# Modelling spine locations on dendrite trees using inhomogeneous Cox point processes

## TL;DR

This paper models the distribution of dendritic spine locations on neuron dendrites using inhomogeneous Cox point processes, revealing clustering patterns and proposing a new statistical model to describe spine arrangements.

## Contribution

It introduces an inhomogeneous Cox process model for spine locations on dendrites, capturing clustering and spatial patterns not explained by simpler models.

## Key findings

- Some spine data fit inhomogeneous Poisson models
- Other data show clustering at larger scales
- The Cox process model captures clustering but has high variance in point counts

## Abstract

Dendritic spines, which are small protrusions on the dendrites of a neuron, are of interest in neuroscience as they are related to cognitive processes such as learning and memory. We analyse the distribution of spine locations on six different dendrite trees from mouse neurons using point process theory for linear networks. Besides some possible small-scale repulsion, { we find that two of the spine point pattern data sets may be described by inhomogeneous Poisson process models}, while the other point pattern data sets exhibit clustering between spines at a larger scale. To model this we propose an inhomogeneous Cox process model constructed by thinning a Poisson process on a linear network with retention probabilities determined by a spatially correlated random field. For model checking we consider network analogues of the empirical $F$-, $G$-, and $J$-functions originally introduced for inhomogeneous point processes on a Euclidean space. The fitted Cox process models seem to catch the clustering of spine locations between spines, but also posses a large variance in the number of points for some of the data sets causing large confidence regions for the empirical $F$- and $G$-functions.