Introductory Story to 3D Spatial Analysis

Spatial statistics are a set of methods used to quantitatively analyze the spatial distribution of individuals or objects within a 2D or 3D space. Since very early in human history, people have been interested in mapping rivers and coasts, positioning trees, mountains or buildings… in other words, they have been interested in the spatial distribution of different elements within the surrounding nature.

Soho District, London 1854. Representation of cholera outbreaks

Fig.1 Soho District, London 1854. Representation of cholera outbreaks

Fig.1 presents a famous example of this type of analysis. It represents a map of the Soho district of London, made by Dr. John Snow during the cholera outbreak in 1854. The spots on this map represent the recorded cases of the disease. Based on this map, Dr. Snow realized that the cholera cases clustered close to specific public wells, which appeared to contain an unknown bacterium. Dr Snow could thus link the propagation of the disease to contaminated water. This simple and historical example illustrates the benefits that can be gained from spatial analyses of human issues.

 

Examples of  different types of point patterns.

Fig.2 Examples of
different types of
point patterns.

Spatial analysis has applications in many different fields and scientific domains: from natural sciences, such as biology or ecology, to human sciences, such as economics. As in the historical example above, individuals or objects are often represented by their positions. In such case, the data to analyze consists of spatial point patterns (Fig.2). One purpose of spatial analysis is first to provide quantitative descriptions of such point patterns, for example based on measured distances between points (Fig.3). Generally, a second objective is to evaluate the absence or existence of rules describing the positioning of points in space.

Quantitative description of a point pattern based on the nearest neighbor.

Fig.3 Quantitative description of a point pattern based on the nearest neighbor.

In such evaluation it is tested whether points are distributed randomly or if they interact with each other, in an attractive (producing clusters) or repulsive way (producing regular patterns) (Fig.2). An ultimate goal in spatial analysis is to quantitatively model (using mathematical formulas or computer algorithms) the rules that govern the spatial positioning of points. By attempting to reproduce real patterns, spatial modeling allows to test hypotheses about spatial organizations.
In the EpiTRAITS project, we are making use of spatial modeling techniques to generate a statistical model of the 3D nuclear architecture of A. thaliana leaf cells. The nucleus of living cells contains various compartments and hosts the genome. Several studies have highlighted the links between the spatial organization of nuclear compartments and nuclear functions, in particular the regulation of genome expression. Our aim is to understand the principles of nuclear organization and its functional significance in plants.

In a first step in this project, we focus on chromocenters, which are plastic and dynamic heterochromatic compartments. Chromocenters appear as bright foci when observing DNA-stained nuclei in confocal microscopy. A major challenge is the large variability of the nuclei in terms of shape, size, and number of compartments, which makes it difficult to identify spatial rules from individual images (Fig.4).

The methodology we develop in the EpiTRAITS project allows to address this issue and to test spatial models on populations of nuclei, based on the processing and analysis of 3D images (Fig.5). Our methodology is developed with a generic point of view and can be applied to model distributions of all kind of objects within a domain based on repeated observations.

In a second step, we will map gene expression inside the nucleus, connecting gene locations with their expression levels. Furthermore, to get insight into the principles of nuclear organisation and its functional significance we will study other nuclear compartments, mutants affecting the spatial organisation of the nucleus, and various different cell types.

DNA-stained nuclei from Arabidopsis leaf cells observed using confocal microscopy.

Fig.4 DNA-stained nuclei from Arabidopsis leaf cells observed using confocal microscopy.

Methodology steps. Microscopic images (A) are processed to identify objects of interest (B). Objects are modeled as spheres and their distribution is modeled based on spatial limitations relative to the nuclear envelope (C) and/or to other objects.

Fig.5 Methodology steps. Microscopic images (A) are processed to identify objects of interest (B). Objects are modeled as spheres and their distribution is modeled based on spatial limitations relative to the nuclear envelope (C) and/or to other objects (D).

 

Bibliography & image sources:

– Dr. Snow case: http://www.ph.ucla.edu/epi/snow/snowcricketarticle.html
– Nuclei images courtesy from K. Sakai (coll. V. Gaudin).
– Spatial models generated by Javier Arpón.