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

On the reliability of the corrected semiempirical quantum chemical method (PM6-DH2) for assigning the protonation states in HIV-1 protease/inhibitor complexes

A novel computational protocol for determining the most probable protonation states in protein/ligand complexes is presented. The method consists in treating large parts of the enzyme using the corrected semiempirical quantum chemical (QM) method – PM6-D2 for optimization and PM6-DH2 for single-point energies – while the rest is calculated using molecular mechanics (MM) within a hybrid QM/MM fashion. The surrounding solvent is approximated by an implicit model. This approach is applied to two model systems, two different carboxylate pairs in one general and one unique HIV-1 protease/inhibitor complex. The effect of the size of the movable QM part is investigated in a series of several sizes, 3-, 6-, 8- and 10-Å regions surrounding the inhibitor. For the smallest region (< 450 atoms) the computationally more costly DFT QM/MM optimizations are performed as a check of the correctness. Proton transfer (PT) phenomena occur at both the PM6-D2 and DFT levels, which underlines the requirement for a QM approach. The barriers of PT are checked in model carboxylic acid pairs using the highly accurate MP2 and CCSD(T) values. An important result of this study is the fine-tuning of the protocol which can be used in further applications; its limitations are also shown, pointing to future developments. The calculations reveal which protonation variants of the active site are the most stable. In conclusion, the presented protocol can also be utilized for defining probable isomers in biomolecular systems. It can also serve as a preparatory step for further interaction-energy and binding-score calculations.

Mechanistic insights into ferredoxin-NADP(H) reductase catalysis involving the conserved glutamate in the active site

Plant-type ferredoxin-NADP(H) reductases (FNRs) are flavoenzymes harboring one molecule of noncovalently bound flavin adenine dinucleotide that catalyze reversible reactions between obligatory one-electron carriers and obligatory two-electron carriers. A glutamate next to the C-terminus is strictly conserved in FNR and has been proposed to function as proton donor/acceptor during catalysis. However, experimental studies of this proposed function led to contradicting conclusions about the role of this glutamate in the catalytic mechanism. In the present work, we study the titration behavior of the glutamate in the active site of FNR using theoretical methods. Protonation probabilities for maize FNR were computed for the reaction intermediates of the catalytic cycle by Poisson-Boltzmann electrostatic calculations and Metropolis Monte Carlo titration. The titration behavior of the highly conserved glutamate was found to vary depending on the bound substrates NADP(H) and ferredoxin and also on the redox states of these substrates and the flavin adenine dinucleotide. Our results support the involvement of the glutamate in the FNR catalytic mechanism not only as a proton donor but also as a key residue for stabilizing and destabilizing reaction intermediates. On the basis of our findings, we propose a model rationalizing the function of the glutamate in the reaction cycle, which allows reinterpretation of previous experimental results.

Predicting pKa

One of the most important physicochemical properties of small molecules and macromolecules are the dissociation constants for any weakly acidic or basic groups, generally expressed as the pK(a) of each group. This is a major factor in the pharmacokinetics of drugs and in the interactions of proteins with other molecules. For both the protein and small molecule cases, we survey the sources of experimental pK(a) values and then focus on current methods for predicting them. Of particular concern is an analysis of the scope, statistical validity, and predictive power of methods as well as their accuracy.

Novel isosteric charge-deficient spermine analogue--1,12-diamino-3,6,9-triazadodecane: synthesis, pK(a) measurement and biological activity

Ionic interactions are essential for the biological functions of the polyamines spermidine and spermine in mammalian physiology. Here, we describe a simple gram scale method to prepare 1,12-diamino-3,6,9-triazadodecane (SpmTrien), an isosteric charge-deficient spermine analogue. The protonation sites of SpmTrien were determined at pH range of 2.2-11.0 using two-dimensional (1)H-(15)N NMR spectroscopy, which proved to be more feasible than conventional methods. The macroscopic pK(a) values of SpmTrien (3.3, 6.3, 8.5, 9.5 and 10.3) are significantly lower than those of 1,12-diamino-4,9-diazadodecane (spermine). The effects of SpmTrien and its parent molecule, 1,8-diamino-3,6-diazaoctane (Trien), on cell growth and polyamine metabolism were investigated in DU145 prostate carcinoma cells. SpmTrien downregulated the biosynthetic enzymes ornithine decarboxylase (ODC) and S-adenosyl-L: -methionine decarboxylase and decreased intracellular polyamine levels, whereas the effects of Trien alone were minor. Interestingly, both SpmTrien and Trien were able to partially overcome growth arrest induced by an ODC inhibitor, alpha-difluoromethylornithine, indicating that they are able to mimic some functions of the natural polyamines. Thus, SpmTrien is a novel tool to influence polyamine interaction sites at the molecular level and offers a new means to study the contribution of the protonation of spermine amino group(s) in the regulation of polyamine-dependent biological processes.

Simulating the proton transfer in gramicidin A by a sequential dynamical Monte Carlo method

The large interest in long-range proton transfer in biomolecules is triggered by its importance for many biochemical processes such as biological energy transduction and drug detoxification. Since long-range proton transfer occurs on a microsecond time scale, simulating this process on a molecular level is still a challenging task and not possible with standard simulation methods. In general, the dynamics of a reactive system can be described by a master equation. A natural way to describe long-range charge transfer in biomolecules is to decompose the process into elementary steps which are transitions between microstates. Each microstate has a defined protonation pattern. Although such a master equation can in principle be solved analytically, it is often too demanding to solve this equation because of the large number of microstates. In this paper, we describe a new method which solves the master equation by a sequential dynamical Monte Carlo algorithm. Starting from one microstate, the evolution of the system is simulated as a stochastic process. The energetic parameters required for these simulations are determined by continuum electrostatic calculations. We apply this method to simulate the proton transfer through gramicidin A, a transmembrane proton channel, in dependence on the applied membrane potential and the pH value of the solution. As elementary steps in our reaction, we consider proton uptake and release, proton transfer along a hydrogen bond, and rotations of water molecules that constitute a proton wire through the channel. A simulation of 8 mus length took about 5 min on an Intel Pentium 4 CPU with 3.2 GHz. We obtained good agreement with experimental data for the proton flux through gramicidin A over a wide range of pH values and membrane potentials. We find that proton desolvation as well as water rotations are equally important for the proton transfer through gramicidin A at physiological membrane potentials. Our method allows to simulate long-range charge transfer in biological systems at time scales, which are not accessible by other methods.

Determination of the microscopic equilibrium dissociation constants for risedronate and its analogues reveals two distinct roles for the nitrogen atom in nitrogen-containing bisphosphonate drugs

Microscopic equilibrium dissociation constants, k as, were determined for four nitrogen-containing bisphosphonates (N-BP): risedronate and its analogues 2-(2-aminophenyl)-1-hydroxyethylidene-1,1-bisphosphonate, NE 11807, and NE 97220. The proportion of each and of analogues 2-(3'-( N-ethyl)pyridinium)-ethylidenebisphosphonate and 2-(3-piperinidyl)-1-hydroxyethylidene-1,1-bisphosphonate, having a positively charged nitrogen and three negative charges on the bisphosphonate group ("carbocation analogue") at pH 7.5, was calculated. When set in order of increasing potency at inhibiting farnesyl diphosphate (FDP) synthase (their intracellular target), the N-BPs are also ranked in order of decreasing mole fraction of carbocation analogue. However, only a weak correlation exists between potency for inhibiting FDP synthase and potency for inhibiting Dictyostelium discoideum growth. It is concluded that, although high potency for inhibiting FDP synthase is favored when the nitrogen atom in a N-BP is uncharged, N-BPs having a positively charged nitrogen can still be potent inhibitors of Dictyostelium growth owing to favorable interaction with a second, unidentified target.

Investigating the mechanisms of photosynthetic proteins using continuum electrostatics

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

Protein-protein binding is often associated with changes in protonation state

pK(a) values of ionizable residues have been calculated using the PROPKA method and structures of 75 protein-protein complexes and their corresponding free forms. These pK(a) values were used to compute changes in protonation state of individual residues, net changes in protonation state of the complex relative to the uncomplexed proteins, and the correction to a binding energy calculated assuming standard protonation states at pH 7. For each complex, two different structures for the uncomplexed form of the proteins were used: the X-ray structures determined for the proteins in the absence of the other protein and the individual protein structures taken from the structure of the complex (referred to as unbound and bound structures, respectively). In 28 and 77% of the cases considered here, protein-protein binding is accompanied by a complete (>95%) or significant (>50%) change in protonation state of at least one residue using unbound structures. Furthermore, in 36 and 61% of the cases, protein-protein binding is accompanied by a complete or significant net change in protonation state of the complex relative to the separated monomers. Using bound structures, the corresponding values are 12, 51, 20, and 48%. Comparison to experimental data suggest that using unbound and bound structures lead to over- and underestimation of binding-induced protonation state changes, respectively. Thus, we conclude that protein-protein binding is often associated with changes in protonation state of amino acid residues and with changes in the net protonation state of the proteins. The pH-dependent correction to the binding energy contributes at least one order of magnitude to the binding constant in 45 and 23%, using unbound and bound structures, respectively.

New protonation microequilibrium treatment in the case of some amino acid and peptide derivatives containing a bis(imidazolyl)methyl group

We present a microequilibrium analysis of a series of amino acid and peptide derivatives containing the chelating bis(imidazol-2-yl)methyl group (BIP, Gly-BIMA, His-BIMA, alpha-Glu-BIMA, gamma-Glu-BIMA, and Phe-His-BIMA). NMR measurements were performed in D2O to follow the deprotonation steps. The software PSEQUAD and a specialized program written in MATLAB were used to determine the macroscopic and microscopic constants. The method assumes that the effect of pH on the chemical shift of an NMR-active nucleus can be interpreted by adding the independent effects of the protonation of individual sites. For derivatives containing histidine (His-BIMA and Phe-His-BIMA), the deprotonation steps of the second imidazole and the His-imidazole significantly overlap. In the Glu derivatives (alpha-Glu-BIMA and gamma-Glu-BIMA), the amino and the second imidazole pK values are separate; the deprotonation processes of the first imidazole nitrogen and the side-chain carboxyl group, however, significantly overlap. In gamma-Glu-BIMA, the deprotonation sequence is carboxylate-imidazole1-imidazole2-amino, while in the case of alpha-Glu-BIMA, it changes to imidazole1-carboxylate-imidazole2-amino, according to the microscopic pk values. The main advantage of the method is that it does not require the synthesis and NMR microequilibrium analysis of substances modeling the individual parts of the target ligand, in contrast to the methods used by others. The method presented here demands slightly more mathematical and computational power, which is readily available today.

Green Fluorescent Protein Ground States: The Influence of a Second Protonation Site near the Chromophore,

The photophysical properties of most green fluorescent protein mutants (GFPs) are strongly affected by pH. This effect must be carefully taken into account when using GFPs as fluorescent probes or indicators. Usually, the pH-dependence of GFPs is rationalized on the basis of the ionization equilibrium of the chromophore phenol group. Yet many different mutants show spectral behavior that cannot be explained by ionization of this group alone. In this study, we propose a general model of protonation comprising two ionization sites (2S model). Steady-state optical measurements at different pH and temperature and pH-jump relaxation experiments were combined to highlight the thermodynamic and kinetic properties of paradigmatically different GFP variants. Our experiments support the 2S model. For the case of mutants in which E222 is the second protonation site, thermodynamic coupling between this residue's and the chromophore's ionization reactions was demonstrated. In agreement with the 2S model predictions, X-ray analysis of one of these mutants showed the presence of two chromophore populations at high pH.

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

Charge transfer through biological macromolecules is essential for many biological processes such as, for instance, photosynthesis and respiration. Protons or electrons are transferred between titratable residues or redox-active cofactors, respectively. Transfer rates between these sites depend on the current charge configuration of neighboring sites. Here, we formulate the kinetics of charge-transfer systems in a microstate formalism. A unique transfer rate constant can be assigned to the interconversion of microstates. Mutual interactions between sites participating in the transfer reactions are naturally taken into account. The formalism is applied to the kinetics of electron transfer in the tetraheme subunit and the special pair of the reaction center of Blastochloris viridis. It is shown that continuum electrostatic calculations can be used in combination with an existing empirical rate law to obtain electron-transfer rate constants. The re-reduction kinetics of the photo-oxidized special pair simulated in a microstate formalism is shown to be in good agreement with experimental data. A flux analysis is used to follow the individual electron-transfer steps.

Influence of the Membrane Potential on the Protonation of Bacteriorhodopsin: Insights from Electrostatic Calculations into the Regulation of Proton Pumping

Proton binding and release are elementary steps for the transfer of protons within proteins, which is a process that is crucial in biochemical catalysis and biological energy transduction. Local electric fields in proteins affect the proton binding energy compared to aqueous solution. In membrane proteins, also the membrane potential affects the local electrostatics and can thus be crucial for protein function. In this paper, we introduce a procedure to calculate the protonation probability of titratable sites of a membrane protein in the presence of a membrane potential. In the framework of continuum electrostatics, we use a modified Poisson-Boltzmann equation to include the influence of the membrane potential. Our method considers that in a transmembrane protein each titratable site is accessible for protons from only one side of the membrane depending on the hydrogen bond pattern of the protein. We show that the protonation of sites receiving their protons from different sides of the membrane is differently influenced by the membrane potential. In addition, the effect of the membrane potential is combined with the effect of the pH gradient resulting from proton pumping. Our method is applied to bacteriorhodopsin, a light-activated proton pump. We find that the proton pumping of this protein might be regulated by Asp115, a conserved residue for which no function has been identified yet. According to our calculations, the interaction of Asp115 with Asp85 leads to the protonation of the latter if the pH gradient or the membrane potential becomes too large. Since Asp85 is the primary proton acceptor in the photocycle, bacteriorhodopsin molecules in which Asp85 is protonated cannot pump protons. Furthermore, we estimate how the membrane potential affects the energetics of the individual proton-transfer reactions of the photocycle. Most reactions, except the initial proton transfer from the Schiff base to Asp85, are influenced. Our calculations give new insights into the mechanism with which bacteriorhodopsin senses the membrane potential and the pH gradient and how the proton pumping is regulated by these parameters.

Theoretical investigation of the behavior of titratable groups in proteins

This paper presents a theoretical analysis of the titration behavior of strongly interacting titratable residues in proteins. Strongly interacting titratable residues exist in many proteins such as for instance bacteriorhodopsin, cytochrome c oxidase, cytochrome bc(1), or the photosynthetic reaction center. Strong interaction between titratable groups can lead to irregular titration behavior. We analyze under which circumstances titration curves can become irregular. We demonstrate that conformational flexibility alone can not lead to irregular titration behavior. Strong interaction between titratable groups is a necessary, but not sufficient condition for irregular titration curves. In addition, the two interacting groups also need to titrate in the same pH-range. These two conditions together lead to irregular titration curves. The mutation of a single residue within a cluster of interacting titratable residues can influence the titration behavior of the other titratable residues in the cluster. We demonstrate this effect on a cluster of four interacting residues. This example underlines that mutational studies directed at identifying the role of a certain titratable residue in a cluster of interacting residues should always be accompanied by an analysis of the effect of the mutation on the titration behavior of the other residues.

Solid–liquid interfacial energy as a tool to estimate shifts in isoelectric points of adsorbed proteins on solid surfaces

This work reports the estimation of isoelectric points (pIs) of adsorbed amino acids and proteins on solid surfaces in the pH range between 3.5-11.0 from a measurement of solid/liquid interfacial energy. The values thus obtained are compared with the pIs determined in solution phase by other methods. Both glass and Teflon have been chosen as model solid surfaces. Close agreement between the reference pI values, obtained by the capillary isoelectric focusing and those obtained at solid/liquid interface is observed within an average difference of 0.04-0.08 pH unit when the pIs are above the pI of glass. For systems whose pIs are far away from that of glass (either in the acidic or highly alkaline range), a large shift in the isoelectric point is observed. In case of Teflon the pIs are closer to the reported values than at glass/liquid interface. This could be due to the fact that Teflon being a hydrophobic surface, its surface is dominated by dispersive forces, which may not be seriously affected by pH changes. The shift in the values at solid/liquid interface compared to that in solution have been examined using an 'image charge approach.'

Negatively Charged Residues and Hydrogen Bonds Tune the Ligand Histidine pKa Values of Rieske Iron−Sulfur Proteins

Rieske proteins carry a redox-active iron-sulfur cluster, which is bound by two histidine and two cysteine side chains. The reduction potential of Rieske proteins depends on pH. This pH dependence can be described by two pK(a) values, which have been assigned to the two iron-coordinating histidines. Rieske proteins are commonly grouped into two major classes: Rieske proteins from quinol-oxidizing cytochrome bc complexes, in which the ligand histidines titrate in the physiological pH range, and bacterial ferredoxin Rieske proteins, in which the ligand histidines are protonated at physiological pH. In the study presented here, we have calculated pK(a) values of the cluster ligand histidines using a combined density functional theory/continuum electrostatics approach. Experimental pK(a) values for a bc-type and a ferredoxin Rieske protein could be reproduced. We could identify functionally important differences between the two proteins: hydrogen bonds toward the cluster, which are present in bc-type Rieske proteins, and negatively charged residues, which are present in ferredoxin Rieske proteins. We removed these differences by mutating the proteins in our calculations. The Rieske centers in the mutated proteins have very similar pK(a) values. We thus conclude that the studied structural differences are the main reason for the different pH-titration behavior of the proteins. Interestingly, the shift caused by neutralizing the negative charges in ferredoxin Rieske proteins is larger than the shift caused by removing the hydrogen bonds toward the cluster in bc-type Rieske proteins.

The Influence of a Transmembrane pH Gradient on Protonation Probabilities of Bacteriorhodopsin: The Structural Basis of the Back-Pressure Effect

Bacteriorhodopsin pumps protons across a membrane using the energy of light. The proton pumping is inhibited when the transmembrane proton gradient that the protein generates becomes larger than four pH units. This phenomenon is known as the back-pressure effect. Here, we investigate the structural basis of this effect by predicting the influence of a transmembrane pH gradient on the titration behavior of bacteriorhodopsin. For this purpose we introduce a method that accounts for a pH gradient in protonation probability calculations. The method considers that in a transmembrane protein, which is exposed to two different aqueous phases, each titratable residue is accessible for protons from one side of the membrane depending on its hydrogen-bond pattern. This method is applied to several ground-state structures of bacteriorhodopsin, which residues already present complicated titration behaviors in the absence of a proton gradient. Our calculations show that a pH gradient across the membrane influences in a non-trivial manner the protonation probabilities of six titratable residues which are known to participate in the proton transfer: D85, D96, D115, E194, E204, and the Schiff base. The residues connected to one side of the membrane are influenced by the pH on the other side because of their long-range electrostatic interactions within the protein. In particular, D115 senses the pH at the cytoplasmic side of the membrane and transmits this information to D85 and the Schiff base. We propose that the strong electrostatic interactions found between D85, D115, and the Schiff base as well as the interplay of their respective protonation states under the influence of a transmembrane pH gradient are responsible for the back-pressure effect on bacteriorhodopsin.