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In this paper, we are concerned with a class of second-order hemivariational inequalities involving history-dependent operators. For the problem, we first derive a semidiscrete scheme by implicit Euler formula and prove its unique solvability. The existence and uniqueness of a solution to the inequality problem is given by Rothe method. As the core part of the paper, we propose a two-step semidiscrete approximation for the problem, provide its unique solvability and obtain its second-order error estimates. The two-step scheme is more accurate than the standard implicit Euler scheme. Finally, we apply the results to a dynamic frictionless contact problem with long memory. [ABSTRACT FROM AUTHOR]

In this paper, we study an optimal control problem for a stationary Navier–Stokes hemivariational inequality with control constraints and its numerical approximation. The hemivariational inequality is the weak formulation of a stationary incompressible fluid flow problem, modeled by the Navier-Stokes equations subject to a nonleak boundary condition and a subdifferential condition of friction type. We investigate the stability of the solution of the hemivariational inequality with respect to perturbations in the density of external force and superpotential, and demonstrate the existence of a solution for the optimal control problem with the external force density as the control. Moreover, we consider the numerical solution of the optimal control problem and show its convergence. As an example and for definiteness, the numerical solution is defined through the finite element method. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying a dynamic adhesive contact model where the body is composed of a viscoelastic material with long memory. The adhesion process is modeled by a bonding field on part of the contact surface and on which the contact and the friction are modeled by nonmonotone Clarke subdifferential conditions with adhesion. Meanwhile, on another part of the contact surface, the contact is comprised of a normal compliance contact condition while the memory effects of the obstacle are considered, the friction is modeled by a version of Coulomb's law of dry friction and the friction bound is dependent on the normal stress. The variational form of the model generates a system of a doubly-history dependent variational–hemivariational inequality as well as a differential equation. Then, on the basis of the proof of abstract variational–hemivariational inequality, the existence and uniqueness results of the contact problem are established. [ABSTRACT FROM AUTHOR]

Motivation Topologically associating domains (TADs) are fundamental building blocks of 3D genome. TAD-like domains in single cells are regarded as the underlying genesis of TADs discovered in bulk cells. Understanding the organization of TAD-like domains helps to get deeper insights into their regulatory functions. Unfortunately, it remains a challenge to identify TAD-like domains on single-cell Hi-C data due to its ultra-sparsity. Results We propose scKTLD, an in silico tool for the identification of TAD-like domains on single-cell Hi-C data. It takes Hi-C contact matrix as the adjacency matrix for a graph, embeds the graph structures into a low-dimensional space with the help of sparse matrix factorization followed by spectral propagation, and the TAD-like domains can be identified using a kernel-based changepoint detection in the embedding space. The results tell that our scKTLD is superior to the other methods on the sparse contact matrices, including downsampled bulk Hi-C data as well as simulated and experimental single-cell Hi-C data. Besides, we demonstrated the conservation of TAD-like domain boundaries at single-cell level apart from heterogeneity within and across cell types, and found that the boundaries with higher frequency across single cells are more enriched for architectural proteins and chromatin marks, and they preferentially occur at TAD boundaries in bulk cells, especially at those with higher hierarchical levels. Availability and implementation scKTLD is freely available at https://github.com/lhqxinghun/scKTLD. [ABSTRACT FROM AUTHOR]

Cost-effective hydrolysis of biomass into sugars for biofuel production requires high-performance low-cost glycoside hydrolase (GH) cocktails that are active under demanding process conditions. Improving the performance of GH cocktails depends on knowledge of many critical parameters, including individual enzyme stabilities, optimal reaction conditions, kinetics, and specificity of reaction. With this information, rate- and/or yield-limiting reactions can be potentially improved through substitution, synergistic complementation, or protein engineering. Given the wide range of substrates and methods used for GH characterization, it is difficult to compare results across a myriad of approaches to identify high performance and synergistic combinations of enzymes. Here, we describe a platform for systematic screening of GH activities using automatic biomass handling, bioconjugate chemistry, robotic liquid handling, and nanostructure-initiator mass spectrometry (NIMS). Twelve well-characterized substrates spanning the types of glycosidic linkages found in plant cell walls are included in the experimental workflow. To test the application of this platform and substrate panel, we studied the reactivity of three engineered cellulases and their synergy of combination across a range of reaction conditions and enzyme concentrations. We anticipate that large-scale screening using the standardized platform and substrates will generate critical datasets to enable direct comparison of enzyme activities for cocktail design.

Harnessing the biotechnological potential of the large number of proteins available in sequence databases requires scalable methods for functional characterization. Here we propose a workflow to address this challenge by combining phylogenomic guided DNA synthesis with high-throughput mass spectrometry and apply it to the systematic characterization of GH1 β-glucosidases, a family of enzymes necessary for biomass hydrolysis, an important step in the conversion of lignocellulosic feedstocks to fuels and chemicals. We synthesized and expressed 175 GH1s, selected from over 2000 candidate sequences to cover maximum sequence diversity. These enzymes were functionally characterized over a range of temperatures and pHs using nanostructure-initiator mass spectrometry (NIMS), generating over 10,000 data points. When combined with HPLC-based sugar profiling, we observed GH1 enzymes active over a broad temperature range and toward many different β-linked disaccharides. For some GH1s we also observed activity toward laminarin, a more complex oligosaccharide present as a major component of macroalgae. An area of particular interest was the identification of GH1 enzymes compatible with the ionic liquid 1-ethyl-3-methylimidazolium acetate ([C2mim][OAc]), a next-generation biomass pretreatment technology. We thus searched for GH1 enzymes active at 70 °C and 20% (v/v) [C2mim][OAc] over the course of a 24-h saccharification reaction. Using our unbiased approach, we identified multiple enzymes of different phylogentic origin with such activities. Our approach of characterizing sequence diversity through targeted gene synthesis coupled to high-throughput screening technologies is a broadly applicable paradigm for a wide range of biological problems.