A methodology for creating mutants of G-protein coupled receptors stabilized in active state by combining statistical thermodynamics and evolutionary molecular engineering.

We challenged the stabilization of a G-protein coupled receptor (GPCR) in the active state solely by multiple amino-acid mutations without the agonist binding. For many GPCRs, the free energy of the active state is higher than that of the inactive state. When the inactive state is stabilized through the lowering of its free energy, the apparent midpoint temperature of thermal denaturation Tm exhibits a significant increase. However, this is not always the case for the stabilization of the active state. We constructed a modified version of our methodology combining statistical thermodynamics and evolutionary molecular engineering, which was recently developed for the inactive state. First, several residues to be mutated are determined using our statistical-thermodynamics theory. Second, a gene (mutant) library is constructed using Escherichia coli cells to efficiently explore most of the mutational space. Third, for the mutant screening, the mutants prepared in accordance with the library are expressed in engineered Saccharomyces cerevisiae YB14 cells which can grow only when a GPCR mutant stabilized in the active state has signaling function. For the adenosine A2A receptor tested, the methodology enabled us to sort out two triple mutants and a double mutant. It was experimentally corroborated that all the mutants exhibit much higher binding affinity for G protein than the wild type. Analyses indicated that the mutations make the structural characteristics shift toward those of the active state. However, only slight increases in Tm resulted from the mutations, suggesting the unsuitability of Tm to the stability measure for the active state.

Hydration properties of a protein at low and high pressures: Physics of pressure denaturation.

Using experimentally determined structures of ubiquitin at 1 and 3000 bar, we generate sufficiently large ensembles of model structures in the native and pressure-induced (denatured) states by means of molecular dynamics simulations with explicit water. We calculate the values of a free-energy function (FEF), which comprises the hydration free energy (HFE) and the intramolecular (conformational) energy and entropy, for the two states at 1 and 3000 bar. The HFE and the conformational entropy, respectively, are calculated using our statistical-mechanical method, which has recently been shown to be accurate, and the Boltzmann-quasi-harmonic method. The HFE is decomposed into a variety of physically insightful components. We show that the FEF of the native state is lower than that of the denatured state at 1 bar, whereas the opposite is true at 3000 bar, thus being successful in reproducing the pressure denaturation. We argue that the following two quantities of hydration play essential roles in the denaturation: the WASA-dependent term in the water-entropy loss upon cavity creation for accommodating the protein (WASA is the water-accessible surface area of the cavity) and the protein-water Lennard-Jones interaction energy. At a high pressure, the mitigation of the serious water crowding in the system is the most important, and the WASA needs to be sufficiently enlarged with the increase in the excluded-volume being kept as small as possible. The denatured structure thus induced is characterized by the water penetration into the protein interior. The pressure denaturation is accompanied by a significantly large gain of water entropy.

How Does the Recently Discovered Peptide MIP Exhibit Much Higher Binding Affinity than an Anticancer Protein p53 for an Oncoprotein MDM2?

An oncoprotein MDM2 binds to the extreme N-terminal peptide region of a tumor suppressor protein p53 (p53NTD) and inhibits its anticancer activity. We recently discovered a peptide named MIP which exhibits much higher binding affinity for MDM2 than p53NTD. Experiments showed that the binding free energy (BFE) of MDM2-MIP is lower than that of MDM2-p53NTD by approximately -4 kcal/mol. Here, we develop a theoretical method which is successful in reproducing this quantitative difference and elucidating its physical origins. It enables us to decompose the BFE into a variety of energetic and entropic components, evaluate their relative magnitudes, and identify the physical factors driving or opposing the binding. It should be applicable also to the assessment of differences among ligands in the binding affinity for a particular receptor, which is a central issue in modern chemistry. In the MDM2 case, the higher affinity of MIP is ascribed to a larger gain of translational, configurational entropy of water upon binding. This result is useful to the design of a peptide possessing even higher affinity for MDM2 as a reliable drug against a cancer.

An accurate and rapid method for calculating hydration free energies of a variety of solutes including proteins.

A new method is developed for calculating hydration free energies (HFEs) of polyatomic solutes. The solute insertion is decomposed into the creation of a cavity in water matching the geometric characteristics of the solute at the atomic level (process 1) and the incorporation of solute-water van der Waals and electrostatic interactions (process 2). The angle-dependent integral equation theory combined with our morphometric approach and the three-dimensional interaction site model theory are applied to processes 1 and 2, respectively. Neither a stage of training nor parameterization is necessitated. For solutes with various sizes including proteins, the HFEs calculated by the new method are compared to those obtained using a molecular dynamics simulation based on solution theory in energy representation (the ER method developed by Matubayasi and co-workers), currently the most reliable tool. The agreement is very good especially for proteins. The new method is characterized by the following: The calculation can rapidly be finished; a solute possessing a significantly large total charge can be handled without difficulty; and since it yields not only the HFE but also its many physically insightful energetic and entropic components, it is best suited to the elucidation of mechanisms of diverse phenomena such as the receptor-ligand binding, different types of molecular recognition, and protein folding, denaturation, and association.

Statistical thermodynamics for the unexpectedly large difference between disaccharide stereoisomers in terms of solubility in water.

We unravel the physical origins of the large difference between cellobiose and maltose, which consist of two ß-1,4 and α-1,4 linked d-glucose units, respectively, in terms of the solubility in water. We construct a thermodynamic theory where the chemical-potential difference between disaccharides in water and in vacuum is identified as the key free-energy function. Its energetic and entropic components are calculated for cellobiose and maltose by statistical-mechanical theories for solute hydration. The disaccharide structures are taken into account at the atomic level and a molecular model is adopted for water. Molecular dynamics simulations are used to account for the conformational fluctuation of a disaccharide molecule, which also enables us to estimate the conformational entropy. We show that the cellobiose/maltose solubility ratio calculated is in good agreement with the experimental value. The solubility becomes much lower for cellobiose due to conformational-entropy and water-entropy effects. The former effect is relevant to higher stability of the intramolecular hydrogen bond between oxygen atoms in the six-membered ring and in the neighboring hydroxyl group: the hydration alters the fluctuation of a molecular conformation to a larger or less regular one, but the degree of this alteration is smaller. The latter effect is attributed to more separation of two hydroxymethyl groups in a molecule, causing lower probability of the overlap of excluded volumes generated by the groups for water molecules. We suggest that physicochemical properties of disaccharides in water become variable depending on the stereoisomerism through hydration effects and the origins of the variety are entropic.

Physical Origin of Thermostabilization by a Quadruple Mutation for the Adenosine A2a Receptor in the Active State.

The G protein-coupled receptors (GPCRs) form a large, physiologically important family of membrane proteins and are currently the most attractive targets for drug discovery. We investigate the physical origin of thermostabilization of the adenosine A2a receptor (A2aR) in the active state, which was experimentally achieved by another research group using the four point mutations: L48A, A54L, T65A, and Q89A. The investigation is performed on the basis of our recently developed physics-based free-energy function (FEF), which has been quite successful for the thermodynamics of GPCRs in the inactive state. The experimental condition for solving the wild-type and mutant crystal structures was substantially different from that for comparing their thermostabilities. Therefore, all-atom molecular dynamics simulations are necessitated, which also allows us to account for the structural fluctuations of the membrane protein. We show that the quadruple mutation leads to the enlargement of the solvent-entropy gain upon protein folding. The solvent is formed by hydrocarbon groups constituting nonpolar chains within the lipid bilayer, and the entropy is relevant to the thermal motion of the hydrocarbon groups. From an energetic point of view (e.g., in terms of protein intramolecular hydrogen bonds), the mutation confers no improvement upon the structural stability of A2aR. The reliability of our FEF and the crucial importance of the solvent-entropy effect have thus been demonstrated for a GPCR in the active state. We are now ready to identify thermostabilizing mutations of GPCRs not only in the inactive state but also in the active one.

Computational Methods for Configurational Entropy Using Internal and Cartesian Coordinates.

The configurational entropy of solute molecules is a crucially important quantity to study various biophysical processes. Consequently, it is necessary to establish an efficient quantitative computational method to calculate configurational entropy as accurately as possible. In the present paper, we investigate the quantitative performance of the quasi-harmonic and related computational methods, including widely used methods implemented in popular molecular dynamics (MD) software packages, compared with the Clausius method, which is capable of accurately computing the change of the configurational entropy upon temperature change. Notably, we focused on the choice of the coordinate systems (i.e., internal or Cartesian coordinates). The Boltzmann-quasi-harmonic (BQH) method using internal coordinates outperformed all the six methods examined here. The introduction of improper torsions in the BQH method improves its performance, and anharmonicity of proper torsions in proteins is identified to be the origin of the superior performance of the BQH method. In contrast, widely used methods implemented in MD packages show rather poor performance. In addition, the enhanced sampling of replica-exchange MD simulations was found to be efficient for the convergent behavior of entropy calculations. Also in folding/unfolding transitions of a small protein, Chignolin, the BQH method was reasonably accurate. However, the independent term without the correlation term in the BQH method was most accurate for the folding entropy among the methods considered in this study, because the QH approximation of the correlation term in the BQH method was no longer valid for the divergent unfolded structures.