Vectors on manifolds

The vector, the dual vector (one-form), components and inner products are defined and discussed. The difference between a vector and a one-form is carefully drawn out, with examples and diagrams. Contravariant and covariant components are described, and the way in which the metric can relate them is carefully explained. The transformation of vector components under a change of coordinate basis is derived.

Applications of Ultrasound-Mediated Drug Delivery and Gene Therapy

Gene therapy has continuously evolved throughout the years since its first proposal to develop more specific and effective transfection, capable of treating a myriad of health conditions. Viral vectors are some of the most common and most efficient vehicles for gene transfer. However, the safe and effective delivery of gene therapy remains a major obstacle. Ultrasound contrast agents in the form of microbubbles have provided a unique solution to fulfill the need to shield the vectors from the host immune system and the need for site specific targeted therapy. Since the discovery of the biophysical and biological effects of microbubble sonification, multiple developments have been made to enhance its applicability in targeted drug delivery. The concurrent development of viral vectors and recent research on dual vector strategies have shown promising results. This review will explore the mechanisms and recent advancements in the knowledge of ultrasound-mediated microbubbles in targeting gene and drug therapy.

An intein-mediated split-nCas9 system for base editing in plants

Virus-assisted delivery of the clustered regularly interspaced short palindromic (CRISPR)/CRISPR-associated (Cas) system represents a promising approach for editing plant genomes. However, the relatively large size of the CRISPR/Cas9 system is challenging to package into viral vectors with confined packaging capacity. To address this technical challenge, we developed a strategy that splits the required CRISPR-Cas9 components across a dual-vector system in which CRISPR-Cas reassembles into an active form following co-infection to achieve targeted genome editing in plant cells. An intein-mediated split system was adapted and optimized in plant cells by successfully demonstrating split-eYGFPuv expression. Using a plant-based biosensor, we demonstrated for the first time that the split-SpnCas9 is capable of inducing efficient base editing in plant cells and identified several valid split sites for future biodesign strategies. Overall, this strategy provides new opportunities to bridge different CRISPR/Cas9 tools including base editor, prime editor, and CRISPR activation with virus-mediated gene editing.

On an Anti-Torqued Vector Field on Riemannian Manifolds

A torqued vector field ξ is a torse-forming vector field on a Riemannian manifold that is orthogonal to the dual vector field of the 1-form in the definition of torse-forming vector field. In this paper, we introduce an anti-torqued vector field which is opposite to torqued vector field in the sense it is parallel to the dual vector field to the 1-form in the definition of torse-forming vector fields. It is interesting to note that anti-torqued vector fields do not reduce to concircular vector fields nor to Killing vector fields and thus, give a unique class among the classes of special vector fields on Riemannian manifolds. These vector fields do not exist on compact and simply connected Riemannian manifolds. We use anti-torqued vector fields to find two characterizations of Euclidean spaces. Furthermore, a characterization of an Einstein manifold is obtained using the combination of a torqued vector field and Fischer–Marsden equation. We also find a condition under which the scalar curvature of a compact Riemannian manifold admitting an anti-torqued vector field is strictly negative.

Metasurface of Combined Semicircular Rings with Orthogonal Slit Pairs for Generation of Dual Vector Beams

Manipulation of multichannel vector beams (VBs) with metasurfaces is an important topic and holds potential applications in information technology. In this paper, we propose a novel metasurface for the generation of dual VBs, which is composed of orthogonal slit pairs arranged on multiple groups of combined semicircular rings (CSRs). A group of CSRs include a right-shifted set and a left-shifted set of semicircular rings, and each set of semicircular rings has two halves of circles with different radii, sharing the same shifted center. Under the illumination of linearly polarized light, the two shifted sets of semicircular rings generate the two VBs at the shifted center positions on the observation plane. The slit units of each set are designed with independent rotation order and initial orientation angle. By adjusting the linear polarization of illumination, both two VBs with their orders and polarization states are independently controlled simultaneously. The principle and design are demonstrated by the finite-difference time domain (FDTD) simulation. The work is of significance for miniatured devices of VB generators and for related applications.

Von Willebrand disease: What does the future hold?

Von Willebrand disease (VWD) is characterized by its heterogeneous clinical manifestation, which complicates its diagnosis and management. The clinical management of VWD has remained essentially unchanged over the last 30 years or so, using von Willebrand factor (VWF) concentrates, desmopressin and anti-fibrinolytic agents as main tools to control bleeding. This is in contrast to hemophilia A, for which a continuous innovative path has led to novel treatment modalities. Despite current VWD management being considered effective, quality-of-life studies consistently reveal a higher than anticipated burden of VWD on patients, which is particularly true for women. Apparently, despite our perceived notion of current therapeutic efficiency, there is space for innovation with the goal to reach superior efficacy. Developing innovative treatments for VWD is complex, especially given the heterogeneity of the disease and the multifunctional nature of VWF. In this perspective article, we describe several potential strategies that could provide the basis for future VWD treatments. These include genetic approaches such as gene therapy using dual-vector adeno-associated virus and transcriptional silencing of mutant alleles. Furthermore, protein-based approaches to increase FVIII levels in VWD-type 3 or 2N patients will be discussed. Finally, antibody-based options to interfere with VWF degradation (for congenital VWD-type 2A or acquired Von Willebrand syndrome-type 2A) or increase endogenous VWF levels (for VWD-type 1) will be presented. By highlighting these potential strategies, we hope to initiate an innovative path, which ultimately would allow us to better serve VWD patients and their specific needs.