The Fascinating Symmetries of Golden Clusters Containing Two Skeletal Elements [M-2] in the Cluster Nucleus

The golden clusters containing two skeletal atoms in the cluster nucleus have been analyzed more carefully with the help of the 4n series method. Their shapes can reasonably and readily be predicted by mapping the [M-2] capped clusters of 3 to 13 nuclearity onto Pivoriunas geometrical model. Some of these clusters were historically categorized as being spherically centered.

Acetylcholine receptor clustering and nuclear movement in muscle fibers in culture.

We have studied the formation of acetylcholine receptor (AChR) clusters and the behavior of myonuclei in rat and chick skeletal muscle cells grown in cell culture. These cells were treated with a factor derived from Torpedo electric extracellular matrix, which causes a large increase in their number of AChR clusters. We found that these clusters were located preferentially in membrane regions above myonuclei. This cluster-nucleus colocalization is explained by our finding that most of the nuclei near clusters remain relatively stationary, while most of those away from clusters are able to translocate throughout the myotube. In some cases, clusters clearly formed first, then nuclei migrated underneath and became immobilized. If clustered AChRs later dispersed, their associated nuclei resumed moving. These results suggest that AChR clustering initiates an extensive cytoskeletal rearrangement that causes the subcluster localization of organelles, potentially providing a stable source of newly synthesized AChRs for insertion into the cluster.

Mathematical approach to the problem of clustering

The mathematical theory of the description of the structure of point-sets in a plane or in space can be applied to the investigation of the distribution of different extragalactic objects. Mathematically we can define rigorously such ideas as cluster, nucleus of cluster, monoor polynuclear structure, background and so on. First we choose a critical distance that determines the scale on which we investigate the distribution of objects. the critical distance plays a similar role to the wavelength of radiation by means of which we investigate the internal structure of matter. It is obvious that the description is different for different critical distances. To obtain a complete picture we have to analyse the evolution of this description as the critical distance changes.