Improvement of Heterologous Soluble Expression of L-amino Acid Oxidase Using Logistic Regression.

Successful implementation of enzymes in practical application hinges on the development of efficient mass production techniques. However, in a heterologous expression system, the protein is often unable to fold correctly and, thus, forms inclusion bodies, resulting in the loss of its original activity. In this study, we present a new and more accurate model for predicting amino acids associated with an increased L-amino acid oxidase (LAO) solubility. Expressing LAO from Rhizoctonia solani in Escherichia coli and combining random mutagenesis and statistical logistic regression, we modified 108 amino acid residues by substituting hydrophobic amino acids with serine and hydrophilic amino acids with alanine. Our results indicated that specific mutations in Euclidean distance, glycine, methionine, and secondary structure increased LAO expression. Furthermore, repeated mutations were performed for LAO based on logistic regression models. The mutated LAO displayed a significantly increased solubility, with the 6-point and 58-point mutants showing a 2.64- and 4.22-fold increase, respectively, compared with WT-LAO. Ultimately, using recombinant LAO in the biotransformation of α-keto acids indicates its great potential as a biocatalyst in industrial production.

Tuning the Trade-Off between Ethane/Ethylene Selectivity and Adsorption Capacity within Isoreticular Microporous Metal-Organic Frameworks by Linker Fine-Fluorination.

The pore dimension and surface property directly dictate the transport of guests, endowing diverse gas selective adsorptions to porous materials. It is highly relevant to construct metal-organic frameworks (MOFs) with designable functional groups that can achieve feasible pore regulation to improve their separation performances. However, the role of functionalization in different positions or degrees within framework on the separation of light hydrocarbon has rarely been emphasized. In this context, four isoreticular MOFs (TKL-104-107) bearing dissimilar fluorination are rationally screened out and afforded intriguing differences in the adsorption behavior of C2 H6 and C2 H4 . Ortho-fluoridation of carboxyl allows TKL-105-107 to exhibit enhanced structural stabilities, impressive C2 H6 adsorption capacities (>125 cm3 g-1 ) and desirable inverse selectivities (C2 H6 over C2 H4 ). The more modified ortho-fluorine group and meta-fluorine group of carboxyl have improved the C2 H6 /C2 H4 selectivity and adsorption capacity, respectively, and the C2 H6 /C2 H4 separation potential can be well optimized via linker fine-fluorination. Meanwhile, dynamic breakthrough experiments proved that TKL-105-107 can be used as highly efficient C2 H6 -selective adsorbents for C2 H4 purification. This work highlights that the purposeful functionalization of pore surfaces facilitates the assembly of highly efficient MOF adsorbents for specific gas separation.

Spherical Parameterization Balancing Angle and Area Distortions.

This work presents a novel framework for spherical mesh parameterization. An efficient angle-preserving spherical parameterization algorithm is introduced, which is based on dynamic Yamabe flow and the conformal welding method with solid theoretic foundation. An area-preserving spherical parameterization is also discussed, which is based on discrete optimal mass transport theory. Furthermore, a spherical parameterization algorithm, which is based on the polar decomposition method, balancing angle distortion and area distortion is presented. The algorithms are tested on 3D geometric data and the experiments demonstrate the efficiency and efficacy of the proposed methods.

Hyperbolic Harmonic Mapping for Surface Registration.

Automatic computation of surface correspondence via harmonic map is an active research field in computer vision, computer graphics and computational geometry. It may help document and understand physical and biological phenomena and also has broad applications in biometrics, medical imaging and motion capture industries. Although numerous studies have been devoted to harmonic map research, limited progress has been made to compute a diffeomorphic harmonic map on general topology surfaces with landmark constraints. This work conquers this problem by changing the Riemannian metric on the target surface to a hyperbolic metric so that the harmonic mapping is guaranteed to be a diffeomorphism under landmark constraints. The computational algorithms are based on Ricci flow and nonlinear heat diffusion methods. The approach is general and robust. We employ our algorithm to study the constrained surface registration problem which applies to both computer vision and medical imaging applications. Experimental results demonstrate that, by changing the Riemannian metric, the registrations are always diffeomorphic and achieve relatively high performance when evaluated with some popular surface registration evaluation standards.

Optimal mass transport for shape matching and comparison.

Surface based 3D shape analysis plays a fundamental role in computer vision and medical imaging. This work proposes to use optimal mass transport map for shape matching and comparison, focusing on two important applications including surface registration and shape space. The computation of the optimal mass transport map is based on Monge-Brenier theory, in comparison to the conventional method based on Monge-Kantorovich theory, this method significantly improves the efficiency by reducing computational complexity from O(n(2)) to O(n) . For surface registration problem, one commonly used approach is to use conformal map to convert the shapes into some canonical space. Although conformal mappings have small angle distortions, they may introduce large area distortions which are likely to cause numerical instability thus resulting failures of shape analysis. This work proposes to compose the conformal map with the optimal mass transport map to get the unique area-preserving map, which is intrinsic to the Riemannian metric, unique, and diffeomorphic. For shape space study, this work introduces a novel Riemannian framework, Conformal Wasserstein Shape Space, by combing conformal geometry and optimal mass transport theory. In our work, all metric surfaces with the disk topology are mapped to the unit planar disk by a conformal mapping, which pushes the area element on the surface to a probability measure on the disk. The optimal mass transport provides a map from the shape space of all topological disks with metrics to the Wasserstein space of the disk and the pullback Wasserstein metric equips the shape space with a Riemannian metric. We validate our work by numerous experiments and comparisons with prior approaches and the experimental results demonstrate the efficiency and efficacy of our proposed approach.

Shape Classification Using Wasserstein Distance for Brain Morphometry Analysis.

Brain morphometry study plays a fundamental role in medical imaging analysis and diagnosis. This work proposes a novel framework for brain cortical surface classification using Wasserstein distance, based on uniformization theory and Riemannian optimal mass transport theory. By Poincare uniformization theorem, all shapes can be conformally deformed to one of the three canonical spaces: the unit sphere, the Euclidean plane or the hyperbolic plane. The uniformization map will distort the surface area elements. The area-distortion factor gives a probability measure on the canonical uniformization space. All the probability measures on a Riemannian manifold form the Wasserstein space. Given any 2 probability measures, there is a unique optimal mass transport map between them, the transportation cost defines the Wasserstein distance between them. Wasserstein distance gives a Riemannian metric for the Wasserstein space. It intrinsically measures the dissimilarities between shapes and thus has the potential for shape classification. To the best of our knowledge, this is the first. work to introduce the optimal mass transport map to general Riemannian manifolds. The method is based on geodesic power Voronoi diagram. Comparing to the conventional methods, our approach solely depends on Riemannian metrics and is invariant under rigid motions and scalings, thus it intrinsically measures shape distance. Experimental results on classifying brain cortical surfaces with different intelligence quotients demonstrated the efficiency and efficacy of our method.

Area-preservation mapping using optimal mass transport.

We present a novel area-preservation mapping/flattening method using the optimal mass transport technique, based on the Monge-Brenier theory. Our optimal transport map approach is rigorous and solid in theory, efficient and parallel in computation, yet general for various applications. By comparison with the conventional Monge-Kantorovich approach, our method reduces the number of variables from O(n2) to O(n), and converts the optimal mass transport problem to a convex optimization problem, which can now be efficiently carried out by Newton's method. Furthermore, our framework includes the area weighting strategy that enables users to completely control and adjust the size of areas everywhere in an accurate and quantitative way. Our method significantly reduces the complexity of the problem, and improves the efficiency, flexibility and scalability during visualization. Our framework, by combining conformal mapping and optimal mass transport mapping, serves as a powerful tool for a broad range of applications in visualization and graphics, especially for medical imaging. We provide a variety of experimental results to demonstrate the efficiency, robustness and efficacy of our novel framework.

Hyperbolic harmonic brain surface registration with curvature-based landmark matching.

Brain Cortical surface registration is required for inter-subject studies of functional and anatomical data. Harmonic mapping has been applied for brain mapping, due to its existence, uniqueness, regularity and numerical stability. In order to improve the registration accuracy, sculcal landmarks are usually used as constraints for brain registration. Unfortunately, constrained harmonic mappings may not be diffeomorphic and produces invalid registration. This work conquer this problem by changing the Riemannian metric on the target cortical surface o a hyperbolic metric, so that the harmonic mapping is guaranteed to be a diffeomorphism while the landmark constraints are enforced as boundary matching condition. The computational algorithms are based on the Ricci flow method and yperbolic heat diffusion. Experimental results demonstrate that, by changing the Riemannian metric, the registrations are always diffeomorphic, with higher qualities in terms of landmark alignment, curvature matching, area distortion and overlapping of region of interests.

1-Methyl-3,5-bis-(3-methyl-phen-yl)benzene.

In the title compound, C(21)H(20), the dihedral angles formed by the central benzene ring with the outer benzene rings are 21.43 (6) and 31.70 (4)°. The crystal packing is stabilized by a weak π-π stacking inter-action, with a centroid-centroid distance of 3.843 (3) Å.

Bis[µ-3-(1H-benzimidazol-2-yl)benzoato]dicopper(I).

The dimeric title complex, [Cu(2)(C(14)H(9)N(2)O(2))(2)], resides on a center of symmetry. In the crystal, the mol-ecules are packed via π-π stacking inter-actions alternating between imidazole and benzene rings [mean inter-planar distances = 3.754 (3) and 3.624 (3) Å]. An inter-molecular N-H⋯O hydrogen bond links the dimers together. The two-coordinate Cu(I) atom displays an O-Cu-N bond angle of 176.3 (2)°. The Cu⋯Cu distance within the dimer is 5.100 (2) Å.