Enhancing the population of the encounter complex affects protein complex formation efficiency.

Optimal charge distribution is considered to be important for efficient formation of protein complexes. Electrostatic interactions guide encounter complex formation that precedes the formation of an active protein complex. However, disturbing the optimized distribution by introduction of extra charged patches on cytochrome c peroxidase does not lead to a reduction in productive encounters with its partner cytochrome c. To test whether a complex with a high population of encounter complex is more easily affected by suboptimal charge distribution, the interactions of cytochrome c mutant R13A with wild-type cytochrome c peroxidase and a variant with an additional negative patch were studied. The complex of the peroxidase and cytochrome c R13A was reported to have an encounter state population of 80%, compared to 30% for the wild-type cytochrome c. NMR analysis confirms the dynamic nature of the interaction and demonstrates that the mutant cytochrome c samples the introduced negative patch. Kinetic experiments show that productive complex formation is fivefold to sevenfold slower at moderate and high ionic strength values for cytochrome c R13A but the association rate is not affected by the additional negative patch on cytochrome c peroxidase, showing that the total charge on the protein surface can compensate for less optimal charge distribution. At low ionic strength (44 mm), the association with the mutant cytochrome c reaches the same high rates as found for wild-type cytochrome c, approaching the diffusion limit.

The Charge Distribution on a Protein Surface Determines Whether Productive or Futile Encounter Complexes Are Formed.

Protein complex formation depends strongly on electrostatic interactions. The distribution of charges on the surface of redox proteins is often optimized by evolution to guide recognition and binding. To test the degree to which the electrostatic interactions between cytochrome c peroxidase (CcP) and cytochrome c (Cc) are optimized, we produced five CcP variants, each with a different charge distribution on the surface. Monte Carlo simulations show that the addition of negative charges attracts Cc to the new patches, and the neutralization of the charges in the regular, stereospecific binding site for Cc abolishes the electrostatic interactions in that region entirely. For CcP variants with the charges in the regular binding site intact, additional negative patches slightly enhance productive complex formation, despite disrupting the optimized charge distribution. Removal of the charges in the regular binding site results in a dramatic decrease in the complex formation rate, even in the presence of highly negative patches elsewhere on the surface. We conclude that additional charge patches can result in either productive or futile encounter complexes, depending on whether negative residues are located also in the regular binding site.

Efficient Encounter Complex Formation and Electron Transfer to Cytochrome†c Peroxidase with an Additional, Distant Electrostatic Binding Site.

Electrostatic interactions can strongly increase the efficiency of protein complex formation. The charge distribution in redox proteins is often optimized to steer a redox partner to the electron transfer active binding site. To test whether the optimized distribution is more important than the strength of the electrostatic interactions, an additional negative patch was introduced on the surface of cytochrome c peroxidase, away from the stereospecific binding site, and its effect on the encounter complex as well as the rate of complex formation was determined. Monte Carlo simulations and paramagnetic relaxation enhancement NMR experiments indicate that the partner, cytochrome c, interacts with the new patch. Unexpectedly, the rate of the active complex formation was not reduced, but rather slightly increased. The findings support the idea that for efficient protein complex formation the strength of the electrostatic interaction is more critical than an optimized charge distribution.

The dynamic complex of cytochrome c6 and cytochrome f studied with paramagnetic NMR spectroscopy.

The rapid transfer of electrons in the photosynthetic redox chain is achieved by the formation of short-lived complexes of cytochrome b6f with the electron transfer proteins plastocyanin and cytochrome c6. A balance must exist between fast intermolecular electron transfer and rapid dissociation, which requires the formation of a complex that has limited specificity. The interaction of the soluble fragment of cytochrome f and cytochrome c6 from the cyanobacterium Nostoc sp. PCC 7119 was studied using NMR spectroscopy and X-ray diffraction. The crystal structures of wild type, M58H and M58C cytochrome c6 were determined. The M58C variant is an excellent low potential mimic of the wild type protein and was used in chemical shift perturbation and paramagnetic relaxation NMR experiments to characterize the complex with cytochrome f. The interaction is highly dynamic and can be described as a pure encounter complex, with no dominant stereospecific complex. Ensemble docking calculations and Monte-Carlo simulations suggest a model in which charge-charge interactions pre-orient cytochrome c6 with its haem edge toward cytochrome f to form an ensemble of orientations with extensive contacts between the hydrophobic patches on both cytochromes, bringing the two haem groups sufficiently close to allow for rapid electron transfer. This model of complex formation allows for a gradual increase and decrease of the hydrophobic interactions during association and dissociation, thus avoiding a high transition state barrier that would slow down the dissociation process.

An ensemble of rapidly interconverting orientations in electrostatic protein-peptide complexes characterized by NMR spectroscopy.

Protein complex formation involves an encounter state in which the proteins are associated in a nonspecific manner and often stabilized by interactions between charged surface patches. Such patches are thought to bind in many different orientations with similar affinity. To obtain experimental evidence for the dynamics in encounter complexes, a model was created using the electron transfer protein plastocyanin and short charged peptides. Three plastocyanins with distinct surface charge distributions were studied. The experimental results from chemical shift perturbations, paramagnetic relaxation enhancement (PRE) NMR, and theoretical results from Monte Carlo simulations indicate the presence of multiple binding orientations that interconvert quickly and are dominated by long-range charge interactions. The PRE data also suggest the presence of highly transient orientations stabilized by short-range interactions.

Loss of electrostatic interactions causes increase of dynamics within the plastocyanin-cytochrome f complex.

Recent studies on the electron transfer complex formed by cytochrome f and plastocyanin from Nostoc revealed that both hydrophobic and electrostatic interactions play a role in the process of complex formation. To study the balance between these two types of interactions in the encounter and the final state, the complex between plastocyanin from Phormidium laminosum and cytochrome f from Nostoc sp. PCC 7119 was investigated using NMR spectroscopy and Monte Carlo docking. Cytochrome f has a highly negative charge. Phormidium plastocyanin is similar to that from Nostoc, but the net charge of the protein is negative rather than positive. NMR titrations of Zn-substituted Phormidium plastocyanin and Nostoc cytochrome f indicated that a complex with an affinity intermediate between those of the Nostoc and Phormidium complexes is formed. Plastocyanin was found in a head-on orientation, as determined using pseudocontact shifts, similar to that in the Phormidium complex, in which the hydrophobic patch represents the main site of interaction on plastocyanin. However, the interaction in the cross-complex is dependent on electrostatics, similar to that in the Nostoc complex. The negative charge of plastocyanin decreases, but not abolishes, the attraction to cytochrome f, resulting in the formation of a more diffuse encounter complex than in the Nostoc case, as could be determined using paramagnetic relaxation spectroscopy. This work illustrates the subtle interplay of electrostatic and hydrophobic interactions in the formation of transient protein complexes. The results are discussed in the context of a model for association on the basis of hydrophobic contacts in the encounter state.

Role of hydrophobic interactions in the encounter complex formation of the plastocyanin and cytochrome f complex revealed by paramagnetic NMR spectroscopy.

Protein complex formation is thought to be at least a two-step process, in which the active complex is preceded by the formation of an encounter complex. The interactions in the encounter complex are usually dominated by electrostatic forces, whereas the active complex is also stabilized by noncovalent short-range forces. Here, the complex of cytochrome f and plastocyanin, electron-transfer proteins involved in photosynthesis, was studied using paramagnetic relaxation NMR spectroscopy. Spin labels were attached to cytochrome f, and the relaxation enhancements of plastocyanin nuclei were measured, demonstrating that a large part of the cytochrome f surface area is sampled by plastocyanin. In contrast, plastocyanin is always oriented with its hydrophobic patch toward cytochrome f. The complex was visualized using ensemble docking, showing that the encounter complex is stabilized by hydrophobic as well as electrostatic interactions. The results suggest a model of electrostatic preorientation before the proteins make contact, followed by the formation of an encounter complex that rapidly leads to electron-transfer active conformations by gradual increase of the overlap of nonpolar surface areas on cytochrome f and plastocyanin. In this model the distinction between the encounter and active complexes vanishes, at least in the case of electron-transfer complexes, which do not require a high degree of specificity.

Thermodynamics of transport through the ammonium transporter Amt-1 investigated with free energy calculations.

Amt-1 from Archaeoglobus fulgidus (AfAmt-1) belongs to the Amt/Rh family of ammonium/ammonia transporting membrane proteins. The transport mode and the precise microscopic permeation mechanism utilized by these proteins are intensely debated. Open questions concern the identity of the transported substrate (ammonia and/or ammonium) and whether the transport is passive or active. To address these questions, we studied the overall thermodynamics of the different transport modes as a function of the environmental conditions. Then, we investigated the thermodynamics of the underlying microscopic transport mechanisms with free energy calculations within a continuum electrostatics model. The formalism developed for this purpose is of general utility in the calculation of binding free energies for ligands with multiple protonation forms or other binding forms. The results of our calculations are compared to the available experimental and theoretical data on Amt/Rh proteins and discussed in light of the current knowledge on the physiological conditions experienced by microorganisms and plants. We found that microscopic models of electroneutral and electrogenic transport modes are in principle thermodynamically viable. However, only the electrogenic variants have a net thermodynamic driving force under the physiological conditions experienced by microorganisms and plants. Thus, the transport mechanism of AfAmt-1 is most likely electrogenic.

GMCT : a Monte Carlo simulation package for macromolecular receptors.

Generalized Monte Carlo titration (GMCT) is a versatile suite of computer programs for the efficient simulation of complex macromolecular receptor systems as for example proteins. The computational model of the system is based on a microstate description of the receptor and an average description of its surroundings in terms of chemical potentials. The receptor can be modeled in great detail including conformational flexibility and many binding sites with multiple different forms that can bind different ligand types. Membrane embedded systems can be modeled including electrochemical potential gradients. Overall properties of the receptor as well as properties of individual sites can be studied with a variety of different Monte Carlo (MC) simulation methods. Metropolis MC, Wang-Landau MC and efficient free energy calculation methods are included. GMCT is distributed as free open source software at www.bisb.uni-bayreuth.de under the terms of the GNU Affero General Public License.

The electronically excited states of LH2 complexes from Rhodopseudomonas acidophila strain 10050 studied by time-resolved spectroscopy and dynamic Monte Carlo simulations. II. Homo-arrays of LH2 complexes reconstituted into phospholipid model membranes.

We performed time-resolved spectroscopy on homoarrays of LH2 complexes from the photosynthetic purple bacterium Rhodopseudomonas acidophila. Variations of the fluorescence transients were monitored as a function of the excitation fluence and the repetition rate of the excitation. These parameters are directly related to the excitation density within the array and to the number of LH2 complexes that still carry a triplet state prior to the next excitation. Comparison of the experimental observations with results from dynamic Monte Carlo simulations for a model cluster of LH2 complexes yields qualitative agreement without the need for any free parameter and reveals the mutual relationship between energy transfer and annihilation processes.

The electronically excited states of LH2 complexes from Rhodopseudomonas acidophila strain 10050 studied by time-resolved spectroscopy and dynamic Monte Carlo simulations. I. Isolated, non-interacting LH2 complexes.

We have employed time-resolved spectroscopy on the picosecond time scale in combination with dynamic Monte Carlo simulations to investigate the photophysical properties of light-harvesting 2 (LH2) complexes from the purple photosynthetic bacterium Rhodopseudomonas acidophila. The variations of the fluorescence transients were studied as a function of the excitation fluence, the repetition rate of the excitation and the sample preparation conditions. Here we present the results obtained on detergent solubilized LH2 complexes, i.e., avoiding intercomplex interactions, and show that a simple four-state model is sufficient to grasp the experimental observations quantitatively without the need for any free parameters. This approach allows us to obtain a quantitative measure for the singlet-triplet annihilation rate in isolated, noninteracting LH2 complexes.

A generalized free energy perturbation theory accounting for end states with differing configuration space volume.

We present a generalized free energy perturbation theory that is inspired by Monte Carlo techniques and based on a microstate description of a transformation between two states of a physical system. It is shown that the present free energy perturbation theory stated by the Zwanzig equation follows as a special case of our theory. Our method uses a stochastic mapping of the end states that associates a given microstate from one ensemble with a microstate from the adjacent ensemble according to a probability distribution. In contrast, previous free energy perturbation methods use a static, deterministic mapping that associates fixed pairs of microstates from the two ensembles. The advantages of our approach are that end states of differing configuration space volume can be treated easily also in the case of discrete configuration spaces and that the method does not require the potentially cumbersome search for an optimal deterministic mapping. The application of our theory is illustrated by some example problems. We discuss practical applications for which our findings could be relevant and point out perspectives for further development of the free energy perturbation theory.

Shifting the equilibrium between the encounter state and the specific form of a protein complex by interfacial point mutations.

Recent experimental studies have confirmed a long-held view that protein complex formation proceeds via a short-lived encounter state. The population of this transient intermediate, stabilized mainly by long-range electrostatic interactions, varies among different complexes. Here we show that the occupancy of the encounter state can be modulated across a broad range by single point mutations of interfacial residues. Using a combination of Monte Carlo simulations and paramagnetic relaxation enhancement NMR spectroscopy, we illustrate that it is possible to both enhance and diminish the binding specificity in an electron transfer complex of yeast cytochrome c (Cc) and cytochrome c peroxidase. The Cc T12A mutation decreases the population of the encounter to 10% as compared with 30% in the wild-type complex. More dramatically, the Cc R13A substitution reverses the relative occupancies of the stereospecific and the encounter forms, with the latter now being the dominant species with the population of 80%. This finding indicates that the encounter state can make a large contribution to the stability of a protein complex. Also, it appears that by adjusting the amount of the encounter through a judicious choice of point mutations, we can remodel the energy landscape of a protein complex and tune its binding specificity.

Visualization of the encounter ensemble of the transient electron transfer complex of cytochrome c and cytochrome c peroxidase.

Recent studies have provided experimental evidence for the existence of an encounter complex, a transient intermediate in the formation of protein complexes. We use paramagnetic relaxation enhancement NMR spectroscopy in combination with Monte Carlo simulations to characterize and visualize the ensemble of encounter orientations in the short-lived electron transfer complex of yeast cytochrome c (Cc) and cytochrome c peroxidase (CcP). The complete conformational space sampled by the protein molecules during the dynamic part of the interaction was mapped experimentally. The encounter complex was described by an electrostatic ensemble of orientations based on Monte Carlo calculations, considering the protein structures in atomic detail. We demonstrate that this visualization of the encounter complex, in combination with the specific complex, is in excellent agreement with the experimental data. Our results indicate that Cc samples only about 15% of the surface area of CcP, surrounding the specific binding interface. The encounter complex is populated for 30% of the time, representing a mere 0.5 kcal/mol difference in the free energies between the two states. This delicate balance is interpreted to be a consequence of the conflicting requirements of fast electron transfer and high turnover of the complex.

McVol - a program for calculating protein volumes and identifying cavities by a Monte Carlo algorithm.

In this paper, we describe a Monte Carlo method for determining the volume of a molecule. A molecule is considered to consist of hard, overlapping spheres. The surface of the molecule is defined by rolling a probe sphere over the surface of the spheres. To determine the volume of the molecule, random points are placed in a three-dimensional box, which encloses the whole molecule. The volume of the molecule in relation to the volume of the box is estimated by calculating the ratio of the random points placed inside the molecule and the total number of random points that were placed. For computational efficiency, we use a grid-cell based neighbor list to determine whether a random point is placed inside the molecule or not. This method in combination with a graph-theoretical algorithm is used to detect internal cavities and surface clefts of molecules. Since cavities and clefts are potential water binding sites, we place water molecules in the cavities. The potential water positions can be used in molecular dynamics calculations as well as in other molecular calculations. We apply this method to several proteins and demonstrate the usefulness of the program. The described methods are all implemented in the program McVol, which is available free of charge from our website at http://www.bisb.uni-bayreuth.de/software.html .

Proton-transfer pathways in photosynthetic reaction centers analyzed by profile hidden markov models and network calculations.

In the bacterial reaction center (bRC) of Rhodobacter sphaeroides, the key residues of proton transfer to the secondary quinone (Q(B)) are known. Also, several possible proton entry points and proton-transfer pathways have been proposed. However, the mechanism of the proton transfer to Q(B) remains unclear. The proton transfer to Q(B) in the bRC of Blastochloris viridis is less explored. To analyze whether the bRCs of different species use the same key residues for proton transfer to Q(B), we determined the conservation of these residues. We performed a multiple-sequence alignment based on profile hidden Markov models. Residues involved in proton transfer but not located at the protein surface are conserved or are only exchanged to functionally similar amino acids, whereas potential proton entry points are not conserved to the same extent. The analysis of the hydrogen-bond network of the bRC from R. sphaeroides and that from B. viridis showed that a large network connects Q(B) with the cytoplasmic region in both bRCs. For both species, all non-surface key residues are part of the network. However, not all proton entry points proposed for the bRC of R. sphaeroides are included in the network in the bRC of B. viridis. From our analysis, we could identify possible proton entry points. These proton entry points differ between the two bRCs. Together, the results of the conservation analysis and the hydrogen-bond network analysis make it likely that the proton transfer to Q(B) is not mediated by distinct pathways but by a large hydrogen-bond network.

Profile hidden Markov models for analyzing similarities and dissimilarities in the bacterial reaction center and photosystem II.

The bacterial photosynthetic reaction center is the evolutionary ancestor of the Photosystem II reaction center. These proteins share the same fold and perform the same biological function. Nevertheless, the details of their molecular reaction mechanism differ. It is of significant biological and biochemical interest to determine which functional characteristics are conserved at the level of the protein sequences. Since the level of sequence identity between the bacterial photosynthetic reaction center and Photosystem II is low, a progressive multiple-sequence alignment leads to errors in identifying the conserved residues. In such a situation, profile hidden Markov models (pHMM) can be used to obtain reliable multiple-sequence alignments. We therefore constructed the pHMM with the help of a sequence alignment based on a structural superposition of both proteins. To validate the multiple-sequence alignments obtained with the pHMM, the conservation of residues with known functional importance was examined. Having confirmed the correctness of the multiple-sequence alignments, we analyzed the conservation of residues involved in hydrogen bonding and redox potential tuning of the cofactors. Our analysis reveals similarities and dissimilarities between the bacterial photosynthetic reaction center and Photosystem II at the protein sequence level, hinting at different charge separation and charge transfer mechanisms. The conservation analysis that we perform in this paper can be considered as a model for analyzing the conservation in proteins with a low level of sequence identity.

Simulating the proton transfer in gramicidin A by a sequential dynamical Monte Carlo method.

The large interest in long-range proton transfer in biomolecules is triggered by its importance for many biochemical processes such as biological energy transduction and drug detoxification. Since long-range proton transfer occurs on a microsecond time scale, simulating this process on a molecular level is still a challenging task and not possible with standard simulation methods. In general, the dynamics of a reactive system can be described by a master equation. A natural way to describe long-range charge transfer in biomolecules is to decompose the process into elementary steps which are transitions between microstates. Each microstate has a defined protonation pattern. Although such a master equation can in principle be solved analytically, it is often too demanding to solve this equation because of the large number of microstates. In this paper, we describe a new method which solves the master equation by a sequential dynamical Monte Carlo algorithm. Starting from one microstate, the evolution of the system is simulated as a stochastic process. The energetic parameters required for these simulations are determined by continuum electrostatic calculations. We apply this method to simulate the proton transfer through gramicidin A, a transmembrane proton channel, in dependence on the applied membrane potential and the pH value of the solution. As elementary steps in our reaction, we consider proton uptake and release, proton transfer along a hydrogen bond, and rotations of water molecules that constitute a proton wire through the channel. A simulation of 8 mus length took about 5 min on an Intel Pentium 4 CPU with 3.2 GHz. We obtained good agreement with experimental data for the proton flux through gramicidin A over a wide range of pH values and membrane potentials. We find that proton desolvation as well as water rotations are equally important for the proton transfer through gramicidin A at physiological membrane potentials. Our method allows to simulate long-range charge transfer in biological systems at time scales, which are not accessible by other methods.

Redox-linked protonation state changes in cytochrome bc1 identified by Poisson-Boltzmann electrostatics calculations.

Cytochrome bc(1) is a major component of biological energy conversion that exploits an energetically favourable redox reaction to generate a transmembrane proton gradient. Since the mechanistic details of the coupling of redox and protonation reactions in the active sites are largely unresolved, we have identified residues that undergo redox-linked protonation state changes. Structure-based Poisson-Boltzmann/Monte Carlo titration calculations have been performed for completely reduced and completely oxidised cytochrome bc(1). Different crystallographically observed conformations of Glu272 and surrounding residues of the cytochrome b subunit in cytochrome bc(1) from Saccharomyces cerevisiae have been considered in the calculations. Coenzyme Q (CoQ) has been modelled into the CoQ oxidation site (Q(o)-site). Our results indicate that both conformational and protonation state changes of Glu272 of cytochrome b may contribute to the postulated gating of CoQ oxidation. The Rieske iron-sulphur cluster could be shown to undergo redox-linked protonation state changes of its histidine ligands in the structural context of the CoQ-bound Q(o)-site. The proton acceptor role of the CoQ ligands in the CoQ reduction site (Q(i)-site) is supported by our results. A modified path for proton uptake towards the Q(i)-site features a cluster of conserved lysine residues in the cytochrome b (Lys228) and cytochrome c(1) subunits (Lys288, Lys289, Lys296). The cardiolipin molecule bound close to the Q(i)-site stabilises protons in this cluster of lysine residues.