Computational study of the absorption spectra of green fluorescent protein mutants

In this work, we present a theoretical study of the relationship between molecular structure and the red-shift in absorption spectra of S65G and S65T green fluorescent protein (GFP) mutants. To identify the effects of the protein environment, we combined results from molecular dynamics (MD) simulations and quantum mechanics/molecular mechanics calculations to obtain structural properties, and applied time-dependent density functional theory to calculate the excitation energies. By using results from the MD simulations, we were able to provide a systematic analysis of the structural details that may effect the red-shift in the absorption spectra when taking into account temperature effects. Furthermore, a detailed study of hydrogen bonding during the MD simulations demonstrated differences between S65G and S65T, for example, regarding hydrogen bonding with Glu222. An analysis of the absorption spectra for different forms of the chromophore emphasized the dominance of the anionic forms in solution for the S65G and S65T GFP mutants.     

Applications of the Cartesian coordinate tensor transfer technique in the simulations of vibrational circular dichroism spectra of oligonucleotides

The application of the Cartesian coordinate tensor transfer (CCT) technique for simulations of the IR absorption and vibrational circular dichroism (VCD) spectra of relatively large nucleic acid fragments is demonstrated on several case studies. The approach is based on direct ab initio calculations of atomic tensors, determining molecular properties, for relatively small fragments, and subsequent transfer of these tensors to the larger systems in Cartesian coordinates. This procedure enables precise computations of vibrational spectra for large biomolecular systems, currently with up to several thousands of atoms. The versatile ability of the CCT methods is emphasized on the examples of VCD and IR absorption spectra calculations for B- and Z-forms of DNA, single-, double-, and triple-stranded RNA helices and DNA structures with different base content and sequences. The development and recent improvements of the methodology are followed, including utilization of the constrained normal mode optimization (NMO) strategy and combined quantum mechanics and molecular dynamics simulations. Advantages, drawbacks, and recommendations for future improvements of the CCT method as applied to nucleic acid spectra calculations are discussed.     

Red fluorescent protein DsRed: Parametrization of its chromophore as an amino acid residue for computer modeling in the OPLS-AA force field

Topology of the neutral form of the DsRed fluorescent protein chromophore as a residue of [(4-cis)-2-[(1-cis)-4-amino-4-oxobutanimidoyl]-4-(4-hydroxybenzylidene)-5-oxo-4,5-dihydro-1H-imidazol-1-yl]acetic acid was calculated with OPLS-AA force field. Use of this topology and molecular dynamics simulation allows calculating the parameters of proteins that contain such residue in their polypeptide chains. The chromophore parameters were obtained by ab initio (RHF/6-31G**) quantum chemical calculations applying density functional theory (B3LYP). Using this chromophore, we have calculated the molecular dynamics trajectory of tetrameric fluorescent protein DsRed in solution at 300 K (4 nsec). Correctness of the chromophore parametrization was revealed by comparison of quantitative characteristics of the chromophore structure obtained from the molecular dynamic simulations of DsRed protein with the quantitative characteristics of the chromophore based on the crystallographic X-ray data of fluorescent protein DsRed (PDB ID: 1ZGO, 1G7K, and 1GGX), and also with the quantitative characteristics of the chromophore obtained by quantum chemical calculations. Inclusion of the neutral form of DsRed protein chromophore topology into the OPLS-AA force field yielded the extended force field OPLS-AA/DsRed. This force field can be used for molecular dynamics calculations of proteins containing the DsRed chromophore. The parameter set presented in this study can be applied for similar extension in any other force fields.     

Photoabsorption of green and red fluorescent protein chromophore anions in vacuo

Photoabsorption properties of green and red fluorescent protein chromophore anions in vacuo were investigated theoretically, based on the experimental results in gas phase [Phys. Rev. Lett. 2001, 87, 228102; Phys. Rev. Lett. 2003, 90, 118103]. Their calculated transition energies in absorption with TD-DFT and ZINDO methods are directly compared to the experimental reports in gas phase, and the calculations with ZINDO method can correctly reproduce the absorption spectra. The orientation and strength of their transition dipole moments were revealed with transition density. We also showed the orientation and result of their intramolecular charge transfer with transition difference density. The calculated results show that with the increase of the extended conjugated system, the orientation of transition dipole moments and the orientation of charge transfer can be reversed. They are the linear responds with the external electric fields. These theoretical results reveal the insight understanding of the photoinduced dynamics of green and red fluorescent protein chromophore anions and cations in vacuo.     

Study of the betulin molecule in a water environment; ab initio and molecular simulation calculations

Ab initio and molecular simulation methods were used in calculations of the neutral individual betulin molecule, and molecular simulations were used to optimize the betulin molecule immersed in various amounts of water. Individual betulin was optimized in different force fields to find the one exhibiting best agreement with ab initio calculations obtained in the Gaussian03 program. Dihedral torsions of active groups of betulin were determined for both procedures, and related calculated structures were compared successfully. The selected force field was used for subsequent optimization of betulin in a water environment, and a conformational search was performed using quench molecular dynamics. The total energies of betulin and its interactions in water bulk were calculated, and the influence of water on betulin structure was investigated.     

Structural Assignment of Spectra by Characterization of Conformational Substates in Bound MbCO

Residue motions of the distal heme pocket and bound CO ligand of carbonmonoxy Myoglobin are studied using a combination of molecular dynamics simulations and quantum chemical methods. Using mixed quantum mechanics/molecular mechanics calculations together with sampling from molecular dynamics simulations (QM/MM(MD)), the experimentally observed spectroscopic A₀ and A₁ substates of the bound CO ligand are assigned to the open and closed conformation of His⁶⁴ and the His_ɛ⁶⁴ tautomer, respectively. Several previously proposed origins of the A₃ substate, including rotamers of the doubly protonated His⁶⁴H⁺ side chain, His⁶⁴H⁺ inside the distal pocket, and cooperative motions with Arg⁴⁵, are investigated with QM/MM(MD). However, the signatures of the calculated infrared spectra do not agree with the experimentally observed ones. For additional insight on this, extensive molecular dynamics simulations are used together with improved electrostatics for the bound ligand. A CO fluctuating charge model is developed to describe the ab initio dipole and quadrupole moments of the bound ligand. CO absorption spectra are then obtained directly from the dynamics simulations. Finally, the electrostatics of the heme pocket is examined in detail in an attempt to determine the structural origins of the observed spectroscopic A-states from MD simulations. However, contrary to related simulations for unbound CO in myoglobin, the shifts and splittings for carbonmonoxy Myoglobin are generally small and difficult to relate to structural change. This suggests that coupling of the CO motion to other degrees of freedom, such as the Fe-CO stretching and bending, is important to correctly describe the dynamics of bound CO in myoglobin.     

Effects of pathological mutations on the stability of a conserved amino acid triad in retinoschisin

A three-dimensional model has been calculated for the discoidin domain of retinoschisin (RS1), the protein involved in the X-linked juvenile retinoschisis. The model allows for a mapping of the pathological retinoschisis missense mutations and a rationale for the structural effects of an evolutionary conserved surface exposed triad (W122-R200-W163). Molecular dynamics simulations of the triad mutants models, together with ab initio energy calculations of the complexes corresponding to the triad show that the observed pathological mutations sensibly destabilize local interactions and the entire fold. Moreover the presented model reveals evidence of a putative site for membrane association.     

First-principles calculations of protein circular dichroism in the near ultraviolet

Electronic transitions in aromatic side chains are responsible for the characteristics of proteins in the near UV. We present the first systematic study of a large number of proteins focused on the accurate calculation of near-UV circular dichroism (CD) spectra. We report new parameter sets derived from ab initio calculations for benzene, phenol, and indole that describe the valence electronic transitions to the (1)L(b), (1)L(a), (1)B(b), and (1)B(a) states in the side chains of amino acids phenylalanine, tyrosine, and tryptophan. CD spectra were calculated, using the matrix method with the new side-chain parameters, for 30 proteins whose CD spectra and crystal structures have been made publicly available. The new parameter sets are fully self-consistent and yield near-UV spectra better than those obtained using previous parameter sets. The mean absolute errors for computed wild-type spectra in the near UV are reduced by a factor of approximately 2. A similiar reduction is found for the near-UV spectra (and difference spectra) of mutants involving aromatic amino acids. Empirical modifications to model vibronic coupling in the side-chain chromophore of phenylalanine offer no overall improvement. Protein CD calculations from first principles coupled with atomic-level modeling enhance the utility and interpretability of CD measurements in the near UV.     

Fast calculation of the infrared spectra of large biomolecules

Vibrational spectra of proteins potentially give insight into biologically significant molecular motion and the proportions of different types of secondary structure. Vibrational spectra can be calculated either from normal modes obtained by diagonalizing the mass-weighted Hessian or from the time autocorrelation function derived from molecular dynamics trajectories. The Hessian matrix is calculated from force fields because it is not practical to calculate the Hessian from quantum mechanics for large molecules. As an alternative to molecular dynamics the spectral response can be calculated from a time autocorrelation derived from numerical solution of the harmonic equations of motion, resulting in calculations at least 4 times faster. Because the calculation also scales linearly with number of atoms, N, it is faster than normal-mode calculations that scale as N ³ for proteins with more then 4,700 atoms. Using this method it is practical to perform all-atom calculations for large biological systems, for example viral capsids, with the order of 10⁵ atoms.     

Mutants of monomeric red fluorescent protein mRFP1 at residue 66: Structure modeling by molecular dynamics and search for correlations with spectral properties

To study the interrelation between the spectral and structural properties of fluorescent proteins, structures of mutants of monomeric red fluorescent protein mRFP1 with all possible point mutations of Glu66 (except replacement by Pro) were simulated by molecular dynamics. A global search for correlations between geometrical structure parameters and some spectral characteristics (absorption maximum wavelength, integral extinction coefficient at the absorption maximum, excitation maximum wavelength, emission maximum wavelength, and quantum yield) was performed for the chromophore and its 6 A environment in mRFP1, Q66A, Q66L, Q66S, Q66C, Q66H, and Q66N. The correlation coefficients (0.81-0.87) were maximal for torsion angles in phenolic and imidazolidine rings as well as for torsion angles in the regions of connection between these rings and chromophore attachment to beta-barrel. The data can be used to predict the spectral properties of fluorescent proteins based on their structures and to reveal promising positions for directed mutagenesis.     

The effect of temperature on FMN absorption spectra in rigid poly(vinyl alcohol) matrices

Electronic absorption spectra of flavomononucleotide (FMN) in poly(vinyl alcohol) films (PVA) were measured over the concentrations ranging from 6.9 x 10(-4) to 6.8 x 10(-1) M and temperatures from 263 to 338 K.The FMN absorption spectra measurements performed at room temperature have shown two ranges of different changes as a function of dye concentration. For concentrations c<10(-1) M (range I) the spectra exhibited regular changes showing an isosbestic point, which evidences the equilibrium between monomers and dimers. However, for range II (c>1.05 x 10(-1) M) the FMN absorption spectra occurred to be almost independent of concentration and they nearly overlapped with the dimer spectrum (within the error limit).Temperature measurements have shown that the FMN absorption spectra in PVA are stable over a wide temperature range.The mean distances between FMN molecules in PVA films are calculated. For maximal concentrations (from the range II), they are below 13.1 A, whereas the mean dimensions of FMN monomers and dimers are 15.8 and 21.1 A, respectively, which indicates that the orientation of dimers and monomers in the PVA film cannot be random at high concentrations. Molecules are partly ordered, adopting approximately parallel orientation, which is in agreement with the calculations of dimer structure by molecular modelling method (MMM).     

Computational strategy for tuning spectral properties of red fluorescent proteins

Computational methods of quantum chemistry are used to characterize structures and vertical excitation energies of the S(0)-S(1) optical transitions in the chromophore binding pockets of the red fluorescent proteins DsRed and of its artificial mutant mCherry. As previously shown, optimizing the equilibrium geometry configurations with B3LYP density functional theory, followed by ZINDO calculations of the electronic excitations, yields positions of the optical bands in good agreement with experimental data. These large scale quantum calculations elucidate the role of the hydrogen bonded network as well as point mutations in the absorption spectra of the DsRed and mCherry proteins. The effect of an external electric field applied to the fluorescent protein chromophores is examined and shows that such fields may result in large shifts in spectral bands. These strategies can be applied for rational design of the fluorescent proteins by site-directed mutagenesis.     

Exciton interactions in synthetic porphyrin dimers

The Soret absorption spectra of six synthetic rigid porphyrin dimers whose crystal structures have been determined are simulated using simple exciton theory. The objective is to test the validity of the point dipole and associated approximations; the electronic interaction parameters are thus calculated using data obtained from the monomer spectra, with no adjustable parameters. Satisfactory agreement between theory and experiment is obtained for one class of dimers but not for a second. This poses a challenge for semiempirical electronic structure methods as to whether improvements over the point dipole calculations can be obtained.     

Ab initio self-consistent field and potential-dependent partial equalization of orbital electronegativity calculations of hydration properties of N-acetyl-N'-methyl-alanineamide

Using a recently developed parallel computation algorithm, ab initio self-consistent field (SCF) calculations were carried out to estimate the relative hydration energies for 12 low-energy conformations of N-acetyl-N'-methyl-alanineamide. The requisite SCF calculations were carried out using 6-31G and 6-31G* basis sets, both in the absence and presence of a perturbing potential arising from a model solvent. The alpha R, alpha L, polyproline II (PII), and pi helical conformations were preferentially stabilized by the solvent potential, whereas conformations with intramolecular hydrogen-bonding C5 and C7 were preferred in the gas phase. Average vicinal nmr coupling constants (JNH-C alpha H), calculated using the total energies of the various solvated conformations, were consistent with observed coupling constants for this peptide in aqueous solution. Substantial alteration of the solute charge density occurred upon equilibration with the reaction field, as was exemplified in changes both in the molecular dipole moments and in atom-centered multipoles, when the molecule was transferred from a medium of low dielectric constant to one of high dielectric constant. In order to model these changes in charge density with an empirical scheme, we have implemented a novel monopolar representation of the solute charge density based on a potential-dependent form of partial equalization of orbital electronegativities (PDPEOE). In the atom-centered point charge PDPEOE representation, charge flows from one region of the solute to another in response to external fields. Hydration energies calculated using the PDPEOE representation are similar to those calculated by the SCF procedure. Also, the PDPEOE calculations yielded changes in molecular dipole moments upon solvation that agreed closely with the changes in the calculated ab initio SCF dipole moments.     

The nature of intermolecular interactions between aromatic amino acid residues

The nature of intermolecular interactions between aromatic amino acid residues has been investigated by a combination of molecular dynamics and ab initio methods. The potential energy surface of various interacting pairs, including tryptophan, phenilalanine, and tyrosine, was scanned for determining all the relevant local minima by a combined molecular dynamics and conjugate gradient methodology with the AMBER force field. For each of these minima, single-point correlated ab initio calculations of the binding energy were performed. The agreement between empirical force field and ab initio binding energies of the minimum energy structures is excellent. Aromatic-aromatic interactions can be rationalized on the basis of electrostatic and van der Waals interactions, whereas charge transfer or polarization phenomena are small for all intermolecular complexes and, particularly, for stacked structures. Proteins 2002;48:117-125.     

Reproduction of correct electrostatic field by charges and dipoles on a closed surface

A general algorithm based on the Green function theorem has been developed to correctly reproduce electrostatic fields inside a closed space by point charges and point dipoles on the surface surrounding the space. For actual computations, limited numbers of point charges, including charge pairs replacing point dipoles, are enough to approximate the inner fields. As examples, reaction fields were reproduced by the current surface charges and dipoles for the dielectric models, where a monopole, dipole, or quadrupole was individually set at the center in a vacuum sphere surrounded by high dielectric continuum. The potentials due to those reaction fields agree well with the analytical ones. As an application of this method to the analysis of the electronic structure of the active site of a protein, a combination of the continuum dielectric model and ab initio molecular orbital calculation was carried out. Other applications to molecular dynamics and quantum mechanical calculations are also discussed.     

Fluorescent proteins: physical-chemical properties and application in cell biology

Green fluorescent protein (GFP) from jellyfish Aequorea victoria is the most extensively studied and widely used in cell biology protein. At present novel naturally occurring GFP-like proteins have been discovered and enhanced mutants of Aequorea GFP have been created. These mutants differ from wild-type GFP by stability, value of quantum yield, absorption and fluorescence spectra position and photochemical properties. GFP-like proteins are the fast growing family. This review is an attempt to characterize the main groups of GFP-like proteins, describe their structure and mechanisms of chromophore formation and summarize the main trends of their utilization as markers and biosensors in cell and molecular biology.     

Density-functional theory and ab initio Hartree-Fork studies on the structural parameters and chemical activity of the free radicals generated by benzoquinone and hydroquinone

Density-functional theory (DFT) calculations were performed for calculation of the theoretical spectra and the chemical activities of free radicals generated by benzoquinone and hydroquinone as well as the transition states, and the calculated spectra were used for the assignment of the frequencies observed in the experimental IR spectra. The calculated geometrical parameters, the predicted IR spectra, and the chemical activities of free radicals and transition states were also compared with those of benzoquinone and hydroquinone. The reactive mechanisms of free radicals generated by benzoquinone and hydroquinone are also discussed using ab initio Hartree-Fork (HF) methods.     

Electric dipole moments of the fluorescent probes Prodan and Laurdan: experimental and theoretical evaluations

Several experimental and theoretical approaches can be used for a comprehensive understanding of solvent effects on the electronic structure of solutes. In this review, we revisit the influence of solvents on the electronic structure of the fluorescent probes Prodan and Laurdan, focusing on their electric dipole moments. These biologically used probes were synthesized to be sensitive to the environment polarity. However, their solvent-dependent electronic structures are still a matter of discussion in the literature. The absorption and emission spectra of Prodan and Laurdan in different solvents indicate that the two probes have very similar electronic structures in both the ground and excited states. Theoretical calculations confirm that their electronic ground states are very much alike. In this review, we discuss the electric dipole moments of the ground and excited states calculated using the widely applied Lippert–Mataga equation, using both spherical and spheroid prolate cavities for the solute. The dimensions of the cavity were found to be crucial for the calculated dipole moments. These values are compared to those obtained by quantum mechanics calculations, considering Prodan in vacuum, in a polarizable continuum solvent, and using a hybrid quantum mechanics–molecular mechanics methodology. Based on the theoretical approaches it is evident that the Prodan dipole moment can change even in the absence of solute–solvent-specific interactions, which is not taken into consideration with the experimental Lippert–Mataga method. Moreover, in water, for electric dipole moment calculations, it is fundamental to consider hydrogen-bonded molecules.