pKa values in proteins determined by electrostatics applied to molecular dynamics trajectories

The Functionality of the DC Pair in a Rhodopsin Guanylyl Cyclase from Catenaria anguillulae

Rhodopsin guanylyl cyclases (RGCs) belong to the class of enzymerhodopsins catalyzing the transition from GTP into the second messenger cGMP, whereas light-regulation of enzyme activity is mediated by a membrane-bound microbial rhodopsin domain, that holds the catalytic center inactive in the dark. Structural determinants for activation of the rhodopsin moiety eventually leading to catalytic activity are largely unknown. Here, we investigate the mechanistic role of the D283-C259 (DC) pair that is hydrogen bonded via a water molecule as a crucial functional motif in the homodimeric C. anguillulae RGC. Based on a structural model of the DC pair in the retinal binding pocket obtained by MD simulation, we analyzed formation and kinetics of early and late photocycle intermediates of the rhodopsin domain wild type and specific DC pair mutants by combined UV-Vis and FTIR spectroscopy at ambient and cryo-temperatures. By assigning specific infrared bands to S-H vibrations of C259 we are able to show that the DC pair residues are tightly coupled. We show that deprotonation of D283 occurs already in the inactive L state as a prerequisite for M state formation, whereas structural changes of C259 occur in the active M state and early cryo-trapped intermediates. We propose a comprehensive molecular model for formation of the M state that activates the catalytic moiety. It involves light induced changes in bond strength and hydrogen bonding of the DC pair residues from the early J state to the active M state and explains the retarding effect of C259 mutants.

Accurately Predicting Protein pKa Values Using Nonequilibrium Alchemy

The stability, solubility, and function of a protein depend on both its net charge and the protonation states of its individual residues. pKa is a measure of the tendency for a given residue to (de)protonate at a specific pH. Although pKa values can be resolved experimentally, theory and computation provide a compelling alternative. To this end, we assess the applicability of a nonequilibrium (NEQ) alchemical free energy method to the problem of pKa prediction. On a data set of 144 residues that span 13 proteins, we report an average unsigned error of 0.77 ± 0.09, 0.69 ± 0.09, and 0.52 ± 0.04 pK for aspartate, glutamate, and lysine, respectively. This is comparable to current state-of-the-art predictors and the accuracy recently reached using free energy perturbation methods (e.g., FEP+). Moreover, we demonstrate that our open-source, pmx-based approach can accurately resolve the pKa values of coupled residues and observe a substantial performance disparity associated with the lysine partial charges in Amber14SB/Amber99SB*-ILDN, for which an underused fix already exists.

Conformational and mechanical stability of the isolated large subunit of membrane-bound [NiFe]-hydrogenase from Cupriavidus necator

Comprising at least a bipartite architecture, the large subunit of [NiFe]-hydrogenase harbors the catalytic nickel-iron site while the small subunit houses an array of electron-transferring Fe-S clusters. Recently, some [NiFe]-hydrogenase large subunits have been isolated showing an intact and redox active catalytic cofactor. In this computational study we have investigated one of these metalloproteins, namely the large subunit HoxG of the membrane-bound hydrogenase from Cupriavidus necator (CnMBH), targeting its conformational and mechanical stability using molecular modelling and long all-atom Gaussian accelerated molecular dynamics (GaMD). Our simulations predict that isolated HoxG is stable in aqueous solution and preserves a large portion of its mechanical properties, but loses rigidity in regions around the active site, in contrast to the MBH heterodimer. Inspired by biochemical data showing dimerization of the HoxG protein and IR measurements revealing an increased stability of the [NiFe] cofactor in protein preparations with higher dimer content, corresponding simulations of homodimeric forms were also undertaken. While the monomeric subunit contains several flexible regions, our data predicts a regained rigidity in homodimer models. Furthermore, we computed the electrostatic properties of models obtained by enhanced sampling with GaMD, which displays a significant amount of positive charge at the protein surface, especially in solvent-exposed former dimer interfaces. These data offer novel insights on the way the [NiFe] core is protected from de-assembly and provide hints for enzyme anchoring to surfaces, which is essential information for further investigations on these minimal enzymes.

Calcium-permeable channelrhodopsins for the photocontrol of calcium signalling

Channelrhodopsins are light-gated ion channels used to control excitability of designated cells in large networks with high spatiotemporal resolution. While ChRs selective for H+, Na+, K+ and anions have been discovered or engineered, Ca2+-selective ChRs have not been reported to date. Here, we analyse ChRs and mutant derivatives with regard to their Ca2+ permeability and improve their Ca2+ affinity by targeted mutagenesis at the central selectivity filter. The engineered channels, termed CapChR1 and CapChR2 for calcium-permeable channelrhodopsins, exhibit reduced sodium and proton conductance in connection with strongly improved Ca2+ permeation at negative voltage and low extracellular Ca2+ concentrations. In cultured cells and neurons, CapChR2 reliably increases intracellular Ca2+ concentrations. Moreover, CapChR2 can robustly trigger Ca2+ signalling in hippocampal neurons. When expressed together with genetically encoded Ca2+ indicators in Drosophila melanogaster mushroom body output neurons, CapChRs mediate light-evoked Ca2+ entry in brain explants.

WiChR, a highly potassium-selective channelrhodopsin for low-light one- and two-photon inhibition of excitable cells

The electric excitability of muscle, heart, and brain tissue relies on the precise interplay of Na+- and K+-selective ion channels. The involved ion fluxes are controlled in optogenetic studies using light-gated channelrhodopsins (ChRs). While non-selective cation-conducting ChRs are well established for excitation, K+-selective ChRs (KCRs) for efficient inhibition have only recently come into reach. Here, we report the molecular analysis of recently discovered KCRs from the stramenopile Hyphochytrium catenoides and identification of a novel type of hydrophobic K+ selectivity filter. Next, we demonstrate that the KCR signature motif is conserved in related stramenopile ChRs. Among them, WiChR from Wobblia lunata features a so far unmatched preference for K+ over Na+, stable photocurrents under continuous illumination, and a prolonged open-state lifetime. Showing high expression levels in cardiac myocytes and neurons, WiChR allows single- and two-photon inhibition at low irradiance and reduced tissue heating. Therefore, we recommend WiChR as the long-awaited efficient and versatile optogenetic inhibitor.

AMOEBA Force Field Trajectories Improve Predictions of Accurate pKa Values of the GFP Fluorophore: The Importance of Polarizability and Water Interactions

Precisely quantifying the magnitude, direction, and biological functions of electric fields in proteins has long been an outstanding challenge in the field. The most widely implemented experimental method to measure such electric fields at a particular residue in a protein has been through changes in pKa of titratable residues. While many computational strategies exist to predict these values, it has been difficult to do this accurately or connect predicted results to key structural or mechanistic features of the molecule. Here, we used experimentally determined pKa values of the fluorophore in superfolder green fluorescent protein (GFP) with amino acid mutations made at position Thr 203 to evaluate the pKa prediction ability of molecular dynamics (MD) simulations using a polarizable force field, AMOEBA. Structure ensembles from AMOEBA were used to calculate pKa values of the GFP fluorophore. The calculated pKa values were then compared to trajectories using a conventional fixed charge force field (Amber03 ff). We found that the position of water molecules included in the pKa calculation had opposite effects on the pKa values between the trajectories from AMOEBA and Amber03 force fields. In AMOEBA trajectories, the inclusion of water molecules within 35 Å of the fluorophore decreased the difference between the predicted and experimental values, resulting in calculated pKa values that were within an average of 0.8 pKa unit from the experimental results. On the other hand, in Amber03 trajectories, including water molecules that were more than 5 Å from the fluorophore increased the differences between the calculated and experimental pKa values. The inaccuracy of pKa predictions determined from Amber03 trajectories was caused by a significant stabilization of the deprotonated chromophore's free energy compared to the result in AMOEBA. We rationalize the cutoffs for explicit water molecules when calculating pKa to better predict the electrostatic environment surrounding the fluorophore buried in GFP. We discuss how the results from this work will assist the prospective prediction of pKa values or other electrostatic effects in a wide variety of folded proteins.

Beating Heart of Cytochrome c Oxidase: The Shared Proton of Heme a3 Propionates

Cytochrome c oxidase (CcO) pumps protons from the N-side to the P-side and consumes electrons from the P-side of the mitochondrial membrane driven by energy gained from reduction of dioxygen to water. ATP synthesis uses the resulting proton gradient and electrostatic potential difference. Since the distance a proton travels through CcO is too large for a one-step transfer process, proton-loading sites (PLS) that can carry protons transiently are necessary. One specific pump-active PLS couples to the redox reaction, thus energizing the proton to move across the membrane against electric potential and proton gradient. The PLS should also prevent proton backflow. Therefore, the propionates of the two redox-active hemes in CcO were suggested as PLS candidates although, according to CcO crystal structures, none of the four propionates can be protonated on account of strong H-bonds. Here, we show that modeling the local structure around heme a₃ propionates enhances significantly their capability of carrying a proton jointly. This was not possible for the propionates of heme a. The modeled structures are stable in molecular dynamics simulations (MDS) and are energetically similar to the crystal structure. Precise electrostatic energy computations of MDS data are used to estimate the pK_A values of all titratable residues in CcO. For the modeled structures, the heme a₃ propionates have pK_A values high enough to host a proton transiently but not too high to fix the proton permanently. The change in pK_A throughout the redox reaction is sufficient to push the proton to the P-side of the membrane and to provide the protons with the necessary amount of energy for ATP synthesis.

Quantification of Local Electric Field Changes at the Active Site of Cytochrome c Oxidase by Fourier Transform Infrared Spectroelectrochemical Titrations

Cytochrome c oxidase (CcO) is a transmembrane protein complex that reduces molecular oxygen to water while translocating protons across the mitochondrial membrane. Changes in the redox states of its cofactors trigger both O₂ reduction and vectorial proton transfer, which includes a proton-loading site, yet unidentified. In this work, we exploited carbon monoxide (CO) as a vibrational Stark effect (VSE) probe at the binuclear center of CcO from Rhodobacter sphaeroides. The CO stretching frequency was monitored as a function of the electrical potential, using Fourier transform infrared (FTIR) absorption spectroelectrochemistry. We observed three different redox states (R₄CO, R₂CO, and O), determined their midpoint potential, and compared the resulting electric field to electrostatic calculations. A change in the local electric field strength of +2.9 MV/cm was derived, which was induced by the redox transition from R₄CO to R₂CO. We performed potential jump experiments to accumulate the R₂CO and R₄CO species and studied the FTIR difference spectra in the protein fingerprint region. The comparison of the experimental and computational results reveals that the key glutamic acid residue E286 is protonated in the observed states, and that its hydrogen-bonding environment is disturbed upon the redox transition of heme a₃. Our experiments also suggest propionate A of heme a₃ changing its protonation state in concert with the redox state of a second cofactor, heme a. This supports the role of propionic acid side chains as part of the proton-loading site.

Computing Protein pKas Using the TABI Poisson–Boltzmann Solver

A common approach to computing protein pKas uses a continuum dielectric model in which the protein is a low dielectric medium with embedded atomic point charges, the solvent is a high dielectric medium with a Boltzmann distribution of ionic charges, and the pKa is related to the electrostatic free energy which is obtained by solving the Poisson–Boltzmann equation. Starting from the model pKa for a titrating residue, the method obtains the intrinsic pKa and then computes the protonation probability for a given pH including site–site interactions. This approach assumes that acid dissociation does not affect protein conformation aside from adding or deleting charges at titratable sites. In this work, we demonstrate our treecode-accelerated boundary integral (TABI) solver for the relevant electrostatic calculations. The pKa computing procedure is enclosed in a convenient Python wrapper which is publicly available at the corresponding author’s website. Predicted results are compared with experimental pKas for several proteins. Among ongoing efforts to improve protein pKa calculations, the advantage of TABI is that it reduces the numerical errors in the electrostatic calculations so that attention can be focused on modeling assumptions.

A Resonance Raman Marker Band Characterizes the Slow and Fast Form of Cytochrome c Oxidase

Cytochrome c oxidase (CcO) in its as-isolated form is known to exist in a slow and fast form, which differ drastically in their ability to bind oxygen and other ligands. While preparation methods have been established that yield either the fast or the slow form of the protein, the underlying structural differences have not been identified yet. Here, we have performed surface enhanced resonance Raman (SERR) spectroscopy of CcO immobilized on electrodes in both forms. SERR spectra obtained in resonance with the heme a₃ metal-to-ligand charge transfer (MLCT) transition at 650 nm displayed a sharp vibrational band at 748 or 750 cm^-1 when the protein was in its slow or fast form, respectively. DFT calculations identified the band as a mode of the His-419 ligand that is sensitive to the oxygen ligand and the protonation state of Tyr-288 within the binuclear complex. Potential-dependent SERR spectroscopy showed a redox-induced change of this band around 525 mV versus Ag/AgCl exclusively for the fast form, which coincides with the redox potential of the Tyr-O/Tyr-O^- transition. Our data points to a peroxide ligand in the resting state of CcO for both forms. The observed frequencies and redox sensitivities of the Raman marker band suggest that a radical Tyr-288 is present in the fast form and a protonated Tyr-288 in the slow form.

Frontiers in Multiscale Modeling of Photoreceptor Proteins

This perspective article highlights the challenges in the theoretical description of photoreceptor proteins using multiscale modeling, as discussed at the CECAM workshop in Tel Aviv, Israel. The participants have identified grand challenges and discussed the development of new tools to address them. Recent progress in understanding representative proteins such as green fluorescent protein, photoactive yellow protein, phytochrome, and rhodopsin is presented, along with methodological developments.

Cholesterol Transport in Wild-Type NPC1 and P691S: Molecular Dynamics Simulations Reveal Changes in Dynamical Behavior

The Niemann–Pick C1 (NPC1) protein is the main protein involved in NPC disease, a fatal lysosomal lipid storage disease. NPC1, containing 1278 amino acids, is comprised of three lumenal domains (N-terminal, middle lumenal, C-terminal) and a transmembrane (TM) domain that contains a five helix bundle referred to as the sterol-sensing domain (SSD). The exact purpose of the SSD is not known, but it is believed that the SSD may bind cholesterol, either as a part of the lipid trafficking pathway or as part of a signaling mechanism. A recent cryo-EM structure has revealed an itraconazole binding site (IBS) in the SSD of human NPC1. Using this structural data, we constructed a model of cholesterol-bound wild-type (WT) and mutant P691S and performed molecular dynamics (MD) simulations of each cholesterol-bound protein. For WT NPC1, cholesterol migrates laterally, in the direction of the lipid bilayer. In the case of P691S, cholesterol is observed for the first time to migrate away from the SSD toward the N-terminal domain via a putative tunnel that connects the IBS with the lumenal domains. Structural features of the IBS are analyzed to identify the causes for different dynamical behavior between cholesterol-bound WT and cholesterol-bound P691S. The side chain of Ser691 in the P691S mutant introduces a hydrogen bond network that is not present in the WT protein. This change is likely responsible for the altered dynamical behavior observed in the P691S mutant and helps explain the disrupted cholesterol trafficking behavior observed in experiments.

Redox-coupled proton pumping drives carbon concentration in the photosynthetic complex I

Photosynthetic organisms capture light energy to drive their energy metabolism, and employ the chemical reducing power to convert carbon dioxide (CO2) into organic molecules. Photorespiration, however, significantly reduces the photosynthetic yields. To survive under low CO2 concentrations, cyanobacteria evolved unique carbon-concentration mechanisms that enhance the efficiency of photosynthetic CO2 fixation, for which the molecular principles have remained unknown. We show here how modular adaptations enabled the cyanobacterial photosynthetic complex I to concentrate CO2 using a redox-driven proton-pumping machinery. Our cryo-electron microscopy structure at 3.2 Å resolution shows a catalytic carbonic anhydrase module that harbours a Zn2+ active site, with connectivity to proton-pumping subunits that are activated by electron transfer from photosystem I. Our findings illustrate molecular principles in the photosynthetic complex I machinery that enabled cyanobacteria to survive in drastically changing CO2 conditions.

MerMAIDs: a family of metagenomically discovered marine anion-conducting and intensely desensitizing channelrhodopsins

Channelrhodopsins (ChRs) are algal light-gated ion channels widely used as optogenetic tools for manipulating neuronal activity. ChRs desensitize under continuous bright-light illumination, resulting in a significant decline of photocurrents. Here we describe a metagenomically identified family of phylogenetically distinct anion-conducting ChRs (designated MerMAIDs). MerMAIDs almost completely desensitize during continuous illumination due to accumulation of a late non-conducting photointermediate that disrupts the ion permeation pathway. MerMAID desensitization can be fully explained by a single photocycle in which a long-lived desensitized state follows the short-lived conducting state. A conserved cysteine is the critical factor in desensitization, as its mutation results in recovery of large stationary photocurrents. The rapid desensitization of MerMAIDs enables their use as optogenetic silencers for transient suppression of individual action potentials without affecting subsequent spiking during continuous illumination. Our results could facilitate the development of optogenetic tools from metagenomic databases and enhance general understanding of ChR function.

A Hierarchical Approach to Predict Conformation-Dependent Histidine Protonation States in Stable and Flexible Proteins

Solution acidity measured by pH is an important environmental factor that affects protein structure. It influences the protonation state of protein residues, which in turn may be coupled to protein conformational changes, unfolding, and ligand binding. It remains difficult to compute and measure the p K_a of individual residues, as well as to relate them to pH-dependent protein transitions. This paper presents a hierarchical approach to compute the p K_a of individual protonatable residues, specifically histidines, coupled with underlying structural changes of a protein. A fast and efficient free energy perturbation (FEP) algorithm has also been developed utilizing a fast implementation of standard molecular dynamics (MD) algorithms. Specifically, a CUDA version of the AMBER MD engine is used in this paper. Eight histidine p K_a's are computed in a diverse set of pH stable proteins to demonstrate the proposed approach's utility and assess the predictive quality of the AMBER FF99SB force field. A reference molecule is carefully selected and tested for convergence. A hierarchical approach is used to model p K_a's of the six histidine residues of the diphtheria toxin translocation domain (DTT), which exhibits a diverse ensemble of individual conformations and pH-dependent unfolding. The hierarchical approach consists of first sampling equilibrium conformational ensembles of a protein with protonated and neutral histidine residues via long equilibrium MD simulations (Flores-Canales, J. C.; et al. bioRxiv, 2019, 572040). A clustering method is then used to identify sampled protein conformations, and p K_a's of histidines in each protein conformation are computed. Finally, an ensemble averaging formalism is developed to compute weighted average histidine p K_a's. These can be compared with an apparent experimentally measured p K_a of the DTT protein and thus allows us to propose a mechanism of pH-dependent unfolding of the DTT protein.

Computational Tools Unravel Putative Sterol Binding Sites in the Lysosomal NPC1 Protein

Two proteins have been linked as the critical components in the molecular mechanisms involved in the Niemann Pick type C (NPC) disease: NPC1, a 140 kDa polytopic membrane-bound protein, and the smaller (132 residues), water-soluble NPC2 protein. NPC1 is believed to act in tandem with NPC2, transferring cholesterol and other sterols out of the LE/Lys compartments. Mutations in either NPC1 or NPC2 can lead to an accumulation of cholesterol and lipids in the LE/Lys, the primary phenotype of the NPC disease, but approximately 95% of identified disease-causing mutations have been mapped to the membrane-bound NPC1 protein. Here, we investigate the full length, membrane-bound NPC1 protein computationally using a combination of molecular modeling, docking, and molecular dynamics (MD) simulations. An analysis of titratable amino acid side chains, several buried in protein pockets, reveals several nonstandard protonation states for the low-pH scenario (pH 5) that is realized in the lysosome. Together with the location of these buried amino acids, docking studies have identified putative lipid binding domains that are in close proximity to amino acids that, when mutated, are connected to NPC1 loss-of-function. Using energy analyses and MD simulations, we analyze these domains as potential cholesterol binding sites and propose the possibility of multiple sterol binding pockets enabling the intramolecular transport of sterol molecules to the transmembrane domain.

Redox-coupled quinone dynamics in the respiratory complex I

Complex I couples the free energy released from quinone (Q) reduction to pump protons across the biological membrane in the respiratory chains of mitochondria and many bacteria. The Q reduction site is separated by a large distance from the proton-pumping membrane domain. To address the molecular mechanism of this long-range proton-electron coupling, we perform here full atomistic molecular dynamics simulations, free energy calculations, and continuum electrostatics calculations on complex I from Thermus thermophilus We show that the dynamics of Q is redox-state-dependent, and that quinol, QH₂, moves out of its reduction site and into a site in the Q tunnel that is occupied by a Q analog in a crystal structure of Yarrowia lipolytica We also identify a second Q-binding site near the opening of the Q tunnel in the membrane domain, where the Q headgroup forms strong interactions with a cluster of aromatic and charged residues, while the Q tail resides in the lipid membrane. We estimate the effective diffusion coefficient of Q in the tunnel, and in turn the characteristic time for Q to reach the active site and for QH₂ to escape to the membrane. Our simulations show that Q moves along the Q tunnel in a redox-state-dependent manner, with distinct binding sites formed by conserved residue clusters. The motion of Q to these binding sites is proposed to be coupled to the proton-pumping machinery in complex I.

Empirical Conversion of pK a Values between Different Solvents and Interpretation of the Parameters: Application to Water, Acetonitrile, Dimethyl Sulfoxide, and Methanol

An empirical conversion method (ECM) that transforms pK _a values of arbitrary organic compounds from one solvent to the other is introduced. We demonstrate the method's usefulness and performance on pK _a conversions involving water and organic solvents acetonitrile (MeCN), dimethyl sulfoxide (Me₂SO), and methanol (MeOH). We focus on the pK _a conversion from the known reference value in water to the other three organic solvents, although such a conversion can also be performed between any pair of the considered solvents. The ECM works with an additive parameter that is specific to a solvent and a molecular family (essentially characterized by a functional group that is titrated). We formally show that the method can be formulated with a single additive parameter, and that the extra multiplicative parameter used in other works is not required. The values of the additive parameter are determined from known pK _a data, and their interpretation is provided on the basis of physicochemical concepts. The data set of known pK _a values is augmented with pK _a values computed with the recently introduced electrostatic transform method, whose validity is demonstrated. For a validation of our method, we consider pK _a conversions for two data sets of titratable compounds. The first data set involves 81 relatively small molecules belonging to 19 different molecular families, with the pK _a data available in all four considered solvents. The second data set involves 76 titratable molecules from 5 additional molecular families. These molecules are typically larger, and their experimental pK _a values are available only in Me₂SO and water. The validation tests show that the agreement between the experimental pK _a data and the ECM predictions is generally good, with absolute errors often on the order of 0.5 pH units. The presence of a few outliers is rationalized, and observed trends with respect to molecular families are discussed.

Role of AP-endonuclease (Ape1) active site residues in stabilization of the reactant enzyme-DNA complex

Apurinic/apyrimidinic endonuclease 1 (Ape1) is an important metal-dependent enzyme in the base excision repair mechanism, responsible for the backbone cleavage of abasic DNA through a phosphate hydrolysis reaction. Molecular dynamics simulations of Ape1 complexed to its substrate DNA performed for models containing 1 or 2 Mg²⁺ -ions as cofactor located at different positions show a complex with 1 metal ion bound on the leaving group site of the scissile phosphate to be the most likely reaction-competent conformation. Active-site residue His309 is found to be protonated based on pKa calculations and the higher conformational stability of the Ape1-DNA substrate complex compared to scenarios with neutral His309. Simulations of the D210N mutant further support the prevalence of protonated His309 and strongly suggest Asp210 as the general base for proton acceptance by a nucleophilic water molecule.

Investigating energy-based pool structure selection in the structure ensemble modeling with experimental distance constraints: The example from a multidomain protein Pub1

The structural variations of multidomain proteins with flexible parts mediate many biological processes, and a structure ensemble can be determined by selecting a weighted combination of representative structures from a simulated structure pool, producing the best fit to experimental constraints such as interatomic distance. In this study, a hybrid structure-based and physics-based atomistic force field with an efficient sampling strategy is adopted to simulate a model di-domain protein against experimental paramagnetic relaxation enhancement (PRE) data that correspond to distance constraints. The molecular dynamics simulations produce a wide range of conformations depicted on a protein energy landscape. Subsequently, a conformational ensemble recovered with low-energy structures and the minimum-size restraint is identified in good agreement with experimental PRE rates, and the result is also supported by chemical shift perturbations and small-angle X-ray scattering data. It is illustrated that the regularizations of energy and ensemble-size prevent an arbitrary interpretation of protein conformations. Moreover, energy is found to serve as a critical control to refine the structure pool and prevent data overfitting, because the absence of energy regularization exposes ensemble construction to the noise from high-energy structures and causes a more ambiguous representation of protein conformations. Finally, we perform structure-ensemble optimizations with a topology-based structure pool, to enhance the understanding on the ensemble results from different sources of pool candidates.

Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation

Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.

The reductive phase of Rhodobacter sphaeroides cytochrome c oxidase disentangled by CO ligation

Cytochrome c oxidase (CcO) is a membrane protein of the respiratory chain that catalytically reduces molecular oxygen (O2) to water while translocating protons across the membrane. The enzyme hosts two copper and two heme iron moieties (heme a/heme a3). The atomic details of the sequential steps that go along with this redox-driven proton translocation are a matter of debate. Particularly for the reductive phase of CcO that precedes oxygen binding experimental data are scarce. Here, we use CcO under anaerobic conditions where carbon monoxide (CO) is bound to heme a3 which in tandem with CuB forms the binuclear center (BNC). Fourier-transform infrared (FTIR) absorption spectroscopy is combined with electro-chemistry to probe different redox and protonation states populated by variation of the external electrostatic potential. With this approach, the redox behavior of heme a and the BNC could be separated and the corresponding redox potentials were determined. We also infer the protonation of one of the propionate side chains of heme a3 to correlate with the oxidation of heme a. Experimental changes in the local electric field surrounding CO bound to heme a3 are determined by their vibrational Stark effect and agree well with electrostatic computations. The comparison of experimental and computational results indicates that changes of the heme a3/CuB redox state are coupled to proton transfer towards heme a3. The latter supports the role of the heme a3 propionate D as proton loading site.

DelPhiForce, a tool for electrostatic force calculations: Applications to macromolecular binding

Long-range electrostatic forces play an important role in molecular biology, particularly in macromolecular interactions. However, calculating the electrostatic forces for irregularly shaped molecules immersed in water is a difficult task. Here, we report a new tool, DelPhiForce, which is a tool in the DelPhi package that calculates and visualizes the electrostatic forces in biomolecular systems. In parallel, the DelPhi algorithm for modeling electrostatic potential at user-defined positions has been enhanced to include triquadratic and tricubic interpolation methods. The tricubic interpolation method has been tested against analytical solutions and it has been demonstrated that the corresponding errors are negligibly small at resolution 4 grids/Å. The DelPhiForce is further applied in the study of forces acting between partners of three protein-protein complexes. It has been demonstrated that electrostatic forces play a dual role by steering binding partners (so that the partners recognize their native interfaces) and exerting an electrostatic torque (if the mutual orientations of the partners are not native-like). The output of DelPhiForce is in a format that VMD can read and visualize, and provides additional options for analysis of protein-protein binding. DelPhiForce is available for download from the DelPhi webpage at http://compbio.clemson.edu/downloadDir/delphiforce.tar.gz © 2017 Wiley Periodicals, Inc.

pH-Dependent absorption spectrum of a protein: a minimal electrostatic model of Anabaena sensory rhodopsin

A minimal electrostatic model is introduced which aims at reproducing and analyzing the visible-light absorption energy shift of a protein with pH.

Continuum Electrostatics Approaches to Calculating pKas and Ems in Proteins

Proteins change their charge state through protonation and redox reactions as well as through binding charged ligands. The free energy of these reactions is dominated by solvation and electrostatic energies and modulated by protein conformational relaxation in response to the ionization state changes. Although computational methods for calculating these interactions can provide very powerful tools for predicting protein charge states, they include several critical approximations of which users should be aware. This chapter discusses the strengths, weaknesses, and approximations of popular computational methods for predicting charge states and understanding the underlying electrostatic interactions. The goal of this chapter is to inform users about applications and potential caveats of these methods as well as outline directions for future theoretical and computational research.

pK(A) in proteins solving the Poisson-Boltzmann equation with finite elements

Knowledge on pK(A) values is an eminent factor to understand the function of proteins in living systems. We present a novel approach demonstrating that the finite element (FE) method of solving the linearized Poisson-Boltzmann equation (lPBE) can successfully be used to compute pK(A) values in proteins with high accuracy as a possible replacement to finite difference (FD) method. For this purpose, we implemented the software molecular Finite Element Solver (mFES) in the framework of the Karlsberg+ program to compute pK(A) values. This work focuses on a comparison between pK(A) computations obtained with the well-established FD method and with the new developed FE method mFES, solving the lPBE using protein crystal structures without conformational changes. Accurate and coarse model systems are set up with mFES using a similar number of unknowns compared with the FD method. Our FE method delivers results for computations of pK(A) values and interaction energies of titratable groups, which are comparable in accuracy. We introduce different thermodynamic cycles to evaluate pK(A) values and we show for the FE method how different parameters influence the accuracy of computed pK(A) values.