Perspective: Structural fluctuation of protein and Anfinsen's thermodynamic hypothesis

Structural Fluctuation, Relaxation, and Folding of Protein: An Approach Based on the Combined Generalized Langevin and RISM/3D-RISM Theories

In 2012, Kim and Hirata derived two generalized Langevin equations (GLEs) for a biomolecule in water, one for the structural fluctuation of the biomolecule and the other for the density fluctuation of water, by projecting all the mechanical variables in phase space onto the two dynamic variables: the structural fluctuation defined by the displacement of atoms from their equilibrium positions, and the solvent density fluctuation. The equation has an expression similar to the classical Langevin equation (CLE) for a harmonic oscillator, possessing terms corresponding to the restoring force proportional to the structural fluctuation, as well as the frictional and random forces. However, there is a distinct difference between the two expressions that touches on the essential physics of the structural fluctuation, that is, the force constant, or Hessian, in the restoring force. In the CLE, this is given by the second derivative of the potential energy among atoms in a protein. So, the quadratic nature or the harmonicity is only valid at the minimum of the potential surface. On the contrary, the linearity of the restoring force in the GLE originates from the projection of the water's degrees of freedom onto the protein's degrees of freedom. Taking this into consideration, Kim and Hirata proposed an ansatz for the Hessian matrix. The ansatz is used to equate the Hessian matrix with the second derivative of the free-energy surface or the potential of the mean force of a protein in water, defined by the sum of the potential energy among atoms in a protein and the solvation free energy. Since the free energy can be calculated from the molecular mechanics and the RISM/3D-RISM theory, one can perform an analysis similar to the normal mode analysis (NMA) just by diagonalizing the Hessian matrix of the free energy. This method is referred to as the Generalized Langevin Mode Analysis (GLMA). This theory may be realized to explore a variety of biophysical processes, including protein folding, spectroscopy, and chemical reactions. The present article is devoted to reviewing the development of this theory, and to providing perspective in exploring life phenomena.

The impact of AlphaFold Protein Structure Database on the fields of life sciences

Arguably, 2020 was the year of high-accuracy protein structure predictions, with AlphaFold 2.0 achieving previously unseen accuracy in the Critical Assessment of Protein Structure Prediction (CASP). In 2021, DeepMind and EMBL-EBI developed the AlphaFold Protein Structure Database to make an unprecedented number of reliable protein structure predictions easily accessible to the broad scientific community. We provide a brief overview and describe the latest developments in the AlphaFold database. We highlight how the fields of data services, bioinformatics, structural biology, and drug discovery are directly affected by the influx of protein structure data. We also show examples of cutting-edge research that took advantage of the AlphaFold database. It is apparent that connections between various fields through protein structures are now possible, but the amount of data poses new challenges. Finally, we give an outlook regarding the future direction of the database, both in terms of data sets and new functionalities.

A theory of chemical reactions in biomolecules in solution: Generalized Langevin mode analysis (GLMA)

The generalized Langevin mode analysis (GLMA) is applied to chemical reactions in biomolecules in solution. The theory sees a chemical reaction in solution as a barrier-crossing process, similar to the Marcus theory. The barrier is defined as the crossing point of two free-energy surfaces that are attributed to the reactant and product of the reaction. It is assumed that both free-energy surfaces are quadratic or harmonic. The assumption is based on the Kim-Hirata theory of structural fluctuation of protein, which proves that the fluctuation around an equilibrium structure is quadratic with respect to the structure or atomic coordinates. The quadratic surface is a composite of many harmonic functions with different modes or frequencies. The height of the activation barrier will be dependent on the mode or frequency-the less the frequency, the lower the barrier. Hence, it is essential to decouple the fluctuational modes into a hierarchical order. GLMA is impeccable for this purpose. It is essential for a theoretical study of chemical reactions to choose a reaction coordinate along which the reaction proceeds. We suppose that the mode whose center of coordinate and/or the frequency changes most before and after the reaction is the one relevant to the chemical reaction and choose the coordinate as the reaction coordinate. The rate of reaction along the reaction coordinate is k_rate=ν⁡exp-ΔF^(†)/k_BT, which is similar to the Marcus expression for the electron transfer reaction. In the equation, ΔF^(†) is the activation barrier defined by ΔF^(†)≡F^(r)Q^†-F^(r)(Q_eq ^(r)), where F^(r)(Q_eq ^(r)) and F^(r)Q^† denote the free energies at equilibrium Q_eq ^(r) and the crossing point Q^†, respectively, both on the free energy surface of the reactant.

Bioprocessing of recombinant proteins from Escherichia coli inclusion bodies: insights from structure-function relationship for novel applications

The formation of inclusion bodies (IBs) during expression of recombinant therapeutic proteins using E. coli is a significant hurdle in producing high-quality, safe, and efficacious medicines. The improved understanding of the structure-function relationship of the IBs has resulted in the development of novel biotechnologies that have streamlined the isolation, solubilization, refolding, and purification of the active functional proteins from the bacterial IBs. Together, this overall effort promises to radically improve the scope of experimental biology of therapeutic protein production and expand new prospects in IBs usage. Notably, the IBs are increasingly used for applications in more pristine areas such as drug delivery and material sciences. In this review, we intend to provide a comprehensive picture of the bio-processing of bacterial IBs, including assessing critical gaps that still need to be addressed and potential solutions to overcome them. We expect this review to be a useful resource for those working in the area of protein refolding and therapeutic protein production.

3D-Beacons: decreasing the gap between protein sequences and structures through a federated network of protein structure data resources

While scientists can often infer the biological function of proteins from their 3-dimensional quaternary structures, the gap between the number of known protein sequences and their experimentally determined structures keeps increasing. A potential solution to this problem is presented by ever more sophisticated computational protein modeling approaches. While often powerful on their own, most methods have strengths and weaknesses. Therefore, it benefits researchers to examine models from various model providers and perform comparative analysis to identify what models can best address their specific use cases. To make data from a large array of model providers more easily accessible to the broader scientific community, we established 3D-Beacons, a collaborative initiative to create a federated network with unified data access mechanisms. The 3D-Beacons Network allows researchers to collate coordinate files and metadata for experimentally determined and theoretical protein models from state-of-the-art and specialist model providers and also from the Protein Data Bank.

Proteins in Wonderland: The Magical World of Pressure

Admitting the "Native", "Unfolded" and "Fibril" states as the three basic generic states of proteins in nature, each of which is characterized with its partial molar volume, here we predict that the interconversion among these generic states N, U, F may be performed simply by making a temporal excursion into the so called "the high-pressure regime", created artificially by putting the system under sufficiently high hydrostatic pressure, where we convert N to U and F to U, and then back to "the low-pressure regime" (the "Anfinsen regime"), where we convert U back to N (U→N). Provided that the solution conditions (temperature, pH, etc.) remain largely the same, the idea provides a general method for choosing N, U, or F of a protein, to a great extent at will, assisted by the proper use of the external perturbation pressure. A successful experiment is demonstrated for the case of hen lysozyme, for which the amyloid fibril state F prepared at 1 bar is turned almost fully back into its original native state N at 1 bar by going through the "the high-pressure regime". The outstanding simplicity and effectiveness of pressure in controlling the conformational state of a protein are expected to have a wide variety of applications both in basic and applied bioscience in the future.

A computational method to simulate global conformational changes of proteins induced by cosolvent

A computational method to investigate the global conformational change of a protein is proposed by combining the linear response path following (LRPF) method and three-dimensional reference interaction site model (3D-RISM) theory, which is referred to as the LRPF/3D-RISM method. The proposed method makes it possible to efficiently simulate protein conformational changes caused by either solutions of varying concentrations or the presence of cosolvent species by taking advantage of the LRPF and 3D-RISM. The proposed method is applied to the urea-induced denaturation of ubiquitin. The LRPF/3D-RISM trajectories successfully simulate the early stage of the denaturation process within the simulation time of 300 ns, whereas no significant structural change is observed even in the 1 μs standard MD simulation. The obtained LRPF/3D-RISM trajectories reproduce the mechanism of the urea denaturation of ubiquitin reported in previous studies, and demonstrate the high efficiency of the method.

Molecular Recognition and Self-Organization in Life Phenomena Studied by a Statistical Mechanics of Molecular Liquids, the RISM/3D-RISM Theory

There are two molecular processes that are essential for living bodies to maintain their life: the molecular recognition, and the self-organization or self-assembly. Binding of a substrate by an enzyme is an example of the molecular recognition, while the protein folding is a good example of the self-organization process. The two processes are further governed by the other two physicochemical processes: solvation and the structural fluctuation. In the present article, the studies concerning the two molecular processes carried out by Hirata and his coworkers, based on the statistical mechanics of molecular liquids or the RISM/3D-RISM theory, are reviewed.

Cavity Particle in Aqueous Solution with a Hydrophobic Solute: Structure, Energetics, and Functionals

Endpoints density functional theory (DFT) provides a framework for calculating the excess chemical potential of a solute in solution using solvent distribution functions obtained from both physical endpoints of a hypothetical charging process which transforms the solvent density from that of the pure liquid to the solution state. In this work, the endpoints DFT equations are formulated in terms of the indirect (solvent-mediated) contribution ω(x) to the solute-solvent potential of mean force, and their connections are established with the conventional DFT expressions which are based on the use of direct correlation functions. ω actually corresponds to the free-energy cost to move a cavity particle (a tagged solvent molecule which interacts with the other solvent molecules but not the solute) from the bulk to the configuration x of a solvent molecule relative to the solute and is a suitable variable to describe the solvent effects on the solute-solvent interactions. HNC and PY type approximations are then used to integrate the DFT charging integral involved in the exact expression for the excess chemical potential. With these approximations, molecular simulations are to be performed at the two endpoints of solute insertion: pure solvent without the solute and the solution system with the fully coupled solute-solvent interaction. An endpoints method thus utilizes the ensembles of intermolecular configurations of physical interest, which are often readily accessible with MD simulations given the present computational power. To illustrate properties of the formulation, we perform simulations of model systems consisting of a cavity particle in an aqueous solution containing a spherical hydrophobic solute of three different sizes from which ω(x) and the solute chemical potential can be calculated using endpoints DFT expressions. These are compared with corresponding results obtained using the approximations needed in order to evaluate the endpoints DFT charging integral when cavity particle simulation data is not available. We analyze a new approximation (two-points quadratic HNC) to the DFT charging integral which captures the correct behavior of the cavity distributions at both endpoints of the solute insertion. The behavior of the cavity particle in simple and complex liquids plays an important role in various theoretical treatments of the solute chemical potential. For pure Lennard-Jones fluids, the free energy to bring a cavity particle from the bulk to the center of a fluid particle is negative. However, for solutes of varying size, this is not generally true for Lennard-Jones fluids or the systems studied in this work. We carry out energetic and structural analyses of the cavity particle in aqueous solution with hydrophobic solutes of varying size and discuss the results in the context of the hydrophobic effect.

Thermoresponsive Polysaccharide Graft Polymer Vesicles with Tunable Size and Structural Memory

Controlling polymer vesicle size is difficult and a major obstacle for their potential use in biomedical applications, such as drug-delivery carriers and nanoreactors. Herein, we report size-tunable polymer vesicles based on self-assembly of a thermoresponsive amphiphilic graft copolymer. Unilamellar polymer vesicles form upon heating chilled polymer solutions, and vesicle size can be tuned in the range of 40-70 nm by adjusting the initial polymer concentration. Notably, the polymer can reversibly switch between a monomer state and a vesicle state in accordance with a cooling/heating cycle, which changes neither the size nor the size distribution of the vesicles. This lack of change suggests that the polymer memorizes a particular vesicle conformation. Given our vesicles' size tunability and structural memory, our research considerably expands the fundamental and practical scope of thermoresponsive amphiphilic graft copolymers and renders amphiphilic graft copolymers useful tools for synthesizing functional self-assembled materials.

The Amyloid as a Ribbon-Like Micelle in Contrast to Spherical Micelles Represented by Globular Proteins

Selected amyloid structures available in the Protein Data Bank have been subjected to a comparative analysis. Classification is based on the distribution of hydrophobicity in amyloids that differ with respect to sequence, chain length, the distribution of beta folds, protofibril structure, and the arrangement of protofibrils in each superfibril. The study set includes the following amyloids: Aβ (1-42), which is listed as Aβ (15-40) and carries the D23N mutation, and Aβ (11-42) and Aβ (1-40), both of which carry the E22Δ mutation, tau amyloid, and α-synuclein. Based on the fuzzy oil drop model (FOD), we determined that, despite their conformational diversity, all presented amyloids adopt a similar structural pattern that can be described as a ribbon-like micelle. The same model, when applied to globular proteins, results in structures referred to as "globular micelles," emerging as a result of interactions between the proteins' constituent residues and the aqueous solvent. Due to their composition, amyloids are unable to attain entropically favorable globular forms and instead attempt to limit contact between hydrophobic residues and water by producing elongated structures. Such structures typically contain quasi hydrophobic cores that stretch along the fibril's long axis. Similar properties are commonly found in ribbon-like micelles, with alternating bands of high and low hydrophobicity emerging as the fibrils increase in length. Thus, while globular proteins are generally consistent with a 3D Gaussian distribution of hydrophobicity, the distribution instead conforms to a 2D Gaussian distribution in amyloid fibrils.

Thermodynamics of Reactions Affected by Medium Reorganization

We present a thermodynamic analysis of the activation barrier for reactions which can be monitored through the difference in the energies of reactants and products defined as the reaction coordinate (electron and atom transfer, enzyme catalysis, etc.). The free-energy surfaces along the reaction coordinate are separated into the enthalpy and entropy surfaces. For the Gaussian statistics of the reaction coordinate, the free-energy surfaces are parabolas, and the entropy surface is an inverted parabola. Its maximum coincides with the transition state for reactions with zero value of the reaction free energy. Maximum entropic depression of the activation barrier, anticipated by the concept of transition-state ensembles, can be achieved for such reactions. From Onsager's reversibility, the entropy of equilibrium fluctuations encodes the entropic component of the activation barrier. The reorganization entropy thus becomes the critical parameter of the theory reducing the problem of activation entropy to the problem of reorganization entropy. Standard solvation theories do not allow reorganization entropy sufficient for the barrier depression. Complex media, characterized by many relaxation processes, need to be involved. Proteins provide several routes for achieving large entropic effects through incomplete (nonergodic) sampling of the complex energy landscape and by facilitating an active role of water in the reaction mechanism.