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This handbook and ready reference presents a combination of statistical, information-theoretic, and data analysis methods to meet the challenge of designing empirical models involving molecular descriptors within bioinformatics.

Context Conformation generation, also known as molecular unfolding (MU), is a crucial step in structure-based drug design, remaining a challenging combinatorial optimization problem. Quantum annealing (QA) has shown great potential for solving certain combinatorial optimization problems over traditional classical methods such as simulated annealing (SA). However, a recent study showed that a 2000-qubit QA hardware was still unable to outperform SA for the MU problem. Here, we propose the use of quantum-inspired algorithm to solve the MU problem, in order to go beyond traditional SA. We introduce a highly compact phase encoding method which can exponentially reduce the representation space, compared with the previous one-hot encoding method. For benchmarking, we tested this new approach on the public QM9 dataset generated by density functional theory (DFT). The root-mean-square deviation between the conformation determined by our approach and DFT is negligible (less than about 0.5Å), which underpins the validity of our approach. Furthermore, the median time-to-target metric can be reduced by a factor of five compared to SA. Additionally, we demonstrate a simulation experiment by MindQuantum using quantum approximate optimization algorithm (QAOA) to reach optimal results. These results indicate that quantum-inspired algorithms can be applied to solve practical problems even before quantum hardware becomes mature. Methods The objective function of MU is defined as the sum of all internal distances between atoms in the molecule, which is a high-order unconstrained binary optimization (HUBO) problem. The degree of freedom of variables is discretized and encoded with binary variables by the phase encoding method. We employ the quantum-inspired simulated bifurcation algorithm for optimization. The public QM9 dataset is generated by DFT. The simulation experiment of quantum computation is implemented by MindQuantum using QAOA.

Metal cations are associated with many biological processes. The effects of these cations on nucleic acids and chromatin were extensively studied in the early stages of nucleic acid and chromatin research. The results revealed that some monovalent and divalent metal cations, including Mg2+, profoundly affect the conformations and stabilities of nucleic acids, the folding of chromatin fibers, and the extent of chromosome condensation. Apart from these effects, there have only been a few reports on the functions of these cations. In 2007 and 2013, however, Mg2+-implicated novel phenomena were found: Mg2+ facilitates or enables both self-assembly of identical double-stranded (ds) DNA molecules and self-assembly of identical nucleosomes in vitro. These phenomena may be deeply implicated in the heterochromatin domain formation and chromatin-based phase separation. Furthermore, a recent study showed that elevation of the intranuclear Mg2+ concentration causes unusual differentiation of mouse ES (embryonic stem) cells. All of these phenomena seem to be closely related to one another. Mg2+ seems to be a key regulator of chromatin dynamics and chromatin-based biological processes.

Internal cavities are important elements in protein structure, dynamics, stability and function. Here we use NMR spectroscopy to investigate the binding of molecular oxygen (O 2 ) to cavities in a well-studied model for ligand binding, the L99A mutant of T4 lysozyme. On increasing the O 2 concentration to 8.9 mM, changes in 1 H, 15 N and 13 C chemical shifts and signal broadening were observed specifically for backbone amide and side chain methyl groups located around the two hydrophobic cavities of the protein. O 2 -induced longitudinal relaxation enhancements for amide and methyl protons could be adequately accounted for by paramagnetic dipolar relaxation. These data provide the first experimental demonstration that O 2 binds specifically to the hydrophobic and not the hydrophilic cavities, in a protein. Molecular dynamics simulations visualized the rotational and translational motions of O 2 in the cavities, as well as the binding and egress of O 2 , suggesting that the channel consisting of helices D, E, G, H and J could be the potential gateway for ligand binding to the protein. Due to strong paramagnetic relaxation effects, O 2 gas-pressure NMR measurements can detect hydrophobic cavities when populated to as little as 1% and thereby provide a general and highly sensitive method for detecting oxygen binding in proteins.

We establish and quantify correlations among the molecular structures, interaction forces, and physical processes associated with light-responsive self-assembled surfactant monolayers or bilayers at interfaces. Using the surface forces apparatus (SFA), the interaction forces between adsorbed monolayers and bilayers of an azobenzene-functionalized surfactant can be drastically and controllably altered by light-induced conversion of trans and cis molecular conformations. These reversible conformation changes affect significantly the shape of the molecules, especially in the hydrophobic region, which induces dramatic transformations of molecular packing in self-assembled structures, causing corresponding modulation of electrostatic double layer, steric hydration, and hydrophobic interactions. For bilayers, the isomerization from trans to cis exposes more hydrophobic groups, making the cis bilayers more hydrophobic, which lowers the activation energy barrier for (hemi) fusion. A quantitative and general model is derived for the interaction potential of charged bilayers that includes the electrostatic double-layer force of the Derjaguin-Landau-Verwey-Overbeek theory, attractive hydrophobic interactions, and repulsive steric-hydration forces. The model quantitatively accounts for the elastic strains, deformations, long-range forces, energy maxima, adhesion minima, as well as the instability (when it exists) as two bilayers breakthrough and (hemi) fuse. These results have several important implications, including quantitative and qualitative understanding of the hydrophobic interaction, which is furthermore shown to be a nonadditive interaction.

Stereochemistry plays a central role in controlling molecular recognition and interaction: the chemical and biological properties of molecules depend not only on the nature of their constituent atoms but also on how these atoms are positioned in space. Chiral specificity is consequently fundamental in chemical biology and pharmacology 1 , 2 and has accordingly been widely studied. Advances in scanning probe microscopies now make it possible to probe chiral phenomena at surfaces at the molecular level. These methods have been used to determine the chirality of adsorbed molecules 3 , 4 , 5 , and to provide direct evidence for chiral discrimination in molecular interactions 6 and the spontaneous resolution of adsorbates into extended enantiomerically pure overlayers 3 , 7 , 8 , 9 . Here we report scanning tunnelling microscopy studies of cysteine adsorbed to a (110) gold surface, which show that molecular pairs formed from a racemic mixture of this naturally occurring amino acid are exclusively homochiral, and that their binding to the gold surface is associated with local surface restructuring. Density-functional theory 10 calculations indicate that the chiral specificity of the dimer formation process is driven by the optimization of three bonds on each cysteine molecule. These findings thus provide a clear molecular-level illustration of the well known three-point contact model 11 , 12 for chiral recognition in a simple bimolecular system.

Confinement of fluorescent dyes is known to enhance fluorescence properties by reducing aggregation and restricting molecular motion, but few studies have attempted to modulate the extent of confinement. In this work, we explored extreme confinement by exploiting the rigid structure of metal–organic frameworks (MOFs). Other than the commonly known restriction of peripheral substituents in fluorescent molecules for aggregation‐induced emission (AIE)‐like effects, the more powerful confinement surprisingly led to buckling of the chromophore core, leading to reduced fluorescence lifetime. We name these effects buckling‐induced quenching (BIQ). By studying 14 dyes in zeolitic‐imidazolate framework 8 (ZIF8), we systematically analyzed their confined behaviors, establishing strong correlations: The reduction of chromophore planarity always leads to a decrease of fluorescence lifetimes, whereas reduction in the longest dimension of the confined molecule, while maintaining chromophore planarity, always leads to an increased lifetime. Confinement in the larger cavities of ZIF71 leads to signs of alleviation, in good agreement with our hypotheses. The BIQ effects provide an important complement for the well‐known confinement effects, and the extreme confinement serves also as an important reference for more subtle effects in various applications. This study investigates the behavior of 14 fluorescent dyes under extreme confinement in metal–organic frameworks. A dragonfly illustration analogizes three states: free flight for unconfined dyes, folded wings for AIE‐like effects, and buckled bodies for BIQ effects. The visual metaphor highlights how extreme spatial restriction alters molecular conformation and fluorescence.

Protein molecular conformation is an important and challenging problem in biophysics. It is to recover the structure of proteins based on limited information such as noised distances, lower and upper bounds on some distances between atoms. In this paper, based on the recent progress in numerical algorithms for Euclidean distance matrix (EDM) optimization problems, we propose a EDM model for protein molecular conformation. We reformulate the problem as a rank-constrained least squares problem with linear equality constraints, box constraints, as well as a cone constraint. Due to the nonconvexity of the problem, we develop a majorized penalty approach to solve the problem. We apply the accelerated block coordinate descent algorithm proposed in Sun et al. (SIAM J Optim 26(2):1072–1100, 2016) to solve the resulting subproblem. Extensive numerical results demonstrate the efficiency of the proposed model.

Nucleation of crystals from solution is fundamental to many natural and industrial processes. In this work, the molecular mechanism of conformational polymorphism nucleation and the links between the molecular conformation in solutions and in crystals were investigated in detail by using 5-nitrofurazone as the model compound. Different polymorphs were prepared, and the conformations in solutions obtained by dissolving different polymorphs were analysed and compared. The solutions of 5-nitrofurazone were proven to contain multiple conformers through quantum chemical computation, Raman spectra analysis, 2D nuclear Overhauser effect spectroscopy spectra analysis and molecular dynamics simulation. The conformational evolution and desolvation path was illustrated according to the 1 H NMR spectra of solutions with different concentrations. Finally, based on all the above analysis, the molecular conformational evolution path during nucleation of 5-nitrofurazone was illustrated. The results presented in this work shed a new light on the molecular mechanism of conformational polymorphism nucleation in solution.