3 research outputs found
On the Directional Derivative of Kemeny's Constant
In a connected graph, Kemeny's constant gives the expected time of a random
walk from an arbitrary vertex to reach a randomly-chosen vertex .
Because of this, Kemeny's constant can be interpreted as a measure of how well
a graph is connected. It is generally unknown how the addition or removal of
edges affects Kemeny's constant. Inspired by the directional derivative of the
normalized Laplacian, we derive the directional derivative of Kemeny's constant
for several graph families. In addition, we find sharp bounds for the
directional derivative of an eigenvalue of the normalized Laplacian and bounds
for the directional derivative of Kemeny's constant
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Structural basis of SARS-CoV-2 Omicron immune evasion and receptor engagement.
The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Omicron variant of concern evades antibody-mediated immunity that comes from vaccination or infection with earlier variants due to accumulation of numerous spike mutations. To understand the Omicron antigenic shift, we determined cryo-electron microscopy and x-ray crystal structures of the spike protein and the receptor-binding domain bound to the broadly neutralizing sarbecovirus monoclonal antibody (mAb) S309 (the parent mAb of sotrovimab) and to the human ACE2 receptor. We provide a blueprint for understanding the marked reduction of binding of other therapeutic mAbs that leads to dampened neutralizing activity. Remodeling of interactions between the Omicron receptor-binding domain and human ACE2 likely explains the enhanced affinity for the host receptor relative to the ancestral virus
Identification and analysis of functional elements in 1% of the human genome by the ENCODE pilot project.
We report the generation and analysis of functional data from multiple, diverse experiments performed on a targeted 1% of the human genome as part of the pilot phase of the ENCODE Project. These data have been further integrated and augmented by a number of evolutionary and computational analyses. Together, our results advance the collective knowledge about human genome function in several major areas. First, our studies provide convincing evidence that the genome is pervasively transcribed, such that the majority of its bases can be found in primary transcripts, including non-protein-coding transcripts, and those that extensively overlap one another. Second, systematic examination of transcriptional regulation has yielded new understanding about transcription start sites, including their relationship to specific regulatory sequences and features of chromatin accessibility and histone modification. Third, a more sophisticated view of chromatin structure has emerged, including its inter-relationship with DNA replication and transcriptional regulation. Finally, integration of these new sources of information, in particular with respect to mammalian evolution based on inter- and intra-species sequence comparisons, has yielded new mechanistic and evolutionary insights concerning the functional landscape of the human genome. Together, these studies are defining a path for pursuit of a more comprehensive characterization of human genome function