How proteins trigger excitation energy transfer in the FMO complex of green sulfur bacteria

A simple electrostatic method for the calculation of optical transition energies of pigments in protein environments is presented and applied to the Fenna-Matthews-Olson (FMO) complex of Prosthecochloris aestuarii and Chlorobium tepidum. The method, for the first time, allows us to reach agreement between experimental optical spectra and calculations based on transition energies of pigments that are calculated in large part independently, rather than fitted to the spectra. In this way it becomes possible to understand the molecular mechanism allowing the protein to trigger excitation energy transfer reactions. The relative shift in excitation energies of the seven bacteriochlorophyll-a pigments of the FMO complex of P. aestuarii and C. tepidum are obtained from calculations of electrochromic shifts due to charged amino acids, assuming a standard protonation pattern of the protein, and by taking into account the three different ligand types of the pigments. The calculations provide an explanation of some of the earlier results for the transition energies obtained from fits of optical spectra. In addition, those earlier fits are verified here by using a more advanced theory of optical spectra, a genetic algorithm, and excitonic couplings obtained from electrostatic calculations that take into account the influence of the dielectric protein environment. The two independent calculations of site energies strongly favor one of the two possible orientations of the FMO trimer relative to the photosynthetic membrane, which were identified by electron microscopic studies and linear dichroism experiments. Efficient transfer of excitation energy to the reaction center requires bacteriochlorophylls 3 and 4 to be the linker pigments. The temporal and spatial transfer of excitation energy through the FMO complex is calculated to proceed along two branches, with transfer times that differ by an order of magnitude.     

Visualization analysis of inter-fragment interaction energies of CRP-cAMP-DNA complex based on the fragment molecular orbital method

A visualization method for inter-fragment interaction energies (IFIEs) of biopolymers is presented on the basis of the fragment molecular orbital (FMO) method. The IFIEs appropriately illustrate the information about the interaction energies between the fragments consisting of amino acids, nucleotides and other molecules. The IFIEs are usually analyzed in a matrix form called an IFIE matrix. Analyzing the IFIE matrix, we detect important fragments for the function of biomolecular systems and quantify the strength of interaction energies based on quantum chemistry, including the effects of charge transfer, electronic polarization and dispersion force. In this study, by analyzing a protein-DNA complex, we report a visual representation of the IFIE matrix, a so-called IFIE map. We comprehensively examine what information the IFIE map contains concerning structures and stabilities of the protein-DNA complex.     

Calculation of chromophore excited state energy shifts in response to molecular dynamics of pigment-protein complexes

The absorption and energy transfer properties of photosynthetic pigments are strongly influenced by their local environment or “site.” Local electrostatic fields vary in time with protein and chromophore molecular movement and thus transiently influence the excited state transition properties of individual chromophores. Site-specific information is experimentally inaccessible in many light-harvesting pigment–proteins due to multiple chromophores with overlapping spectra. Full quantum mechanical calculations of each chromophores excited state properties are too computationally demanding to efficiently calculate the changing excitation energies along a molecular dynamics trajectory in a pigment–protein complex. A simplified calculation of electrostatic interactions with each chromophores ground to excited state transition, the so-called charge density coupling (CDC) for site energy, CDC, has previously been developed to address this problem. We compared CDC to more rigorous quantum chemical calculations to determine its accuracy in computing excited state energy shifts and their fluctuations within a molecular dynamics simulation of the bacteriochlorophyll containing light-harvesting Fenna–Mathews–Olson (FMO) protein. In most cases CDC calculations differed from quantum mechanical (QM) calculations in predicting both excited state energy and its fluctuations. The discrepancies arose from the inability of CDC to account for the differing effects of charge on ground and excited state electron orbitals. Results of our study show that QM calculations are indispensible for site energy computations and the quantification of contributions from different parts of the system to the overall site energy shift. We suggest an extension of QM/MM methodology of site energy shift calculations capable of accounting for long-range electrostatic potential contributions from the whole system, including solvent and ions.     

Molecular bases for human complement C7 polymorphisms,C7*3 and C7*4

Complement C7 is one of the components of membrane attack complex (MAC) generated by the terminal complement cascade. C7 protein is polymorphic and most of its polymorphisms have been identified using isoelectric focusing (IEF), which detects protein charge differences. To date, the molecular bases of the polymorphisms detected by IEF have not been determined. In this paper, we describe the structural bases of two C7 IEF-detected polymorphisms, C7*3 and C7*4, both of which are common in Asian populations. C7*3 resulted from substitution of cysteine (Cys) at amino acid residue 106 by charged arginine (Arg; C106R), while charged lysine (Lys) at amino acid residue 398 was replaced by neutral glutamine (Gln; K398Q) in C7*4. As C7*3 is hypomorphic, it is important to study its possible associations with diseases such as immunological disorders and infections. We present genetic bases for this C7 polymorphism, which we determined using polymerase chain reaction (PCR)-based genotyping, a simple and accurate method suitable for large-scale studies.     

Site specific mutants of beta-galactosidase show that Tyr-503 is unimportant in Mg2+ binding but that Glu-461 is very important and may be a ligand to Mg2+

The Mg2+ concentrations required for half maximal activity, the dissociation constants, and the free energies of binding for Mg2+ bound to wild type beta-galactosidase and several site specific mutants are reported. The mutants have one of the following substitutions: Glu-461 substituted with Asp, Gln, Gly, His, or Lys; or Tyr-503 substituted with Phe, His or Cys. Substitutions for Tyr-503 had little effect on the affinity of the enzyme for Mg2+, implying that Tyr-503 is not involved in Mg2+ binding. Neutrally charged amino acids substituted for the negatively charged Glu-461 significantly decreased the affinity of the enzyme for Mg2+ and substitution of positively charged amino acids at this position further decreased the affinity. On the other hand, substitution by Asp (negative charge) at position 461 had no effect on the binding. Thus, the negatively charged side chain of Glu-461 is important for divalent cation binding to beta-galactosidase.     

Membrane bending is critical for the stability of voltage sensor segments in the membrane

The interaction between membrane proteins and the surrounding membrane is becoming increasingly appreciated for its role in regulating protein function, protein localization, and membrane morphology. In particular, recent studies have suggested that membrane deformation is needed to stably accommodate proteins harboring charged amino acids in their transmembrane (TM) region, as it is energetically prohibitive to bury charge in the hydrophobic core of the bilayer. Unfortunately, current computational methods are poorly equipped for describing such deformations, as atomistic simulations are often too short to observe large-scale membrane reorganization and most continuum approaches assume a flat membrane. Previously, we developed a method that overcomes these shortcomings by using elasticity theory to characterize equilibrium membrane distortions in the presence of a TM protein, while using traditional continuum electrostatic and nonpolar energy models to determine the energy of the protein in the membrane. Here, we linked the elastostatics, electrostatics, and nonpolar numeric solvers to permit the calculation of energies for nontrivial membrane deformations. We then coupled this procedure to a robust search algorithm that identifies optimal membrane shapes for a TM protein of arbitrary chemical composition. This advance now permits us to explore a host of biological phenomena that were beyond the scope of our original method. We show that the energy required to embed charged residues in the membrane can be highly nonadditive, and our model provides a simple mechanical explanation for this nonadditivity. Our results also predict that isolated voltage sensor segments do not insert into rigid membranes, but membrane bending dramatically stabilizes these proteins in the bilayer despite their high charge content. Additionally, we use the model to explore hydrophobic mismatch with regard to nonpolar peptides and mechanosensitive channels. Our method is in quantitative agreement with molecular dynamics simulations at a tiny fraction of the computational cost.     

Ions from the Hofmeister series and osmolytes: effects on proteins in solution and in the crystallization process

Sephadex G-10 gel sieving chromatography, Jones-Dole viscosity B coefficients, and solution neutron and X-ray diffraction are used to show that small ions of high charge density (e.g., sulfate, phosphate, the carboxylate, sodium, and fluoride) are strongly hydrated (kosmotropes) whereas large monovalent ions of low charge density (e.g., ammonium, chloride, potassium, and the positively charged amino acid side chains) are weakly hydrated (chaotropes). The heats of solution of the crystalline alkali halides are then used to show that only oppositely charged ions of equal water affinity spontaneously form inner sphere ion pairs, and that this controls ion binding to proteins. The net charge on a protein is a major determinant of its solubility. Finally, the surface potential difference and surface tension at an air-salt solution interface are used to generate a simple model for how ions affect protein stability and solubility through indirect interactions at the protein-solution interface. A few comments about small neutral osmolytes are also included.     

Protein contributions to redox potentials of homologous rubredoxins: an energy minimization study.

The energetic contributions of the protein to the redox potential in an iron-sulfur protein are studied via energy minimization, comparing homologous rubredoxins from Clostridium pasteurianum, Desulfovibrio gigas, Desulfovibrio vulgaris, and Pyrococcus furiosus. The reduction reaction was divided into 1) the change in the redox site charge without allowing the protein to respond and 2) the relaxation of the protein in response to the new charge state, focusing on the latter. The energy minimizations predict structural relaxation near the redox site that agrees well with that in crystal structures of oxidized and reduced P. furiosus rubredoxin, but underpredicts it far from the redox site. However, the relaxation energies from the energy-minimized structures agree well with those from the crystal structures, because the polar groups near the redox site are the main determinants and the charged groups are all located at the surface and thus are screened dielectrically. Relaxation energies are necessary for good agreement with experimentally observed differences in reduction energies between C. pasteurianum and the other three rubredoxins. Overall, the relaxation energy is large (over 500 mV) from both the energy-minimized and the crystal structures. In addition, the range in the relaxation energy for the different rubredoxins is large (300 mV), because even though the structural perturbations of the polar groups are small, they are very near the redox site. Thus the relaxation energy is an important factor to consider in reduction energetics.     

Investigation of the role of electrostatic charge in activation of the Escherichia coli response regulator CheY

In a two-component regulatory system, an important means of signal transduction in microorganisms, a sensor kinase phosphorylates a response regulator protein on an aspartyl residue, resulting in activation. The active site of the response regulator is highly charged (containing a lysine, the phosphorylatable aspartate, two additional aspartates involved in metal binding, and an Mg(2+) ion), and introduction of the dianionic phosphoryl group results in the repositioning of charged moieties. Furthermore, substitution of one of the Mg(2+)-coordinating aspartates with lysine or arginine in the Escherichia coli chemotaxis response regulator CheY results in phosphorylation-independent activation. In order to examine the consequences of altered charge distribution for response regulator activity and to identify possible additional amino acid substitutions that result in phosphorylation-independent activation, we made 61 CheY mutants in which residues close to the site of phosphorylation (Asp57) were replaced by various charged amino acids. Most substitutions (47 of 61) resulted in the complete loss of CheY activity, as measured by the inability to support clockwise flagellar rotation. However, 10 substitutions, all introducing a new positive charge, resulted in the loss of chemotaxis but in the retention of some clockwise flagellar rotation. Of the mutants in this set, only the previously identified CheY13DK and CheY13DR mutants displayed clockwise activity in the absence of the CheA sensor kinase. The absence of negatively charged substitution mutants with residual activity suggests that the introduction of additional negative charges into the active site is particularly deleterious for CheY function. Finally, the spatial distribution of positions at which amino acid substitutions are functionally tolerated or not tolerated is consistent with the presently accepted mechanism of response regulator activation and further suggests a possible role for Met17 in signal transduction by CheY.     

Influence of key residues on the reaction mechanism of the cAMP-dependent protein kinase

The reaction mechanism of the catalytic phosphoryl transfer of cAMP-dependent protein kinase (cAPK) was investigated by semi-empirical AM1 molecular orbital computations of an active site model system derived from the crystal structure of the catalytic subunit of the enzyme. The activation barrier is calculated as 20.7 kcal mol(-1) and the reaction itself to be exothermic by 12.2 kcal mol(-1). The active site residue Asp166, which was often proposed to act as a catalytic base, does not accept a proton in any of the reaction steps. Instead, the hydroxyl hydrogen of serine is shifted to the simultaneously transferred phosphate group of ATP. Although the calculated transition state geometry indicates an associative phosphoryl transfer, no concentration of negative charge is found. To study the influence of protein mutations on the reaction mechanism, we compared two-dimensional energy hypersurfaces of the protein kinase wild-type model and a corresponding mutant in which Asp166 was replaced by alanine. Surprisingly, they show similar energy profiles despite the experimentally known decrease of catalytic activity for corresponding mutants. Furthermore, a model structure was examined, where the charged NH3 group of Lys168 was replaced by a neutral methyl group. The energetic hypersurface of this hypothetical mutant shows two possible pathways for phosphoryl transfer, which both require significantly higher activation energies than the other systems investigated, while the energetic stabilization of the reaction product is similar in all systems. As the position of the amino acid side chains and the substrate peptide is virtually unchanged in all model systems, our results suggest that the exchange of Asp166 by other amino acid is less important to the phosphoryl transfer itself, but crucial to maintain the configuration of the active site in vivo. The positively charged side chain of Lys168, however, is necessary to stabilize the intermediate reaction states, particularly the side chain of the substrate peptide.     

Role of charged residues in the catalytic mechanism of hepatitis C virus NS3 protease: electrostatic precollision guidance and transition-state stabilization

Maturational cleavage of the hepatitis C virus polyprotein involves the viral chymotrypsin-like serine protease NS3. The substrate binding site of this enzyme is unusually flat and featureless. We here show that NS3 has a highly asymmetric charge distribution that is characterized by strong positive potentials in the vicinity of its active site and in the S5/S6 region. Using electrostatic potential calculations, we identified determinants of this positive potential, and the role of six different residues was explored by site-directed mutagenesis. Mutation of residues in the vicinity of the active site led to changes in k(cat) values of a peptide substrate indicating that basic amino acids play a role in the stabilization of the transition state. Charge neutralization in the S5/S6 region increased the K(m) values of peptide substrates in a manner that depended on the presence of negatively charged residues in the P5 and P6 positions. K(i) values of hexapeptide acids spanning P6-P1 (product inhibitors) were affected by charge neutralization in both the active site region and the S5/S6 region. Pre-steady-state kinetic data showed that the electrostatic surface potential is used by this enzyme to enhance collision rates between peptidic ligands and the active site. Calculations of the interaction energies of protease-substrate or protease-inhibitor complexes showed that electrostatic interaction energies oppose the formation of a tightly bound complex due to an unfavorable change in the desolvation energy. We propose that desolvation costs are minimized by avoiding the formation of individual ion pair interactions through the use of clusters of positively charged residues in the generation of local electrostatic potentials.     

Stability of 100 homo and heterotypic coiled-coil a-a' pairs for ten amino acids (A, L, I, V, N, K, S, T, E, and R)

We present the thermal stability monitored by circular dichroism (CD) spectroscopy at 222 nm of 100 heterodimers that contain all possible coiled-coil a-a' pairs for 10 amino acids (I, V, L, N, A, K S, T, E, and R). This includes the stability of 36 heterodimers for 6 amino acids (I, V, L, N, A, and K) previously described and 64 new heterodimers including the 4 amino acids (S, T, E, and R). We have calculated a double mutant alanine thermodynamic cycle to determine a-a' pair coupling energies to evaluate which a-a' pairs encourage specific dimerization partners. The four new homotypic a-a' pairs (T-T, S-S, R-R, E-E) are repulsive relative to A-A and have destabilizing coupling energies. Among the 90 heterotypic a-a' pairs, the stabilizing coupling energies contain lysine or arginine paired with either an aliphatic or a polar amino acid. The range in coupling energies for each amino acid reveals its potential to regulate dimerization specificity. The a-a' pairs containing isoleucine and asparagine have the greatest range in coupling energies and thus contribute dramatically to dimerization specificity, which is to encourage homodimerization. In contrast, the a-a' pairs containing charged amino acids (K, R, and E) show the least range in coupling energies and promiscuously encourage heterodimerization.     

Redox potential of the Rieske iron-sulfur protein: Quantum-chemical and electrostatic study

Quantum-chemical study of structures, energies, and effective partial charge distribution for several models of the Rieske protein redox center is performed in terms of the B3LYP density functional method in combination with the broken symmetry approach using three different atomic basis sets. The structure of the redox complex optimized in vacuum differs markedly from that inside the protein. This means that the protein matrix imposes some stress on the active site resulting in distortion of its structure. The redox potentials calculated for the real active site structure are in a substantially better agreement with the experiment than those calculated for the idealized structure. This shows an important role of the active site distortion in tuning its redox potential. The reference absolute electrode potential of the standard hydrogen electrode is used that accounts for the correction caused by the water surface potential. Electrostatic calculations are performed in the framework of the polarizable solute model. Two dielectric permittivities of the protein are employed: the optical permittivity for calculation of the intraprotein electric field, and the static permittivity for calculation of the dielectric response energy. Only this approach results in a reasonable agreement of the calculated and experimental redox potentials.     

Measurements of interbilayer forces and protein adsorption on uncharged lipid bilayers displaying poly(ethylene glycol) chains

Poly(ethylene glycol) (PEG)-stabilized liposomes were recently shown to exhibit differences in cell uptake that were linked to the liposome charge. To determine the differences and similarities between charged and uncharged PEG-decorated liposomes, we directly measured the forces between two supported, neutral bilayers with terminally grafted PEG chains. The measurements were performed with the surface force apparatus. The force profiles were similar to those measured with negatively charged PEG conjugates of 1, 2-distearoyl-sn-glycero-3-phosphatidyl ethanolamine (DSPE), except that they lacked the longer ranged electrostatic repulsion observed with the charged compound. Theories for simple polymers describe the forces between end-grafted polymer chains on neutral bilayers. The force measurements were complemented by surface plasmon resonance studies of protein adsorption onto these layers. The lack of electrostatic forces reduced the adsorption of positively charged proteins and enhanced the adsorption of negatively charged ones. The absence of charge also allowed us to determine how membrane charge and the polymer grafting density independently affect protein adsorption on the coated membranes. Such studies suggest the physical basis of the different interactions of charged and uncharged liposomes with proteins and cells.     

A mechanism for the evolution of phosphorylation sites

Protein phosphorylation provides a mechanism for the rapid, reversible control of protein function. Phosphorylation adds negative charge to amino acid side chains, and negatively charged amino acids (Asp/Glu) can sometimes mimic the phosphorylated state of a protein. Using a comparative genomics approach, we show that nature also employs this trick in reverse by evolving serine, threonine, and tyrosine phosphorylation sites from Asp/Glu residues. Structures of three proteins where phosphosites evolved from acidic residues (DNA topoisomerase II, enolase, and C-Raf) show that the relevant acidic residues are present in salt bridges with conserved basic residues, and that phosphorylation has the potential to conditionally restore the salt bridges. The evolution of phosphorylation sites from glutamate and aspartate provides a rationale for why phosphorylation sometimes activates proteins, and helps explain the origins of this important and complex process.     

Extreme differences in charge changes during protein evolution

Summary The maintenance of a proper distribution of charged amino acid residues might be expected to be an important factor in protein evolution. We therefore compared the inferred changes in charge during the evolution of 43 protein families with the changes expected on the basis of random base substitutions. It was found that certain proteins, like the eye lens crystallins and most histones, display an extreme avoidance of changes in charge. Other proteins, like phospholipase A2 and ferredoxin, apparently have sustained more charged replacements than expected, suggesting a positive selection for changes in charge. Depending on function and structure of a protein, charged residues apparently can be important targets for selective forces in protein evolution. It appears that actual biased codon usage tends to decrease the proportion of charged amino acid replacements. The influence of nonrandomness of mutations is more equivocal. Genes that use the mitochondrial instead of the universal code lower the probability that charge changes will occur in the encoded proteins.     

Kinetics of reduction by free flavin semiquinones of algal cytochromes and plastocyanin

It had been shown that plastocyanin and cytochrome c-553 are functionally interchangeable in algae and that the physiological electron transfer reactions are sensitive to ionic strength. The isoelectric points of these proteins range from very acidic to basic depending upon species, and naturally occurring amino acid substitutions of charged residues have been shown to affect the kinetics of electron transfer, presumably through alteration of protein net charge. We have now shown that these naturally occurring amino acid substitutions also affect the kinetics of nonphysiological electron transfer reactions, and that we can quantitate the extent of nonconservation of charge. The reduction of plant and algal proteins by FMN semiquinone is sensitive to ionic strength and the effects can be correlated with net protein charge with regard to sign, but not to magnitude, with the charge at the site of electron transfer varying from +3 through 0 to -3. We had previously observed in a large variety of electron transfer proteins from bacteria (G. Tollin, T. E. Meyer, and M. A. Cusanovich (1986) Biochim. Biophys. Acta 853, 29-41) that charge localized at the site of electron transfer, rather than net protein charge, was more likely to affect kinetics. This also appears to be the case with the algal proteins. By comparison of protein structures, we have been able to predict which substitutions are likely to be responsible for the kinetic effects in the algal proteins and to discuss the implications of such changes for function.     

Extracting the Excitonic Hamiltonian of the Fenna-Matthews-Olson Complex Using Three-Dimensional Third-Order Electronic Spectroscopy

We extend traditional two-dimensional (2D) electronic spectroscopy into a third Fourier dimension without the use of additional optical interactions. By acquiring a set of 2D spectra evenly spaced in waiting time and dividing the area of the spectra into voxels, we can eliminate population dynamics from the data and transform the waiting time dimension into frequency space. The resultant 3D spectrum resolves quantum beating signals arising from excitonic coherences along the waiting frequency dimension, thereby yielding up to 2n-fold redundancy in the set of frequencies necessary to construct a complete set of n excitonic transition energies. Using this technique, we have obtained, to our knowledge, the first fully experimental set of electronic eigenstates for the Fenna-Matthews-Olson (FMO) antenna complex, which can be used to improve theoretical simulations of energy transfer within this protein. Whereas the strong diagonal peaks in the 2D rephasing spectrum of the FMO complex obscure all but one of the crosspeaks at 77 K, extending into the third dimension resolves 19 individual peaks. Analysis of the independently collected nonrephasing data provides the same information, thereby verifying the calculated excitonic transition energies. These results enable one to calculate the Hamiltonian of the FMO complex in the site basis by fitting to the experimental linear absorption spectrum.     

An energetic scale for equilibrium H/D fractionation factors illuminates hydrogen bond free energies in proteins

Equilibrium H/D fractionation factors have been extensively employed to qualitatively assess hydrogen bond strengths in protein structure, enzyme active sites, and DNA. It remains unclear how fractionation factors correlate with hydrogen bond free energies, however. Here we develop an empirical relationship between fractionation factors and free energy, allowing for the simple and quantitative measurement of hydrogen bond free energies. Applying our empirical relationship to prior fractionation factor studies in proteins, we find: [1] Within the folded state, backbone hydrogen bonds are only marginally stronger on average in α‐helices compared to β‐sheets by ～0.2 kcal/mol. [2] Charge‐stabilized hydrogen bonds are stronger than neutral hydrogen bonds by ～2 kcal/mol on average, and can be as strong as –7 kcal/mol. [3] Changes in a few hydrogen bonds during an enzyme catalytic cycle can stabilize an intermediate state by –4.2 kcal/mol. [4] Backbone hydrogen bonds can make a large overall contribution to the energetics of conformational changes, possibly playing an important role in directing conformational changes. [5] Backbone hydrogen bonding becomes more uniform overall upon ligand binding, which may facilitate participation of the entire protein structure in events at the active site. Our energetic scale provides a simple method for further exploration of hydrogen bond free energies.