Deriving a germinal center lymphocyte migration model from two-photon data

Abstract

Recently, two-photon imaging has allowed intravital tracking of lymphocyte migration and cellular interactions during germinal center (GC) reactions. The implications of two-photon measurements obtained by several investigators are currently the subject of controversy. With the help of two mathematical approaches, we reanalyze these data. It is shown that the measured lymphocyte migration frequency between the dark and the light zone is quantitatively explained by persistent random walk of lymphocytes. The cell motility data imply a fast intermixture of cells within the whole GC in approximately 3 h, and this does not allow for maintenance of dark and light zones. The model predicts that chemotaxis is active in GCs to maintain GC zoning and demonstrates that chemotaxis is consistent with two-photon lymphocyte motility data. However, the model also predicts that the chemokine sensitivity is quickly down-regulated. On the basis of these fi ndings, we formulate a novel GC lymphocyte migration model and propose its verifi cation by new two-photon experiments that combine the measurement of B cell migration with that of specifi c chemokine receptor expression levels. In addition, we discuss some statistical limitations for the interpretation of two-photon cell motility measurements in general.

Models of Cell Migration

“…5.1), led to the development of the transient chemotaxis concept for activated B cells in follicles [140], which was later supported by an independent investigation [142]. According to this model, a stable chemokine gradient guides the lymphocytes to their respective compartments.…”

“…For example, it has been proposed that if two cells in a 2-D simulation have vectors for the direction of migration with a negative scalar product, then the two cells will exchange position on the lattice. Such an exchange algorithm might even be important in 3-D cases [140] when the density of cells is high and the artifact of suppressed motility is inferred by the discretization of space.…”

“…In the simplest representation, a cell is shown as a point in space, with each point describing a trajectory [72, [140][141][142]. When the mechanical properties of the migrating cells are not particularly relevant, this approach is most suitable.…”

“…6.2.1) was used to investigate B-cell chemotaxis, affinity maturation, and the recycling hypothesis [140,142,[177][178][179]. A regular lattice model for the cells was simultaneously used as a reaction-diffusion grid for the chemokines CXCL12 and CXCL13, which established stable gradients in the germinal center environment.…”

Imaging immunity

“…Techniques for cell tracking may induce interference effects in measured speed distributions. Data show that active chemotaxis of lymphocytes can still be compatible with results suggesting pure random walk with important implications for the interpretation of two-photon data [18]. Interpretation of complex imaging data goes beyond statistical tools and ideally includes mathematical modelling and simulation tools in order to set the data into functional context.…”