Tomohiko Hayashi

Binding of an RNA aptamer and a partial peptide of a prion protein: crucial importance of water entropy in molecular recognition

It is a central issue to elucidate the new type of molecular recognition accompanied by a global structural change of a molecule upon binding to its targets. Here we investigate the driving force for the binding of R12 (a ribonucleic acid aptamer) and P16 (a partial peptide of a prion protein) during which P16 exhibits the global structural change. We calculate changes in thermodynamic quantities upon the R12–P16 binding using a statistical-mechanical approach combined with molecular models for water which is currently best suited to studies on hydration of biomolecules. The binding is driven by a water-entropy gain originating primarily from an increase in the total volume available to the translational displacement of water molecules in the system. The energy decrease due to the gain of R12–P16 attractive (van der Waals and electrostatic) interactions is almost canceled out by the energy increase related to the loss of R12–water and P16–water attractive interactions. We can explain the general experimental result that stacking of flat moieties, hydrogen bonding and molecular-shape and electrostatic complementarities are frequently observed in the complexes. It is argued that the water-entropy gain is largely influenced by the geometric characteristics (overall shapes, sizes and detailed polyatomic structures) of the biomolecules.

Accurate evaluation of the absorption maxima of retinal proteins based on a hybrid QM/MM method

Here we improved our hybrid QM/MM methodology (Houjou et al. J Phys Chem B 2001, 105, 867) for evaluating the absorption maxima of photoreceptor proteins. The renewed method was applied to evaluation of the absorption maxima of several retinal proteins and photoactive yellow protein. The calculated absorption maxima were in good agreement with the corresponding experimental data with a computational error of <10 nm. In addition, our calculations reproduced the experimental gas‐phase absorption maxima of model chromophores (protonated all‐trans retinal Schiff base and deprotonated thiophenyl‐p‐coumarate) with the same accuracy. It is expected that our methodology allows for definitive interpretation of the spectral tuning mechanism of retinal proteins.

Mechanism of One-to-Many Molecular Recognition Accompanying Target-Dependent Structure Formation: For the Tumor Suppressor p53 Protein as an Example.

The new type of molecular recognition, in which an intrinsically disordered region (IDR) of a protein binds to many different target proteins with target-dependent structure formation, is indispensable to the expression of life phenomena and also implicated in a number of diseases. According to the prevailing view, the physicochemical factors responsible for the binding are also target dependent. Here we consider an IDR of the tumor suppressor p53 protein, p53CTD, as an important example related to carcinogenesis and analyze its binding to four targets accompanying the formation of target-dependent structures (i.e., helix, sheet, and two different coils) using our statistical-mechanical method combined with molecular models for water. We find that all of the seemingly different binding processes are driven by a large gain of the translational, configurational entropy of water in the system. The gain originates from sufficiently high shape complementarity on the atomic level within the p53CTD-target interface. It is also required that the electrostatic complementarity be ensured as much as possible to compensate for the dehydration. Such complementarities are achieved in harmony with the portion of the target to which p53CTD binds, leading to a large diversity of structures of p53CTD formed upon binding: If they are not achievable, the binding does not occur. This finding is made possible only by calculating the changes in thermodynamic quantities upon binding and decomposing them into physically insightful components.

ATP-induced conformational changes of nucleotide-binding domains in an ABC transporter. Importance of the water-mediated entropic force.

ATP binding cassette (ABC) proteins belong to a superfamily of active transporters. Recent experimental and computational studies have shown that binding of ATP to the nucleotide binding domains (NBDs) of ABC proteins drives the dimerization of NBDs, which, in turn, causes large conformational changes within the transmembrane domains (TMDs). To elucidate the active substrate transport mechanism of ABC proteins, it is first necessary to understand how the NBD dimerization is driven by ATP binding. In this study, we selected MalKs (NBDs of a maltose transporter) as a representative NBD and calculated the free-energy change upon dimerization using molecular mechanics calculations combined with a statistical thermodynamic theory of liquids, as well as a method to calculate the translational, rotational, and vibrational entropy change. This combined method is applied to a large number of snapshot structures obtained from molecular dynamics simulations containing explicit water molecules. The results suggest that the NBD dimerization proceeds with a large gain of water entropy when ATP molecules bind to the NBDs. The energetic gain arising from direct NBD-NBD interactions is canceled by the dehydration penalty and the configurational-entropy loss. ATP hydrolysis induces a loss of the shape complementarity between the NBDs, which leads to the dissociation of the dimer, due to a decrease in the water-entropy gain and an increase in the configurational-entropy loss. This interpretation of the NBD dimerization mechanism in concert with ATP, especially focused on the water-mediated entropy force, is potentially applicable to a wide variety of the ABC transporters.

Water based on a molecular model behaves like a hard-sphere solvent for a nonpolar solute when the reference interaction site model and related theories are employed.

For neutral hard-sphere solutes, we compare the reduced density profile of water around a solute g(r), solvation free energy μ, energy U, and entropy S under the isochoric condition predicted by the two theories: dielectrically consistent reference interaction site model (DRISM) and angle-dependent integral equation (ADIE) theories. A molecular model for water pertinent to each theory is adopted. The hypernetted-chain (HNC) closure is employed in the ADIE theory, and the HNC and Kovalenko-Hirata (K-H) closures are tested in the DRISM theory. We also calculate g(r), U, S, and μ of the same solute in a hard-sphere solvent whose molecular diameter and number density are set at those of water, in which case the radial-symmetric integral equation (RSIE) theory is employed. The dependences of μ, U, and S on the excluded volume and solvent-accessible surface area are analyzed using the morphometric approach (MA). The results from the ADIE theory are in by far better agreement with those from computer simulations available for g(r), U, and μ. For the DRISM theory, g(r) in the vicinity of the solute is quite high and becomes progressively higher as the solute diameter d U increases. By contrast, for the ADIE theory, it is much lower and becomes further lower as d U increases. Due to unphysically positive U and significantly larger |S|, μ from the DRISM theory becomes too high. It is interesting that μ, U, and S from the K-H closure are worse than those from the HNC closure. Overall, the results from the DRISM theory with a molecular model for water are quite similar to those from the RSIE theory with the hard-sphere solvent. Based on the results of the MA analysis, we comparatively discuss the different theoretical methods for cases where they are applied to studies on the solvation of a protein.

Statistical Thermodynamics for Actin-Myosin Binding: The Crucial Importance of Hydration Effects

Actomyosin is an important molecular motor, and the binding of actin and myosin is an essential research target in biophysics. Nevertheless, the physical factors driving or opposing the binding are still unclear. Here, we investigate the role of water in actin-myosin binding using the most reliable statistical-mechanical method currently available for assessing biomolecules immersed in water. This method is characterized as follows: water is treated not as a dielectric continuum but as an ensemble of molecules; the polyatomic structures of proteins are taken into consideration; and the binding free energy is decomposed into physically insightful entropic and energetic components by accounting for the hydration effect to its full extent. We find that the actin-myosin binding brings large gains of electrostatic and Lennard-Jones attractive interactions. However, these gains are accompanied by even larger losses of actin-water and myosin-water electrostatic and LJ attractive interactions. Although roughly half of the energy increase due to the losses is cancelled out by the energy decrease arising from structural reorganization of the water released upon binding, the remaining energy increase is still larger than the energy decrease brought by the gains mentioned above. Hence, the net change in system energy is positive, which opposes binding. Importantly, the binding is driven by a large gain of configurational entropy of water, which surpasses the positive change in system energy and the conformational entropy loss occurring for actin and myosin. The principal physical origin of the large water-entropy gain is as follows: the actin-myosin interface is closely packed with the achievement of high shape complementarity on the atomic level, leading to a large increase in the total volume available to the translational displacement of water molecules in the system and a resultant reduction of water crowding (i.e., entropic correlations among water molecules).

On the physics of thermal-stability changes upon mutations of a protein

It is of great interest from both scientific and practical viewpoints to theoretically predict the thermal-stability changes upon mutations of a protein. However, such a prediction is an intricate task. Up to now, significantly many approaches for the prediction have been reported in the literature. They always include parameters which are adjusted so that the prediction results can be best fitted to the experimental data for a sufficiently large set of proteins and mutations. The inclusion is necessitated to achieve satisfactorily high prediction performance. A problem is that the resulting values of the parameters are often physically meaningless, and the physicochemical factors governing the thermal-stability changes upon mutations are rather ambiguous. Here, we develop a new measure of the thermal stability. Protein folding is accompanied by a large gain of water entropy (the entropic excluded-volume (EV) effect), loss of protein conformational entropy, and increase in enthalpy. The enthalpy increase originates primarily from the following: The energy increase due to the break of protein-water hydrogen bonds (HBs) upon folding cannot completely be cancelled out by the energy decrease brought by the formation of protein intramolecular HBs. We develop the measure on the basis of only these three factors and apply it to the prediction of the thermal-stability changes upon mutations. As a consequence, an approach toward the prediction is obtained. It is distinguished from the previously reported approaches in the following respects: The parameters adjusted in the manner mentioned above are not employed at all, and the entropic EV effect, which is ascribed to the translational displacement of water molecules coexisting with the protein in the system, is fully taken into account using a molecular model for water. Our approach is compared with one of the most popular approaches, FOLD-X, in terms of the prediction performance not only for single mutations but also for double, triple, and higher-fold (up to sevenfold) mutations. It is shown that on the whole our approach and FOLD-X exhibit almost the same performance despite that the latter uses the adjusting parameters. For multiple mutations, however, our approach is far superior to FOLD-X. Five multiple mutations for staphylococcal nuclease lead to highly enhanced stabilities, but we find that this high enhancement arises from the entropic EV effect. The neglect of this effect in FOLD-X is a principal reason for its ill success. A conclusion is that the three factors mentioned above play essential roles in elucidating the thermal-stability changes upon mutations.

Unraveling protein folding mechanism by analyzing the hierarchy of models with increasing level of detail

Taking protein G with 56 residues for a case study, we investigate the mechanism of protein folding. In addition to its native structure possessing α-helix and β-sheet contents of 27% and 39%, respectively, we construct a number of misfolded decoys with a wide variety of α-helix and β-sheet contents. We then consider a hierarchy of 8 different models with increasing level of detail in terms of the number of entropic and energetic physical factors incorporated. The polyatomic structure is always taken into account, but the side chains are removed in half of the models. The solvent is formed by either neutral hard spheres or water molecules. Protein intramolecular hydrogen bonds (H-bonds) and protein-solvent H-bonds (the latter is present only in water) are accounted for or not, depending on the model considered. We then apply a physics-based free-energy function (FEF) corresponding to each model and investigate which structures are most stabilized. This special approach taken on a step-by-step basis enables us to clarify the role of each physical factor in contributing to the structural stability and separately elucidate its effect. Depending on the model employed, significantly different structures such as very compact configurations with no secondary structures and configurations of associated α-helices are optimally stabilized. The native structure can be identified as that with lowest FEF only when the most detailed model is employed. This result is significant for at least the two reasons: The most detailed model considered here is able to capture the fundamental aspects of protein folding notwithstanding its simplicity; and it is shown that the native structure is stabilized by a complex interplay of minimal multiple factors that must be all included in the description. In the absence of even a single of these factors, the protein is likely to be driven towards a different, more stable state.

Full-Quantum chemical calculation of the absorption maximum of bacteriorhodopsin: a comprehensive analysis of the amino acid residues contributing to the opsin shift

Herein, the absorption maximum of bacteriorhodopsin (bR) is calculated using our recently developed method in which the whole protein can be treated quantum mechanically at the level of INDO/S-CIS//ONIOM (B3LYP/6-31G(d,p): AMBER). The full quantum mechanical calculation is shown to reproduce the so-called opsin shift of bR with an error of less than 0.04 eV. We also apply the same calculation for 226 different bR mutants, each of which was constructed by replacing any one of the amino acid residues of the wild-type bR with Gly. This substitution makes it possible to elucidate the extent to which each amino acid contributes to the opsin shift and to estimate the inter-residue synergistic effect. It was found that one of the most important contributions to the opsin shift is the electron transfer from Tyr185 to the chromophore upon excitation. We also indicate that some aromatic (Trp86, Trp182) and polar (Ser141, Thr142) residues, located in the vicinity of the retinal polyene chain and the β-ionone ring, respectively, play an important role in compensating for the large blue-shift induced by both the counterion residues (Asp85, Asp212) and an internal water molecule (W402) located near the Schiff base linkage. In particular, the effect of Trp86 is comparable to that of Tyr185. In addition, Ser141 and Thr142 were found to contribute to an increase in the dipole moment of bR in the excited state. Finally, we provide a complete energy diagram for the opsin shift together with the contribution of the chromophore-protein steric interaction.

Statistical Thermodynamics on the Binding of Biomolecules

The binding of biomolecules in water plays an essential role in the expression of life phenomena. In this chapter, we show that the underlying mechanism of this binding can be clarified by calculating the thermodynamic quantities based on statistical mechanics. The three types of biomolecule binding are analyzed within a theoretical framework: (I) the binding between a soft peptide (a portion of protein) and a rigid RNA, (II) the one-to-many molecular recognition by a soft peptide accompanying target-dependent structuring, and (III) the actin–myosin binding. Types (I) and (II) are related to pharmacological applications, and type (III) is an elementary process for muscle contraction. These apparently different binding processes share the same underlying mechanism, which can be characterized using a unified theoretical framework. The binding is driven by a large gain of water entropy in the entire system. This gain primarily originates from the reduction of “water crowding,” which is attributed to a large overlap of the biomolecule excluded volumes (EV) upon binding, referred to as the entropic EV effect. Such a large EV overlap is achieved by the formation of sufficiently high shape complementarity on an atomic level within the binding interface. The electrostatic complementarity within the interface is ensured as much as possible to compensate for the energetic loss due to dehydration. Although the elimination of biomolecule fluctuations within the binding interface causes a large conformational entropy loss, it is surpassed by these complementarity formations when the binding is accomplished.