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J Theor Biol. 2012 Feb 21;295:59-67. doi: 10.1016/j.jtbi.2011.11.001. Epub 2011 Nov 12.

T-cell movement on the reticular network.

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Department of Mathematics, University of Auckland, Auckland, New Zealand.


The idea that the apparently random motion of T cells in lymph nodes is a result of movement on a reticular network (RN) has received support from dynamic imaging experiments and theoretical studies. We present a mathematical representation of the RN consisting of edges connecting vertices that are randomly distributed in three-dimensional space, and models of lymphocyte movement on such networks including constant speed motion along edges and Brownian motion, not in three-dimensions, but only along edges. The simplest model, in which a cell moves with a constant speed along edges, is consistent with mean-squared displacement proportional to time over intervals long enough to include several changes of direction. A non-random distribution of turning angles is one consequence of motion on a preformed network. Confining cell movement to a network does not, in itself, increase the frequency of cell-cell encounters.

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