Theoretical investigation of infrared spectra and pocket dynamics of photodissociated carbonmonoxy myoglobin

Molecular dynamics simulations of the photodissociated state of carbonmonoxy myoglobin (MbCO) are presented using a fluctuating charge model for CO. A new three-point charge model is fitted to high-level ab initio calculations of the dipole and quadrupole moment functions taken from the literature. The infrared spectrum of the CO molecule in the heme pocket is calculated using the dipole moment time autocorrelation function and shows good agreement with experiment. In particular, the new model reproduces the experimentally observed splitting of the CO absorption spectrum. The splitting of 3-7 cm(-1) (compared to the experimental value of 10 cm(-1)) can be directly attributed to the two possible orientations of CO within the docking site at the edge of the distal heme pocket (the B states), as previously suggested on the basis of experimental femtosecond time-resolved infrared studies. Further information on the time evolution of the position and orientation of the CO molecule is obtained and analyzed. The calculated difference in the free energy between the two possible orientations (Fe...CO and Fe...OC) is 0.3 kcal mol(-1) and agrees well with the experimentally estimated value of 0.29 kcal mol(-1). A comparison of the new fluctuating charge model with an established fixed charge model reveals some differences that may be critical for the correct prediction of the infrared spectrum and energy barriers. The photodissociation of CO from the myoglobin mutant L29F using the new model shows rapid escape of CO from the distal heme pocket, in good agreement with recent experimental data. The effect of the protein environment on the multipole moments of the CO ligand is investigated and taken into account in a refined model. Molecular dynamics simulations with this refined model are in agreement with the calculations based on the gas-phase model. However, it is demonstrated that even small changes in the electrostatics of CO alter the details of the dynamics.     

Libraries of atomic multipole moments for precise modeling of electrostatic properties of amino acids

Summary Contemporary theoretical models used in describing electrostatic properties of amino acids in polypeptides rely usually on atomic point charges. Recently noted defects of such models in reproducing protein folding originate from the inadequate representation of the electrostatic term, in particular inability of atomic charges to account for local anisotropy of molecular charge distribution. Such defects could be corrected by multicenter multipole moments derived directly from any high quality quantum chemical wavefunctions. This is illustrated by comparison of monopole and multipole electrostatic interactions between some amino acids within glutathione S-transferase.High quality Point Charge Models (PCM) can be derived analytically from multipole moment databases. Preliminary results suggest that torsional potentials are controlled by electrostatic interactions of atomic multipoles.Examples illustrating various uses of multicenter multipole moment databases of protein building blocks in modeling various properties of amino acids and polypeptides have been described, including calculation of molecular electrostatic potentials, electric fields, interactions between amino acid residues, estimates of pK_a shifts and changes in catalytic activity induced by amino acid substitutions in mutated enzymes.     

Low temperature photodissociation studies of ferrous hemoglobin and myoglobin complexes by Mössbauer spectroscopy

⁵⁷Fe-enriched complexes of hemoglobin and myoglobin with CO and O₂ were photodissociated at 4.2°K, and the resulting spectra were compared with those of the deoxy forms. Differences in both quadrupole splitting and isomer shift were noted for each protein, the photoproducts having smaller isomer shift and larger quadrupole splitting than the deoxy forms. The photoproducts of HbCO and HbCO₂ had narrow absorption lines, indicating a well-defined iron environment. The corresponding myoglobin species had broader absorption lines, as did both deoxy forms. The weak absorption lines of photodissociated NO complexes appeared to be wide, possibly indicating magnetic interaction with the unpaired electron of the nearby NO.     

Kinetic studies of the reactions of O2 and NO with reduced Thermus thermophilus ba3 and bovine aa3 using photolabile carriers

The reactions of molecular oxygen (O₂) and nitric oxide (NO) with reduced Thermus thermophilus (Tt) ba₃ and bovine heart aa₃ were investigated by time-resolved optical absorption spectroscopy to establish possible relationships between the structural diversity of these enzymes and their reaction dynamics. To determine whether the photodissociated carbon monoxide (CO) in the CO flow-flash experiment affects the ligand binding dynamics, we monitored the reactions in the absence and presence of CO using photolabile O₂ and NO complexes. The binding of O₂/NO to reduced ba₃ in the absence of CO occurs with a second-order rate constant of 1 × 10⁹ M^? 1 s^? 1. This rate is 10-times faster than for the mammalian enzyme, and which is attributed to structural differences in the ligand channels of the two enzymes. Moreover, the O₂/NO binding in ba₃ is 10-times slower in the presence of the photodissociated CO while the rates are the same for the bovine enzyme. This indicates that the photodissociated CO directly or indirectly impedes O₂ and NO access to the active site in Tt ba₃, and that traditional CO flow-flash experiments do not accurately reflect the O₂ and NO binding kinetics in ba₃. We suggest that in ba₃ the binding of O₂ (NO) to heme a₃^2 + causes rapid dissociation of CO from Cu_B⁺ through steric or electronic effects or, alternatively, that the photodissociated CO does not bind to Cu_B⁺. These findings indicate that structural differences between Tt ba₃ and the bovine aa₃ enzyme are tightly linked to mechanistic differences in the functions of these enzymes. This article is part of a Special Issue entitled: Respiratory Oxidases.     

Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions

We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance the extent of the charge distribution–the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Å from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Å ) is half that of the point multipole expansion up to the octupole order.     

Structure and coordination of CuB in the Acidianus ambivalens aa 3 quinol oxidase heme–copper center

The coordination environment of the Cu_B center of the quinol oxidase from Acidianus ambivalens, a type B heme–copper oxygen reductase, was investigated by Fourier transform (FT) IR and extended X-ray absorption fine structure (EXAFS) spectroscopy. The comparative structural chemistry of dinuclear Fe–Cu sites of the different types of oxygen reductases is of great interest. Fully reduced A. ambivalens quinol oxidase binds CO at the heme a ₃ center, with ν(CO)=1,973 cm⁻¹. On photolysis, the CO migrated to the Cu_B center, forming a Cu_B^I–CO complex with ν(CO)=2,047 cm⁻¹. Raising the temperature of the samples to 25°C did not result in a total loss of signal in the FTIR difference spectrum although the intensity of these signals was reduced sevenfold. This observation is consistent with a large energy barrier against the geminate rebinding of CO to the heme iron from Cu_B, a restricted limited access at the active-site pocket for a second binding, and a kinetically stable Cu_B–CO complex in A. ambivalens aa ₃. The Cu_B center was probed in a number of different states using EXAFS spectroscopy. The oxidized state was best simulated by three histidines and a solvent O scatterer. On reduction, the site became three-coordinate, but in contrast to the bo ₃ enzyme, there was no evidence for heterogeneity of binding of the coordinated histidines. The Cu_B centers in both the oxidized and the reduced enzymes also appeared to contain substoichiometric amounts (0.2 mol equiv) of nonlabile chloride ion. EXAFS data of the reduced carbonylated enzyme showed no difference between dark and photolyzed forms. The spectra could be well fit by 2.5 imidazoles, 0.5 Cl⁻ and 0.5 CO ligands. This arrangement of scatterers would be consistent with about half the sites remaining as unligated Cu(his)₃ and half being converted to Cu(his)₂Cl⁻CO, a 50/50 ratio of Cu(his)₂Cl⁻ and Cu(his)₃CO, or some combination of these formulations. Electronic Supplementary Material Supplementary material is available for this article at .     

Low temperature photodissociation studies of ferrous hemoglobin and myoglobin complexes by M?ssbauer spectroscopy.

57Fe-enriched complexes of hemoglobin and myoglobin with CO and O2 were photodissociated at 4.2 degrees K, and the resulting spectra were compared with those of the deoxy forms. Differences in both quadrupole splitting and isomer shift were noted for each protein, the photoproducts having smaller isomer shift and larger quadrupole splitting than the deoxy forms. The photoproducts of HbCO and HbO2 had narrow absorption lines, indicating a well-defined iron environment. The corresponding myoglobin species had broader absorption lines, as did both deoxy forms. The weak absorption lines of photodissociated NO complexes appeared to be wide, possibly indicating magnetic interaction with the unpaired electron of the nearby NO.     

Revealing substitution effects on the strength and nature of halogen-hydride interactions: a theoretical study

A quantum chemistry study was carried out to investigate the strength and nature of halogen bond interactions in HXeH···XCCY complexes, where X = Cl, Br and Y = H, F, Cl, Br, CN, NC, C₂H, CH₃, OH, SH, NH₂. Examination of the electrostatic potentials V(r) of the XCCY molecules reveals that the addition of substituents has a significant effect upon the most positive electrostatic potential on the surface of the interacting halogen atom. We found that the magnitude of atomic charges and multipole moments depends upon the halogen atom X and is rather sensitive to the electron-withdrawing/donating power of the remainder of the molecule. An excellent correlation was found between the most positive electrostatic potentials on the halogen atom and the interaction energies. For either HXeH···ClCCY or HXeH···BrCCY complexes, an approximate linear correlation between the interaction energies and halogens multipole moments are established, indicating that the electrostatic and polarization interactions are responsible for the stability of the complexes. According to energy decomposition analysis, it is revealed that the electrostatic interactions are the major source of the attraction in the HXeH···XCCY complexes. Furthermore, the changes in the electrostatic term are mainly responsible for the dependence of interaction energy on the halogen atom.

Contributions of dipole moments, quadrupole moments, and molecular polarizabilities to the anesthetic potency of fluorobenzenes

Previous studies have emphasized the role of molecular polarizability and electric moments, especially dipole and quadrupole moments, in binding of drugs to sites of action. A recent publication of ED50s that prevent response to a noxious stimulus for eight fluorobenzenes has made it possible to compare anesthetic potency with ab initio Hartree-Fock calculations of molecular polarizability as well as dipole and quadrupole moments. Fluorobenzenes provide a stringent test of the role of electric moments in anesthetic potency because individual dipole moments range from 0 to 2.84 debye (D) while the quadrupole moment of benzene is large and negative (-30 x 10(-40) C m(2)), that of hexafluorobenzene is large and positive (30 x 10(-40) C m(2)), and that of 1,3,5-trifluorobenzene is nearly zero. We found that anesthetic potency of fluorobenzenes was not affected by the presence of either dipole or quadrupole moments. This result is surprising because fluoroalkanes and fluorocycloalkanes are most potent when half fluorinated and are usually not anesthetics when perfluorinated. The results suggest that electrostatic interactions are not important for binding of fluorobenzenes at sites of anesthetic action and that these sites are different from those that bind conventional anesthetics.     

Modulating carbon monoxide binding affinity and kinetics in myoglobin: the roles of the distal histidine and the heme pocket docking site

 Myoglobin has long served as a model system for understanding the relations between protein structure, dynamics, and function. Its ability to discriminate between toxic CO and vital O₂, two small ligands that are almost equivalent in size and dipole moment, has attracted much attention. To understand discrimination and reversible ligand-binding in Mb, both the bound state and the "docked" state that leads to binding need to be studied. We have reported previously the nearly linear Fe–C–O geometry of bound CO and the nearly orthogonal geometry of docked CO [Lim et al. (1995), Science 269 : 962]. With the exception of X-ray structures, a preponderance of evidence points to a nearly linear Fe–C–O geometry and calls into question the proposal that the highly conserved distal histidine forces CO to bind in a nonoptimal geometry. The differences between the bound CO structures determined using IR and X-ray methods might arise from a water molecule hydrogen bonded to the distal histidine in some of the unit cells. Discrimination by Mb is manifested not only thermodynamically but also kinetically. Time-resolved CO rebinding studies that compare Mb with microperoxidase suggest that the heme pocket docking site in Mb exerts steric control of the ligand rebinding rate, slowing the rate of CO binding by a factor of more than 10⁴. Received, accepted: 23 May 1997     

Spherical tensor multipolar electrostatics and smooth particle mesh Ewald summation: a theoretical study

The point-charge approximation, typically used by classical molecular mechanics force-fields, can be overcome by a multipolar expansion. For decades multipole moments were only used in the context of the rigid body approximation but recently it has become possible to combine multipolar electrostatics with molecular flexibility. The program DL_MULTI, which is derived from DL_POLY_2, includes efficient multipolar Ewald functionality up to the hexadecapole moment but the code is restricted to rigid bodies. The incorporation of flexibility into DL_MULTI would cause too large an impact on its architecture whereas the package DL_POLY_4 offers a more attractive and sustainable route to handle multipolar electrostatics. This package inherently handles molecular flexibility, which warrants sufficiently transferable atoms or atoms that are “knowledgeable” about their chemical environment (as made possible by quantum chemical topology and machine learning). DL_MULTI uses the spherical multipole formalism, which is mathematically more involved than the Cartesian one but which is more compact. DL_POLY_4 uses the computationally efficient method of smooth particle mesh Ewald (SPME) summation, which has also been parallellized by others. Therefore, combining the strengths of DL_POLY_4 and DL_MULTI poses the challenge of merging SPME with multipolar electrostatics by spherical multipole. In an effort to recast as clearly as possible the principles behind DL_MULTI, its key equations have been reformulated by the more streamlined route involving the algebra of complex numbers, and some of these equations’ peculiarities clarified. This article explores theoretically the repercussions of the merging of SPME with spherical multipole electrostatics (as implemented in DL_MULTI). Difficulties in design and implementation of possible future code are discussed.     

Cα torsion angles as a flexible criterion to extract secrets from a molecular dynamics simulation

A multipolar, polarizable electrostatic method for future use in a novel force field is described. Quantum Chemical Topology (QCT) is used to partition the electron density of a chemical system into atoms, then the machine learning method Kriging is used to build models that relate the multipole moments of the atoms to the positions of their surrounding nuclei. The pilot system serine is used to study both the influence of the level of theory and the set of data generator methods used. The latter consists of: (i) sampling of protein structures deposited in the Protein Data Bank (PDB), or (ii) normal mode distortion along either (a) Cartesian coordinates, or (b) redundant internal coordinates. Wavefunctions for the sampled geometries were obtained at the HF/6-31G(d,p), B3LYP/apc-1, and MP2/cc-pVDZ levels of theory, prior to calculation of the atomic multipole moments by volume integration. The average absolute error (over an independent test set of conformations) in the total atom-atom electrostatic interaction energy of serine, using Kriging models built with the three data generator methods is 11.3 kJ mol^-1 (PDB), 8.2 kJ mol^-1 (Cartesian distortion), and 10.1 kJ mol^-1 (redundant internal distortion) at the HF/6-31G(d,p) level. At the B3LYP/apc-1 level, the respective errors are 7.7 kJ mol^-1, 6.7 kJ mol^-1, and 4.9 kJmol^-1, while at the MP2/cc-pVDZ level they are 6.5 kJ mol^-1, 5.3 kJ mol^-1, and 4.0 kJmol^-1. The ranges of geometries generated by the redundant internal coordinate distortion and by extraction from the PDB are much wider than the range generated by Cartesian distortion. The atomic multipole moment and electrostatic interaction energy predictions for the B3LYP/apc-1 and MP2/cc-pVDZ levels are similar, and both are better than the corresponding predictions at the HF/6-31G(d,p) level.     

The effect of quaternary structure on the state of the α and β subunits within nitrosyl haemoglobin: Low temperature photodissociation and the ESR spectra

Photodissociation of nitrosyl haemoglobin and nitrosyl hybrids, in which either the α or β subunit is in the nitrosyl form has been studied at liquid helium temperature (4.2°K) by electron spin resonance and optical absorption spectroscopy. In the presence of inositol hexaphosphate, the photodissociated form of nitrosyl haemoglobin showed an anomalous absorption spectrum in the near infrared region. The experiments with nitrosyl hybrids showed that the α^NO subunit within the T state haemoglobin is predominantly responsible for the anomalous photodissociated form and the ESR spectrum with three distinct hyperfines. The ESR spectrum of α₂^NOβ₂^deoxy with inositol hexaphosphate appeared to be very similar to that of the 5-coordinated NO-haem complexes but the absorption spectrum of its photodissociated form was similar to none of protoporphyrin Fe(II) derivatives so far reported. This result suggests that the anomalous photodissociated form may be attributable to some structural distortion of porphyrin or a new electronic state of the haem with different spin state from that of deoxyhaemoglobin.     

A Simple Force-Motion Relation for Migrating Cells Revealed by Multipole Analysis of Traction Stress

For biophysical understanding of cell motility, the relationship between mechanical force and cell migration must be uncovered, but it remains elusive. Since cells migrate at small scale in dissipative circumstances, the inertia force is negligible and all forces should cancel out. This implies that one must quantify the spatial pattern of the force instead of just the summation to elucidate the force-motion relation. Here, we introduced multipole analysis to quantify the traction stress dynamics of migrating cells. We measured the traction stress of Dictyostelium discoideum cells and investigated the lowest two moments, the force dipole and quadrupole moments, which reflect rotational and front-rear asymmetries of the stress field. We derived a simple force-motion relation in which cells migrate along the force dipole axis with a direction determined by the force quadrupole. Furthermore, as a complementary approach, we also investigated fine structures in the stress field that show front-rear asymmetric kinetics consistent with the multipole analysis. The tight force-motion relation enables us to predict cell migration only from the traction stress patterns.     

A Simple Force-Motion Relation for Migrating Cells Revealed by Multipole Analysis of Traction Stress

For biophysical understanding of cell motility, the relationship between mechanical force and cell migration must be uncovered, but it remains elusive. Since cells migrate at small scale in dissipative circumstances, the inertia force is negligible and all forces should cancel out. This implies that one must quantify the spatial pattern of the force instead of just the summation to elucidate the force-motion relation. Here, we introduced multipole analysis to quantify the traction stress dynamics of migrating cells. We measured the traction stress of Dictyostelium discoideum cells and investigated the lowest two moments, the force dipole and quadrupole moments, which reflect rotational and front-rear asymmetries of the stress field. We derived a simple force-motion relation in which cells migrate along the force dipole axis with a direction determined by the force quadrupole. Furthermore, as a complementary approach, we also investigated fine structures in the stress field that show front-rear asymmetric kinetics consistent with the multipole analysis. The tight force-motion relation enables us to predict cell migration only from the traction stress patterns.     

Multipole representation of an eccentric dipole and an eccentric double-layer

Recently a theorem for representing current generators in a volume conductor by the superposition of a central dipole, quadrupole, octopole, etc., has been established by G. C. K. Yeh, J. Martinek, and H. de Beaumont (Bull. Math. Biophysics,20, 203–16, 1958). This theorem makes possible the representation of any discrete or line, surface- or volume-distributed current source by a unique model which can be determined for each given case by surface potential measurements and closed form analysis. In this paper the multipole representations of an eccentric dipole and an eccentric double-layer are obtained in terms of the various parameters of the assumed singularities, and the contributions to surface potentials due to each of the multipoles are compared. Certain numerical results corresponding to those of E. Frank (Amer. Heart J.,46, 364–78, 1953) are carried out and compared. Furthermore, the multipole representation of a partially damaged double-layer is also determined and compared with that of an undamaged one. It is concluded that within the range of parameters corresponding to human subjects the higher-order multipoles can contribute significantly to the surface potentials compared with the dipole. This investigation was supported by the National Heart Institute under a research grant H-2263(c).     

Multipole representations of current generators in a volume conductor

As far as the potential distribution outside the current generators is concerned, any current source distribution may be replaced by a suitable collection of multipoles. If these current generators lie close to the geometrical center of the volume conductor, a central dipole is a good approximation for potentials at surface points which are at considerable distances from the center. For better accuracy and for points close to the center, additional singularities such as a central quadrupole, a central octopole, etc., should be included. Potential expressions due to such multipoles in a spherical conductor can be obtained in closed forms by means of the “interior sphere theorem”. This paper presents a method for determining successively better multipole representations of the current generators in a homogeneous conducting sphere by measuring surface potentials at a successively increasing number of points. It is shown that Einthoven's triangle and Wilson's tetrahedron in the theory of electrocardiography are first and second approximations of this method. This concept also applies to conductors of other shapes. This investigation was supported by The National Heart Institute under a research grant H-2263(c).