Simulation of the Electron Transfer between the Tetraheme Subunit and the Special Pair of the Photosynthetic Reaction Center Using a Microstate Description

Undulating Free Energy Landscapes Buffer Redox Chains from Environmental Fluctuations

Roller-coaster or undulating free energy landscapes, with alternating high and low potential cofactors, occur frequently in biological redox chains. Yet, there is little understanding of the possible advantages created by these landscapes. We examined the tetraheme subunit associated with Blastochloris viridis reaction centers, comparing the dynamics of the native protein and of hypothetical (in silico) mutants. We computed the variation in the total number of electrons in wild type (WT) and mutant tetrahemes connected to an electron reservoir in the presence of a time-varying potential, as a model for a fluctuating redox environment. We found that roller-coaster free energy landscapes buffer the redox cofactor populations from these fluctuations. The WT roller-coaster landscape slows forward and backward electron transfer in the face of fluctuations, and may offer the advantage of sustaining the reduction of essential cofactors, such as the chlorophyll special pair in photosynthesis, even though an undulating landscape introduces thermodynamically uphill steps in multistep redox chains.

Virtual Model Compound Approach for Calculating Redox Potentials of [Fe2S2]-Cys4 Centers in Proteins - Structure Quality Matters

The midpoint potential of the [Fe2S2]-Cys4-cluster in proteins is known to vary between -200 and -450 mV. This variation is caused by the different electrostatic environment of the cluster in the respective proteins. Continuum electrostatics can quantify the impact of the protein environment on the redox potential. Thus, if the redox potential of a [Fe2S2]-Cys4-cluster model compound in aqueous solution would be known, then redox potentials in various protein complexes could be calculated. However, [Fe2S2]-Cys4-cluster models are not water-soluble, and thus, their redox potential can not be measured in aqueous solution. To overcome this problem, we introduce a method that we call Virtual Model Compound Approach (VMCA) to extrapolate the model redox potential from known redox potentials of proteins. We carefully selected high-resolution structures for our analysis and divide them into a fit set, for fitting the model redox potential, and an independent test set, to check the validity of the model redox potential. However, from our analysis, we realized that the some structures can not be used as downloaded from the PDB but had to be re-refined in order to calculate reliable redox potentials. Because of the re-refinement, we were able to significantly reduce the standard deviation of our derived model redox potential for the [Fe2S2]-Cys4-cluster from 31 mV to 10 mV. As the model redox potential, we obtained -184 mV. This model redox potential can be used to analyze the redox behavior of [Fe2S2]-Cys4-clusters in larger protein complexes.

Computational Biochemistry-Enzyme Mechanisms Explored

Understanding enzyme mechanisms is a major task to achieve in order to comprehend how living cells work. Recent advances in biomolecular research provide huge amount of data on enzyme kinetics and structure. The analysis of diverse experimental results and their combination into an overall picture is, however, often challenging. Microscopic details of the enzymatic processes are often anticipated based on several hints from macroscopic experimental data. Computational biochemistry aims at creation of a computational model of an enzyme in order to explain microscopic details of the catalytic process and reproduce or predict macroscopic experimental findings. Results of such computations are in part complementary to experimental data and provide an explanation of a biochemical process at the microscopic level. In order to evaluate the mechanism of an enzyme, a structural model is constructed which can be analyzed by several theoretical approaches. Several simulation methods can and should be combined to get a reliable picture of the process of interest. Furthermore, abstract models of biological systems can be constructed combining computational and experimental data. In this review, we discuss structural computational models of enzymatic systems. We first discuss various models to simulate enzyme catalysis. Furthermore, we review various approaches how to characterize the enzyme mechanism both qualitatively and quantitatively using different modeling approaches.

The open, the closed, and the empty: time-resolved fluorescence spectroscopy and computational analysis of RC-LH1 complexes from Rhodopseudomonas palustris

We studied the time-resolved fluorescence of isolated RC-LH1 complexes from Rhodopseudomonas palustris as a function of the photon fluence and the repetition rate of the excitation laser. Both parameters were varied systematically over 3 orders of magnitude. On the basis of a microstate description we developed a quantitative model for RC-LH1 and obtained very good agreement between experiments and elaborate simulations based on a global master equation approach. The model allows us to predict the relative population of RC-LH1 complexes with the special pair in the neutral state or in the oxidized state P(+) and those complexes that lack a reaction center.

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.

A mathematical view on the decoupled sites representation

The decoupled sites representation (DSR) is a theoretical instrument which allows to regard complex pH titration curves of biomolecules with several interacting proton binding sites as composition of isolated, non-interacting sites, each with a standard Henderson-Hasselbalch titration curve. In this work, we present the mathematical framework in which the DSR is embedded and give mathematical proofs for several statements in the periphery of the DSR. These proofs also identify exceptions. To apply the DSR to any molecule, it is necessary to extend the set of binding energies from R to a stripe within C. An important observation in this context is that even positive interaction energies (repulsion) between the binding sites will not guarantee real binding energies in the decoupled system, at least if the molecule has more than four proton binding sites. Moreover, we show that for a given overall titration curve it is not only possible to find a corresponding system with an interaction energy of zero but with any arbitrary fix interaction energy. This result also effects practical work as it shows that for any given titration curve, there is an infinite number of corresponding hypothetical molecules. Furthermore, this implies that--using a common definition of cooperative binding on the level of interaction energies--a meaningful measure of cooperativity between the binding sites cannot be defined solely on the basis of the overall titration. Consequently, all measures of cooperativity based on the overall binding curve do not measure the type of cooperativity commonly defined on the basis of interaction energies. Understanding the DSR mathematically provides the basis of transferring the DSR to biomolecules with different types of interacting ligands, such as protons and electrons, which play an important role within electron transport chains like in photosynthesis.

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.

Distinguishing two groups of flavin reductases by analyzing the protonation state of an active site carboxylic acid

Flavin-containing reductases are involved in a wide variety of physiological reactions such as photosynthesis, nitric oxide synthesis, and detoxification of foreign compounds, including therapeutic drugs. Ferredoxin-NADP(H)-reductase (FNR) is the prototypical enzyme of this family. The fold of this protein is highly conserved and occurs as one domain of several multidomain enzymes such as the members of the diflavin reductase family. The enzymes of this family have emerged as fusion of a FNR and a flavodoxin. Although the active sites of these enzymes are very similar, different enzymes function in opposite directions, that is, some reduce oxidized nicotinamide adenine dinucleotide phosphate (NADP(+)) and some oxidize reduced nicotinamide adenine dinucleotide phosphate (NADPH). In this work, we analyze the protonation behavior of titratable residues of these enzymes through electrostatic calculations. We find that a highly conserved carboxylic acid in the active site shows a different titration behavior in different flavin reductases. This residue is deprotonated in flavin reductases present in plastids, but protonated in bacterial counterparts and in diflavin reductases. The protonation state of the carboxylic acid may also influence substrate binding. The physiological substrate for plastidic enzymes is NADP(+), but it is NADPH for the other mentioned reductases. In this article, we discuss the relevance of the environment of this residue for its protonation and its importance in catalysis. Our results allow to reinterpret and explain experimental data.

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.

Investigating the mechanisms of photosynthetic proteins using continuum electrostatics

Computational methods based on continuum electrostatics are widely used in theoretical biochemistry to analyze the function of proteins. Continuum electrostatic methods in combination with quantum chemical and molecular mechanical methods can help to analyze even very complex biochemical systems. In this article, applications of these methods to proteins involved in photosynthesis are reviewed. After giving a short introduction to the basic concepts of the continuum electrostatic model based on the Poisson-Boltzmann equation, we describe the application of this approach to the docking of electron transfer proteins, to the comparison of isofunctional proteins, to the tuning of absorption spectra, to the analysis of the coupling of electron and proton transfer, to the analysis of the effect of membrane potentials on the energetics of membrane proteins, and to the kinetics of charge transfer reactions. Simulations as those reviewed in this article help to analyze molecular mechanisms on the basis of the structure of the protein, guide new experiments, and provide a better and deeper understanding of protein functions.

Cooperative interaction of high-potential hemes in the cytochrome subunit of the photosynthetic reaction center of bacterium Ectothiorhodospira shaposhnikovii

Cooperative interaction of the high-potential hemes (C(h)) in the cytochrome subunit of the photosynthesizing bacterium Ectothiorhodospira shaposhnikovii was studied by comparing redox titration curves of the hemes under the conditions of pulse photoactivation inducing single turnover of electron-transport chain and steady-state photoactivation, as well as by analysis of the kinetics of laser-induced oxidation of cytochromes by reaction center (RC). A mathematical model of the processes of electron transfer in cytochrome-containing RC was considered. Theoretical analysis revealed that the reduction of one heme C(h) facilitated the reduction of the other heme, which was equivalent to a 60 mV positive shift of the midpoint potential. In addition, reduction of the second heme C(h) caused a three- to four-fold acceleration of the electron transfer from the cytochrome subunit to RC.

An extended dead-end elimination algorithm to determine gap-free lists of low energy states

Proteins are flexible systems and commonly populate several functionally important states. To understand protein function, these states and their energies have to be identified. We introduce an algorithm that allows the determination of a gap-free list of the low energy states. This algorithm is based on the dead-end elimination (DEE) theorem and is termed X-DEE (extended DEE). X-DEE is applicable to discrete systems whose state energy can be formulated as pairwise interaction between sites and their intrinsic energies. In this article, the computational performance of X-DEE is analyzed and discussed. X-DEE is implemented to determine the lowest energy protonation states of proteins, a problem to which DEE has not been applied so far. We use X-DEE to calculate a list of low energy protonation states for two bacteriorhodopsin structures that represent the first proton transfer step of the bacteriorhodopsin photocycle.