Elisa Bombarda

pH-Dependent pKa Values in Proteins—A Theoretical Analysis of Protonation Energies with Practical Consequences for Enzymatic Reactions

Because of their central importance for understanding enzymatic mechanisms, pK(a) values are of great interest in biochemical research. It is common practice to determine pK(a) values of amino acid residues in proteins from NMR or FTIR titration curves by determining the pH at which the protonation probability is 50%. The pH dependence of the free energy required to protonate this residue is then determined from the linear relationship DeltaG(prot) = RT ln 10 (pH-pK(a)), where R is the gas constant and T the absolute temperature. However, this approach neglects that there can be important electrostatic interactions in the proteins that can shift the protonation energy. Even if the titration curves seem to have a standard sigmoidal shape, the protonation energy of an individual site in a protein may depend nonlinearly on pH. To account for this nonlinear dependence, we show that it is required to introduce pK(a) values for individual sites in proteins that depend on pH. Two different definitions are discussed. One definition is based on a rearranged Henderson-Hasselbalch equation, and the other definition is based on an equation that was used by Tanford and Roxby to approximate titration curves of proteins. In the limiting case of weak interactions, the two definitions lead to nearly the same pK(a) value. We discuss how these two differently defined pK(a) values are related to the free energy change required to protonate a site. Using individual site pK(a) values, we demonstrate on simple model systems that the interactions between protonatable residues in proteins can help to maintain the energy required to protonate a site in the protein nearly constant over a wide pH range. We show with the example of RNase T1 that such a mechanism to keep the protonation energy constant is used in enzymes. The pH dependence of pK(a) values may be an important concept in enzyme catalysis. Neglecting this concept, important features of enzymes may be missed, and the enzymatic mechanism may not be fully understood.

Thermodynamics of Zn2+ binding to Cys2His2 and Cys2HisCys zinc fingers and a Cys4 transcription factor site.

The thermodynamics of Zn(2+) binding to three peptides corresponding to naturally occurring Zn-binding sequences in transcription factors have been quantified with isothermal titration calorimetry (ITC). These peptides, the third zinc finger of Sp1 (Sp1-3), the second zinc finger of myelin transcription factor 1 (MyT1-2), and the second Zn-binding sequence of the DNA-binding domain of glucocorticoid receptor (GR-2), bind Zn(2+) with Cys(2)His(2), Cys(2)HisCys, and Cys(4) coordination, respectively. Circular dichroism confirms that Sp1-3 and MyT1-2 have considerable and negligible Zn-stabilized secondary structure, respectively, and indicate only a small amount for GR-2. The pK(a)s of the Sp1-3 cysteines and histidines were determined by NMR and used to estimate the number of protons displaced by Zn(2+) at pH 7.4. ITC was also used to determine this number, and the two methods agree. Subtraction of buffer contributions to the calorimetric data reveals that all three peptides have a similar affinity for Zn(2+), which has equal enthalpy and entropy components for Sp1-3 but is more enthalpically disfavored and entropically favored with increasing Cys ligands. The resulting enthalpy-entropy compensation originates from the Zn-Cys coordination, as subtraction of the cysteine deprotonation enthalpy results in a similar Zn(2+)-binding enthalpy for all three peptides, and the binding entropy tracks with the number of displaced protons. Metal and protein components of the binding enthalpy and entropy have been estimated. While dominated by Zn(2+) coordination to the cysteines and histidines, other residues in the sequence affect the protein contributions that modulate the stability of these motifs.

On the involvement of electron transfer reactions in the fluorescence decay kinetics heterogeneity of proteins

Time‐resolved fluorescence study of single tryptophan‐containing proteins, nuclease, ribonuclease T1, protein G, glucagon, and mastoparan, has been carried out. Three different methods were used for the analysis of fluorescence decays: the iterative reconvolution method, as reviewed and developed in our laboratory, the maximum entropy method, and the recent method that we called “energy transfer” method. All the proteins show heterogeneous fluorescence kinetics (multiexponential decay). The origin of this heterogeneity is interpreted in terms of current theories of electron transfer process, which treat the electron transfer process as a radiationless transition. The theoretical electron transfer rate was calculated assuming the peptide bond carbonyl as the acceptor site. The good agreement between experimental and theoretical electron‐transfer rates leads us to suggest that the electron‐transfer process is the principal quenching mechanism of Trp fluorescence in proteins, resulting in heterogeneous fluorescence kinetics. Furthermore, the origin of apparent homogeneous fluorescence kinetics (monoexponential decay) in some proteins also can be explained on the basis of electron‐transfer mechanism.

Time-Resolved Fluorescence Investigation of the Human Immunodeficiency Virus Type 1 Nucleocapsid Protein: Influence of the Binding of Nucleic Acids

Depending on the HIV-1 isolate, MN or BH10, the nucleocapsid protein, NCp7, corresponds to a 55- or 71-amino acid length product, respectively. The MN NCp7 contains a single Trp residue at position 37 in the distal zinc finger motif, and the BH10 NCp7 contains an additional Trp, at position 61 in the C-terminal chain. The time-resolved intensity decay parameters of the zinc-saturated BH10 NCp7 were determined and compared to those of single-Trp-containing derivatives. The fluorescence decay of BH10 NCp7 could be clearly represented as a linear combination (with respect to both lifetimes and fractional intensities) of the individual emitting Trp residues. This suggested the absence of interactions between the two Trp residues, a feature that was confirmed by molecular modeling and fluorescence energy transfer studies. In the presence of tRNAPhe, taken as a RNA model, the same conclusions hold true despite the large fluorescence decrease induced by the binding of tRNAPhe. Indeed, the fluorescence of Trp37 appears almost fully quenched, in keeping with a stacking of this residue with the bases of tRNAPhe. Despite the multiple binding sites in tRNAPhe, the large prevalence of ultrashort lifetimes, associated with the stacking of Trp37, suggests that this stacking constitutes a major feature in the binding process of NCp7 to nucleic acids. In contrast, Trp61 only stacked to a small extent with tRNAPhe. The behavior of this residue in the tRNAPhe-NCp7 complexes appeared to be rather heterogeneous, suggesting that it does not constitute a major determinant in the binding process. Finally, our data suggested that the binding of NCp7 proteins from the two HIV-1 strains to nonspecific nucleic acid sequences was largely similar.

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.

Continuum electrostatic investigations of charge transfer processes in biological molecules using a microstate description

Charge transfer through biological macromolecules is essential for many biological processes such as for instance photosynthesis and respiration. In these processes, protons or electrons are transferred between titratable residues or redox-active cofactors, respectively. Often their transfer is tightly coupled. Computational methods based on continuum electrostatics are widely used in theoretical biochemistry to analyze the function of even very complex biochemical systems. These methods allow one to consider the pH and the redox potential of the solution as well as explicitly considering membrane potentials in the calculations. Combining continuum electrostatic calculations with a statistical thermodynamic analysis, it is possible to calculate equilibrium parameters such as protonation or oxidation probabilities. Moreover, it is also possible to simulate reaction kinetics by using parameters calculated from continuum electrostatics. One needs to consider that the transfer rate between two sites depends on the current charge configuration of neighboring sites. 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. This 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 rate law to obtain electron transfer rate constants. The relaxation electron transfer kinetics after photo-oxidation of the special pair of photosynthetic reaction center is simulated by a microstate formalism and it is shown to be in good agreement with experimental data. A flux analysis is used to follow the individual electron transfer steps. This method of simulating the complex kinetics of biomolecules based on structural data is a first step on the way from structural biology to systems biology.

pK(a) values and redox potentials of proteins. What do they mean

Abstract In this article, we review a microstate model that uses protonation and redox microstates in order to understand the complex pH and redox titration of proteins and other polyelectrolytes. From this model, it becomes obvious that it is impossible to assign pKa values or redox potentials to individual protonatable or redox-active sites in a protein in which many of such sites interact. Instead each site is associated with many microscopic equilibrium constants that may lead to irregular or even non-monotonic titration curves of some groups. The microstate model provides a closed theoretical framework to discuss such phenomena.

Continuum Electrostatic Analysis of Proteins

Electrostatic interactions play an important role in many biochemical processes. The continuum electrostatics model, which originates from the Poisson-Boltzmann equation, provides a framework to represent the electrostatics properties of proteins together with their ligands and how these properties are influenced by the solvent; all this with limited computational costs. Therefore, methods based on continuum electrostatics are ideal to analyze bio-molecular processes in their own environment. In this review, first we illustrate the physical basis of the Poisson-Boltzmann equation, then we discuss the strategy to obtain its solution, i.e. the electrostatic potential, and which information can be deducted from it. Afterwards, we report how methods based on continuum electrostatics can be applied to analyze the interactions of proteins, in particular electron transfer proteins, and to calculate the probabilities of protonation and redox states of proteins. Furthermore, we outline how continuum electrostatics allows to access also the non-equilibrium behavior of bio-molecular systems.

Continuum Electrostatic Calculation on Bovine Rhodopsin: Protonation and the Effect of the Membrane Potential

In this work, we calculate the protonation probabilities of titratable residues of bovine rhodopsin using the Poisson–Boltzmann equation. We also consider the influence of the membrane potential. Our results indicate that at physiological pH, the titratable groups directly involved in photosensing, namely Glu113, Glu181 and the retinal Schiff base, are charged. In contrast, the residues Asp83, Glu122 and His211, which are buried in the membrane, are uncharged. However, as these later residues are localized in the middle of the membrane, they are exposed to the membrane potential more strongly, which may have important functional implications. Despite of their large distance, Asp83 and Glu122 interact relatively strongly. As these two residues are in contact with opposite sides of the membrane, the membrane potential has different effects on them, which allows an enhancement of the membrane potential signal. An analysis of the different contributions to the protonation energy indicates that conformational changes that reduce the desolvation penalty of Asp83, Glu122 and His211 may lead to a complex protonation pattern change that allows an influence of the membrane potential on the function of rhodopsin. The high degree of evolutionary conservation of these three buried residues supports the idea of their functional importance. Our results are in‐line with many experimental findings and lead to new ideas that can be experimentally tested.

Theoretical Analysis of Electron Transfer in Proteins: From Simple Proteins to Complex Machineries

Electron transferplays a central role in many biological processes such as, for instance, photosynthesis or oxidative phosphorylation, but also in other bioenergetic processes such as denitrification or sulfate and sulfite reduction. Moreover, electron transfer is a key step in many enzymatic reactions. The framework of Marcus theory provides the theoretical basis to describe the kinetics of these reactions. The parameters to calculate rate constants can be estimated using protein crystal structures. Namely, the electronic coupling is related to the edge-to-edge distance between the redox-active sites. The reaction free energy and the reorganization energy can be obtained, for instance, from continuum electrostatic calculations. However, to perform complicated tasks, proteins often combine many redox cofactors and couple the redox reactions to protonation reactions or conformational changes. Moreover, electron transfer proteins are often embedded in membranes, and thus membrane potential and concentration gradients influence the reactions. One approach to describe such complex systems is the so-called microstate model, in which each state of a system is represented by a vector in which each component defines the status of each site (for instance oxidized or reduced, protonated or deprotonated). On the basis of this microstate description, it is possible to calculate the thermodynamics and kinetics of a complex protein system. In this article, we will review the principle features of the microstate model and explain how the parameters of the microstate model can be calculated using continuum electrostatics. The microstate model provides the theoretical framework to go from molecular structures to the mechanism of complex protein machines.