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Cryo-electron microscopy (cryo-EM) is an important experimental technique for the structural analysis of biomolecules that are difficult or impossible to crystallize. The three-dimensional structure of a biomolecule can be reconstructed using two-dimensional electron-density maps, which are experimentally sampled via the electron beam irradiation of vitreous ice in which the target biomolecules are embedded. One assumption required for this reconstruction is that the orientation of the biomolecules in the vitreous ice is isotropic. However, this is not always the case and two-dimensional electron-density maps are often sampled using preferred biomolecular orientations, which can make reconstruction difficult or impossible. Compensation for under-represented views is computationally feasible for the reconstruction of three-dimensional electron density maps, but one must know whether or not there is any missing information in the sampled two-dimensional electron density maps. Thus, a measure to identify whether a cryo-EM data is obtained from the bio­molecules adopting preferred orientations is required. In the present study, we propose a measure for which the geometry of manifold projected onto a low-dimensional space is used. To show the usefulness of the measure, we perform simulations for cryo-EM experiment of a protein. It is found that the geometry of manifold projected onto a two-dimensional space for a protein adopting a preferred biomolecular orientation is significantly different from that for a protein adopting a uniform orientation. This result suggests that the geometry of manifold projected onto a low-dimensional space can be used for the measure for the identification that the biomolecules adopt preferred orientations.

We review a general framework of pressure effects on the structures formed by entropically driven self-assembly (for example, denaturation of proteins from their native structure and dissociation of ordered structure of the amyloid fibril occur at high pressures). In the framework, the translational entropy of water is an essential factor. Our findings are as follows: at low pressures, the structures almost minimizing the excluded volume (EV) generated for water molecules are stable. On the other hand, at high pressures, the structures possessing the largest possible water-accessible surface area together with sufficiently small EV become more stable. These characteristics are consistent with experimental observations.

The hydration free energy (HFE) is a crucially important physical quantity to discuss various chemical processes in aqueous solutions. Although an explicit-solvent computation with molecular dynamics (MD) simulations is a preferable treatment of the HFE, huge computational load has been inevitable for large, complex solutes like proteins. In the present paper, we propose an efficient computation method for the HFE. In our method, the HFE is computed as a sum of (UUV)/2 (UUV) is the ensemble average of the sum of pair interaction energy between solute and water molecule) and the water reorganization term mainly reflecting the excluded volume effect. Since (UUV) can readily be computed through a MD of the system composed of solute and water, an efficient computation of the latter term leads to a reduction of computational load. We demonstrate that the water reorganization term can quantitatively be calculated using the morphometric approach (MA) which expresses the term as the linear combinations of the four geometric measures of a solute and the corresponding coefficients determined with the energy representation (ER) method. Since the MA enables us to finish the computation of the solvent reorganization term in less than 0.1 s once the coefficients are determined, the use of the MA enables us to provide an efficient computation of the HFE even for large, complex solutes. Through the applications, we find that our method has almost the same quantitative performance as the ER method with substantial reduction of the computational load. [ABSTRACT FROM AUTHOR]

Analyzing the structure of proteins in terms of their structural polymorphism has been recently performed using their two-dimensional electron-density maps obtained through cryo-electron microscopy (cryo-EM) experiments. In performing such analyses for a protein, the initial step is to classify its maps in terms of its structural polymorphism. Although current programs used for analyzing cryo-EM experimental data implement classification algorithms, they require the number of classes as input prior to conducting the classification. However, the number of classes is generally unknown, and choosing the wrong number of classes leads to difficulties in performing the structural analyses. Manifold learning is a candidate to resolve this issue because it has been successfully used for the classification of twodimensional electron-density maps. However, a low signal-to-noise ratio of the maps would lead to the failure of the classification, especially for small proteins. Here, we investigated the effects of a low-pass filter, which can reduce noise, on the classification of two-dimensional electron-density maps using manifold learning. We performed a simulation for a cryo-EM experiment of a small protein that predominantly adopts two states. We found that while the classification failed for the raw two-dimensional electron-density maps, it was successful for the maps where a low-pass filter was applied. We also investigated the dependence of the filter’s parameters on the classification and found a relation between the values of the parameters and the degree of success of the classification. [ABSTRACT FROM AUTHOR]

Markov state models (MSMs) have enabled us to analyze the long-time behaviors of protein motions using molecular dynamics (MD) simulation data. To construct the model, protein conformations must be classified into states. We have recently shown that an MSM constructed using the classification results obtained via manifold learning performs better when calculating the time series of an observable as compared with an MSM constructed using the K-center method for classification [R. Ito and T. Yoshidome, Chem. Phys. Lett. 691, 22 (2018)]. Our classification protocol involved a visual classification step. We investigated the performance of an MSM, constructed using an automatic classification method that was a hybrid of the manifold learning, K-means method, and the silhouette score. The time evolution of an observable obtained using MSM was in good agreement with that obtained directly through MD. [ABSTRACT FROM AUTHOR]

Coherent x-ray diffraction imaging (CXDI) enables us to visualize noncrystalline sample particles with micrometer to submicrometer dimensions. Using x-ray free-electron laser (XFEL) sources, two-dimensional diffraction patterns are collected from fresh samples supplied to the irradiation area in the "diffraction-beforedestruction" scheme. A recent significant increase in the intensity of the XFEL pulse is promising and will allow us to visualize the three-dimensional structures of proteins using XFEL-CXDI in the future. For the protocol proposed for molecular structure determination using future XFEL-CXDI [T. Oroguchi and M. Nakasako, Phys. Rev. E 87. 022712 (2013)], we require an algorithm that can classify the data in accordance with the structural polymorphism of proteins arising from their conformational dynamics. However, most of the algorithms proposed primarily require the numbers of conformational classes, and then the results are biased by the numbers. To improve this point, here we examine whether a method based on the manifold concept can classify simulated XFEL-CXDI data with respect to the structural polymorphism of a protein that predominantly adopts two states. After random sampling of the conformations of the two states and in-between states from the trajectories of molecular dynamics simulations, a diffraction pattern is calculated from each conformation. Classification was performed by using our custom-made program suite named ENMA, in which the diffusion map (DM) method developed based on the manifold concept was implemented. We successfully classify most of the projection electron density maps phase retrieved from diffraction patterns into each of the two states and in-between conformations without the knowledge of the number of conformational classes. We also examined the classification of the projection electron density maps of each of the three states with respect to the Euler angle. The present results suggest that the DM method is imperative for future applications of XFEL-CXDI experiments for proteins, and clarify issues to be taken care of in the future application. [ABSTRACT FROM AUTHOR]