Random walk informed heterogeneity detection reveals how the lymph node conduit network influences T cells collective exploration behavior

Abstract

Random walks on networks are widely used to model stochastic processes such as search strategies, transportation problems or disease propagation. A prominent example of such process is the dynamics of naive T cells within the lymph node while they are scanning for antigens. The observed T cells trajectories in small sub-volumes of the lymph node are well modeled as a random walk and they have been shown to follow the lymphatic conduit network as substrate for migration. One can then ask how does the connectivity patterns of the lymph node conduit network affect the T cells collective exploration behavior. In particular, does the network display properties that are uniform across the whole volume of the lymph node or can we distinguish some heterogeneities? We propose a workflow to accurately and efficiently define and compute these quantities on large networks, which enables us to characterize heterogeneities within a very large published dataset of Lymph Node Conduit Network. To establish the significance of our results, we compared the results obtained on the lymph node to null models of varying complexity. We identified significantly heterogeneous regions characterized as “remote regions” at the poles and next to the medulla, while a large portion of the network promotes uniform exploration by T cells. Lymph nodes are organs in which actors of the immune system meet. In particular, the encounter between the naive T cells and their specific antigens occurs in lymph nodes. This event triggers the adaptive immune response. T cells movement has been shown to be well described as a random walk, at least when they are measured on small sub-volumes of the lymph node. In parallel, it was shown that T-cells migrate following the lymphatic conduit network that span the lymph nodes. In this study, we ask, how does the connectivity pattern of the conduit network on which T cells move influences their collective exploration behavior? Are there regions in the lymph node conduit network which have distinct random walk related properties? The topological reconstruction of the lymph node conduit network was recently made available. The network is very large (about 200 000 nodes) and appears very regular, with most nodes being connected to three neighbours. We propose a workflow to detect heterogeneities in such large and quasi-regular networks, building on random walk on network tools, and the measure of two features which we interpret using a series of generated null models for comparison. We show that the lymph node conduit network displays remotely accessible regions at both poles and near medulla, with however most of the network promoting uniform exploration.