ABSTRACT
Spatial patterns of cells and other biological elements drive both physiologic and pathologic processes within tissues. While many imaging and transcriptomic methods document tissue organization, discerning these patterns is challenging, especially when they involve multiple elements in complex arrangements. To address this challenge, we present Spatial Patterning Analysis of Cellular Ensembles (SPACE), an R package for analysis of high-plex spatial data. SPACE is compatible with any data collection modality that records values (i.e., categorical cell/structure types or quantitative expression levels) at fixed spatial coordinates (i.e., 2d pixels or 3d voxels). SPACE detects not only broad patterns of co-occurrence but also context-dependent associations, quantitative gradients and orientations, and other organizational complexities. Via a robust information theoretic framework, SPACE explores all possible ensembles of tissue elements - single elements, pairs, triplets, and so on - and ranks the most strongly patterned ensembles. For single images, rankings reflect patterns that differ from random assortment. For sets of images, rankings reflect patterns that differ across sample groups (e.g., genotypes, treatments, timepoints, etc.). Further tools then thoroughly characterize the nature of each pattern for intuitive interpretation. We validate SPACE and demonstrate its advantages using murine lymph node images for which ground truth has been defined. We then use SPACE to detect new patterns across varied datasets, including tumors and tuberculosis granulomas.
ABSTRACT
Human immunodeficiency virus (HIV) infection is a major public health concern with 1.2 million people living with HIV in the United States. The role of nutrition in general, and albumin/globulin in particular in HIV progression has long been recognized. However, no mathematical models exist to describe the interplay between HIV and albumin/globulin. In this paper, we present a family of models of HIV and the two protein components albumin and globulin. We use albumin, globulin, viral load and target cell data from simian immunodeficiency virus (SIV)-infected monkeys to perform model selection on the family of models. We discover that the simplest model accurately and uniquely describes the data. The selection of the simplest model leads to the observation that albumin and globulin do not impact the infection rate of target cells by the virus and the clearance of the infected target cells by the immune system. Moreover, the recruitment of target cells and immune cells are modeled independently of globulin in the selected model. Mathematical analysis of the selected model reveals that the model has an infection-free equilibrium and a unique infected equilibrium when the immunological reproduction number is above one. The infection-free equilibrium is locally stable when the immunological reproduction number is below one, and unstable when the immunological reproduction number is greater than one. The infection equilibrium is locally stable whenever it exists. To determine the parameters of the best fitted model we perform structural and practical identifiability analysis. The structural identifiability analysis reveals that the model is identifiable when the immune cell infection rate is fixed at a value obtained from the literature. Practical identifiability reveals that only seven of the sixteen parameters are practically identifiable with the given data. Practical identifiability of parameters performed with synthetic data sampled a lot more frequently reveals that only two parameters are practically unidentifiable. We conclude that experiments that will improve the quality of the data can help improve the parameter estimates and lead to better understanding of the interplay of HIV and albumin-globulin metabolism.
