M. R. Gunner

Comparing Photosynthetic and Photovoltaic Efficiencies and Recognizing the Potential for Improvement

Comparing photosynthetic and photovoltaic efficiencies is not a simple issue. Although both processes harvest the energy in sunlight, they operate in distinctly different ways and produce different types of products: biomass or chemical fuels in the case of natural photosynthesis and nonstored electrical current in the case of photovoltaics. In order to find common ground for evaluating energy-conversion efficiency, we compare natural photosynthesis with present technologies for photovoltaic-driven electrolysis of water to produce hydrogen. Photovoltaic-driven electrolysis is the more efficient process when measured on an annual basis, yet short-term yields for photosynthetic conversion under optimal conditions come within a factor of 2 or 3 of the photovoltaic benchmark. We consider opportunities in which the frontiers of synthetic biology might be used to enhance natural photosynthesis for improved solar energy conversion efficiency.

Combining Conformational Flexibility and Continuum Electrostatics for Calculating pK a s in Proteins

Protein stability and function relies on residues being in their appropriate ionization states at physiological pH. In situ residue pK(a)s also provides a sensitive measure of the local protein environment. Multiconformation continuum electrostatics (MCCE) combines continuum electrostatics and molecular mechanics force fields in Monte Carlo sampling to simultaneously calculate side chain ionization and conformation. The response of protein to charges is incorporated both in the protein dielectric constant (epsilon(prot)) of four and by explicit conformational changes. The pK(a) of 166 residues in 12 proteins was determined. The root mean square error is 0.83 pH units, and >90% have errors of <1 pH units whereas only 3% have errors >2 pH units. Similar results are found with crystal and solution structures, showing that the methods explicit conformational sampling reduces sensitivity to the initial structure. The outcome also changes little with protein dielectric constant (epsilon(prot) 4-20). Multiconformation continuum electrostatics titrations show coupling of conformational flexibility and changes in ionization state. Examples are provided where ionizable side chain position (protein G), Asn orientation (lysozyme), His tautomer distribution (RNase A), and phosphate ion binding (RNase A and H) change with pH. Disallowing these motions changes the calculated pK(a).

Incorporating protein conformational flexibility into the calculation of pH-dependent protein properties

A method for combining calculations of residue pKas with changes in the position of polar hydrogens has been developed. The Boltzmann distributions of proton positions in hydroxyls and neutral titratable residues are found in the same Monte Carlo sampling procedure that determines the amino acid ionization states at each pH. Electrostatic, Lennard-Jones potentials, and torsion angle energies are considered at each proton position. Many acidic and basic residues are found to have significant electrostatic interactions with either a water- or hydroxyl-containing side chain. Protonation state changes are coupled to reorientation of the neighboring hydroxyl dipoles, resulting in smaller free energy differences between neutral and ionized residues than when the protein is held rigid. Multiconformation pH titration gives better agreement with the experimental pKas for triclinic hen egg lysozyme than conventional rigid protein calculations. The hydroxyl motion significantly increases the protein dielectric response, making it sensitive to the composition of the local protein structure. More than one conformer per residue is often found at a given pH, providing information about the distribution of low-energy lysozyme structures.

MCCE2: Improving protein pKa calculations with extensive side chain rotamer sampling

Multiconformation continuum electrostatics (MCCE) explores different conformational degrees of freedom in Monte Carlo calculations of protein residue and ligand pKas. Explicit changes in side chain conformations throughout a titration create a position dependent, heterogeneous dielectric response giving a more accurate picture of coupled ionization and position changes. The MCCE2 methods for choosing a group of input heavy atom and proton positions are described. The pKas calculated with different isosteric conformers, heavy atom rotamers and proton positions, with different degrees of optimization are tested against a curated group of 305 experimental pKas in 33 proteins. QUICK calculations, with rotation around Asn and Gln termini, sampling His tautomers and torsion minimum hydroxyls yield an RMSD of 1.34 with 84% of the errors being <1.5 pH units. FULL calculations adding heavy atom rotamers and side chain optimization yield an RMSD of 0.90 with 90% of the errors <1.5 pH unit. Good results are also found for pKas in the membrane protein bacteriorhodopsin. The inclusion of extra side chain positions distorts the dielectric boundary and also biases the calculated pKas by creating more neutral than ionized conformers. Methods for correcting these errors are introduced. Calculations are compared with multiple X‐ray and NMR derived structures in 36 soluble proteins. Calculations with X‐ray structures give significantly better pKas. Results with the default protein dielectric constant of 4 are as good as those using a value of 8. The MCCE2 program can be downloaded from http://www.sci.ccny.cuny.edu/∼mcce.

Structural-functional role of chloride in photosystem II.

Chloride binding in photosystem II (PSII) is essential for photosynthetic water oxidation. However, the functional roles of chloride and possible binding sites, during oxygen evolution, remain controversial. This paper examines the functions of chloride based on its binding site revealed in the X-ray crystal structure of PSII at 1.9 Å resolution. We find that chloride depletion induces formation of a salt bridge between D2-K317 and D1-D61 that could suppress the transfer of protons to the lumen.

A pragmatic approach to structure based calculation of coupled proton and electron transfer in proteins

The coupled motion of electrons and protons occurs in many proteins. Using appropriate tools for calculation, the three-dimensional protein structure can show how each protein modulates the observed electron and proton transfer reactions. Some of the assumptions and limitations involved in calculations that rely on continuum electrostatics to calculate the energy of charges in proteins are outlined. Approaches that mix molecular mechanics and continuum electrostatics are described. Three examples of the analysis of reactions in photosynthetic reaction centers are given: comparison of the electrochemistry of hemes in different sites; analysis of the role of the protein in stabilizing the early charge separated state in photosynthesis; and calculation of the proton uptake and protein motion coupled to the electron transfer from the primary (Q(A)) to secondary (Q(B)) quinone. Different mechanisms for stabilizing intra-protein charged cofactors are highlighted in each reaction.

Backbone Dipoles Generate Positive Potentials in all Proteins: Origins and Implications of the Effect

Asymmetry in packing the peptide amide dipole results in larger positive than negative regions in proteins of all folding motifs. The average side chain potential in 305 proteins is 109 +/- 30 mV (2. 5 +/- 0.7 kcal/mol/e). Because the backbone has zero net charge, the non-zero potential is unexpected. The larger oxygen at the negative and smaller proton at the positive end of the amide dipole yield positive potentials because: 1) at allowed phi and psi angles residues come off the backbone into the positive end of their own amide dipole, avoiding the large oxygen; and 2) amide dipoles with their carbonyl oxygen surface exposed and amine proton buried make the protein interior more positive. Twice as many amides have their oxygens exposed than their amine protons. The distribution of acidic and basic residues shows the importance of the bias toward positive backbone potentials. Thirty percent of the Asp, Glu, Lys, and Arg are buried. Sixty percent of buried residues are acids, only 40% bases. The positive backbone potential stabilizes ionization of 20% of the acids by >3 pH units (-4.1 kcal/mol). Only 6.5% of the bases are equivalently stabilized by negative regions. The backbone stabilizes bound anions such as phosphates and rarely stabilizes bound cations.

The pKa Cooperative: A collaborative effort to advance structure-based calculations of pKa values and electrostatic effects in proteins†

The pKa Cooperative (http://www.pkacoop.org) was organized to advance development of accurate and useful computational methods for structure‐based calculation of pKa values and electrostatic energies in proteins. The Cooperative brings together laboratories with expertise and interest in theoretical, computational, and experimental studies of protein electrostatics. To improve structure‐based energy calculations, it is necessary to better understand the physical character and molecular determinants of electrostatic effects. Thus, the Cooperative intends to foment experimental research into fundamental aspects of proteins that depend on electrostatic interactions. It will maintain a depository for experimental data useful for critical assessment of methods for structure‐based electrostatics calculations. To help guide the development of computational methods, the Cooperative will organize blind prediction exercises. As a first step, computational laboratories were invited to reproduce an unpublished set of experimental pKa values of acidic and basic residues introduced in the interior of staphylococcal nuclease by site‐directed mutagenesis. The pKa values of these groups are unique and challenging to simulate owing to the large magnitude of their shifts relative to normal pKa values in water. Many computational methods were tested in this first Blind Prediction Challenge and critical assessment exercise. A workshop was organized in the Telluride Science Research Center to objectively assess the performance of many computational methods tested on this one extensive data set. This volume of Proteins: Structure, Function, and Bioinformatics introduces the pKa Cooperative, presents reports submitted by participants in the Blind Prediction Challenge, and highlights some of the problems in structure‐based calculations identified during this exercise. Proteins 2011;

Analysis of the electrochemistry of hemes with Ems spanning 800 mV

The free energy of heme reduction in different proteins is found to vary over more than 18 kcal/mol. It is a challenge to determine how proteins manage to achieve this enormous range of Ems with a single type of redox cofactor. Proteins containing 141 unique hemes of a‐, b‐, and c‐type, with bis‐His, His‐Met, and aquo‐His ligation were calculated using Multi‐Conformation Continuum Electrostatics (MCCE). The experimental Ems range over 800 mV from −350 mV in cytochrome c3 to 450 mV in cytochrome c peroxidase (vs. SHE). The quantitative analysis of the factors that modulate heme electrochemistry includes the interactions of the heme with its ligands, the solvent, the protein backbone, and sidechains. MCCE calculated Ems are in good agreement with measured values. Using no free parameters the slope of the line comparing calculated and experimental Ems is 0.73 (R2 = 0.90), showing the method accounts for 73% of the observed Em range. Adding a +160 mV correction to the His‐Met c‐type hemes yields a slope of 0.97 (R2 = 0.93). With the correction 65% of the hemes have an absolute error smaller than 60 mV and 92% are within 120 mV. The overview of heme proteins with known structures and Ems shows both the lowest and highest potential hemes are c‐type, whereas the b‐type hemes are found in the middle Em range. In solution, bis‐His ligation lowers the Em by ≈205 mV relative to hemes with His‐Met ligands. The bis‐His, aquo‐His, and His‐Met ligated b‐type hemes all cluster about Ems which are ≈200 mV more positive in protein than in water. In contrast, the low potential bis‐His c‐type hemes are shifted little from in solution, whereas the high potential His‐Met c‐type hemes are raised by ≈300 mV from solution. The analysis shows that no single type of interaction can be identified as the most important in setting heme electrochemistry in proteins. For example, the loss of solvation (reaction field) energy, which raises the Em, has been suggested to be a major factor in tuning in situ Ems. However, the calculated solvation energy vs. experimental Em shows a slope of 0.2 and R2 of 0.5 thus correlates weakly with Ems. All other individual interactions show even less correlation with Em. However the sum of these terms does reproduce the range of observed Ems. Therefore, different proteins use different aspects of their structures to modulate the in situ heme electrochemistry. This study also shows that the calculated Ems are relatively insensitive to different heme partial charges and to the protein dielectric constant used in the simulation. Proteins 2009.

The importance of the protein in controlling the electrochemistry of heme metalloproteins: methods of calculation and analysis

Abstract The importance of electrostatic effects in determining the free energy of redox reactions in proteins such as cytochromes and iron-sulfur complexes is well established. Several theoretical techniques have been used to analyze how the protein and its environment combine to produce the observed electrochemical midpoints. The free energy of changing the cofactor charge is influenced by the distribution of charges and dipoles in the protein, solvent and ions surrounding the protein, and by the redistribution of these charges and dipoles coupled to the reaction. An outline of a consistent view for calculating these effects will be presented and compared with other theoretical models. Heme redox potentials in yeast cytochrome c and the cytochrome subunit of photosynthetic reaction centers will be calculated to show how these protein structures produce the observed electrochemistry.