Spatial Statistics

In the following 3 notebooks, we will learn how to assess spatial relationships between objects. Our focus will be on clustering and co-localisation.

Notebook Lessons

Each notebook will focus on a question:

• Notebook 1: Does a protein cluster?

• Notebook 2: Do two different protein clusters co-localize?

• Notebook 3: Does a protein localize to a cellular compartment?

To answer these questions, we will introduce the following concepts:

Concept	Purpose
Complete Spatial Randomness method	A null distribution where all object locations are randomly distributed
KD-tree	A data structure for efficient nearest neighbor search
Nearest Neighbor relationship	A formalism to establish spatial relationships between objects
Nearest Neighbor Distance	A metric to quantify spatial relationships between objects
Clark-Evans Index	An index that reports whether a distribution of objects is randomly distributed
Ripley's L	A method to assess the length scale of clustering / dispersion

Dataset

Our data consists of fluorescence images with five channels:

Channel	Staining	Staining Description
0	Hoechst	Nuclear stain
1	Phalloidin	F-actin stain; whole cell marker
2	Protein A	Spot pattern
3	Protein B	Spot pattern
4	Protein C	Spot pattern