Measuring aggregation of events about a mass using spatial point pattern methods

Abstract

We present a methodology that detects event aggregation about a mass surface using 3-dimensional study regions with a point pattern and a mass present. The Aggregation about a Mass function determines aggregation, randomness, or repulsion of events with respect to the mass surface. Our method closely resembles Ripley’s K function but is modified to discern the pattern about the mass surface. We briefly state the definition and derivation of Ripley’s K function and explain how the Aggregation about a Mass function is different. We develop the novel function according to the definition: the Aggregation about a Mass function times the intensity is the expected number of events within a distance h of a mass. Special consideration of edge effects is taken in order to make the function invariant to the location of the mass within the study region. Significance of aggregation or repulsion is determined using simulation envelopes. A simulation study is performed to inform researchers how the Aggregation about a Mass function performs under different types of aggregation. Finally, we apply the Aggregation about a Mass function to neuroscience as a novel analysis tool by examining the spatial pattern of neurotransmitter release sites as events about a neuron.

Possible frequent multiple mitochondrial DNA copies in a single nucleoid in HeLa cells

“…Either, so-called dimerization hTFAM mutant was overexpressed, being unable to dimerize, hence unable to crosslink mtDNA chains; or an L6-bending mutant of hTFAM was overexpressed, which cannot bend mtDNA. Both mutations affected mtDNA replication and transcription, as reported previously 46 , 47 . When visualized by anti -DNA 3D dSTORM, 143B knockin cells overexpressing either one of hTFAM mutants exhibited similar nucleoid diameter distribution as the parental cells, reduced to diameters only up to 200 nm (Fig.…”

“…The 3D Ripley’s K -function then expresses the expected number of events (points) within the distance r from a randomly selected point 47 . Let’s assume a volume of interest in which n points (events) exist with distances d ij (point i , point j ).…”