Probabilistic analysis for identifying the driving force of protein folding

Solvent-Environment Dependence of the Excess Chemical Potential and Its Computation Scheme Formulated through Error Minimization

Solvent environment may significantly affect the equilibria involving flexible solute species, such as proteins and polymers. In the present work, a computation scheme is formulated for the change in the excess chemical potential of a flexible solute molecule upon variation of the solvent condition. The formulation adopts the scheme of error minimization in parallel to the method of Bennett acceptance ratio, and an exact expression is presented that provides the change in the excess chemical potential from solvation free energies computed in two solvent conditions of interest. The formulated scheme is applied to n-hexanol as the solute in water and n-octanol as the two solvent systems and to an oligomer of ethylene glycol as the solute in water with urea or NaCl added as a cosolvent. It is demonstrated that the change in the excess chemical potential of the solute due to the variation of the solvent condition (composition) can be obtained from the solvation free energies calculated over ∼10 to ∼102 solute configurations, without referring to any intermediate states between the two solvent conditions concerned. The connection to the solvent-condition dependence of the solute structure is further discussed for the systems of the ethylene-glycol oligomer, and the role is addressed for the probability distribution functions of the cosolvent-induced changes in the solvation free energies.

Statistical-Mechanics Analyses on Thermodynamics of Protein Folding Constructed by Privalov and Co-Workers

Privalov and co-workers estimated the changes in hydration enthalpy and entropy upon ubiquitin unfolding and their temperature dependences denoted by ΔHhyd(T) and ΔShyd(T), respectively, from experimentally measured enthalpies and entropies of transfer of various model compounds from gaseous phase to water. We calculate ΔHhyd(T) and ΔShyd(T) for ubiquitin by our statistical-mechanics theory where molecular and atomistic models are employed for water and protein structure, respectively. ΔHhyd(T) and ΔShyd(T) calculated are in remarkably good agreement with those estimated by Privalov and co-workers. By examining relative magnitudes and signs of the changes in a variety of constituents of ΔHhyd(T) and ΔShyd(T), we confirm that the hydrophobic effect is an essential force driving a protein to fold. Detailed and comprehensive explanations are given for our claim that the prevailing views of the hydrophobic effect are not capable of elucidating its weakening at low temperatures, whereas our updated view is. We find out problematic points of the changes in enthalpy and entropy upon protein unfolding denoted by ΔH°(T) and ΔS°(T), respectively, which are measured using the differential scanning calorimetry at low pH, suggesting a theoretical method of calculating ΔH°(T) and ΔS°(T) at pH ∼ 7.

Physical pictures of rotation mechanisms of F1- and V1-ATPases: Leading roles of translational, configurational entropy of water

We aim to develop a theory based on a concept other than the chemo-mechanical coupling (transduction of chemical free energy of ATP to mechanical work) for an ATP-driven protein complex. Experimental results conflicting with the chemo-mechanical coupling have recently emerged. We claim that the system comprises not only the protein complex but also the aqueous solution in which the protein complex is immersed and the system performs essentially no mechanical work. We perform statistical-mechanical analyses on V₁-ATPase (the A₃B₃DF complex) for which crystal structures in more different states are experimentally known than for F₁-ATPase (the α₃β₃γ complex). Molecular and atomistic models are employed for water and the structure of V₁-ATPase, respectively. The entropy originating from the translational displacement of water molecules in the system is treated as a pivotal factor. We find that the packing structure of the catalytic dwell state of V₁-ATPase is constructed by the interplay of ATP bindings to two of the A subunits and incorporation of the DF subunit. The packing structure represents the nonuniformity with respect to the closeness of packing of the atoms in constituent proteins and protein interfaces. The physical picture of rotation mechanism of F₁-ATPase recently constructed by Kinoshita is examined, and common points and differences between F₁- and V₁-ATPases are revealed. An ATP hydrolysis cycle comprises binding of ATP to the protein complex, hydrolysis of ATP into ADP and Pi in it, and dissociation of ADP and Pi from it. During each cycle, the chemical compounds bound to the three A or β subunits and the packing structure of the A₃B₃ or α₃β₃ complex are sequentially changed, which induces the unidirectional rotation of the central shaft for retaining the packing structure of the A₃B₃DF or α₃β₃γ complex stabilized for almost maximizing the water entropy. The torque driving the rotation is generated by water with no input of chemical free energy. The presence of ATP is indispensable as a trigger of the torque generation. The ATP hydrolysis or synthesis reaction is tightly coupled to the rotation of the central shaft in the normal or inverse direction through the water-entropy effect.

Solvation energetics of proteins and their aggregates analyzed by all-atom molecular dynamics simulations and the energy-representation theory of solvation

Solvation is a controlling factor for the structure and function of proteins. This article addresses the effects of solvation from an energetic perspective for the fluctuations and cosolvent-induced changes in protein structures and the equilibrium of aggregate formation for a peptide. A theoretical framework to analyze the solvation effects with an explicit solvent is introduced by adopting the energy-representation theory of solvation, and the connection of the solvation free energy to the protein structure and the aggregation tendency is quantitatively described in combination with all-atom molecular dynamics simulations. The interaction components that govern the solvation effects on the structural variations of proteins are further identified through correlation analysis, and a computational scheme to assess the shift of an aggregation equilibrium due to the addition of a cosolvent is provided.

Accurate and rapid calculation of hydration free energy and its physical implication for biomolecular functions

Here we review a new method for calculating a hydration free energy (HFE) of a solute and discuss its physical implication for biomolecular functions in aqueous environments. The solute hydration is decomposed into processes 1 and 2. A cavity matching the geometric characteristics of the solute at the atomic level is created in process 1. Solute-water van der Waals and electrostatic interaction potentials are incorporated in process 2. The angle-dependent integral equation theory combined with our morphometric approach is applied to process 1, and the three-dimensional reference interaction site model theory is employed for process 2. Molecular models are adopted for water. The new method is characterized by the following. Solutes with various sizes including proteins can be treated in the same manner. It is almost as accurate as the molecular dynamics simulation despite its far smaller computational burden. It enables us to handle a solute possessing a significantly large total charge without difficulty. The HFE can be decomposed into a variety of physically insightful, energetic, and entropic components. It is best suited to the elucidation of mechanisms of protein folding, pressure and cold denaturation of a protein, and different types of molecular recognition.

The Hydration Shell of Monomeric and Dimeric Insulin Studied by Terahertz Time-Domain Spectroscopy

Protein aggregation is believed to be a significant biological mechanism related to neurodegenerative disease, which makes the early-stage detection of aggregates a major concern. We demonstrated the use of terahertz (THz) time-domain spectroscopy to study protein-water interaction of monomeric and dimeric bovine insulin in aqueous samples. Regulated by changing pH and verified by size-exclusion chromatography and dynamic light scattering, we then measured their concentration-dependent changes in THz absorption between 0.5 and 3.0 THz and quantitatively deduced the extended hydration shell thickness by cubic distribution model and random distribution model. Under a random distribution assumption, the extended hydration thickness is 15.4 ± 0.4 Å for monomeric insulin and 17.5 ± 0.5 Å for dimeric insulin, with the hydration number of 6700 and 11,000, respectively. The hydration number of dimeric insulin is not twice but 1.64 times that of monomeric insulin, further supported by the ratio of solvent-accessible surface area. This "1.64-times" relation probably originates from the structural and conformational changes accompanied with dimerization. Combined with the investigations on insulin samples with different single amino acid mutations, residue B24 is believed to play an important role in the dimerization process. It is demonstrated that THz time-domain spectroscopy is a useful tool and has the sensitivity to provide the hydration information of different protein aggregates at an early stage.