Electrostatics of Proteins: Principles, Models and Applications

Braun‐Sand, Sonja; Warshel, Arieh

doi:10.1002/9783527619498.ch7

Cited by 9 publications

(20 citation statements)

References 202 publications

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“…In fact, our early related prediction65 has been confirmed experimentally in the case of triosephosphate isomerse 74. Furthermore, our prediction75 of the small effect of the Helix dipole in the KscA channel has been just confirmed experimentally 76…”

Section: Discussionsupporting

confidence: 73%

The barrier for proton transport in aquaporins as a challenge for electrostatic models: The role of protein relaxation in mutational calculations

2006

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The origin of the barrier for proton transport through the aquaporin channel is a problem of general interest. It is becoming increasingly clear that this barrier is not attributable to the orientation of the water molecules across the channel but rather to the electrostatic penalty for moving the proton charge to the center of the channel. However, the reason for the high electrostatic barrier is still rather controversial. It has been argued by some workers that the barrier is due to the so-called NPA motif and/or to the helix macrodipole or to other specific elements. However, our works indicated that the main reason for the high barrier is the loss of the generalized solvation upon moving the proton charge from the bulk to the center of the channel and that this does not reflect a specific repulsive electrostatic interaction but the absence of sufficient electrostatic stabilization. At this stage it seems that the elucidation and clarification of the origin of the electrostatic barrier can serve as an instructive test case for electrostatic models. Thus, we reexamine the free-energy surface for proton transport in aquaporins using the microscopic free-energy perturbation/umbrella sampling (FEP/US) and the empirical valence bond/umbrella sampling (EVB/US) methods as well as the semimacroscopic protein dipole Langevin dipole model in its linear response approximation version (the PDLD/S-LRA). These extensive studies help to clarify the nature of the barrier and to establish the "reduced solvation effect" as the primary source of this barrier. That is, it is found that the barrier is associated with the loss of the generalized solvation energy (which includes of course all electrostatic effects) upon moving the proton charge from the bulk solvent to the center of the channel. It is also demonstrated that the residues in the NPA region and the helix dipole cannot be considered as the main reasons for the electrostatic barrier. Furthermore, our microscopic and semimacroscopic studies clarify the problems with incomplete alternative calculations, illustrating that the effects of various electrostatic elements are drastically overestimated by macroscopic calculations that use a low dielectric constant and do not consider the protein reorganization. Similarly, it is pointed out that microscopic potential of mean force calculations that do not evaluate the electrostatic barrier relative to the bulk water cannot be used to establish the origin of the electrostatic barrier. The relationship between the present study and calculations of pK(a)s in protein interiors is clarified, pointing out that approaches that are applied to study the aquaporin barrier should be validated by pK(a)s calculations. Such calculations also help to clarify the crucial role of solvation energies in establishing the barrier in aquaporins.

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Section: Discussionsupporting

confidence: 73%

The barrier for proton transport in aquaporins as a challenge for electrostatic models: The role of protein relaxation in mutational calculations

2006

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“…Soon thereafter, Linderstrom‐Lang recognized that the net charge on a protein would influence the ionization of individual groups, and incorporated this into the first model developed to understand the acid/base properties of a protein (Linderstrom‐Lang 1924). An important contribution by Tanford and Kirkwood triggered an intense interest in the factors that determine the pK values of the ionizable groups of proteins that continues to the present day (Tanford and Kirkwood 1957; Braun‐Sand and Warshel 2005). The net charge on a protein varies with pH, and is determined by the content and the pK values of the ionizable groups (Tanford 1962).…”

Section: Pk Values For the Ionizable Groups In Proteins From The Litementioning

confidence: 99%

pK values of the ionizable groups of proteins

et al. 2006

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We have used potentiometric titrations to measure the pK values of the ionizable groups of proteins in alanine pentapeptides with appropriately blocked termini. These pentapeptides provide an improved model for the pK values of the ionizable groups in proteins. Our pK values determined in 0.1 M KCl at 25°C are: 3.67 6 0.03 (a-carboxyl), 3.67 6 0.04 (Asp), 4.25 6 0.05 (Glu), 6.54 6 0.04 (His), 8.00 6 0.03 (a-amino), 8.55 6 0.03 (Cys), 9.84 6 0.11 (Tyr), and 10.40 6 0.08 (Lys). The pK values of some groups differ from the Nozaki and Tanford (N&T) pK values often used in the literature: Asp (3.67 this work vs. 4.0 N&T); His (6.54 this work vs. 6.3 N&T); a-amino (8.00 this work vs. 7.5 N&T); Cys (8.55 this work vs. 9.5 N&T); and Tyr (9.84 this work vs. 9.6 N&T). Our pK values will be useful to those who study pK perturbations in folded and unfolded proteins, and to those who use theory to gain a better understanding of the factors that determine the pK values of the ionizable groups of proteins.Keywords: pK values; protein ionizable groups; pH titration; peptide model compounds The acid/base properties of proteins have been studied since 1917, when Sorensen, who first defined pH in 1909, showed that egg albumin is an ampholyte (Sorensen et al. 1917). Soon thereafter, Linderstrom-Lang recognized that the net charge on a protein would influence the ionization of individual groups, and incorporated this into the first model developed to understand the acid/base properties of a protein (Linderstrom-Lang 1924). An important contribution by Tanford and Kirkwood triggered an intense interest in the factors that determine the pK values of the ionizable groups of proteins that continues to the present day (Tanford and Kirkwood 1957;Braun-Sand and Warshel 2005). The net charge on a protein varies with pH, and is determined by the content and the pK values of the ionizable groups (Tanford 1962). Thus, the pK values of the ionizable groups are important to biochemists because they influence the structure, stability, solubility, and the many functions of proteins (Tanford 1968;Pace 1975;Fersht 1985;Matthew et al. 1985;Anderson et al. 1990;Ries-Kautt and Ducruix 1997;Shaw et al. 2001;Bartlett et al. 2002).In early studies aimed at interpreting titration curves of proteins, Tanford (1962) introduced the term intrinsic pK (pK int ). He defined the term as the pK an ionizable group would have when the net charge on the molecule is zero. When proteins fold, the perturbations of the pKs of the ionizable groups on the surface of the protein from the pK int values are usually small, and are determined mainly by charge-charge interactions with other ionizable groups (Laurents et al. 2003). However, if these groups are partially or fully buried in the protein interior, large positive and negative perturbations often occur, and it is important that we understand why (Schutz and Warshel 2001). Experimental studies of these perturbations have been reported by several groups (see, for example, Garcia-Moreno et al. 1997;Giletto and Pac...

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“…enzyme catalysis22,24,124–126, proton transport, electron transport127, protein-protein interactions128–132, and molecular motors125). For both classes it is crucial to have the ability to accurately evaluate the corresponding electrostatic energy if we are interested in any quantitative structure function correlation in proteins104,133–143. Here, we will focus only on the first class and even in this case we will mainly consider solvation and pK a calculations by ab initio QM/MM-FEP approaches.…”

Section: Introductionmentioning

confidence: 99%

Progress in Ab Initio QM/MM Free-Energy Simulations of Electrostatic Energies in Proteins: Accelerated QM/MM Studies of pK_a, Redox Reactions and Solvation Free Energies

2008

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Hybrid quantum mechanical / molecular mechanical (QM/MM) approaches have been used to provide a general scheme for chemical reactions in proteins. However, such approaches still present a major challenge to computational chemists, not only because of the need for very large computer time in order to evaluate the QM energy but also because of the need for proper computational sampling. This review focuses on the sampling issue in QM/MM evaluations of electrostatic energies in proteins. We chose this example since electrostatic energies play a major role in controlling the function of proteins and are key to the structure-function correlation of biological molecules. Thus, the correct treatment of electrostatics is essential for the accurate simulation of biological systems. Although we will be presenting here different types of QM/MM calculations of electrostatic energies (and related properties), our focus will be on pK a calculations. This reflects the fact that pK a of ionizable groups in proteins provide one of the most direct benchmarks for the accuracy of electrostatic models of macromolecules. While pK a calculations by semimacroscopic models have given reasonable results in many cases, existing attempts to perform pK a calculations using QM/ MM-FEP have led to large discrepancies between calculated and experimental values. In this work, we accelerate our QM/MM calculations using an updated mean charge distribution and a classical reference potential. We examine both a surface residue (Asp3) of the bovine pancreatic trypsin inhibitor, as well as a residue buried in a hydrophobic pocket (Lys102) of the T4-lysozyme mutant. We demonstrate that by using this approach, we are able to reproduce the relevant sidechain pK a s with an accuracy of 3 kcal/mol. This is well within the 7 kcal/mol energy difference observed in studies of enzymatic catalysis, and is thus sufficient accuracy to determine the main contributions to the catalytic energies of enzymes. We also provide an overall perspective of the potential of QM/ MM calculations in general evaluations of electrostatic free energies, pointing out that our approach should provide a very powerful and accurate tool to predict the electrostatics of not only solution but also enzymatic reactions, as well as the solvation free energies of even larger systems, such as nucleic acid bases incorporated into DNA.

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Electrostatics of Proteins: Principles, Models and Applications

Cited by 9 publications

References 202 publications

The barrier for proton transport in aquaporins as a challenge for electrostatic models: The role of protein relaxation in mutational calculations

The barrier for proton transport in aquaporins as a challenge for electrostatic models: The role of protein relaxation in mutational calculations

pK values of the ionizable groups of proteins

Progress in Ab Initio QM/MM Free-Energy Simulations of Electrostatic Energies in Proteins: Accelerated QM/MM Studies of pK_a, Redox Reactions and Solvation Free Energies

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Electrostatics of Proteins: Principles, Models and Applications

Cited by 9 publications

References 202 publications

The barrier for proton transport in aquaporins as a challenge for electrostatic models: The role of protein relaxation in mutational calculations

The barrier for proton transport in aquaporins as a challenge for electrostatic models: The role of protein relaxation in mutational calculations

pK values of the ionizable groups of proteins

Progress in Ab Initio QM/MM Free-Energy Simulations of Electrostatic Energies in Proteins: Accelerated QM/MM Studies of pKa, Redox Reactions and Solvation Free Energies

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Progress in Ab Initio QM/MM Free-Energy Simulations of Electrostatic Energies in Proteins: Accelerated QM/MM Studies of pK_a, Redox Reactions and Solvation Free Energies