Microscopic pKa analysis of Glu286 in cytochrome c oxidase (Rhodobacter sphaeroides): toward a calibrated molecular model

Hybrid Quantum Mechanical/Molecular Mechanical Methods For Studying Energy Transduction in Biomolecular Machines

Hybrid quantum mechanical/molecular mechanical (QM/MM) methods have become indispensable tools for the study of biomolecules. In this article, we briefly review the basic methodological details of QM/MM approaches and discuss their applications to various energy transduction problems in biomolecular machines, such as long-range proton transports, fast electron transfers, and mechanochemical coupling. We highlight the particular importance for these applications of balancing computational efficiency and accuracy. Using several recent examples, we illustrate the value and limitations of QM/MM methodologies for both ground and excited states, as well as strategies for calibrating them in specific applications. We conclude with brief comments on several areas that can benefit from further efforts to make QM/MM analyses more quantitative and applicable to increasingly complex biological problems.

Electric fields control water-gated proton transfer in cytochrome c oxidase

Aerobic life is powered by membrane-bound enzymes that catalyze the transfer of electrons to oxygen and protons across a biological membrane. Cytochrome c oxidase (CcO) functions as a terminal electron acceptor in mitochondrial and bacterial respiratory chains, driving cellular respiration and transducing the free energy from O₂ reduction into proton pumping. Here we show that CcO creates orientated electric fields around a nonpolar cavity next to the active site, establishing a molecular switch that directs the protons along distinct pathways. By combining large-scale quantum chemical density functional theory (DFT) calculations with hybrid quantum mechanics/molecular mechanics (QM/MM) simulations and atomistic molecular dynamics (MD) explorations, we find that reduction of the electron donor, heme a, leads to dissociation of an arginine (Arg438)-heme a₃ D-propionate ion-pair. This ion-pair dissociation creates a strong electric field of up to 1 V Å^-1 along a water-mediated proton array leading to a transient proton loading site (PLS) near the active site. Protonation of the PLS triggers the reduction of the active site, which in turn aligns the electric field vectors along a second, "chemical," proton pathway. We find a linear energy relationship of the proton transfer barrier with the electric field strength that explains the effectivity of the gating process. Our mechanism shows distinct similarities to principles also found in other energy-converting enzymes, suggesting that orientated electric fields generally control enzyme catalysis.

O to bR transition in bacteriorhodopsin occurs through a proton hole mechanism

Extensive classical and quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations are used to establish the structural features of the O state in bacteriorhodopsin (bR) and its conversion back to the bR ground state. The computed free energy surface is consistent with available experimental data for the kinetics and thermodynamics of the O to bR transition. The simulation results highlight the importance of the proton release group (PRG, consisting of Glu194/204) and the conserved arginine 82 in modulating the hydration level of the protein cavity. In particular, in the O state, deprotonation of the PRG and downward rotation of Arg82 lead to elevated hydration level and a continuous water network that connects the PRG to the protonated Asp85. Proton exchange through this water network is shown by ∼0.1-μs semiempirical QM/MM free energy simulations to occur through the generation and propagation of a proton hole, which is relayed by Asp212 and stabilized by Arg82. This mechanism provides an explanation for the observation that the D85S mutant of bacteriorhodopsin pumps chloride ions. The electrostatics-hydration coupling mechanism and the involvement of all titration states of water are likely applicable to many biomolecules involved in bioenergetic transduction.

Electron Transfer Coupled to Conformational Dynamics in Cell Respiration

Cellular respiration is a fundamental process required for energy production in many organisms. The terminal electron transfer complex in mitochondrial and many bacterial respiratory chains is cytochrome c oxidase (CcO). This converts the energy released in the cytochrome c/oxygen redox reaction into a transmembrane proton electrochemical gradient that is used subsequently to power ATP synthesis. Despite detailed knowledge of electron and proton transfer paths, a central question remains as to whether the coupling between electron and proton transfer in mammalian mitochondrial forms of CcO is mechanistically equivalent to its bacterial counterparts. Here, we focus on the conserved span between H376 and G384 of transmembrane helix (TMH) X of subunit I. This conformationally-dynamic section has been suggested to link the redox activity with the putative H pathway of proton transfer in mammalian CcO. The two helix X mutants, Val380Met (V380M) and Gly384Asp (G384D), generated in the genetically-tractable yeast CcO, resulted in a respiratory-deficient phenotype caused by the inhibition of intra-protein electron transfer and CcO turnover. Molecular aspects of these variants were studied by long timescale atomistic molecular dynamics simulations performed on wild-type and mutant bovine and yeast CcOs. We identified redox- and mutation-state dependent conformational changes in this span of TMH X of bovine and yeast CcOs which strongly suggests that this dynamic module plays a key role in optimizing intra-protein electron transfers.

Investigating the Many Roles of Internal Water in Cytochrome c Oxidase

Cytochrome c oxidase (C cO) is the terminal enzyme in the respiratory electron transport chain. As part of its catalytic cycle, C cO transfers protons to its Fe-Cu binuclear center (BNC) to reduce oxygen, and in addition, it pumps protons across the mitochondrial inner, or bacterial, membrane where it is located. It is believed that this proton transport is facilitated by a network of water chains inside the enzyme. Here we present an analysis of the hydration of C cO, including the BNC region, using a semi-empirical hydration program, Dowser++, recently developed in our group. Using high-resolution X-ray data, we show that Dowser++ predictions match very accurately the water molecules seen in the D- and K-channels of C cO, as well as in the vicinity of its BNC. Moreover, Dowser++ predicts many more internal water molecules than is typically seen in the experiment. However, no significant hydration of the catalytic cavity in C cO described recently in the literature is observed. As Dowser++ itself does not account for structural changes of the protein, this result supports the earlier assessment that the proposed wetting transition in the catalytic cavity can only either be due to structural rearrangements of BNC, possibly induced by the charges during the catalytic cycle, or occur transiently, in concert with the proton transfer. Molecular dynamics simulations were performed to investigate the global dynamic nature of Dowser++ waters in C cO, and the results suggest a consistent explanation as to why some predicted water molecules would be missing in the experimental structures. Furthermore, in light of the significant protein hydration predicted by Dowser++, the dielectric constant of the hydrated cavities in C cO was also investigated using the Fröhlich-Kirkwood model; the results indicate that in the cavities where water is packed sufficiently densely the dielectric constant can approach values comparable even to that of bulk water.

Oxygen Activation and Energy Conservation by Cytochrome c Oxidase

This review focuses on the type A cytochrome c oxidases (CcO), which are found in all mitochondria and also in several aerobic bacteria. CcO catalyzes the respiratory reduction of dioxygen (O₂) to water by an intriguing mechanism, the details of which are fairly well understood today as a result of research for over four decades. Perhaps even more intriguingly, the membrane-bound CcO couples the O₂ reduction chemistry to translocation of protons across the membrane, thus contributing to generation of the electrochemical proton gradient that is used to drive the synthesis of ATP as catalyzed by the rotary ATP synthase in the same membrane. After reviewing the structure of the core subunits of CcO, the active site, and the transfer paths of electrons, protons, oxygen, and water, we describe the states of the catalytic cycle and point out the few remaining uncertainties. Finally, we discuss the mechanism of proton translocation and the controversies in that area that still prevail.

Validating the Water Flooding Approach by Comparing It to Grand Canonical Monte Carlo Simulations

The study of the function of proteins on a quantitative level requires consideration of the water molecules in and around the protein. This requirement presents a major computational challenge due to the fact that the insertion of water molecules can have a very high activation barrier and would require a long simulation time. Recently, we developed a water flooding (WF) approach which is based on a postprocessing Monte Carlo ranking of possible water configurations. This approach appears to provide a very effective way for assessing the insertion free energies and determining the most likely configurations of the internal water molecules. Although the WF approach was used effectively in modeling challenging systems that have not been addressed reliably by other microscopic approaches, it was not validated by a comparison to the more rigorous grand canonical Monte Carlo (GCMC) method. Here we validate the WF approach by comparing its performance to that of the GCMC method. It is found that the WF approach reproduces the GCMC results in well-defined test cases but does so much faster. This established the WF approach as a useful strategy for finding correct water configurations in proteins and thus to provide a powerful way for studies of the functions of proteins.

Cavity hydration dynamics in cytochrome c oxidase and functional implications

Cytochrome c oxidase (CcO) is a transmembrane protein that uses the free energy of O₂ reduction to generate the proton concentration gradient across the membrane. The regulation of competitive proton transfer pathways has been established to be essential to the vectorial transport efficiency of CcO, yet the underlying mechanism at the molecular level remains lacking. Recent studies have highlighted the potential importance of hydration-level change in an internal cavity that connects the proton entrance channel, the site of O₂ reduction, and the putative proton exit route. In this work, we use atomistic molecular dynamics simulations to investigate the energetics and timescales associated with the volume fluctuation and hydration-level change in this central cavity. Extensive unrestrained molecular dynamics simulations (accumulatively [Formula: see text]4 [Formula: see text]s) and free energy computations for different chemical states of CcO support a model in which the volume and hydration level of the cavity are regulated by the protonation state of a propionate group of heme a₃ and, to a lesser degree, the redox state of heme a and protonation state of Glu286. Markov-state model analysis of [Formula: see text]2-[Formula: see text]s trajectories suggests that hydration-level change occurs on the timescale of 100-200 ns before the proton-loading site is protonated. The computed energetic and kinetic features for the cavity wetting transition suggest that reversible hydration-level change of the cavity can indeed be a key factor that regulates the branching of proton transfer events and therefore contributes to the vectorial efficiency of proton transport.

QM/MM Analysis of Transition States and Transition State Analogues in Metalloenzymes

Enzymology is approaching an era where many problems can benefit from computational studies. While ample challenges remain in quantitatively predicting behavior for many enzyme systems, the insights that often come from computations are an important asset for the enzymology community. Here we provide a primer for enzymologists on the types of calculations that are most useful for mechanistic problems in enzymology. In particular, we emphasize the integration of models that range from small active-site motifs to fully solvated enzyme systems for cross-validation and dissection of specific contributions from the enzyme environment. We then use a case study of the enzyme alkaline phosphatase to illustrate specific application of the methods. The case study involves examination of the binding modes of putative transition state analogues (tungstate and vanadate) to the enzyme. The computations predict covalent binding of these ions to the enzymatic nucleophile and that they adopt the trigonal bipyramidal geometry of the expected transition state. By comparing these structures with transition states found through free energy simulations, we assess the degree to which the transition state analogues mimic the true transition states. Technical issues worth treating with care as well as several remaining challenges to quantitative analysis of metalloenzymes are also highlighted during the discussion.

Multiscale simulations reveal key features of the proton-pumping mechanism in cytochrome c oxidase

Cytochrome c oxidase (CcO) reduces oxygen to water and uses the released free energy to pump protons across the membrane. We have used multiscale reactive molecular dynamics simulations to explicitly characterize (with free-energy profiles and calculated rates) the internal proton transport events that enable proton pumping during first steps of oxidation of the fully reduced enzyme. Our results show that proton transport from amino acid residue E286 to both the pump loading site (PLS) and to the binuclear center (BNC) are thermodynamically driven by electron transfer from heme a to the BNC, but that the former (i.e., pumping) is kinetically favored whereas the latter (i.e., transfer of the chemical proton) is rate-limiting. The calculated rates agree with experimental measurements. The backflow of the pumped proton from the PLS to E286 and from E286 to the inside of the membrane is prevented by large free-energy barriers for the backflow reactions. Proton transport from E286 to the PLS through the hydrophobic cavity and from D132 to E286 through the D-channel are found to be strongly coupled to dynamical hydration changes in the corresponding pathways and, importantly, vice versa.

Coupling between protonation and conformation in cytochrome c oxidase: Insights from constant-pH MD simulations

Cytochrome c oxidases (CcOs) are the terminal enzymes of the respiratory chain in mitochondria and most bacteria. These enzymes reduce dioxygen (O(2)) to water and, simultaneously, generate a transmembrane electrochemical proton gradient. Despite their importance in the aerobic metabolism and the large amount of structural and biochemical data available for the A1-type CcO family, there is still no consensually accepted description of the molecular mechanisms operating in this protein. A substantial number of questions about the CcO's working mechanism remain to be answered, including how the protonation behavior of some key residues is modulated during a reduction cycle and how is the conformation of the protein affected by protonation. The main objective of this work was to study the protonation-conformation coupling in CcOs and identify the molecular factors that control the protonation state of some key residues. In order to directly capture the interplay between protonation and conformational effects, we have performed constant-pH MD simulations of an A1-type CcO inserted into a lipid bilayer in two redox states (oxidized and reduced) at physiological pH. From the simulations, we were able to identify several groups with unusual titration behavior that are highly dependent on the protein redox state, including the A-propionate from heme a and the D-propionate from heme a3, two key groups possibly involved in proton pumping. The protonation state of these two groups is heavily influenced by subtle conformational changes in the protein (notably of R481(I) and R482(I)) and by small changes in the hydrogen bond network.

The role of the K-channel and the active-site tyrosine in the catalytic mechanism of cytochrome c oxidase

The active site of cytochrome c oxidase (CcO) comprises an oxygen-binding heme, a nearby copper ion (CuB), and a tyrosine residue that is covalently linked to one of the histidine ligands of CuB. Two proton-conducting pathways are observed in CcO, namely the D- and the K-channels, which are used to transfer protons either to the active site of oxygen reduction (substrate protons) or for pumping. Proton transfer through the D-channel is very fast, and its role in efficient transfer of both substrate and pumped protons is well established. However, it has not been fully clear why a separate K-channel is required, apparently for the supply of substrate protons only. In this work, we have analysed the available experimental and computational data, based on which we provide new perspectives on the role of the K-channel. Our analysis suggests that proton transfer in the K-channel may be gated by the protonation state of the active-site tyrosine (Tyr244) and that the neutral radical form of this residue has a more general role in the CcO mechanism than thought previously. This article is part of a Special Issue entitled 'EBEC 2016: 19th European Bioenergetics Conference, Riva del Garda, Italy, July 2-6, 2016', edited by Prof. Paolo Bernardi.

Computationally Efficient Multiscale Reactive Molecular Dynamics to Describe Amino Acid Deprotonation in Proteins

An important challenge in the simulation of biomolecular systems is a quantitative description of the protonation and deprotonation process of amino acid residues. Despite the seeming simplicity of adding or removing a positively charged hydrogen nucleus, simulating the actual protonation/deprotonation process is inherently difficult. It requires both the explicit treatment of the excess proton, including its charge defect delocalization and Grotthuss shuttling through inhomogeneous moieties (water and amino residues), and extensive sampling of coupled condensed phase motions. In a recent paper (J. Chem. Theory Comput. 2014, 10, 2729-2737), a multiscale approach was developed to map high-level quantum mechanics/molecular mechanics (QM/MM) data into a multiscale reactive molecular dynamics (MS-RMD) model in order to describe amino acid deprotonation in bulk water. In this article, we extend the fitting approach (called FitRMD) to create MS-RMD models for ionizable amino acids within proteins. The resulting models are shown to faithfully reproduce the free energy profiles of the reference QM/MM Hamiltonian for PT inside an example protein, the ClC-ec1 H(+)/Cl(-) antiporter. Moreover, we show that the resulting MS-RMD models are computationally efficient enough to then characterize more complex 2-dimensional free energy surfaces due to slow degrees of freedom such as water hydration of internal protein cavities that can be inherently coupled to the excess proton charge translocation. The FitRMD method is thus shown to be an effective way to map ab initio level accuracy into a much more computationally efficient reactive MD method in order to explicitly simulate and quantitatively describe amino acid protonation/deprotonation in proteins.

Microscopic basis for kinetic gating in Cytochrome c oxidase: insights from QM/MM analysis

Understanding the mechanism of vectorial proton pumping in biomolecules requires establishing the microscopic basis for the regulation of both thermodynamic and kinetic features of the relevant proton transfer steps.

Understanding the mechanism of vectorial proton pumping in biomolecules requires establishing the microscopic basis for the regulation of both thermodynamic and kinetic features of the relevant proton transfer steps. For the proton pump cytochrome c oxidase, while the regulation of thermodynamic driving force for key proton transfers has been discussed in great detail, the microscopic basis for the control of proton transfer kinetics has been poorly understood. Here we carry out extensive QM/MM free energy simulations to probe the kinetics of relevant proton transfer steps and analyze the effects of local structure and hydration level. We show that protonation of the proton loading site (PLS, taken to be a propionate of heme a₃) requires a concerted process in which a key glutamic acid (Glu286H) delivers the proton to the PLS while being reprotonated by an excess proton coming from the D-channel. The concerted nature of the mechanism is a crucial feature that enables the loading of the PLS before the cavity containing Glu286 is better hydrated to lower its pK_a to experimentally measured range; the charged rather than dipolar nature of the process also ensures a tight coupling with heme a reduction, as emphasized by Siegbahn and Blomberg. In addition, we find that rotational flexibility of the PLS allows its protonation before that of the binuclear center (the site where oxygen gets reduced to water). Together with our recent study (P. Goyal, et al., Proc. Natl. Acad. Sci. U. S. A., 2013, 110, 18886–18891) that focused on the modulation of Glu286 pK_a, the current work suggests a mechanism that builds in a natural sequence for the protonation of the PLS prior to that of the binuclear center. This provides microscopic support to the kinetic constraints revealed by kinetic network analysis as essential elements that ensure an efficient vectorial proton transport in cytochrome c oxidase.

Molecular simulation of water and hydration effects in different environments: challenges and developments for DFTB based models

We discuss the description of water and hydration effects that employs an approximate density functional theory, DFTB3, in either a full QM or QM/MM framework. The goal is to explore, with the current formulation of DFTB3, the performance of this method for treating water in different chemical environments, the magnitude and nature of changes required to improve its performance, and factors that dictate its applicability to reactions in the condensed phase in a QM/MM framework. A relatively minor change (on the scale of kBT) in the O-H repulsive potential is observed to substantially improve the structural properties of bulk water under ambient conditions; modest improvements are also seen in dynamic properties of bulk water. This simple change also improves the description of protonated water clusters, a solvated proton, and to a more limited degree, a solvated hydroxide. By comparing results from DFTB3 models that differ in the description of water, we confirm that proton transfer energetics are adequately described by the standard DFTB3/3OB model for meaningful mechanistic analyses. For QM/MM applications, a robust parametrization of QM-MM interactions requires an explicit consideration of condensed phase properties, for which an efficient sampling technique was developed recently and is reviewed here. The discussions help make clear the value and limitations of DFTB3 based simulations, as well as the developments needed to further improve the accuracy and transferability of the methodology.

Changing hydration level in an internal cavity modulates the proton affinity of a key glutamate in cytochrome c oxidase

Cytochrome c oxidase contributes to the transmembrane proton gradient by removing two protons from the high-pH side of the membrane each time the binuclear center active site is reduced. One proton goes to the binuclear center, whereas the other is pumped to the low-pH periplasmic space. Glutamate 286 (Glu286) has been proposed to serve as a transiently deprotonated proton donor. Using unrestrained atomistic molecular dynamics simulations, we show that the size of and water distribution in the hydrophobic cavity that holds Glu286 is controlled by the protonation state of the propionic acid of heme a3, a group on the proton outlet pathway. Protonation of the propionate disrupts hydrogen bonding to two side chains, allowing a loop to swing open. Continuum electrostatics and atomistic free-energy perturbation calculations show that the resultant changes in hydration and electrostatic interactions lower the Glu proton affinity by at least 5 kcal/mol. These changes in the internal hydration level occur in the absence of major conformational transitions and serve to stabilize needed transient intermediates in proton transport. The trigger is not the protonation of the Glu of interest, but rather the protonation of a residue ∼10 Å away. Thus, unlike local water penetration to stabilize a new charge, this finding represents a specific role for water molecules in the protein interior, mediating proton transfers and facilitating ion transport.

Bayesian model aggregation for ensemble-based estimates of protein pKa values

This article investigates an ensemble-based technique called Bayesian Model Averaging (BMA) to improve the performance of protein amino acid pKa predictions. Structure-based pKa calculations play an important role in the mechanistic interpretation of protein structure and are also used to determine a wide range of protein properties. A diverse set of methods currently exist for pKa prediction, ranging from empirical statistical models to ab initio quantum mechanical approaches. However, each of these methods are based on a set of conceptual assumptions that can effect a model's accuracy and generalizability for pKa prediction in complicated biomolecular systems. We use BMA to combine eleven diverse prediction methods that each estimate pKa values of amino acids in staphylococcal nuclease. These methods are based on work conducted for the pKa Cooperative and the pKa measurements are based on experimental work conducted by the García-Moreno lab. Our cross-validation study demonstrates that the aggregated estimate obtained from BMA outperforms all individual prediction methods with improvements ranging from 45 to 73% over other method classes. This study also compares BMA's predictive performance to other ensemble-based techniques and demonstrates that BMA can outperform these approaches with improvements ranging from 27 to 60%. This work illustrates a new possible mechanism for improving the accuracy of pKa prediction and lays the foundation for future work on aggregate models that balance computational cost with prediction accuracy.

Current advances in research of cytochrome c oxidase

The function of cytochrome c oxidase as a biomolecular nanomachine that transforms energy of redox reaction into protonmotive force across a biological membrane has been subject of intense research, debate, and controversy. The structure of the enzyme has been solved for several organisms; however details of its molecular mechanism of proton pumping still remain elusive. Particularly, the identity of the proton pumping site, the key element of the mechanism, is still open to dispute. The pumping mechanism has been for a long time one of the key unsolved issues of bioenergetics and biochemistry, but with the accelerating progress in this field many important details and principles have emerged. Current advances in cytochrome oxidase research are reviewed here, along with a brief discussion of the most complete proton pumping mechanism proposed to date, and a molecular basis for control of its efficiency.

Molecular mechanisms for generating transmembrane proton gradients

Membrane proteins use the energy of light or high energy substrates to build a transmembrane proton gradient through a series of reactions leading to proton release into the lower pH compartment (P-side) and proton uptake from the higher pH compartment (N-side). This review considers how the proton affinity of the substrates, cofactors and amino acids are modified in four proteins to drive proton transfers. Bacterial reaction centers (RCs) and photosystem II (PSII) carry out redox chemistry with the species to be oxidized on the P-side while reduction occurs on the N-side of the membrane. Terminal redox cofactors are used which have pKas that are strongly dependent on their redox state, so that protons are lost on oxidation and gained on reduction. Bacteriorhodopsin is a true proton pump. Light activation triggers trans to cis isomerization of a bound retinal. Strong electrostatic interactions within clusters of amino acids are modified by the conformational changes initiated by retinal motion leading to changes in proton affinity, driving transmembrane proton transfer. Cytochrome c oxidase (CcO) catalyzes the reduction of O2 to water. The protons needed for chemistry are bound from the N-side. The reduction chemistry also drives proton pumping from N- to P-side. Overall, in CcO the uptake of 4 electrons to reduce O2 transports 8 charges across the membrane, with each reduction fully coupled to removal of two protons from the N-side, the delivery of one for chemistry and transport of the other to the P-side.

Charging free energy calculations using the Generalized Solvent Boundary Potential (GSBP) and periodic boundary condition: a comparative analysis using ion solvation and oxidation free energy in proteins

Free energy simulations using a finite sphere boundary condition rather than a periodic boundary condition (PBC) are attractive in the study of very large biomolecular systems. To understand the quantitative impact of various approximations in such simulations, we compare charging free energies in both solution and protein systems calculated in a linear response framework with the Generalized Solvent Boundary Potential (GSBP) and PBC simulations. For simple ions in solution, we find good agreements between GSBP and PBC charging free energies, once the relevant correction terms are taken into consideration. For PBC simulations with the particle-mesh-Ewald for long-range electrostatics, the contribution (ΔG(P-M)) due to the use of a particle rather than molecule based summation scheme in real space is found to be significant, as pointed out by Hünenberger and co-workers. For GSBP, when the inner region is close to be charge neutral, the key correction is the overpolarization of water molecules at the inner/outer dielectric boundary; the magnitude of the correction (ΔG(s-pol)), however, is relatively small. For charging (oxidation) free energy in proteins, the situation is more complex, although good agreement between GSBP and PBC can still be obtained when care is exercised. The smooth dielectric boundary approximation inherent to GSBP tends to make significant errors when the inner region is featured with a high net charge. However, the error can be corrected with Poisson-Boltzmann calculations using snapshots from GSBP simulations in a straightforward and robust manner. Because of the more complex charge and solvent distributions, the magnitudes of ΔG(P-M) and ΔG(s-pol) in protein simulations appear to be different from those derived for solution simulations, leading to uncertainty in directly comparing absolute charging free energies from PBC and GSBP simulations for protein systems. The relative charging/oxidation free energies, however, are robust. With the linear response approximation, for the specific protein system (CueR) studied, the effect of freezing the protein structure in the outer region is found to be small, unless a very small (8 Å) inner region is used; even in the latter case, the result is substantially improved when the nearby metal binding loop is allowed to respond to metal oxidation. The implications of these results to the applicability of GSBP to complex biomolecules and in ab initio QM/MM simulations are discussed.

Proton uptake and pKa changes in the uncoupled Asn139Cys variant of cytochrome c oxidase

Cytochrome c oxidase (CytcO) is a membrane-bound enzyme that links electron transfer from cytochrome c to O(2) to proton pumping across the membrane. Protons are transferred through specific pathways that connect the protein surface with the catalytic site as well as the proton input with the proton output sides. Results from earlier studies have shown that one site within the so-called D proton pathway, Asn139, located ~10 Å from the protein surface, is particularly sensitive to mutations that uncouple the O(2) reduction reaction from the proton pumping activity. For example, none of the Asn139Asp (charged) or Asn139Thr (neutral) mutant CytcOs pump protons, although the proton-uptake rates are unaffected. Here, we have investigated the Asn139Cys and Asn139Cys/Asp132Asn mutant CytcOs. In contrast to other structural variants investigated to date, the Cys side chain may be either neutral or negatively charged in the experimentally accessible pH range. The data show that the Asn139Cys and Asn139Asp mutations result in the same changes of the kinetic and thermodynamic parameters associated with the proton transfer. The similarity is not due to introduction of charge at position 139, but rather introduction of a protonatable group that modulates the proton connectivity around this position. These results illuminate the mechanism by which CytcO couples electron transfer to proton pumping.

Three-dimensional stress field around a membrane protein: atomistic and coarse-grained simulation analysis of gramicidin A

Using both atomistic and coarse-grained (CG) models, we compute the three-dimensional stress field around a gramicidin A (gA) dimer in lipid bilayers that feature different degrees of negative hydrophobic mismatch. The general trends in the computed stress field are similar at the atomistic and CG levels, supporting the use of the CG model for analyzing the mechanical features of protein/lipid/water interfaces. The calculations reveal that the stress field near the protein-lipid interface exhibits a layered structure with both significant repulsive and attractive regions, with the magnitude of the stress reaching 1000 bar in certain regions. Analysis of density profiles and stress field distributions helps highlight the Trp residues at the protein/membrane/water interface as mechanical anchors, suggesting that similar analysis is useful for identifying tension sensors in other membrane proteins, especially membrane proteins involved in mechanosensation. This work fosters a connection between microscopic and continuum mechanics models for proteins in complex environments and makes it possible to test the validity of assumptions commonly made in continuum mechanics models for membrane mediated processes. For example, using the calculated stress field, we estimate the free energy of membrane deformation induced by the hydrophobic mismatch, and the results for regions beyond the annular lipids are in general consistent with relevant experimental data and previous theoretical estimates using elasticity theory. On the other hand, the assumptions of homogeneous material properties for the membrane and a bilayer thickness at the protein/lipid interface being independent of lipid type (e.g., tail length) appear to be oversimplified, highlighting the importance of annular lipids of membrane proteins. Finally, the stress field analysis makes it clear that the effect of even rather severe hydrophobic mismatch propagates to only about two to three lipid layers, thus putting a limit on the range of cooperativity between membrane proteins in crowded cellular membranes.

A density functional and quantum Monte Carlo study of glutamic acid in vacuo and in a dielectric continuum medium

We present density functional theory (DFT) and quantum Monte Carlo (QMC) calculations of the glutamic acid and glutamate ion in vacuo and in various dielectric continuum media within the polarizable continuum model (PCM). In DFT, we employ the integral equation formalism variant of PCM while, in QMC, we use a PCM scheme we have developed to include both surface and volume polarization. We investigate the gas-phase protonation thermochemistry of the glutamic acid using a large set of structural conformations, and find that QMC is in excellent agreement with the best available theoretical and experimental results. For the solvated glutamic acid and glutamate ion, we perform DFT calculations for dielectric constants, ε, between 4 and 78. We find that the glutamate ion in the zwitterionic form is more stable than the non-zwitterionic form over the whole range of dielectric constants, while the glutamic acid is more stable in its non-zwitterionic form at ε = 4. The dielectric constant at which the two glutamic acid species have the same energy depends on the cavity size and lies between 5 and 12.5. We validate these results with QMC for the two limiting values of the dielectric constant, and find qualitative agreement with DFT even though the solvent polarization is less pronounced at the QMC level.

From static structure to living protein: computational analysis of cytochrome c oxidase main-chain flexibility

Crystallographic structure and deuterium accessibility comparisons of CcO in different redox states have suggested conformational changes of mechanistic significance. To predict the intrinsic flexibility and low energy motions in CcO, this work has analyzed available high-resolution crystallographic structures with ProFlex and elNémo computational methods. The results identify flexible regions and potential conformational changes in CcO that correlate well with published structural and biochemical data and provide mechanistic insights. CcO is predicted to undergo rotational motions on the interior and exterior of the membrane, driven by transmembrane helical tilting and bending, coupled with rocking of the β-sheet domain. Consequently, the proton K-pathway becomes sufficiently flexible for internal water molecules to alternately occupy upper and lower parts of the pathway, associated with conserved Thr-359 and Lys-362 residues. The D-pathway helices are found to be relatively rigid, with a highly flexible entrance region involving the subunit I C-terminus, potentially regulating the uptake of protons. Constriction and dilation of hydrophobic channels in RsCcO suggest regulation of the oxygen supply to the binuclear center. This analysis points to coupled conformational changes in CcO and their potential to influence both proton and oxygen access.

Capturing the energetics of water insertion in biological systems: the water flooding approach

Consistent description of the effect of internal water in proteins has been a major challenge for both simulation and experimental studies. Describing this effect has been particularly important and elusive in cases of charges in protein interiors. Here, we present a new microscopic method that provides an efficient way for simulating the energetics of water insertion. Instead of performing explicit Monte Carlo (MC) moves on the insertion process, which generally involves an enormous number of rejected attempts, our method is based on generating trial configurations with excess amount of internal water, estimating the relevant free energy by the linear response approximation, and then using a postprocessing MC treatment to filter out a limited number of configurations from a large possible set. Our approach is validated on particularly challenging test cases including the pK(a) of the V66D mutation in Staphylococcal nuclease, Glu286 in cytochrome c oxidase (CcO) and the energetics of a protonated water molecule in the D channel of CcO. The new postprocessing method allows us to reproduce the relevant energetics of highly unstable charges in protein interiors using fully microscopic calculations and provides a substantial improvement over regular microscopic free energy estimates. This advance established the effectiveness of our water insertion strategy in challenging cases that have not been addressed successfully by other microscopic methods. Furthermore, our study provides a new exciting view on the crucial effect of water penetration in key biological systems as well as a new view on the nature of the dielectric in protein interiors.

Expanding the view of proton pumping in cytochrome c oxidase through computer simulation

In cytochrome c oxidase (CcO), a redox-driven proton pump, protons are transported by the Grotthuss shuttling via hydrogen-bonded water molecules and protonatable residues. Proton transport through the D-pathway is a complicated process that is highly sensitive to alterations in the amino acids or the solvation structure in the channel, both of which can inhibit proton pumping and enzymatic activity. Simulations of proton transport in the hydrophobic cavity showed a clear redox state dependence. To study the mechanism of proton pumping in CcO, multi-state empirical valence bond (MS-EVB) simulations have been conducted, focusing on the proton transport through the D-pathway and the hydrophobic cavity next to the binuclear center. The hydration structures, transport pathways, effects of residues, and free energy surfaces of proton transport were revealed in these MS-EVB simulations. The mechanistic insight gained from them is herein reviewed and placed in context for future studies.

Insights into the mechanism of proton transport in cytochrome c oxidase

Cytochrome c oxidase (CcO), known as complex IV of the electron transport chain, plays several important roles in aerobic cellular respiration. Electrons transferred from cytochrome c to CcO's catalytic site reduce molecular oxygen and produce a water molecule. These electron transfers also drive active proton pumping from the matrix (N-side) to intermembrane region (P-side) in mitochondria; the resultant proton gradient activates ATP synthase to produce ATP from ADP. Although the existence of the coupling between the electron transfer and the proton transport (PT) is established experimentally, its mechanism is not yet fully understood at the molecular level. In this work, it is shown why the reduction of heme a is essential for proton pumping. This is demonstrated via novel reactive molecular dynamics (MD) simulations that can describe the Grotthuss shuttling associated with the PT as well as the dynamic delocalization of the excess proton electronic charge defect. Moreover, the "valve" role of the Glu242 residue (bovine CcO notation) and the gate role of d-propionate of heme a(3) (PRDa3) in the explicit PT are explicitly demonstrated for the first time. These results provide conclusive evidence for the CcO proton transporting mechanism inferred from experiments, while deepening the molecular level understanding of the CcO proton switch.

Gating and regulation of the cytochrome c oxidase proton pump

As a consumer of 95% of the oxygen we breathe, cytochrome c oxidase plays a major role in the energy balance of the cell. Regulation of its oxygen reduction and proton pumping activity is therefore critical to physiological function in health and disease. The location and structure of pathways for protons that are required to support cytochrome c oxidase activity are still under debate, with respect to their requirements for key residues and fixed waters, and how they are gated to prevent (or allow) proton backflow. Recent high resolution structures of bacterial and mammalian forms reveal conserved lipid and steroid binding sites as well as redox-linked conformational changes that provide new insights into potential regulatory ligands and gating modes. Mechanistic interpretation of these findings and their significance for understanding energy regulation is discussed.

Coupled electron and proton transfer reactions during the O→E transition in bovine cytochrome c oxidase

A combined DFT/electrostatic approach is employed to study the coupling of proton and electron transfer reactions in cytochrome c oxidase (CcO) and its proton pumping mechanism. The coupling of the chemical proton to the internal electron transfer within the binuclear center is examined for the O→E transition. The novel features of the His291 pumping model are proposed, which involve timely well-synchronized sequence of the proton-coupled electron transfer reactions. The obtained pK(a)s and E(m)s of the key ionizable and redox-active groups at the different stages of the O→E transition are consistent with available experimental data. The PT step from E242 to H291 is examined in detail for various redox states of the hemes and various conformations of E242 side-chain. Redox potential calculations of the successive steps in the reaction cycle during the O→E transition are able to explain a cascade of equilibria between the different intermediate states and electron redistribution between the metal centers during the course of the catalytic activity. All four electrometric phases are discussed in the light of the obtained results, providing a robust support for the His291 model of proton pumping in CcO.

Glu-286 rotation and water wire reorientation are unlikely the gating elements for proton pumping in cytochrome C oxidase

One of the key unresolved issues regarding proton pumping in cytochrome c oxidase (CcO) is the identity of the gating element that prevents the backflow of protons. In this study, we analyze two popular proposals for this element: isomerization of the key branching residue (Glu-286) and (re)orientation of water molecules in the hydrophobic cavity. Using a multifaceted set of computational analyses that involve CcO embedded in either an implicit or explicit treatment of lipid membrane, we show that neither Glu-286 nor active-site water likely constitutes the gating element. Detailed energetic and structural analyses of the simulation results indicate that the gating-relevant properties of these structural motifs observed in previous work are likely a result of the simplified computational models employed in those studies.

Reduction potentials and acidity constants of Mn superoxide dismutase calculated by QM/MM free-energy methods

We used two theoretical methods to estimate reduction potentials and acidity constants in Mn superoxide dismutase (MnSOD), namely combined quantum mechanical and molecular mechanics (QM/MM) thermodynamic cycle perturbation (QTCP) and the QM/MM-PBSA approach. In the latter, QM/MM energies are combined with continuum solvation energies calculated by solving the Poisson-Boltzmann equation (PB) or by the generalised Born approach (GB) and non-polar solvation energies calculated from the solvent-exposed surface area. We show that using the QTCP method, we can obtain accurate and precise estimates of the proton-coupled reduction potential for MnSOD, 0.30±0.01 V, which compares favourably with experimental estimates of 0.26-0.40 V. However, the calculated potentials depend strongly on the DFT functional used: The B3LYP functional gives 0.6 V more positive potentials than the PBE functional. The QM/MM-PBSA approach leads to somewhat too high reduction potentials for the coupled reaction and the results depend on the solvation model used. For reactions involving a change in the net charge of the metal site, the corresponding results differ by up to 1.3 V or 24 pK(a) units, rendering the QM/MM-PBSA method useless to determine absolute potentials. However, it may still be useful to estimate relative shifts, although the QTCP method is expected to be more accurate.

Proton storage site in bacteriorhodopsin: new insights from quantum mechanics/molecular mechanics simulations of microscopic pK(a) and infrared spectra

Identifying the group that acts as the proton storage/loading site is a challenging but important problem for understanding the mechanism of proton pumping in biomolecular proton pumps, such as bacteriorhodopsin (bR) and cytochrome c oxidase. Recent experimental studies of bR propelled the idea that the proton storage/release group (PRG) in bR is not an amino acid but a water cluster embedded in the protein. We argue that this idea is at odds with our knowledge of protein electrostatics, since invoking the water cluster as the PRG would require the protein to raise the pK(a) of a hydronium by almost 11 pK(a) units, which is difficult considering known cases of pK(a) shifts in proteins. Our recent quantum mechanics/molecular mechanics (QM/MM) simulations suggested an alternative "intermolecular proton bond" model in which the stored proton is shared between two conserved Glu residues (194 and 204). Here we show that this model leads to microscopic pK(a) values consistent with available experimental data and the functional requirement of a PRG. Extensive QM/MM simulations also show that, independent of a number of technical issues, such as the influence of QM region size, starting X-ray structure, and nuclear quantum effects, the "intermolecular proton bond" model is qualitatively consistent with available spectroscopic data. Potential of mean force calculations show explicitly that the stored proton strongly prefers the pair of Glu residues over the water cluster. The results and analyses help highlight the importance of considering protein electrostatics and provide arguments for why the "intermolecular proton bond" model is likely applicable to the PRG in biomolecular proton pumps in general.

The mechanism for proton pumping in cytochrome c oxidase from an electrostatic and quantum chemical perspective

The mechanism for proton pumping in cytochrome c oxidase in the respiratory chain, has for decades been one of the main unsolved problems in biochemistry. However, even though several different suggested mechanisms exist, many of the steps in these mechanisms are quite similar and constitute a general consensus framework for discussing proton pumping. When these steps are analyzed, at least three critical gating situations are found, and these points are where the suggested mechanisms in general differ. The requirements for gating are reviewed and analyzed in detail, and a mechanism is suggested, where solutions for all the gating situations are formulated. This mechanism is based on an electrostatic analysis of a kinetic experiment fior the O to E transition. The key component of the mechanism is a positively charged transition state. An electron on heme a opens the gate for proton transfer from the N-side to a pump loading site (PLS). When the negative charge of the electron is compensated by a chemical proton, the positive transition state prevents backflow from the PLS to the N-side at the most critical stage of the pumping process. The mechanism has now been tested by large model DFT calculations, and these calculations give strong support for the suggested mechanism.

Proton-pumping mechanism of cytochrome c oxidase: a kinetic master-equation approach

Cytochrome c oxidase is an efficient energy transducer that reduces oxygen to water and converts the released chemical energy into an electrochemical membrane potential. As a true proton pump, cytochrome c oxidase translocates protons across the membrane against this potential. Based on a wealth of experiments and calculations, an increasingly detailed picture of the reaction intermediates in the redox cycle has emerged. However, the fundamental mechanism of proton pumping coupled to redox chemistry remains largely unresolved. Here we examine and extend a kinetic master-equation approach to gain insight into redox-coupled proton pumping in cytochrome c oxidase. Basic principles of the cytochrome c oxidase proton pump emerge from an analysis of the simplest kinetic models that retain essential elements of the experimentally determined structure, energetics, and kinetics, and that satisfy fundamental physical principles. The master-equation models allow us to address the question of how pumping can be achieved in a system in which all reaction steps are reversible. Whereas proton pumping does not require the direct modulation of microscopic reaction barriers, such kinetic gating greatly increases the pumping efficiency. Further efficiency gains can be achieved by partially decoupling the proton uptake pathway from the active-site region. Such a mechanism is consistent with the proposed Glu valve, in which the side chain of a key glutamic acid shuttles between the D channel and the active-site region. We also show that the models predict only small proton leaks even in the absence of turnover. The design principles identified here for cytochrome c oxidase provide a blueprint for novel biology-inspired fuel cells, and the master-equation formulation should prove useful also for other molecular machines. .

Application of the SCC-DFTB method to neutral and protonated water clusters and bulk water

The self-consistent charge density functional tight-binding (SCC-DFTB) method has been actively employed to study proton-transfer processes in biological systems. Recent studies in the literature employing SCC-DFTB reported that the method favors the Zundel form of the hydrated proton over the Eigen form, both in gas-phase water clusters and in bulk water, in disagreement with both higher-level calculations and experimental data. In this work, we explore the performance of SCC-DFTB for protonated gas-phase water clusters and bulk water (the latter both with and without an excess proton) with a modified O-H repulsive potential reported in our earlier work and with on-site third-order expansion of the DFT energy. Our results show that, with the proper set of published parameters, SCC-DFTB does correctly favor the Eigen form of the hydrated proton as compared to the Zundel form, both in gas-phase clusters and in the bulk; the amphiphilic character of the hydrated proton discussed in the literature has also been observed. The analyses do, however, bring forth remaining limitations in terms of the solvation structure around the hydrated proton as well as the structure of bulk water, which can guide future improvements of the method.

DFTB3: Extension of the self-consistent-charge density-functional tight-binding method (SCC-DFTB)

The self-consistent-charge density-functional tight-binding method (SCC-DFTB) is an approximate quantum chemical method derived from density functional theory (DFT) based on a second-order expansion of the DFT total energy around a reference density. In the present study we combine earlier extensions and improve them consistently with, first, an improved Coulomb interaction between atomic partial charges, and second, the complete third-order expansion of the DFT total energy. These modifications lead us to the next generation of the DFTB methodology called DFTB3, which substantially improves the description of charged systems containing elements C, H, N, O, and P, especially regarding hydrogen binding energies and proton affinities. As a result, DFTB3 is particularly applicable to biomolecular systems. Remaining challenges and possible solutions are also briefly discussed.

Modeling and simulation of ion-coupled and ATP-driven membrane proteins

The molecular mechanisms of membrane proteins that are activated either by ions or by ATP are just beginning to come into focus, as long-awaited structural data are revealed. This information is being leveraged and supplemented to great effect by molecular modeling and computer simulation studies. Important examples include the homology modeling of eukaryotic protein structures based on distantly related templates, as well as the use of internal structural symmetry for modeling different states in conformational cycles. Molecular simulation studies have elucidated the location and coordination structure of ion binding sites, and explained their selectivity, while also providing tantalizing insights into the mechanisms that couple conformational change to ion translocation or ATP hydrolysis.

pH-sensitive membrane peptides (pHLIPs) as a novel class of delivery agents

Abstract Here we review a novel class of delivery vehicles based on pH-sensitive, moderately polar membrane peptides, which we call pH (Low) Insertion Peptides (pHLIPs), that target cells located in the acidic environment found in many diseased tissues, including tumours. Acidity targeting by pHLIPs is achieved as a result of helix formation and transmembrane insertion. In contrast to the earlier technologies based on cell-penetrating peptides, pHLIPs act as monomeric membrane-inserting peptides that translocate one terminus across a membrane into the cytoplasm, while the other terminus remains in the extracellular space, locating the peptide in the membrane lipid bilayer. Therefore pHLIP has a dual delivery capability: it can tether cargo molecules or nanoparticles to the surfaces of cells in diseased tissues and/or it can move a cell-impermeable cargo molecule across the membrane into the cytoplasm. The source of energy for moving polar molecules attached to pHLIP through the hydrophobic layer of a membrane bilayer is the membrane-associated folding of the polypeptide. A drop in pH leads to the protonation of negatively charged residues (Asp or Glu), which enhances peptide hydrophobicity, increasing the affinity of the peptide for the lipid bilayer and triggering peptide folding and subsequent membrane insertion. The process is accompanied by the release of energy that can be utilized to move cell-impermeable cargo across a membrane. That the mechanism is now understood, and that targeting of tumours in mice has been shown, suggest a number of future applications of the pHLIP technology in the diagnosis and treatment of disease.

Multiconformation continuum electrostatics analysis of the effects of a buried Asp introduced near heme a in Rhodobacter sphaeroides cytochrome c oxidase

Cytochrome c oxidase (CcO) reduces O(2) to water via a series of proton-coupled electron transfers, generating a transmembrane electrochemical gradient. Coupling electron and proton transfer requires changing the pK(a) values of buried residues at each stage in the reaction cycle. Heme a is a key cofactor in the CcO electron transfer chain. Mutation of Ser44 to Asp has been reported [Mills, D. A., et al. (2008) Biochemistry 47, 11499-11509], changing the hydrogen bond acceptor from His102, the heme a axial ligand in Rhodobactor sphaeroides CcO. This adds an acidic residue to the CcO interior. The electrochemical behavior of heme a in wild-type and S44D CcO is compared using the continuum electrostatics program MCCE. The introduced, deeply buried Asp remains ionized at physiological pH only when the nearby heme is oxidized. Heme a reduction is now calculated to be strongly coupled to Asp proton binding, while with Ser44, it is weakly coupled to small protonation shifts at multiple sites, increasing the pH dependence in the mutant. At pH 7, the partially ionized Asp 44 is calculated to lower the heme redox potential by 50 mV as expected given the thermodynamics of coupled electron and proton transfers. This highlights an curious finding in the experimental results where a low Asp pK(a) is found together with a stabilized reduced heme. The stabilization of a heme oxidation in a model complex by a hydrogen bond to the axial His ligand calculated with continuum electrostatics and with density functional theory were in good agreement.