Beyond co-localization: inferring spatial interactions between sub-cellular structures from microscopy images

Sub-cellular structures interact in numerous direct and indirect ways in order to fulfill cellular functions. While direct molecular interactions crucially depend on spatial proximity, other interactions typically result in spatial correlations between the interacting structures. Such correlations are the target of microscopy-based co-localization analysis, which can provide hints of potential interactions. Two complementary approaches to co-localization analysis can be distinguished: intensity correlation methods capitalize on pattern discovery, whereas object-based methods emphasize detection power.

We first reinvestigate the classical co-localization measure in the context of spatial point pattern analysis. This allows us to unravel the set of implicit assumptions inherent to this measure and to identify potential confounding factors commonly ignored. We generalize object-based co-localization analysis to a statistical framework involving spatial point processes. In this framework, interactions are understood as position co-dependencies in the observed localization patterns. The framework is based on a model of effective pairwise interaction potentials and the specification of a null hypothesis for the expected pattern in the absence of interaction. Inferred interaction potentials thus reflect all significant effects that are not explained by the null hypothesis. Our model enables the use of a wealth of well-known statistical methods for analyzing experimental data, as demonstrated on synthetic data and in a case study considering virus entry into live cells. We show that the classical co-localization measure typically under-exploits the information contained in our data.

We establish a connection between co-localization and spatial interaction of sub-cellular structures by formulating the object-based interaction analysis problem in a spatial statistics framework based on nearest-neighbor distance distributions. We provide generic procedures for inferring interaction strengths and quantifying their relative statistical significance from sets of discrete objects as provided by image analysis methods. Within our framework, an interaction potential can either refer to a phenomenological or a mechanistic model of a physico-chemical interaction process. This increased flexibility in designing and testing different hypothetical interaction models can be used to quantify the parameters of a specific interaction model or may catalyze the discovery of functional relations.