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Abstract We present analytical results of the fundamental properties of the one-dimensional (1D) Hubbard model with a repulsive interaction. The new model results with arbitrary external fields include: (I) using the exact solutions of the Bethe ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. We then investigate the gapped excitations in terms of the spin string and the $k-\mathrm{\Lambda }$string bound states at arbitrary driving fields, showing subtle differences in spin magnons and charge $\eta$-pair excitations. (II) For a high-density and high spin magnetization region, i.e. near the quadruple critical point, we further analytically obtain the thermodynamic properties, dimensionless ratios and scaling functions near quantum phase transitions. (III) Importantly, we give the general scaling functions at quantum criticality for arbitrary filling and interaction strength. These can directly apply to other integrable models. (IV) Based on the fractional excitations and the scaling laws, the spin-incoherent Luttinger liquid (SILL) with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of conformal field theory. We also, for the first time, obtain the analytical results of the thermodynamics for the SILL. (V) Finally, to capture deeper insights into the Mott insulator and interaction-driven criticality, we further study the double occupancy and propose its associated contact and contact susceptibilities, through which an adiabatic cooling scheme based upon quantum criticality is proposed. In this scenario, we build up general relations among arbitrary external- and internal-potential-driven quantum phase transitions, providing a comprehensive understanding of quantum criticality. Our methods offer rich perspectives of quantum integrability and offer promising guidance for future experiments with interacting electrons and ultracold atoms, both with and without a lattice. 

Although the one-dimensional repulsive Fermi-Hubbard model has been intensively studied over many decades, a rigorous understanding of many aspects of the model is still lacking. In this work, based on the solutions to the thermodynamic Bethe ansatz equations, we provide a rigorous study on the following. (1) We calculate the fractional excitations of the system in various phases, from which we identify the parameter regime featuring the spin-incoherent Luttinger liquid (SILL). We investigate the universal properties and the asymptotic of correlation functions of the SILL. (2) We study the interaction-driven phase transition and the associated criticality, and build up an essential connection between the contact susceptibilities and the variations of density, magnetization, and entropy with respect to the interaction strength. As an application of these concepts, which hold true for higher-dimensional systems, we propose a quantum cooling scheme based on the interaction-driven refrigeration cycle. 

Abstract AAA+ proteases degrade intracellular proteins in a highly specific manner.E. coliClpXP, for example, relies on a C-terminal ssrA tag or other terminal degron sequences to recognize proteins, which are then unfolded by ClpX and subsequently translocated through its axial channel and into the degradation chamber of ClpP for proteolysis. Prior cryo-EM structures reveal that the ssrA tag initially binds to a ClpX conformation in which the axial channel is closed by a pore-2 loop. Here, we show that substrate-free ClpXP has a nearly identical closed-channel conformation. We destabilize this closed-channel conformation by deleting residues from the ClpX pore-2 loop. Strikingly, open-channel ClpXP variants degrade non-native proteins lacking degrons faster than the parental enzymes in vitro but degraded GFP-ssrA more slowly. When expressed inE. coli, these open channel variants behave similarly to the wild-type enzyme in assays of filamentation and phage-Mu plating but resulted in reduced growth phenotypes at elevated temperatures or when cells were exposed to sub-lethal antibiotic concentrations. Thus, channel closure is an important determinant of ClpXP degradation specificity. 

Preaxial dominance in the mesopodium is limited to distal carpals/tarsals and facilitates digit reduction in early tetrapods. 

Biologically active ligands (e.g., RGDS from fibronectin) play critical roles in the development of chemically defined biomaterials. However, recent decades have shown only limited progress in discovering novel extracellular matrix–protein–derived ligands for translational applications. Through motif analysis of evolutionarily conserved RGD-containing regions in laminin (LM) and peptide-functionalized hydrogel microarray screening, we identified a peptide (a1) that showed superior supports for endothelial cell (EC) functions. Mechanistic studies attributed the results to the capacity of a1 engaging both LM- and Fn-binding integrins. RNA sequencing of ECs in a1-functionalized hydrogels showed ~60% similarities with Matrigel in “vasculature development” gene ontology terms. Vasculogenesis assays revealed the capacity of a1-formulated hydrogels to improve EC network formation. Injectable alginates functionalized with a1 and MMPQK (a vascular endothelial growth factor–mimetic peptide with a matrix metalloproteinase–degradable linker) increased blood perfusion and functional recovery over decellularized extracellular matrix and (RGDS + MMPQK)–functionalized hydrogels in an ischemic hindlimb model, illustrating the power of this approach.