Relations between Protonation Constants and Titration Curves in Polyprotic Acids: A Critical View

Resolving coupled pH titrations using alchemical free energy calculations

In a protein, nearby titratable sites can be coupled: the (de)protonation of one may affect the other. The degree of this interaction depends on several factors and can influence the measured p K a . Here, we derive a formalism based on double free energy differences ( Δ Δ G ) for quantifying the individual site p K a values of coupled residues. As Δ Δ G values can be obtained by means of alchemical free energy calculations, the presented approach allows for a convenient estimation of coupled residue p K a s in practice. We demonstrate that our approach and a previously proposed microscopic p K a formalism, can be combined with alchemical free energy calculations to resolve pH-dependent protein p K a values. Toy models and both, regular and constant-pH molecular dynamics simulations, alongside experimental data, are used to validate this approach. Our results highlight the insights gleaned when coupling and microstate probabilities are analyzed and suggest extensions to more complex enzymatic contexts. Furthermore, we find that naïvely computed p K a values that ignore coupling, can be significantly improved when coupling is accounted for, in some cases reducing the error by half. In short, alchemical free energy methods can resolve the p K a values of both uncoupled and coupled residues.

Why is the Omicron main protease of SARS-CoV-2 less stable than its wild-type counterpart? A crystallographic, biophysical, and theoretical study of the free enzyme and its complex with inhibitor 13b-K

During the continuing evolution of SARS-CoV-2, the Omicron variant of concern emerged in the second half of 2021 and has been dominant since November that year. Along with its sublineages, it has maintained a prominent role ever since. The Nsp5 main protease (Mpro) of the Omicron virus is characterized by a single dominant mutation, P132H. Here we determined the X-ray crystal structures of the P132H mutant (or O-Mpro) as free enzyme and in complex with the Mpro inhibitor, the alpha-ketoamide 13b-K, and we conducted enzymology, biophysical as well as theoretical studies to characterize the O-Mpro. We found that O-Mpro has a similar overall structure and binding with 13b-K; however, it displays lower enzymatic activity and lower thermal stability compared to the WT-Mpro (with "WT" referring to the original Wuhan-1 strain). Intriguingly, the imidazole ring of His132 and the carboxylate plane of Glu240 are in a stacked configuration in the X-ray structures determined here. The empirical folding free energy calculations suggest that the O-Mpro dimer is destabilized relative to the WT-Mpro due to the less favorable van der Waals interactions and backbone conformation in the individual protomers. The all-atom continuous constant pH molecular dynamics (MD) simulations reveal that His132 and Glu240 display coupled titration. At pH 7, His132 is predominantly neutral and in a stacked configuration with respect to Glu240 which is charged. In order to examine whether the Omicron mutation eases the emergence of further Mpro mutations, we also determined crystal structures of the relatively frequent P132H+T169S double mutant but found little evidence for a correlation between the two sites.

Energy coupling and stoichiometry of Zn2+/H+ antiport by the prokaryotic cation diffusion facilitator YiiP

YiiP from Shewanella oneidensis is a prokaryotic Zn2+/H+ antiporter that serves as a model for the Cation Diffusion Facilitator (CDF) superfamily, members of which are generally responsible for homeostasis of transition metal ions. Previous studies of YiiP as well as related CDF transporters have established a homodimeric architecture and the presence of three distinct Zn2+ binding sites named A, B, and C. In this study, we use cryo-EM, microscale thermophoresis and molecular dynamics simulations to address the structural and functional roles of individual sites as well as the interplay between Zn2+ binding and protonation. Structural studies indicate that site C in the cytoplasmic domain is primarily responsible for stabilizing the dimer and that site B at the cytoplasmic membrane surface controls the structural transition from an inward facing conformation to an occluded conformation. Binding data show that intramembrane site A, which is directly responsible for transport, has a dramatic pH dependence consistent with coupling to the proton motive force. A comprehensive thermodynamic model encompassing Zn2+ binding and protonation states of individual residues indicates a transport stoichiometry of 1 Zn2+ to 2-3 H+ depending on the external pH. This stoichiometry would be favorable in a physiological context, allowing the cell to use the proton gradient as well as the membrane potential to drive the export of Zn2+.

Thermodynamically consistent determination of free energies and rates in kinetic cycle models

Kinetic and thermodynamic models of biological systems are commonly used to connect microscopic features to system function in a bottom-up multiscale approach. The parameters of such models-free energy differences for equilibrium properties and in general rates for equilibrium and out-of-equilibrium observables-have to be measured by different experiments or calculated from multiple computer simulations. All such parameters necessarily come with uncertainties so that when they are naively combined in a full model of the process of interest, they will generally violate fundamental statistical mechanical equalities, namely detailed balance and an equality of forward/backward rate products in cycles due to Hill. If left uncorrected, such models can produce arbitrary outputs that are physically inconsistent. Here, we develop a maximum likelihood approach (named multibind) based on the so-called potential graph to combine kinetic or thermodynamic measurements to yield state-resolved models that are thermodynamically consistent while being most consistent with the provided data and their uncertainties. We demonstrate the approach with two theoretical models, a generic two-proton binding site and a simplified model of a sodium/proton antiporter. We also describe an algorithm to use the multibind approach to solve the inverse problem of determining microscopic quantities from macroscopic measurements and, as an example, we predict the microscopic p K a values and protonation states of a small organic molecule from 1D NMR data. The multibind approach is applicable to any thermodynamic or kinetic model that describes a system as transitions between well-defined states with associated free energy differences or rates between these states. A Python package multibind, which implements the approach described here, is made publicly available under the MIT Open Source license.

Thermodynamically consistent determination of free energies and rates in kinetic cycle models

Kinetic and thermodynamic models of biological systems are commonly used to connect microscopic features to system function in a bottom-up multiscale approach. The parameters of such models-free energy differences for equilibrium properties and in general rates for equilibrium and out-of-equilibrium observables-have to be measured by different experiments or calculated from multiple computer simulations. All such parameters necessarily come with uncertainties so that when they are naively combined in a full model of the process of interest, they will generally violate fundamental statistical mechanical equalities, namely detailed balance and an equality of forward/backward rate products in cycles due to T. Hill. If left uncorrected, such models can produce arbitrary outputs that are physically inconsistent. Here we develop a maximum likelihood approach (named multibind ) based on the so-called potential graph to combine kinetic or thermodynamic measurements to yield state resolved models that are thermodynamically consistent while being most consistent with the provided data and their uncertainties. We demonstrate the approach with two theoretical models, a generic two-proton binding site and a simplified model of a sodium/proton antiporter. We also describe an algorithm to use the multibind approach to solve the inverse problem of determining microscopic quantities from macroscopic measurements and as an example we predict the microscopic p K a s and protonation states of a small organic molecule from 1D NMR data. The multibind approach is applicable to any thermodynamic or kinetic model that describes a system as transitions between well-defined states with associated free energy differences or rates between these states. A Python package multibind , which implements the approach described here, is made publicly available under the MIT Open Source license.

WHY IT MATTERS

The increase in computational efficiency and rapid advances in methodology for quantitative free energy and rate calculations has allowed for the construction of increasingly complex thermodynamic or kinetic "bottom-up" models of chemical and biological processes. These multi-scale models serve as a framework for analyzing aspects of cellular function in terms of microscopic, molecular properties and provide an opportunity to connect molecular mechanisms to cellular function. The underlying model parameters-free energy differences or rates-are constrained by thermodynamic identities over cycles of states but these identities are not necessarily obeyed during model construction, thus potentially leading to inconsistent models. We address these inconsistencies through the use of a maximum likelihood approach for free energies and rates to adjust the model parameters in such a way that they are maximally consistent with the input parameters and exactly fulfill the thermodynamic cycle constraints. This approach enables formulation of thermodynamically consistent multi-scale models from simulated or experimental measurements.

PKAD-2: New entries and expansion of functionalities of the database of experimentally measured pKa's of proteins

Almost all biological reactions are pH dependent and understanding the origin of pH dependence requires knowledge of the pKa's of ionizable groups. Here we report a new edition of PKAD, the PKAD-2, which is a database of experimentally measured pKa's of proteins, both wild type and mutant proteins. The new additions include 117 wild type and 54 mutant pKa values, resulting in total 1742 experimentally measured pKa's. The new edition of PKAD-2 includes 8 new wild type and 12 new mutant proteins, resulting in total of 220 proteins. This new edition incorporates a visual 3D image of the highlighted residue of interest within the corresponding protein or protein complex. Hydrogen bonds were identified, counted, and implemented as a search feature. Other new search features include the number of neighboring residues <4A from the heaviest atom of the side chain of a given amino acid. Here, we present PKAD-2 with the intention to continuously incorporate novel features and current data with the goal to be used as benchmark for computational methods.

Energy Coupling and Stoichiometry of Zn2+/H+ Antiport by the Cation Diffusion Facilitator YiiP

YiiP is a prokaryotic Zn2+/H+ antiporter that serves as a model for the Cation Diffusion Facilitator (CDF) superfamily, members of which are generally responsible for homeostasis of transition metal ions. Previous studies of YiiP as well as related CDF transporters have established a homodimeric architecture and the presence of three distinct Zn2+ binding sites named A, B, and C. In this study, we use cryo-EM, microscale thermophoresis and molecular dynamics simulations to address the structural and functional roles of individual sites as well as the interplay between Zn2+ binding and protonation. Structural studies indicate that site C in the cytoplasmic domain is primarily responsible for stabilizing the dimer and that site B at the cytoplasmic membrane surface controls the structural transition from an inward facing conformation to an occluded conformation. Binding data show that intramembrane site A, which is directly responsible for transport, has a dramatic pH dependence consistent with coupling to the proton motive force. A comprehensive thermodynamic model encompassing Zn2+ binding and protonation states of individual residues indicates a transport stoichiometry of 1 Zn2+ to 2-3 H+ depending on the external pH. This stoichiometry would be favorable in a physiological context, allowing the cell to use the proton gradient as well as the membrane potential to drive the export of Zn2+.

The role of conformational change and key glutamic acid residues in the ClC-ec1 antiporter

The triple glutamine (Q) mutant (QQQ) structure of a Cl-/H+ antiporter from Escherichia coli (ClC-ec1) displaying a novel backbone arrangement has been used to challenge the long-held notion that Cl-/H+ antiporters do not operate through large conformational motions. The QQQ mutant substitutes the glutamine residue for an external glutamate E148, an internal glutamate E203, and a third glutamate E113 that hydrogen-bonds with E203. However, it is unknown if QQQ represents a physiologically relevant state, as well as how the protonation of the wild-type glutamates relates to the global dynamics. We herein apply continuous constant-pH molecular dynamics to investigate the H+-coupled dynamics of ClC-ec1. Although any large-scale conformational rearrangement upon acidification would be due to the accumulation of excess charge within the protein, protonation of the glutamates significantly impacts mainly the local structure and dynamics. Despite the fact that the extracellular pore enlarges at acidic pHs, an occluded ClC-ec1 within the active pH range of 3.5-7.5 requires a protonated E148 to facilitate extracellular Cl- release. E203 is also involved in the intracellular H+ transfer as an H+ acceptor. The water wire connection of E148 with the intracellular solution is regulated by the charge states of the E113/E203 dyad with coupled proton titration. However, the dynamics extracted from our simulations are not QQQ-like, indicating that the QQQ mutant does not represent the behavior of the wild-type ClC-ec1. These findings reinforce the necessity of having a protonatable residue at the E203 position in ClC-ec1 and suggest that a higher level of complexity exists for the intracellular H+ transfer in Cl-/H+ antiporters.

GPU-Accelerated All-Atom Particle-Mesh Ewald Continuous Constant pH Molecular Dynamics in Amber

Constant pH molecular dynamics (MD) simulations sample protonation states on the fly according to the conformational environment and user specified pH conditions; however, the current accuracy is limited due to the use of implicit-solvent models or a hybrid solvent scheme. Here, we report the first GPU-accelerated implementation, parametrization, and validation of the all-atom continuous constant pH MD (CpHMD) method with particle-mesh Ewald (PME) electrostatics in the Amber22 pmemd.cuda engine. The titration parameters for Asp, Glu, His, Cys, and Lys were derived for the CHARMM c22 and Amber ff14sb and ff19sb force fields. We then evaluated the PME-CpHMD method using the asynchronous pH replica-exchange titration simulations with the c22 force field for six benchmark proteins, including BBL, hen egg white lysozyme (HEWL), staphylococcal nuclease (SNase), thioredoxin, ribonuclease A (RNaseA), and human muscle creatine kinase (HMCK). The root-mean-square deviation from the experimental pK_a's of Asp, Glu, His, and Cys is 0.76 pH units, and the Pearson's correlation coefficient for the pK_a shifts with respect to model values is 0.80. We demonstrated that a finite-size correction or much enlarged simulation box size can remove a systematic error of the calculated pK_a's and improve agreement with experiment. Importantly, the simulations captured the relevant biology in several challenging cases, e.g., the titration order of the catalytic dyad Glu35/Asp52 in HEWL and the coupled residues Asp19/Asp21 in SNase, the large pK_a upshift of the deeply buried catalytic Asp26 in thioredoxin, and the large pK_a downshift of the deeply buried catalytic Cys283 in HMCK. We anticipate that PME-CpHMD will offer proper pH control to improve the accuracies of MD simulations and enable mechanistic studies of proton-coupled dynamical processes that are ubiquitous in biology but remain poorly understood due to the lack of experimental tools and limitation of current MD simulations.

Fully Symmetric Cyclodextrin Polycarboxylates: How to Determine Reliable Protonation Constants from NMR Titration Data

Acid-base properties of cyclodextrins (CDs), persubstituted at C-6 by 3-mercaptopropionic acid, sualphadex (Suα-CD), subetadex (Suβ-CD) and sugammadex (Suγ-CD, the antidote of neuromuscular blocking steroids) were studied by ¹H NMR-pH titrations. For each CD, the severe overlap in protonation steps prevented the calculation of macroscopic pK_a values using the standard data fitting model. Considering the full symmetry of polycarboxylate structures, we reduced the number of unknown NMR parameters in the "Q-fitting" or the novel "equidistant macroscopic" evaluation approaches. These models already provided pK_a values, but some of them proved to be physically unrealistic, deceptively suggesting cooperativity in carboxylate protonations. The latter problem could be circumvented by adapting the microscopic site-binding (cluster expansion) model by Borkovec, which applies pairwise interactivity parameters to quantify the mutual basicity-decreasing effect of carboxylate protonations. Surprisingly, only a single averaged interactivity parameter could be calculated reliably besides the carboxylate 'core' microconstant for each CD derivative. The speciation of protonation isomers hence could not be resolved, but the optimized microscopic basicity parameters could be converted to the following sets of macroscopic pK_a values: 3.84, 4.35, 4.81, 5.31, 5.78, 6.28 for Suα-CD; 3.82, 4.31, 4.73, 5.18, 5.64, 6.06, 6.54 for Suβ-CD and 3.83, 4.28, 4.65, 5.03, 5.43, 5.81, 6.18, 6.64 for Suγ-CD. The pH-dependent charge of these compounds can now be accurately calculated, in support of designing new analytical methods to exploit their charge-dependent molecular recognition such as in cyclodextrin-aided chiral capillary electrophoresis.

Identification and characterization of alternative sites and molecular probes for SARS-CoV-2 target proteins

Three protein targets from SARS-CoV-2, the viral pathogen that causes COVID-19, are studied: the main protease, the 2′-O-RNA methyltransferase, and the nucleocapsid (N) protein. For the main protease, the nucleophilicity of the catalytic cysteine C145 is enabled by coupling to three histidine residues, H163 and H164 and catalytic dyad partner H41. These electrostatic couplings enable significant population of the deprotonated state of C145. For the RNA methyltransferase, the catalytic lysine K6968 that serves as a Brønsted base has significant population of its deprotonated state via strong coupling with K6844 and Y6845. For the main protease, Partial Order Optimum Likelihood (POOL) predicts two clusters of biochemically active residues; one includes the catalytic H41 and C145 and neighboring residues. The other surrounds a second pocket adjacent to the catalytic site and includes S1 residues F140, L141, H163, E166, and H172 and also S2 residue D187. This secondary recognition site could serve as an alternative target for the design of molecular probes. From in silico screening of library compounds, ligands with predicted affinity for the secondary site are reported. For the NSP16-NSP10 complex that comprises the RNA methyltransferase, three different sites are predicted. One is the catalytic core at the conserved K-D-K-E motif that includes catalytic residues D6928, K6968, and E7001 plus K6844. The second site surrounds the catalytic core and consists of Y6845, C6849, I6866, H6867, F6868, V6894, D6895, D6897, I6926, S6927, Y6930, and K6935. The third is located at the heterodimer interface. Ligands predicted to have high affinity for the first or second sites are reported. Three sites are also predicted for the nucleocapsid protein. This work uncovers key interactions that contribute to the function of the three viral proteins and also suggests alternative sites for ligand design.

Electrostatic fingerprints of catalytically active amino acids in enzymes

The computed electrostatic and proton transfer properties are studied for 20 enzymes that represent all six major enzyme commission classes and a variety of different folds. The properties of aspartate, glutamate, and lysine residues that have been previously experimentally determined to be catalytically active are reported. The catalytic aspartate and glutamate residues studied here are strongly coupled to at least one other aspartate or glutamate residue and often to multiple other carboxylate residues with intrinsic pK_a differences less than 1 pH unit. Sometimes these catalytic acidic residues are also coupled to a histidine residue, such that the intrinsic pK_a of the acidic residue is higher than that of the histidine. All catalytic lysine residues studied here are strongly coupled to tyrosine or cysteine residues, wherein the intrinsic pK_a of the anion-forming residue is higher than that of the lysine. Some catalytic lysines are also coupled to other lysines with intrinsic pK_a differences within 1 pH unit. Some evidence of the possible types of interactions that facilitate nucleophilicity is discussed. The interactions reported here provide important clues about how side chain functional groups that are weak Brønsted acids or bases for the free amino acid in solution can achieve catalytic potency and become strong acids, bases or nucleophiles in the enzymatic environment.

Reverse Protonation of Buried Ion-Pairs in Staphylococcal Nuclease Mutants

Although buried titratable residues in protein cavities are often of major functional importance, it is generally challenging to understand their properties such as the ionization state and factors of stabilization based on experimental studies alone. A specific set of examples involve buried Glu-Lys pairs in a series of variants of Staphylococcal nuclease, for which recent structural and thermodynamic studies appeared to suggest that both the stability and the ionization state of the buried Glu-Lys pair are sensitive to its orientation (i.e., Glu23-Lys36 vs Lys23-Glu36). To further clarify the situation, especially ionization states of the buried Glu-Lys pairs, we have conducted extensive molecular dynamics simulations and free energy computations. Microsecond molecular dynamics simulations show that the hydration level of the cavity depends on the orientation of the buried ion-pair therein as well as its ionization state; free energy simulations recapitulate the relative stability of Glu23-Lys36 (EK) vs Lys23-Glu36 (KE) mutants measured experimentally, although the difference is similar in magnitude regardless of the ionization state of the Glu-Lys pair. A complementary set of free energy simulations strongly suggests that, in contrast to the original suggestion in the experimental analysis, the Glu and Lys residues prefer to adopt their charge-neutral rather than the ionized states. This result is consistent with the low dielectric constant computed for water in the cavity, which makes it difficult for the protein cavity to stabilize a pair of charged Glu-Lys residues, even with water penetration. The current study highlights the role of free energy simulations in understanding the ionization state of buried titratable residues and the relevant energetic contributions, forming the basis for the rational design of buried charge networks in proteins.

Amino acid interactions that facilitate enzyme catalysis

Interactions in enzymes between catalytic and neighboring amino acids and how these interactions facilitate catalysis are examined. In examples from both natural and designed enzymes, it is shown that increases in catalytic rates may be achieved through elongation of the buffer range of the catalytic residues; such perturbations in the protonation equilibria are, in turn, achieved through enhanced coupling of the protonation equilibria of the active ionizable residues with those of other ionizable residues. The strongest coupling between protonation states for a pair of residues that deprotonate to form an anion (or a pair that accept a proton to form a cation) is achieved when the difference in the intrinsic pK_as of the two residues is approximately within 1 pH unit. Thus, catalytic aspartates and glutamates are often coupled to nearby acidic residues. For an anion-forming residue coupled to a cation-forming residue, the elongated buffer range is achieved when the intrinsic pK_a of the anion-forming residue is higher than the intrinsic pK_a of the (conjugate acid of the) cation-forming residue. Therefore, the high pK_a, anion-forming residues tyrosine and cysteine make good coupling partners for catalytic lysine residues. For the anion-cation pairs, the optimum difference in intrinsic pK_as is a function of the energy of interaction between the residues. For the energy of interaction ε expressed in units of (ln 10)RT, the optimum difference in intrinsic pK_as is within ∼1 pH unit of ε.

Analysis of electrostatic coupling throughout the laboratory evolution of a designed retroaldolase

The roles of local interactions in the laboratory evolution of a highly active, computationally designed retroaldolase (RA) are examined. Partial Order Optimum Likelihood (POOL) is used to identify catalytically important amino acid interactions in several RA95 enzyme variants. The series RA95.5, RA95.5–5, RA95.5–8, and RA95.5–8F, representing progress along an evolutionary trajectory with increasing activity, is examined. Computed measures of coupling between charged states of residues show that, as evolution proceeds and higher activities are achieved, electrostatic coupling between the biochemically active amino acids and other residues is increased. In silico residue scanning suggests multiple coupling partners for the catalytic lysine K83. The effects of two predicted partners, Y51 and E85, are tested using site‐directed mutagenesis and kinetic analysis of the variants Y51F and E85Q. The Y51F variants show decreases in k_cat relative to wild type, with the greatest losses observed for the more evolved constructs; they also exhibit significant decreases in k_cat/K_M across the series. Only modest decreases in k_cat/K_M are observed for the E85Q variants with little effect on k_cat. Computed metrics of the degree of coupling between protonation states rise significantly as evolution proceeds and catalytic turnover rate increases. Specifically, the charge state of the catalytic lysine K83 becomes more strongly coupled to those of other amino acids as the enzyme evolves to a better catalyst.

Polyprotic Acids and Beyond—An Algebraic Approach

For an N-protic acid–base system, the set of nonlinear equations (i.e., mass action and balance laws) provides a simple analytical solution/formula for any integer N ≥ 1. The approach is applicable for the general case of zwitterionic acids HNA+Z (e.g., amino acids, NTA, and EDTA), which includes (i) the “ordinary acids” as a special case (Z = 0) and (ii) surface complexation. Examples are presented for N = 1 to 6. The high-N perspective allows the classification of equivalence points (including isoionic and isoelectric points). Principally, there are two main approaches to N-protic acids: one from hydrochemistry and one “outside inorganic hydrochemistry”. They differ in many ways: the choice of the reference state (either HNA or A−N), the reaction type (dissociation or association), the type/nature of the acidity constants, and the structure of the formulas. Once the (nonlinear) conversion between the two approaches is established, we obtain a systematics of acidity constants (macroscopic, microscopic, cumulative, and Simms). Finally, from the viewpoint of statistical mechanics (canonical isothermal–isobaric ensemble), buffer capacities, buffer intensities, and higher pH derivatives are actually fluctuations in the form of variance, skewness, and kurtosis.

Charge Interactions in a Highly Charge-Depleted Protein

Electrostatic forces are important for protein folding and are favored targets of protein engineering. However, interactions between charged residues are difficult to study because of the complex network of interactions found in most proteins. We have designed a purposely simple system to investigate this problem by systematically introducing individual and pairs of charged and titratable residues in a protein otherwise free of such residues. We used constant pH molecular dynamics simulations, NMR spectroscopy, and thermodynamic double mutant cycles to probe the structure and energetics of the interaction between the charged residues. We found that the partial burial of surface charges contributes to a shift in pK_a value, causing an aspartate to titrate in the neutral pH range. Additionally, the interaction between pairs of residues was found to be highly context dependent, with some pairs having no apparent preferential interaction, while other pairs would engage in coupled titration forming a highly stabilized salt bridge. We find good agreement between experiments and simulations and use the simulations to rationalize our observations and to provide a detailed mechanistic understanding of the electrostatic interactions.

Overview of the SAMPL6 pKa challenge: evaluating small molecule microscopic and macroscopic pKa predictions

The prediction of acid dissociation constants (pKa) is a prerequisite for predicting many other properties of a small molecule, such as its protein-ligand binding affinity, distribution coefficient (log D), membrane permeability, and solubility. The prediction of each of these properties requires knowledge of the relevant protonation states and solution free energy penalties of each state. The SAMPL6 pKa Challenge was the first time that a separate challenge was conducted for evaluating pKa predictions as part of the Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) exercises. This challenge was motivated by significant inaccuracies observed in prior physical property prediction challenges, such as the SAMPL5 log D Challenge, caused by protonation state and pKa prediction issues. The goal of the pKa challenge was to assess the performance of contemporary pKa prediction methods for drug-like molecules. The challenge set was composed of 24 small molecules that resembled fragments of kinase inhibitors, a number of which were multiprotic. Eleven research groups contributed blind predictions for a total of 37 pKa distinct prediction methods. In addition to blinded submissions, four widely used pKa prediction methods were included in the analysis as reference methods. Collecting both microscopic and macroscopic pKa predictions allowed in-depth evaluation of pKa prediction performance. This article highlights deficiencies of typical pKa prediction evaluation approaches when the distinction between microscopic and macroscopic pKas is ignored; in particular, we suggest more stringent evaluation criteria for microscopic and macroscopic pKa predictions guided by the available experimental data. Top-performing submissions for macroscopic pKa predictions achieved RMSE of 0.7-1.0 pKa units and included both quantum chemical and empirical approaches, where the total number of extra or missing macroscopic pKas predicted by these submissions were fewer than 8 for 24 molecules. A large number of submissions had RMSE spanning 1-3 pKa units. Molecules with sulfur-containing heterocycles or iodo and bromo groups were less accurately predicted on average considering all methods evaluated. For a subset of molecules, we utilized experimentally-determined microstates based on NMR to evaluate the dominant tautomer predictions for each macroscopic state. Prediction of dominant tautomers was a major source of error for microscopic pKa predictions, especially errors in charged tautomers. The degree of inaccuracy in pKa predictions observed in this challenge is detrimental to the protein-ligand binding affinity predictions due to errors in dominant protonation state predictions and the calculation of free energy corrections for multiple protonation states. Underestimation of ligand pKa by 1 unit can lead to errors in binding free energy errors up to 1.2 kcal/mol. The SAMPL6 pKa Challenge demonstrated the need for improving pKa prediction methods for drug-like molecules, especially for challenging moieties and multiprotic molecules.

Continuous Constant pH Molecular Dynamics Simulations of Transmembrane Proteins

Many membrane channels, transporters, and receptors utilize a pH gradient or proton coupling to drive functionally relevant conformational transitions. Conventional molecular dynamics simulations employ fixed protonation states, thus neglecting the coupling between protonation and conformational equilibria. Here we describe the membrane-enabled hybrid-solvent continuous constant pH molecular dynamics method for capturing atomic details of proton-coupled conformational dynamics of transmembrane proteins. Example protocols from our recent application studies of proton channels and ion/substrate transporters are discussed.

Exploring the pH-Dependent Structure-Dynamics-Function Relationship of Human Renin

Renin is a pepsin-like aspartyl protease and an important drug target for the treatment of hypertension; despite three decades' research, its pH-dependent structure-function relationship remains poorly understood. Here, we employed continuous constant pH molecular dynamics (CpHMD) simulations to decipher the acid/base roles of renin's catalytic dyad and the conformational dynamics of the flap, which is a common structural feature among aspartyl proteases. The calculated pK_a's suggest that catalytic Asp38 and Asp226 serve as the general base and acid, respectively, in agreement with experiment and supporting the hypothesis that renin's neutral optimum pH is due to the substrate-induced pK_a shifts of the aspartic dyad. The CpHMD data confirmed our previous hypothesis that hydrogen bond formation is the major determinant of the dyad pK_a order. Additionally, our simulations showed that renin's flap remains open regardless of pH, although a Tyr-inhibited state is occasionally formed above pH 5. These findings are discussed in comparison to the related aspartyl proteases, including β-secretases 1 and 2, cathepsin D, and plasmepsin II. Our work represents a first step toward a systematic understanding of the pH-dependent structure-dynamics-function relationships of pepsin-like aspartyl proteases that play important roles in biology and human disease states.

Alternative proton-binding site and long-distance coupling in Escherichia coli sodium-proton antiporter NhaA

Escherichia coli NhaA is a prototypical sodium-proton antiporter responsible for maintaining cellular ion and volume homeostasis by exchanging two protons for one sodium ion; despite two decades of research, the transport mechanism of NhaA remains poorly understood. Recent crystal structure and computational studies suggested Lys300 as a second proton-binding site; however, functional measurements of several K300 mutants demonstrated electrogenic transport, thereby casting doubt on the role of Lys300. To address the controversy, we carried out state-of-the-art continuous constant pH molecular dynamics simulations of NhaA mutants K300A, K300R, K300Q/D163N, and K300Q/D163N/D133A. Simulations suggested that K300 mutants maintain the electrogenic transport by utilizing an alternative proton-binding residue Asp133. Surprisingly, while Asp133 is solely responsible for binding the second proton in K300R, Asp133 and Asp163 jointly bind the second proton in K300A, and Asp133 and Asp164 jointly bind two protons in K300Q/D163N. Intriguingly, the coupling between Asp133 and Asp163 or Asp164 is enabled through the proton-coupled hydrogen-bonding network at the flexible intersection of two disrupted helices. These data resolve the controversy and highlight the intricacy of the compensatory transport mechanism of NhaA mutants. Alternative proton-binding site and proton sharing between distant aspartates may represent important general mechanisms of proton-coupled transport in secondary active transporters.

Interfacial water and ion distribution determine ζ potential and binding affinity of nanoparticles to biomolecules

The molecular features that dictate interactions between functionalized nanoparticles and biomolecules are not well understood. This is in part because for highly charged nanoparticles in solution, establishing a clear connection between the molecular features of surface ligands and common experimental observables such as ζ potential requires going beyond the classical models based on continuum and mean field models. Motivated by these considerations, molecular dynamics simulations are used to probe the electrostatic properties of functionalized gold nanoparticles and their interaction with a charged peptide in salt solutions. Counterions are observed to screen the bare ligand charge to a significant degree even at the moderate salt concentration of 50 mM. As a result, the apparent charge density and ζ potential are largely insensitive to the bare ligand charge densities, which fall in the range of ligand densities typically measured experimentally for gold nanoparticles. While this screening effect was predicted by classical models such as the Manning condensation theory, the magnitudes of the apparent surface charge from microscopic simulations and mean-field models are significantly different. Moreover, our simulations found that the chemical features of the surface ligand (e.g., primary vs. quaternary amines, heterogeneous ligand lengths) modulate the interfacial ion and water distributions and therefore the interfacial potential. The importance of interfacial water is further highlighted by the observation that introducing a fraction of hydrophobic ligands enhances the strength of electrostatic binding of the charged peptide. Finally, the simulations highlight that the electric double layer is perturbed upon binding interactions. As a result, it is the bare charge density rather than the apparent charge density or ζ potential that better correlates with binding affinity of the nanoparticle to a charged peptide. Overall, our study highlights the importance of molecular features of the nanoparticle/water interface and underscores a set of design rules for the modulation of electrostatic driven interactions at nano/bio interfaces.

GPU-Accelerated Implementation of Continuous Constant pH Molecular Dynamics in Amber: pKa Predictions with Single-pH Simulations

We present a GPU implementation of the continuous constant pH molecular dynamics (CpHMD) based on the most recent generalized Born implicit-solvent model in the pmemd engine of the Amber molecular dynamics package. To test the accuracy of the tool for rapid pK_a predictions, a series of 2 ns single-pH simulations were performed for over 120 titratable residues in 10 benchmark proteins that were previously used to test the various continuous CpHMD methods. The calculated pK_a's showed a root-mean-square deviation of 0.80 and correlation coefficient of 0.83 with respect to experiment. Also, 90% of the pK_a's were converged with estimated errors below 0.1 pH units. Surprisingly, this level of accuracy is similar to our previous replica-exchange simulations with 2 ns per replica and an exchange attempt frequency of 2 ps^-1 (Huang, Harris, and Shen J. Chem. Inf. Model. 2018 , 58 , 1372 - 1383 ). Interestingly, for the linked titration sites in two enzymes, although residue-specific protonation state sampling in the single-pH simulations was not converged within 2 ns, the protonation fraction of the linked residues appeared to be largely converged, and the experimental macroscopic pK_a values were reproduced to within 1 pH unit. Comparison with replica-exchange simulations with different exchange attempt frequencies showed that the splitting between the two macroscopic pK_a's is underestimated with frequent exchange attempts such as 2 ps^-1, while single-pH simulations overestimate the splitting. The same trend is seen for the single-pH vs replica-exchange simulations of a hydrogen-bonded aspartyl dyad in a much larger protein. A 2 ns single-pH simulation of a 400-residue protein takes about 1 h on a single NVIDIA GeForce RTX 2080 graphics card, which is over 1000 times faster than a CpHMD run on a single CPU core of a high-performance computing cluster node. Thus, we envision that GPU-accelerated continuous CpHMD may be used in routine pK_a predictions for a variety of applications, from assisting MD simulations with protonation state assignment to offering pH-dependent corrections of binding free energies and identifying reactive hot spots for covalent drug design.

Predicting Catalytic Proton Donors and Nucleophiles in Enzymes: How Adding Dynamics Helps Elucidate the Structure-Function Relationships

Despite the relevance of understanding structure-function relationships, robust prediction of proton donors and nucleophiles in enzyme active sites remains challenging. Here we tested three types of state-of-the-art computational methods to calculate the p K_a's of the buried and hydrogen bonded catalytic dyads in five enzymes. We asked the question what determines the p K_a order, i.e., what makes a residue proton donor vs a nucleophile. The continuous constant pH molecular dynamics simulations captured the experimental p K_a orders and revealed that the negative nucleophile is stabilized by increased hydrogen bonding and solvent exposure as compared to the proton donor. Surprisingly, this simple trend is not apparent from crystal structures and the static structure-based calculations. While the generality of the findings awaits further testing via a larger set of data, they underscore the role of dynamics in bridging enzyme structures and functions.

Complexity in pH-Dependent Ribozyme Kinetics: Dark pKa Shifts and Wavy Rate-pH Profiles

Charged bases occur in RNA enzymes, or ribozymes, where they play key roles in catalysis. Cationic bases donate protons and perform electrostatic catalysis, while anionic bases accept protons. We previously published simulations of rate-pH profiles for ribozymes in terms of species plots for the general acid and general base that have been useful for understanding how ribozymes respond to pH. In that study, we did not consider interaction between the general acid and general base or interaction with other species on the RNA. Since that report, diverse small ribozyme classes have been discovered, many of which have charged nucleobases or metal ions in the active site that can either directly interact and participate in catalysis or indirectly interact as "influencers". Herein, we simulate experimental rate-pH profiles in terms of species plots in which reverse protonated charged nucleobases interact. These analyses uncover two surprising features of pH-dependent enzyme kinetics. (1) Cooperativity between the general acid and general base enhances population of the functional forms of a ribozyme and manifests itself as hidden or "dark" pK_a shifts, real pK_a shifts that accelerate the reaction but are not readily observed by standard experimental approaches, and (2) influencers favorably shift the pK_as of proton-transferring nucleobases and manifest themselves as "wavy" rate-pH profiles. We identify parallels with the protein enzyme literature, including reverse protonation and wavelike behavior, while pointing out that RNA is more prone to reverse protonation. The complexities uncovered, which arise from simple pairwise interactions, should aid deconvolution of complex rate-pH profiles for RNA and protein enzymes and suggest veiled catalytic devices for promoting catalysis that can be tested by experiment and calculation.

Conformational dynamics of cathepsin D and binding to a small-molecule BACE1 inhibitor

BACE1 is a major therapeutic target for prevention and treatment of Alzheimer's disease. Developing inhibitors that can selectively target BACE1 in favor of other proteases, especially cathepsin D (CatD), has presented significant challenges. Here, we investigate the conformational dynamics and protonation states of BACE1 and CatD using continuous constant pH molecular dynamics with pH replica-exchange sampling protocol. Despite similar structure, BACE1 and CatD exhibit markedly different active site dynamics. BACE1 displays pH-dependent flap dynamics that controls substrate accessibility, while the CatD flap is relatively rigid and remains open in the pH range 2.5-6. Interestingly, although each protease hydrolyzes peptide bonds, the protonation states of the catalytic dyads are different within the active pH range. The acidic and basic components of the BACE1 catalytic dyad are clear, while either aspartic acid of the CatD catalytic dyad could play the role of acid or base. Finally, we investigate binding of the inhibitor LY2811376 developed by Eli Lilly to BACE1 and CatD. Surprisingly, in the enzyme active pH range, LY2811376 forms a stronger salt bridge with the catalytic dyad in CatD than in BACE1, which might explain the retinal toxicity of the inhibitor related to off-target inhibition of CatD. This work highlights the complexity and challenge in structure-based drug design where receptor-ligand binding induces protonation state change in both the protein and the inhibitor. © 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.

Monomolecular pyrenol-derivatives as multi-emissive probes for orthogonal reactivities

Chameleons in a test tube: up to four easily distinguishable emission colors result from conversion by two hydrolytic enzymes at opposite reaction sites.

Modelling the acid/base 1H NMR chemical shift limits of metabolites in human urine

INTRODUCTION

Despite the use of buffering agents the ¹H NMR spectra of biofluid samples in metabolic profiling investigations typically suffer from extensive peak frequency shifting between spectra. These chemical shift changes are mainly due to differences in pH and divalent metal ion concentrations between the samples. This frequency shifting results in a correspondence problem: it can be hard to register the same peak as belonging to the same molecule across multiple samples. The problem is especially acute for urine, which can have a wide range of ionic concentrations between different samples.

OBJECTIVES

To investigate the acid, base and metal ion dependent ¹H NMR chemical shift variations and limits of the main metabolites in a complex biological mixture.

METHODS

Urine samples from five different individuals were collected and pooled, and pre-treated with Chelex-100 ion exchange resin. Urine samples were either treated with either HCl or NaOH, or were supplemented with various concentrations of CaCl₂, MgCl₂, NaCl or KCl, and their ¹H NMR spectra were acquired.

RESULTS

Nonlinear fitting was used to derive acid dissociation constants and acid and base chemical shift limits for peaks from 33 identified metabolites. Peak pH titration curves for a further 65 unidentified peaks were also obtained for future reference. Furthermore, the peak variations induced by the main metal ions present in urine, Na⁺, K⁺, Ca²⁺ and Mg²⁺, were also measured.

CONCLUSION

These data will be a valuable resource for ¹H NMR metabolite profiling experiments and for the development of automated metabolite alignment and identification algorithms for ¹H NMR spectra.

Interpretation of pH-activity profiles for acid-base catalysis from molecular simulations

The measurement of reaction rate as a function of pH provides essential information about mechanism. These rates are sensitive to the pK(a) values of amino acids directly involved in catalysis that are often shifted by the enzyme active site environment. Experimentally observed pH-rate profiles are usually interpreted using simple kinetic models that allow estimation of "apparent pK(a)" values of presumed general acid and base catalysts. One of the underlying assumptions in these models is that the protonation states are uncorrelated. In this work, we introduce the use of constant pH molecular dynamics simulations in explicit solvent (CpHMD) with replica exchange in the pH-dimension (pH-REMD) as a tool to aid in the interpretation of pH-activity data of enzymes and to test the validity of different kinetic models. We apply the methods to RNase A, a prototype acid-base catalyst, to predict the macroscopic and microscopic pK(a) values, as well as the shape of the pH-rate profile. Results for apo and cCMP-bound RNase A agree well with available experimental data and suggest that deprotonation of the general acid and protonation of the general base are not strongly coupled in transphosphorylation and hydrolysis steps. Stronger coupling, however, is predicted for the Lys41 and His119 protonation states in apo RNase A, leading to the requirement for a microscopic kinetic model. This type of analysis may be important for other catalytic systems where the active forms of the implicated general acid and base are oppositely charged and more highly correlated. These results suggest a new way for CpHMD/pH-REMD simulations to bridge the gap with experiments to provide a molecular-level interpretation of pH-activity data in studies of enzyme mechanisms.

Multiscale methods for computational RNA enzymology

RNA catalysis is of fundamental importance to biology and yet remains ill-understood due to its complex nature. The multidimensional "problem space" of RNA catalysis includes both local and global conformational rearrangements, changes in the ion atmosphere around nucleic acids and metal ion binding, dependence on potentially correlated protonation states of key residues, and bond breaking/forming in the chemical steps of the reaction. The goal of this chapter is to summarize and apply multiscale modeling methods in an effort to target the different parts of the RNA catalysis problem space while also addressing the limitations and pitfalls of these methods. Classical molecular dynamics simulations, reference interaction site model calculations, constant pH molecular dynamics (CpHMD) simulations, Hamiltonian replica exchange molecular dynamics, and quantum mechanical/molecular mechanical simulations will be discussed in the context of the study of RNA backbone cleavage transesterification. This reaction is catalyzed by both RNA and protein enzymes, and here we examine the different mechanistic strategies taken by the hepatitis delta virus ribozyme and RNase A.

pH-dependent random coil (1)H, (13)C, and (15)N chemical shifts of the ionizable amino acids: a guide for protein pK a measurements

The pK a values and charge states of ionizable residues in polypeptides and proteins are frequently determined via NMR-monitored pH titrations. To aid the interpretation of the resulting titration data, we have measured the pH-dependent chemical shifts of nearly all the (1)H, (13)C, and (15)N nuclei in the seven common ionizable amino acids (X = Asp, Glu, His, Cys, Tyr, Lys, and Arg) within the context of a blocked tripeptide, acetyl-Gly-X-Gly-amide. Alanine amide and N-acetyl alanine were used as models of the N- and C-termini, respectively. Together, this study provides an essentially complete set of pH-dependent intra-residue and nearest-neighbor reference chemical shifts to help guide protein pK a measurements. These data should also facilitate pH-dependent corrections in algorithms used to predict the chemical shifts of random coil polypeptides. In parallel, deuterium isotope shifts for the side chain (15)N nuclei of His, Lys, and Arg in their positively-charged and neutral states were also measured. Along with previously published results for Asp, Glu, Cys, and Tyr, these deuterium isotope shifts can provide complementary experimental evidence for defining the ionization states of protein residues.

The intrinsic view of ionization equilibria of polyprotic molecules

The described intrinsic approach massively reduces the parameter number to describe microequilibria. The resulting intrinsic parameters yield insight into the protonation of polyprotic molecules.

Charge-leveling and proper treatment of long-range electrostatics in all-atom molecular dynamics at constant pH

Recent development of constant pH molecular dynamics (CpHMD) methods has offered promise for adding pH-stat in molecular dynamics simulations. However, until now the working pH molecular dynamics (pHMD) implementations are dependent in part or whole on implicit-solvent models. Here we show that proper treatment of long-range electrostatics and maintaining charge neutrality of the system are critical for extending the continuous pHMD framework to the all-atom representation. The former is achieved here by adding forces to titration coordinates due to long-range electrostatics based on the generalized reaction field method, while the latter is made possible by a charge-leveling technique that couples proton titration with simultaneous ionization or neutralization of a co-ion in solution. We test the new method using the pH-replica-exchange CpHMD simulations of a series of aliphatic dicarboxylic acids with varying carbon chain length. The average absolute deviation from the experimental pK(a) values is merely 0.18 units. The results show that accounting for the forces due to extended electrostatics removes the large random noise in propagating titration coordinates, while maintaining charge neutrality of the system improves the accuracy in the calculated electrostatic interaction between ionizable sites. Thus, we believe that the way is paved for realizing pH-controlled all-atom molecular dynamics in the near future.

Mechanistic insights into reversible photoactivation in proteins of the GFP family

Light-controlled modification of the fluorescence emission properties of proteins of the GFP family is of crucial importance for many imaging applications including superresolution microscopy. Here, we have studied the reversibly photoswitchable fluorescent protein mIrisGFP using optical spectroscopy. By analyzing the pH dependence of isomerization and protonation equilibria and the isomerization kinetics, we have obtained insight into the coupling of the chromophore to the surrounding protein moiety and a better understanding of the photoswitching mechanism. A different acid-base environment of the chromophore's protonating group in its two isomeric forms, which can be inferred from the x-ray structures of IrisFP, is key to the photoswitching function and ensures that isomerization and protonation are correlated. Amino acids near the chromophore, especially Glu212, rearrange upon isomerization, and Glu212 protonation modulates the chromophore pK(a). In mIrisGFP, the cis chromophore protonates in two steps, with pK(cis) of 5.3 and 6, which is much lower than pK(trans) (>10). Based on these results, we have put forward a mechanistic scheme that explains how the combination of isomeric and acid-base properties of the chromophore in its protein environment can produce negative and positive photoswitching modes.

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

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

Resolution of microscopic protonation enthalpies of polyprotic molecules by means of cluster expansions

Cluster expansion techniques are used to obtain microconstants and microenthalpies of protonation reactions. The approach relies on the analysis of macroscopic protonation constants and protonation enthalpies within a homologous series. Various linear aliphatic polyamines are considered, including 3,4-tri (spermidine), 3,4,3-tet (spermine), and 2,2,2,2-pent. Besides the full resolution of the microscopic protonation equilibria, one obtains information on the temperature dependence of the microstate probabilities. We find that the concentrations of the dominant microspecies increase with increasing temperature. Due to the large negative protonation enthalpies that are typical for amines, higher temperatures generally favor the less protonated species.

GMCT : a Monte Carlo simulation package for macromolecular receptors

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

Dissecting electrostatic interactions in Bacillus circulans xylanase through NMR-monitored pH titrations

NMR-monitored pH titration curves of proteins provide a rich source of structural and electrostatic information. Although relatively straightforward to measure, interpreting pH-dependent chemical shift changes to obtain site-specific acid dissociation constants (pK (A) values) is challenging. In order to analyze the biphasic titrations exhibited by the side chain (13)C(γ) nuclei of the nucleophilic Glu78 and general acid/base Glu172 in Bacillus circulans xylanase, we have revisited the formalism for the ionization equilibria of two coupled acidic residues. In general, fitting NMR-monitored pH titration curves for such a system will only yield the two macroscopic pK (A) values that reflect the combined effects of both deprotonation reactions. However, through the use of mutations complemented with ionic strength-dependent measurements, we are able to extract the four microscopic pK (Ai) values governing the branched acid/base equilibria of Glu78 and Glu172 in BcX. These data, confirmed through theoretical calculations, help explain the pH-dependent mechanism of this model GH11 xylanase by demonstrating that the kinetically determined pK (A) values and hence catalytic roles of these two residues result from their electrostatic coupling.

Determination of copper(II) ion concentration by lifetime measurements of green fluorescent protein

The understanding of cellular processes and functions and the elucidation of their physiological mechanisms is an important aim in the life sciences. One important aspect is the uptake and the release of essential substances as well as their interactions with the cellular environment. As green fluorescent protein (GFP) can be genetically encoded in cells it can be used as an internal sensor giving a deeper insight into biochemical pathways. Here we report that the presence of copper(II) ions leads to a decrease of the fluorescence lifetime (τ(fl)) of GFP and provide evidence for Förster resonance energy transfer (FRET) as the responsible quenching mechanism. We identify the His(6)-tag as the responsible binding site for Cu(2+) with a dissociation constant K(d) = 9 ± 2 μM and a Förster radius R(0) = 2.1 ± 0.1 nm. The extent of the lifetime quenching depends on [Cu(2+)] which is comprehended by a mathematical titration model. We envision that Cu(2+) can be quantified noninvasively and in real-time by measuring τ(fl) of GFP.

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

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