What Is the Dielectric Constant of a Protein When Its Backbone Is Fixed?

Biologically relevant small variations of intra-cellular pH can have significant effect on stability of protein-DNA complexes, including the nucleosome

Stability of a protein-ligand complex may be sensitive to pH of its environment. Here we explore, computationally, stability of a set of protein-nucleic acid complexes using fundamental thermodynamic linkage relationship. The nucleosome, as well as an essentially random selection of 20 protein complexes with DNA or RNA, are included in the analysis. An increase in intra-cellular/intra-nuclear pH destabilizes most complexes, including the nucleosome. We propose to quantify the effect by ΔΔG^0.3-the change in the binding free energy due to pH increase of 0.3 units, corresponding to doubling of the H ⁺ activity; variations of pH of this amplitude can occur in living cells, including in the course of the cell cycle, and in cancer cells relative to normal ones. We suggest, based on relevant experimental findings, a threshold of biological significance of 1 2 k B T ( ∼ 0.3 k c a l / m o l ) for changes of stability of chromatin-related protein-DNA complexes: a change in the binding affinity above the threshold may have biological consequences. We find that for 70% of the examined complexes, Δ Δ G 0.3 > 1 2 k B T (for 10%, ΔΔG^0.3 is between 3 and 4 k _B T). Thus, small but relevant variations of intra-nuclear pH of 0.3 may have biological consequences for many protein-nucleic acid complexes. The binding affinity between the histone octamer and its DNA, which directly affects the DNA accessibility in the nucleosome, is predicted to be highly sensitive to intra-nuclear pH. A variation of 0.3 units results in ΔΔG^0.3 ∼ 10k _B T ( ∼ 6 k c a l / m o l ) ; for spontaneous unwrapping of 20 bp long entry/exit fragments of the nucleosomal DNA, ΔΔG^0.3 = 2.2k _B T; partial disassembly of the nucleosome into the tetrasome is characterized by ΔΔG^0.3 = 5.2k _B T. The predicted pH -induced modulations of the nucleosome stability are significant enough to suggest that they may have consequences relevant to the biological function of the nucleosome. Accessibility of the nucleosomal DNA is predicted to positively correlate with pH variations during the cell cycle; an increase in intra-cellular pH seen in cancer cells is predicted to lead to a more accessible nucleosomal DNA; a drop in pH associated with apoptosis is predicted to make nucleosomal DNA less accessible. We speculate that processes that depend on accessibility to the DNA in the nucleosomes, such as transcription or DNA replication, might become upregulated due to relatively small, but nevertheless realistic increases of intra-nuclear pH.

Probing the solvation of the α-helix with extended amide III bands in Raman optical activity

Experimental and theoretical Raman optical activity (ROA) study of α-helical peptides and proteins has suggested that the relative intensity of two extended amide III ROA bands at ∼1340 cm^-1 (I band) and ∼1300 cm^-1 (II band) can be used to monitor the permittivity of the surrounding medium of the α-helix. So far, the ROA intensity ratio, I_I/I_II, has been interpreted from two different viewpoints. The first one is in terms of a direct effect of permittivity around the α-helix. The second one is based on a structural equilibrium of two types of α-helical structures, "hydrated" and "unhydrated" ones. In the present study, temperature- and solvent-dependences of I_I/I_II are measured for highly-α-helical peptides and compared to the theoretical spectra while varying the permittivity or the type of α-helical structure. A fragment method with partial optimization in the normal modes is adopted in density functional theory calculations. The main features of the experimental spectra and a trend of the observed I_I/I_II are well reproduced by the simulations, which leads us to a conclusion that the I_I/I_II is dominantly governed by a direct influence of the permittivity of the environment and just accessorily by the equilibrium of the two types of α-helices. The simulations also opposed the conventional assignments of the I and II bands to "hydrated" and "unhydrated" α-helical structures, respectively. In the case of α-helical proteins, solvent exposure of the α-helix may be monitored by the ROA ratio.

Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems

pH is a critical parameter for biological and technological systems directly related with electrical charges. It can give rise to peculiar electrostatic phenomena, which also makes them more challenging. Due to the quantum nature of the process, involving the forming and breaking of chemical bonds, quantum methods should ideally by employed. Nevertheless, due to the very large number of ionizable sites, different macromolecular conformations, salt conditions, and all other charged species, the CPU time cost simply becomes prohibitive for computer simulations, making this a quite complex problem. Simplified methods based on Monte Carlo sampling have been devised and will be reviewed here, highlighting the updated state-of-the-art of this field, advantages, and limitations of different theoretical protocols for biomolecular systems (proteins and nucleic acids). Following a historical perspective, the discussion will be associated with the applications to protein interactions with other proteins, polyelectrolytes, and nanoparticles.

Simple models for nonpolar solvation: Parameterization and testing

Implicit solvent models are important for many biomolecular simulations. The polarity of aqueous solvent is essential and qualitatively captured by continuum electrostatics methods like Generalized Born (GB). However, GB does not account for the solvent-induced interactions between exposed hydrophobic sidechains or solute-solvent dispersion interactions. These "nonpolar" effects are often modeled through surface area (SA) energy terms, which lack realism, create mathematical singularities, and have a many-body character. We have explored an alternate, Lazaridis-Karplus (LK) gaussian energy density for nonpolar effects and a dispersion (DI) energy term proposed earlier, associated with GB electrostatics. We parameterized several combinations of GB, SA, LK, and DI energy terms, to reproduce 62 small molecule solvation free energies, 387 protein stability changes due to point mutations, and the structures of 8 protein loops. With optimized parameters, the models all gave similar results, with GBLK and GBDILK giving no performance loss compared to GBSA, and mean errors of 1.7 kcal/mol for the stability changes and 2 Å deviations for the loop conformations. The optimized GBLK model gave poor results in MD of the Trpcage mini-protein, but parameters optimized specifically for MD performed well for Trpcage and three other small proteins. Overall, the LK and DI nonpolar terms are valid alternatives to SA treatments for a range of applications. © 2017 Wiley Periodicals, Inc.

Comparing pairwise-additive and many-body generalized Born models for acid/base calculations and protein design

Generalized Born (GB) solvent models are common in acid/base calculations and protein design. With GB, the interaction between a pair of solute atoms depends on the shape of the protein/solvent boundary and, therefore, the positions of all solute atoms, so that GB is a many-body potential. For compute-intensive applications, the model is often simplified further, by introducing a mean, native-like protein/solvent boundary, which removes the many-body property. We investigate a method for both acid/base calculations and protein design that uses Monte Carlo simulations in which side chains can explore rotamers, bind/release protons, or mutate. The fluctuating protein/solvent dielectric boundary is treated in a way that is numerically exact (within the GB framework), in contrast to a mean boundary. Its originality is that it captures the many-body character while retaining the residue-pairwise complexity given by a fixed boundary. The method is implemented in the Proteus protein design software. It yields a slight but systematic improvement for acid/base constants in nine proteins and a significant improvement for the computational design of three PDZ domains. It eliminates a source of model uncertainty, which will facilitate the analysis of other model limitations. © 2017 Wiley Periodicals, Inc.

Computational Design of the Tiam1 PDZ Domain and Its Ligand Binding

PDZ domains direct protein-protein interactions and serve as models for protein design. Here, we optimized a protein design energy function for the Tiam1 and Cask PDZ domains that combines a molecular mechanics energy, Generalized Born solvent, and an empirical unfolded state model. Designed sequences were recognized as PDZ domains by the Superfamily fold recognition tool and had similarity scores comparable to natural PDZ sequences. The optimized model was used to redesign the two PDZ domains, by gradually varying the chemical potential of hydrophobic amino acids; the tendency of each position to lose or gain a hydrophobic character represents a novel hydrophobicity index. We also redesigned four positions in the Tiam1 PDZ domain involved in peptide binding specificity. The calculated affinity differences between designed variants reproduced experimental data and suggest substitutions with altered specificities.

An improved quantum biochemistry description of the glutamate–GluA2 receptor binding within an inhomogeneous dielectric function framework

A new methodology to define the inhomogeneous dielectric constant of protein residues, to apply to the calculation of protein–ligand properties such as the electrostatic interaction.

Continuum Electrostatics Approaches to Calculating pKas and Ems in Proteins

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

Protein:Ligand binding free energies: A stringent test for computational protein design

A computational protein design method is extended to allow Monte Carlo simulations where two ligands are titrated into a protein binding pocket, yielding binding free energy differences. These provide a stringent test of the physical model, including the energy surface and sidechain rotamer definition. As a test, we consider tyrosyl-tRNA synthetase (TyrRS), which has been extensively redesigned experimentally. We consider its specificity for its substrate l-tyrosine (l-Tyr), compared to the analogs d-Tyr, p-acetyl-, and p-azido-phenylalanine (ac-Phe, az-Phe). We simulate l- and d-Tyr binding to TyrRS and six mutants, and compare the structures and binding free energies to a more rigorous "MD/GBSA" procedure: molecular dynamics with explicit solvent for structures and a Generalized Born + Surface Area model for binding free energies. Next, we consider l-Tyr, ac- and az-Phe binding to six other TyrRS variants. The titration results are sensitive to the precise rotamer definition, which involves a short energy minimization for each sidechain pair to help relax bad contacts induced by the discrete rotamer set. However, when designed mutant structures are rescored with a standard GBSA energy model, results agree well with the more rigorous MD/GBSA. As a third test, we redesign three amino acid positions in the substrate coordination sphere, with either l-Tyr or d-Tyr as the ligand. For two, we obtain good agreement with experiment, recovering the wildtype residue when l-Tyr is the ligand and a d-Tyr specific mutant when d-Tyr is the ligand. For the third, we recover His with either ligand, instead of wildtype Gln.

Unstable, metastable, or stable halogen bonding interaction involving negatively charged donors? A statistical and computational chemistry study

The noncovalent halogen bonding could be attributed to the attraction between the positively charged σ-hole and a nucleophile. Quantum mechanics (QM) calculation indicated that the negatively charged organohalogens have no positively charged σ-hole on their molecular surface, leading to a postulation of repulsion between negatively charged organohalogens and nucleophiles in vacuum. However, PDB survey revealed that 24% of the ligands with halogen bonding geometry could be negatively charged. Moreover, 36% of ionizable drugs in CMC (Comprehensive Medicinal Chemistry) are possibly negatively charged at pH 7.0. QM energy scan showed that the negatively charged halogen bonding is probably metastable in vacuum. However, the QM calculated bonding energy turned negative in various solvents, suggesting that halogen bonding with negatively charged donors should be stable in reality. Indeed, QM/MM calculation on three crystal structures with negatively charged ligands revealed that the negatively charged halogen bonding was stable. Hence, we concluded that halogen bonding with negatively charged donors is unstable or metastable in vacuum but stable in protein environment, and possesses similar geometric and energetic characteristics as conventional halogen bonding. Therefore, negatively charged organohalogens are still effective halogen bonding donors for medicinal chemistry and other applications.

Uncovering pH-dependent transient states of proteins with buried ionizable residues

The role of pH in regulating biological activity is ubiquitous, and understanding pH-mediated activity has traditionally relied on analyzing static biomolecular structures of highly populated ground states solved near physiological pH. However, recent advances have shown the increasing importance of transiently populated states, the characterization of which is extremely challenging but made plausible with the development of techniques such as relaxation dispersion NMR spectroscopy. To unlock the pH dependence of these transient states with atomistic-level details, we applied the recently developed explicit solvent constant pH molecular dynamics (CPHMD(MSλD)) framework to a series of staphylococcal nuclease (SNase) mutants with buried ionizable residues and probed their dynamics in different pH environments. Among our key findings is the existence of open states in all SNase mutants containing "buried" residues with highly shifted pKa's, where local solvation around the protonation site was observed. The calculated pKa demonstrated good agreement with experimental pKa's, with a low average unsigned error of 1.3 pKa units and correlation coefficient R(2) = 0.78. Sampling both open and closed states in their respective pH range, where they are expected to be dominant, was necessary to reproduce experimental pKa's, and in the most extreme examples of pKa shifts measured, it can be interpreted that the open-state structures are transient at physiological pH, contributing a small population of 1-2%. This suggests that buried ionizable residues can trigger conformational fluctuations that may be observed as transient-state structures at physiological pH. Furthermore, the coupled relationship of both open and closed states and their role in recapitulating macroscopic experimental observables suggest that structural analysis of buried residues may benefit from looking at structural pairs, as opposed to the conventional approach of looking at a single static ground-state conformation.