligand to the active site. Higher moments of the enzyme's charge distribution are also important. However, for a series of mutations for which the direction of the enzyme dipole moment is constant within a few degrees, one observes a gradual decrease in the diffusional encounter rate constant with the number of neutralized residues. On the other hand, for other mutants that change the direction of the dipole moment from that of the wild type, the calculated encounter rate constants can be very close to that of the wild type. The present work yields two new insights to the kinetics of acetylcholinesterase. First, evolution appears to have built a redundant electrostatic steering capability into this important enzyme through the overall distribution of its thousands of partially charged atoms. And second, roughly half of the rate enhancement due to electrostatics arises from steering of the substrate outside the enzyme; the other half of the rate enhancement arises from improved trapping of the substrate after it has entered the gorge. The computational results reproduce qualitatively, and help to rationalize, many surprising experimental results obtained recently for human acetylcholinesterase.

Active site of bee venom phospholipase A2: the role of histidine-34, aspartate-64 and tyrosine-87

In bee venom phospholipase A2, histidine-34 probably functions as a Brønsted base to deprotonate the attacking water. Aspartate-64 and tyrosine-87 form a hydrogen bonding network with histidine-34. We have prepared mutants at these positions and studied their kinetic properties. The mutant in which histidine-34 is changed to glutamine is catalytically inactive, while the mutants in which aspartate-64 is changed to asparagine or alanine (interfacial turnover numbers are reduced by 50-100-fold) or in which tyrosine-87 is changed to phenylalanine (no change in turnover number) retain good activity. The interfacial Michaelis constants are changed by less than 10-fold for all mutants. Molecular simulations suggest that mutation of aspartate-64 and tyrosine-87 should yield enzymes that retain a native-like structure and support catalysis. The pKa of the histidine-34 imidazole was deduced from the pH-rate profile and from the pH dependence of the rate of histidine-34 alkylation by 2-bromo-4'-nitroacetophenone. The pKa is increased about one-half unit by the tyrosine-87 mutation and reduced about one-half unit by the aspartate-64 to asparagine mutation, while in the aspartate-64 to alanine mutant the pKa is unchanged. These pKas are generally consistent with results of electrostatic calculations and suggest that the hydrogen bond between aspartate-64 and histidine-34 is not unusually strong. The hydrogen bonding network linking tyrosine-87 to aspartate-64 and aspartate-64 to histidine-34 is not critical for catalysis.

Binding of tacrine and 6-chlorotacrine by acetylcholinesterase

Multiconfiguration thermodynamic integration was used to determine the relative binding strength of tacrine and 6-chlorotacrine by Torpedo californica acetylcholinesterase. 6-Chlorotacrine appears to be bound stronger by 0.7+/-0.4 kcal/mol than unsubstituted tacrine when the active site triad residue His-440 is deprotonated. This result is in excellent agreement with experimental inhibition data on electric eel acetylcholinesterase. Electrostatic Poisson-Boltzmann calculations confirm that order of binding strength, resulting in deltaG of binding of -2.9 and -3.3 kcal/mol for tacrine and chlorotacrine, respectively, and suggest inhibitor binding does not occur when His-440 is charged. Our results suggest that electron density redistribution upon tacrine chlorination is mainly responsible for the increased attraction potential between pronated inhibitor molecule and adjacent aromatic groups of Phe-330 and Trp-84.

Electrooptical analysis of α-chymotrypsin at physiological salt concentration

The electric dichroism of alpha-chymotrypsin has been measured in a buffer containing 0.1 M Na(+), 10 mM Mg(2+) and 25 mM Tris-cacodylate pH 7.2. The reduced dichroism as a function of the electric field strength can be represented by the orientation function for permanent dipoles and is not consistent with the orientation function for induced dipoles. After correction for the internal directing field, the dipole moment is 1.1 x 10(-27) Cm (+/- 10%), corresponding to 340 D, at 20 degrees C. The assignment of the permanent dipole moment is confirmed by the shape of the dichroism rise curves, which require two exponentials with amplitudes of opposite sign for fitting. The dichroism decay time constants measured in the range of temperatures between 2 and 30 degrees C indicate a temperature induced change of the structure, which is equivalent to an increase of the hydrodynamic radius from r = 26.6 A at 2 degrees C to 28.5 A at 30 degrees C. Our results demonstrate that electrooptical investigations of proteins with a high time resolution can be extended to physiological salt concentrations without serious problems by use of appropriate instruments.

Computation of the dipole moments of proteins

A simple and computationally feasible procedure for the calculation of net charges and dipole moments of proteins at arbitrary pH and salt conditions is described. The method is intended to provide data that may be compared to the results of transient electric dichroism experiments on protein solutions. The procedure consists of three major steps: (i) calculation of self energies and interaction energies for ionizable groups in the protein by using the finite-difference Poisson-Boltzmann method, (ii) determination of the position of the center of diffusion (to which the calculated dipole moment refers) and the extinction coefficient tensor for the protein, and (iii) generation of the equilibrium distribution of protonation states of the protein by a Monte Carlo procedure, from which mean and root-mean-square dipole moments and optical anisotropies are calculated. The procedure is applied to 12 proteins. It is shown that it gives hydrodynamic and electrical parameters for proteins in good agreement with experimental data.