Potential Anti-COVID-19 Therapeutics that Block the Early Stage of the Viral Life Cycle: Structures, Mechanisms, and Clinical Trials

The ongoing pandemic of coronavirus disease-2019 (COVID-19) is being caused by severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2). The disease continues to present significant challenges to the health care systems around the world. This is primarily because of the lack of vaccines to protect against the infection and the lack of highly effective therapeutics to prevent and/or treat the illness. Nevertheless, researchers have swiftly responded to the pandemic by advancing old and new potential therapeutics into clinical trials. In this review, we summarize potential anti-COVID-19 therapeutics that block the early stage of the viral life cycle. The review presents the structures, mechanisms, and reported results of clinical trials of potential therapeutics that have been listed in clinicaltrials.gov. Given the fact that some of these therapeutics are multi-acting molecules, other relevant mechanisms will also be described. The reviewed therapeutics include small molecules and macromolecules of sulfated polysaccharides, polypeptides, and monoclonal antibodies. The potential therapeutics target viral and/or host proteins or processes that facilitate the early stage of the viral infection. Frequent targets are the viral spike protein, the host angiotensin converting enzyme 2, the host transmembrane protease serine 2, and clathrin-mediated endocytosis process. Overall, the review aims at presenting update-to-date details, so as to enhance awareness of potential therapeutics, and thus, to catalyze their appropriate use in combating the pandemic.

Algorithms Based on Path Contraction Carrying Weights for Enumerating Subtrees of Tricyclic Graphs

The subtree number index of a graph, defined as the number of subtrees, attracts much attention recently. Finding a proper algorithm to compute this index is an important but difficult problem for a general graph. Even for unicyclic and bicyclic graphs, it is not completely trivial, though it can be figured out by try and error. However, it is complicated for tricyclic graphs. This paper proposes path contraction carrying weights (PCCWs) algorithms to compute the subtree number index for the nontrivial case of bicyclic graphs and all 15 cases of tricyclic graphs, based on three techniques: PCCWs, generating function and structural decomposition. Our approach provides a foundation and useful methods to compute subtree number index for graphs with more complicated cycle structures and can be applied to investigate the novel structural property of some important nanomaterials such as the pentagonal carbon nanocone.

Structural Pluralism in Gerald Finzi’s Earth and Air and Rain

The genre of song cycle is complex and heterogeneous. As well as attracting significant contention in relation to matters of typology, the inherent aesthetic issues that arise from any intermedial union of words and music are compounded in the potential narrative consequences of the song cycle. Advocating melopoetic practices, my research seeks to examine the different cycle structures that emerge within the twentieth-century, English repertory. Gerald Finzi’s Earth and Air and Rain, composed in 1936, has a somewhat ambiguous genesis and complex history in performance and publication. This article explores the work’s potential to be characterized by structural pluralism; that is, the possibility that there may be more than one way of understanding and navigating the cycle’s structure. The genre of song cycle is complex and heterogeneous. As well as attracting significant contention in relation to matters of typology, the inherent aesthetic issues that arise from any intermedial union of words and music are compounded in the potential narrative consequences of the song cycle. Advocating melopoetic practices, my research seeks to examine the different cycle structures that emerge within the twentieth-century, English repertory. Gerald Finzi’s Earth and Air and Rain, composed in 1936, has a somewhat ambiguous genesis and complex history in performance and publication. This article explores the work’s potential to be characterized by structural pluralism; that is, the possibility that there may be more than one way of understanding and navigating the cycle’s structure.

A New Framework for Analysis of Coevolutionary Systems—Directed Graph Representation and Random Walks

Studying coevolutionary systems in the context of simplified models (i.e., games with pairwise interactions between coevolving solutions modeled as self plays) remains an open challenge since the rich underlying structures associated with pairwise-comparison-based fitness measures are often not taken fully into account. Although cyclic dynamics have been demonstrated in several contexts (such as intransitivity in coevolutionary problems), there is no complete characterization of cycle structures and their effects on coevolutionary search. We develop a new framework to address this issue. At the core of our approach is the directed graph (digraph) representation of coevolutionary problems that fully captures structures in the relations between candidate solutions. Coevolutionary processes are modeled as a specific type of Markov chains—random walks on digraphs. Using this framework, we show that coevolutionary problems admit a qualitative characterization: a coevolutionary problem is either solvable (there is a subset of solutions that dominates the remaining candidate solutions) or not. This has an implication on coevolutionary search. We further develop our framework that provides the means to construct quantitative tools for analysis of coevolutionary processes and demonstrate their applications through case studies. We show that coevolution of solvable problems corresponds to an absorbing Markov chain for which we can compute the expected hitting time of the absorbing class. Otherwise, coevolution will cycle indefinitely and the quantity of interest will be the limiting invariant distribution of the Markov chain. We also provide an index for characterizing complexity in coevolutionary problems and show how they can be generated in a controlled manner.