Simulation and Modeling of the Rhodobacter sphaeroides Bacterial Reaction Center: Structure and Interactions

Refined definition of the critical micelle concentration and application to alkyl maltosides used in membrane protein research

The critical micelle concentration (CMC) of nonionic detergents is defined as the breaking point in the monomer concentration as a function of the total detergent concentration, identified by setting the third derivate of this function to zero. Combined with a mass action model for micelle formation, this definition yields analytic formulae for the concentration ratio of monomers to total detergent at the CMC and the relationship between the CMC and the free energy of micellization g mic. The theoretical breaking point is shown to coincide with the breaking point of the experimental titration curve, if the fluorescence enhancement of 8-anilino-1-naphthalene-sulfonic acid (ANS) or a similar probe dye is used to monitor micelle formation. Application to a series of n-alkyl-β-d-maltosides with the number of carbon atoms in the alkyl chain ranging from 8 to 12 demonstrates the good performance of a molecular thermodynamic model, in which the free energy of micellization is given by g mic = σΦ + g pack + g st. In this model, σ is a fit parameter with the dimension of surface tension, Φ represents the change in area of hydrophobic molecular surfaces in contact with the aqueous phase, and g pack and g st are contributions, respectively, from alkyl chain packing in the micelle interior and steric repulsion of detergent head groups. The analysis of experimental data from different sources shows that varying experimental conditions such as co-solutes in the aqueous phase can be accounted for by adapting only σ, if the co-solutes do not bind to the detergent to an appreciable extent. The model is considered a good compromise between theory and practicability to be applied in the context of in vitro investigations of membrane proteins.

Perturbations of Native Membrane Protein Structure in Alkyl Phosphocholine Detergents: A Critical Assessment of NMR and Biophysical Studies

Membrane proteins perform a host of vital cellular functions. Deciphering the molecular mechanisms whereby they fulfill these functions requires detailed biophysical and structural investigations. Detergents have proven pivotal to extract the protein from its native surroundings. Yet, they provide a milieu that departs significantly from that of the biological membrane, to the extent that the structure, the dynamics, and the interactions of membrane proteins in detergents may considerably vary, as compared to the native environment. Understanding the impact of detergents on membrane proteins is, therefore, crucial to assess the biological relevance of results obtained in detergents. Here, we review the strengths and weaknesses of alkyl phosphocholines (or foscholines), the most widely used detergent in solution-NMR studies of membrane proteins. While this class of detergents is often successful for membrane protein solubilization, a growing list of examples points to destabilizing and denaturing properties, in particular for α-helical membrane proteins. Our comprehensive analysis stresses the importance of stringent controls when working with this class of detergents and when analyzing the structure and dynamics of membrane proteins in alkyl phosphocholine detergents.

Energetics of bacterial photosynthesis

We report the results of extensive numerical simulations and theoretical calculations of electronic transitions in the reaction center of Rhodobacter sphaeroides photosynthetic bacterium. The energetics and kinetics of five electronic transitions related to the kinetic scheme of primary charge separation have been analyzed and compared to experimental observations. Nonergodic formulation of the reaction kinetics is required for the calculation of the rates due to a severe breakdown of the system ergodicity on the time scale of primary charge separation, with the consequent inapplicability of the standard canonical prescription to calculate the activation barrier. Common to all reactions studied is a significant excess of the charge-transfer reorganization energy from the width of the energy gap fluctuations over that from the Stokes shift of the transition. This property of the hydrated proteins, breaking the linear response of the thermal bath, allows the reaction center to significantly reduce the reaction free energy of near-activationless electron hops and thus raise the overall energetic efficiency of the biological charge-transfer chain. The increase of the rate of primary charge separation with cooling is explained in terms of the temperature variation of induction solvation, which dominates the average donor-acceptor energy gap for all electronic transitions in the reaction center. It is also suggested that the experimentally observed break in the Arrhenius slope of the primary recombination rate, occurring near the temperature of the dynamical transition in proteins, can be traced back to a significant drop of the solvent reorganization energy close to that temperature.

Energetics and kinetics of primary charge separation in bacterial photosynthesis

We report the results of molecular dynamics (MD) simulations and formal modeling of the free-energy surfaces and reaction rates of primary charge separation in the reaction center of Rhodobacter sphaeroides. Two simulation protocols were used to produce MD trajectories. Standard force-field potentials were employed in the first protocol. In the second protocol, the special pair was made polarizable to reproduce a high polarizability of its photoexcited state observed by Stark spectroscopy. The charge distribution between covalent and charge-transfer states of the special pair was dynamically adjusted during the simulation run. We found from both protocols that the breadth of electrostatic fluctuations of the protein/water environment far exceeds previous estimates, resulting in about 1.6 eV reorganization energy of electron transfer in the first protocol and 2.5 eV in the second protocol. Most of these electrostatic fluctuations become dynamically frozen on the time scale of primary charge separation, resulting in much smaller solvation contributions to the activation barrier. While water dominates solvation thermodynamics on long observation times, protein emerges as the major thermal bath coupled to electron transfer on the picosecond time of the reaction. Marcus parabolas were obtained for the free-energy surfaces of electron transfer by using the first protocol, while a highly asymmetric surface was obtained in the second protocol. A nonergodic formulation of the diffusion-reaction electron-transfer kinetics has allowed us to reproduce the experimental results for both the temperature dependence of the rate and the nonexponential decay of the population of the photoexcited special pair.

Molecular dynamics simulations of GlpF in a micelle vs in a bilayer: conformational dynamics of a membrane protein as a function of environment

Octyl glucoside (OG) is a detergent widely employed in structural and functional studies of membrane proteins. To better understand the nature of protein-OG interactions, molecular dynamics simulations (duration 10 ns) have been used to explore an alpha-helical membrane protein, GlpF, in OG micelles and in DMPC bilayers. Greater conformational drift of the extramembraneous protein loops, from the initial X-ray structure, is seen for the GlpF-OG simulations than for the GlpF-DMPC simulation. The mobility of the transmembrane alpha-helices is approximately 1.3x higher in the GlpF-OG than the GlpF-DMPC simulations. The detergent is seen to form an irregular torus around the protein. The presence of the protein leads to a small perturbation in the behavior of the alkyl chains in the OG micelle, namely an approximately 15% increase in the trans-gauche(-)-gauche(+) transition time. Aromatic side chains (Trp, Tyr) and basic side chains (Arg, Lys) play an important role in both protein-detergent (OG) and protein-lipid (DMPC) interactions.

Interaction of zwitterionic penicillins with the OmpF channel facilitates their translocation

To study translocation of beta-lactam antibiotics of different size and charge across the outer bacterial membrane, we combine an analysis of ion currents through single trimeric outer membrane protein F (OmpF) porins in planar lipid bilayers with molecular dynamics simulations. Because the size of penicillin molecules is close to the size of the narrowest part of the OmpF pore, penicillins occlude the pore during their translocation. Favorably interacting penicillins cause time-resolvable transient blockages of the small-ion current through the channel and thereby provide information about their dynamics within the pore. Analyzing these random fluctuations, we find that ampicillin and amoxicillin have a relatively high affinity for OmpF. In contrast, no or only a weak interaction is detected for carbenicillin, azlocillin, and piperacillin. Molecular dynamics simulations suggest a possible pathway of these drugs through the OmpF channel and rationalize our experimental findings. For zwitterionic ampicillin and amoxicillin, we identify a region of binding sites near the narrowest part of the channel pore. Interactions with these sites partially compensate for the entropic cost of drug confinement by the channel. Whereas azlocillin and piperacillin are clearly too big to pass through the channel constriction, dianionic carbenicillin does not find an efficient binding region in the constriction zone. Carbenicillin's favorable interactions are limited to the extracellular vestibule. These observations confirm our earlier suggestion that a set of high-affinity sites at the narrowest part of the OmpF channel improves a drug's ability to cross the membrane via the pore.

Rewiring photosynthesis: engineering wrong-way electron transfer in the purple bacterial reaction centre

The purple bacterial reaction centre uses light energy to separate charge across the cytoplasmic membrane, reducing ubiquinone and oxidizing a c-type cytochrome. The protein possesses a macroscopic structural two-fold symmetry but displays a strong functional asymmetry, with only one of two available membrane-spanning branches of cofactors (the so-called A-branch) being used to catalyse photochemical charge separation. The factors underlying this functional asymmetry have been the subject of study for many years but are still not fully understood. Site-directed mutagenesis has been partially successful in rerouting electron transfer along the normally inactive B-branch, allowing comparison of the kinetics of equivalent electron transfer reactions on the two branches. Both the primary and secondary electron transfer steps on the B-branch appear to be considerably slower than their A-branch counterparts. The effectiveness of different mutations in rerouting electron transfer along the B-branch of cofactors is discussed.

Proton binding to proteins: a free-energy component analysis using a dielectric continuum model

Proton binding plays a critical role in protein structure and function. We report pK(a) calculations for three aspartates in two proteins, using a linear response approach, as well as a "standard" Poisson-Boltzmann approach. Averaging over conformations from the two endpoints of the proton-binding reaction, the protein's atomic degrees of freedom are explicitly modeled. Treating macroscopically the protein's electronic polarizability and the solvent, a meaningful model is obtained, without adjustable parameters. It reproduces qualitatively the electrostatic potentials, proton-binding free energies, Marcus reorganization free energies, and pK(a) shifts from explicit solvent molecular dynamics simulations, and the pK(a) shifts from experiment. For thioredoxin Asp-26, which has a large pK(a) upshift, we correctly capture the balance between unfavorable carboxylate desolvation and favorable interactions with a nearby lysine; similarly for RNase A Asp-14, which has a large pK(a) downshift. For the unshifted thioredoxin Asp-20, desolvation by the protein cavity is overestimated by 2.9 pK(a) units; several effects could explain this. "Standard" Poisson-Boltzmann methods sidestep this problem by using a large, ad hoc protein dielectric; but protein charge-charge interactions are then incorrectly downscaled, giving an unbalanced description of the reaction and a large error for the shifted pK(a) values of Asp-26 and Asp-14.

Investigation of B-branch electron transfer by femtosecond time resolved spectroscopy in a Rhodobacter sphaeroides reaction centre that lacks the QA ubiquinone

The dynamics of electron transfer in a membrane-bound Rhodobacter sphaeroides reaction centre containing a combination of four mutations were investigated by transient absorption spectroscopy. The reaction centre, named WAAH, has a mutation that causes the reaction centre to assemble without a Q(A) ubiquinone (Ala M260 to Trp), a mutation that causes the replacement of the H(A) bacteriopheophytin with a bacteriochlorophyll (Leu M214 to His) and two mutations that remove acidic groups close to the Q(B) ubiquinone (Glu L212 to Ala and Asp L213 to Ala). Previous work has shown that the Q(B) ubiquinone is reduced by electron transfer along the so-called inactive cofactor branch (B-branch) in the WAAH reaction centre (M.C. Wakeham, M.G. Goodwin, C. McKibbin, M.R. Jones, Photo-accumulation of the P(+)Q(B)(-) radical pair state in purple bacterial reaction centres that lack the Q(A) ubiquinone, FEBS Letters 540 (2003) 234-240). In the present study the dynamics of electron transfer in the membrane-bound WAAH reaction centre were studied by femtosecond transient absorption spectroscopy, and the data analysed using a compartmental model. The analysis indicates that the yield of Q(B) reduction via the B-branch is approximately 8% in the WAAH reaction centre, consistent with results from millisecond time-scale kinetic spectroscopy. Possible contributions to this yield of the constituent mutations in the WAAH reaction centre and the membrane environment of the complex are discussed.

Microscopic Mechanism of Antibiotics Translocation through a Porin

OmpF from the outer membrane of Escherichia coli is a general porin considered to be the main pathway for beta-lactam antibiotics. The availability of a high-resolution crystal structure of OmpF and new experimental techniques at the single-molecule level have opened the way to the investigation of the microscopic mechanisms that allow the passage of antibiotics through bacterial pores. We applied molecular dynamics simulations to investigate the translocation process of ampicillin (Amp) through OmpF. Using a recent algorithm capable of accelerating molecular dynamics simulations we have been able to obtain a reaction path for the translocation of Amp through OmpF. The mechanism of passage depends both on the internal degrees of freedom of Amp and on interactions of Amp with OmpF. Understanding this mechanism would help us design more efficient antibiotics and shed light on nature's way of devising channels able to enhance the transport of molecules through membranes.