Ernst-Walter Knapp

Multivalency as a Chemical Organization and Action Principle

Multivalent interactions can be applied universally for a targeted strengthening of an interaction between different interfaces or molecules. The binding partners form cooperative, multiple receptor-ligand interactions that are based on individually weak, noncovalent bonds and are thus generally reversible. Hence, multi- and polyvalent interactions play a decisive role in biological systems for recognition, adhesion, and signal processes. The scientific and practical realization of this principle will be demonstrated by the development of simple artificial and theoretical models, from natural systems to functional, application-oriented systems. In a systematic review of scaffold architectures, the underlying effects and control options will be demonstrated, and suggestions will be given for designing effective multivalent binding systems, as well as for polyvalent therapeutics.

α-Helices direct excitation energy flow in the Fenna–Matthews–Olson protein

In photosynthesis, light is captured by antenna proteins. These proteins transfer the excitation energy with almost 100% quantum efficiency to the reaction centers, where charge separation takes place. The time scale and pathways of this transfer are controlled by the protein scaffold, which holds the pigments at optimal geometry and tunes their excitation energies (site energies). The detailed understanding of the tuning of site energies by the protein has been an unsolved problem since the first high-resolution crystal structure of a light-harvesting antenna appeared >30 years ago [Fenna RE, Matthews BW (1975) Nature 258:573–577]. Here, we present a combined quantum chemical/electrostatic approach to compute site energies that considers the whole protein in atomic detail and provides the missing link between crystallography and spectroscopy. The calculation of site energies of the Fenna–Matthews–Olson protein results in optical spectra that are in quantitative agreement with experiment and reveals an unexpectedly strong influence of the backbone of two α-helices. The electric field from the latter defines the direction of excitation energy flow in the Fenna–Matthews–Olson protein, whereas the effects of amino acid side chains, hitherto thought to be crucial, largely compensate each other. This result challenges the current view of how energy flow is regulated in pigment–protein complexes and demonstrates that attention has to be paid to the backbone architecture.

Oxygen-evolving Mn cluster in photosystem II: the protonation pattern and oxidation state in the high-resolution crystal structure.

Extensive quantum chemical DFT calculations were performed on the high-resolution (1.9 Å) crystal structure of photosystem II in order to determine the protonation pattern and the oxidation states of the oxygen-evolving Mn cluster. First, our data suggest that the experimental structure is not in the S(1)-state. Second, a rather complete set of possible protonation patterns is studied, resulting in very few alternative protonation patterns whose relevance is discussed. Finally, we show that the experimental structure is a mixture of states containing highly reduced forms, with the largest contribution (almost 60%) from the S(-3)-state, Mn(II,II,III,III).

Recent advances in anion–π interactions

Over the past 10 years, anion–π interaction has been recognized as an important weak force that may occur between anionic systems and electron-deficient aromatics. Lately, this supramolecular contact has experienced a rapidly growing interest, as reflected by numerous recent literature reports. The present paper highlights the tremendous progress achieved in the field by emphasizing three important studies involving anion–π interactions published in 2010. In addition, a pioneering search of the Protein Data Bank (PDB) reveals short anion–π contacts in some protein structures.

How to guarantee optimal stability for most representative structures in the Protein Data Bank.

We proposed recently an optimization method to derive energy parameters for simplified models of protein folding. The method is based on the maximization of the thermodynamic average of the overlap between protein native structures and a Boltzmann ensemble of alternative structures. Such a condition enforces protein models whose ground states are most similar to the corresponding native states. We present here an extensive testing of the method for a simple residue‐residue contact energy function and for alternative structures generated by threading. The optimized energy function guarantees high stability and a well‐correlated energy landscape to most representative structures in the PDB database. Failures in the recognition of the native structure can be attributed to the neglect of interactions between different chains in oligomeric proteins or with cofactors. When these are taken into account, only very few X‐ray structures are not recognized. Most of them are short inhibitors or fragments and one is a structure that presents serious inconsistencies. Finally, we discuss the reasons that make NMR structures more difficult to recognize. Proteins 2001;44:79–96.

Metal Ligand Aromatic Cation–π Interactions in Metalloproteins: Ligands Coordinated to Metal Interact with Aromatic Residues

Cation-pi interactions between aromatic residues and cationic amino groups in side chains and have been recognized as noncovalent bonding interactions relevant for molecular recognition and for stabilization and definition of the native structure of proteins. We propose a novel type of cation-pi interaction in metalloproteins; namely interaction between ligands coordinated to a metal cation--which gain positive charge from the metal--and aromatic groups in amino acid side chains. Investigation of crystal structures of metalloproteins in the Protein Data Bank (PDB) has revealed that there exist quite a number of metalloproteins in which aromatic rings of phenylalanine, tyrosine, and tryptophan are situated close to a metal center interacting with coordinated ligands. Among these ligands are amino acids such as asparagine, aspartate, glutamate, histidine, and threonine, but also water and substrates like ethanol. These interactions play a role in the stability and conformation of metalloproteins, and in some cases may also be directly involved in the mechanism of enzymatic reactions, which occur at the metal center. For the enzyme superoxide dismutase, we used quantum chemical computation to calculate that Trp163 has an interaction energy of 10.09 kcal mol(-1) with the ligands coordinated to iron.

Calculated pH-dependent population and protonation of carbon-monoxy-myoglobin conformers.

X-ray structures of carbonmonoxymyoglobin (MbCO) are available for different pH values. We used conventional electrostatic continuum methods to calculate the titration behavior of MbCO in the pH range from 3 to 7. For our calculations, we considered five different x-ray structures determined at pH values of 4, 5, and 6. We developed a Monte Carlo method to sample protonation states and conformations at the same time so that we could calculate the population of the considered MbCO structures at different pH values and the titration behavior of MbCO for an ensemble of conformers. To increase the sampling efficiency, we introduced parallel tempering in our Monte Carlo method. The calculated population probabilities show, as expected, that the x-ray structures determined at pH 4 are most populated at low pH, whereas the x-ray structure determined at pH 6 is most populated at high pH, and the population of the x-ray structures determined at pH 5 possesses a maximum at intermediate pH. The calculated titration behavior is in better agreement with experimental results compared to calculations using only a single conformation. The most striking feature of pH-dependent conformational changes in MbCO-the rotation of His-64 out of the CO binding pocket-is reproduced by our calculations and is correlated with a protonation of His-64, as proposed earlier.

Optimizing pKA computation in proteins with pH adapted conformations

pKA in proteins are determined by electrostatic energy computations using a small number of optimized protein conformations derived from crystal structures. In these protein conformations hydrogen positions and geometries of salt bridges on the protein surface were determined self‐consistently with the protonation pattern at three pHs (low, ambient, and high). Considering salt bridges at protein surfaces is most relevant, since they open at low and high pH. In the absence of these conformational changes, computed pK  Acomp of acidic (basic) groups in salt bridges underestimate (overestimate) experimental pK  Aexp , dramatically. The pK  Acomp for 15 different proteins with 185 known pK  Aexp yield an RMSD of 1.12, comparable with two other methods. One of these methods is fully empirical with many adjustable parameters. The other is also based on electrostatic energy computations using many non‐optimized side chain conformers but employs larger dielectric constants at short distances of charge pairs that diminish their electrostatic interactions. These empirical corrections that account implicitly for additional conformational flexibility were needed to describe the energetics of salt bridges appropriately. This is not needed in the present approach. The RMSD of the present approach improves if one considers only strongly shifted pK  Aexp in contrast to the other methods under these conditions. Our method allows interpreting pK  Acomp in terms of pH dependent hydrogen bonding pattern and salt bridge geometries. A web service is provided to perform pKA computations. Proteins 2008.

Redox Potential of Quinones in Both Electron Transfer Branches of Photosystem I

The redox potentials of the two electron transfer (ET) active quinones in the central part of photosystem I (PSI) were determined by evaluating the electrostatic energies from the solution of the Poisson-Boltzmann equation based on the crystal structure. The calculated redox potentials are -531 mV for A1A and -686 mV for A1B. From these results we conclude the following. (i) Both branches are active with a much faster ET in the B-branch than in the A-branch. (ii) The measured lifetime of 200-290 ns of reduced quinones agrees with the estimate for the A-branch and corroborates with an uphill ET from this quinone to the iron-sulfur cluster as observed in recent kinetic measurements. (iii) The electron paramagnetic resonance spectroscopic data refer to the A-branch quinone where the corresponding ET is uphill in energy. The negative redox potential of A1 in PSI is primarily because of the influence from the negatively charged FX, in contrast to the positive shift on the quinone redox potential in bacterial reaction center and PSII that is attributed to the positively charged non-heme iron atom. The conserved residue Asp-B575 changes its protonation state after quinone reduction. The difference of 155 mV in the quinone redox potentials of the two branches were attributed to the conformation of the backbone with a large contribution from Ser-A692 and Ser-B672 and to the side chain of Asp-B575, whose protonation state couples differently with the formation of the quinone radicals.

Calculation of protonation patterns in proteins with structural relaxation and molecular ensembles - application to the photosynthetic reaction center

Abstract The conventional method to determine protonation patterns of proteins was extended by explicit consideration of structural relaxation. The inclusion of structural relaxation was achieved by alternating energy minimization with the calculation of protonation pattern in an iterative manner until consistency of minimized structure and protonation pattern was reached. We applied this method to the bacterial photosynthetic reaction center (bRC) of Rps. viridis and could show that the relaxation procedure accounts for the nuclear polarization and therefore allows one to lower the dielectric constant for the protein from the typically chosen value of ɛp = 4 to a value of ɛp = 2 without fundamentally changing the results. Owing to the lower dielectric shielding at ɛp = 2, the charges of the titratable groups interact more strongly, which leads to sampling problems during Monte Carlo titration. We solved this problem by introducing triple moves in addition to the conventional single and double moves. We also present a new method that considers ensembles of protein conformations for the calculation of protonation patterns. Our method was successfully applied to calculate the redox potential differences of the quinones in the bRC using the relaxed structures for the different redox states of the quinones.