Simulating T-cell motility in the lymph node paracortex with a packed lattice geometry

Abstract

Agent-based simulation modelling of T-cell trafficking, activation and proliferation in the lymph node paracortex requires a model for cell motility. Such a model must be able to reproduce the observed random-walk behaviour of T cells, while accommodating large numbers of tightly packed cells, and must be computationally efficient. We report the development of a motility model, based on a three-dimensional lattice geometry, that meets these objectives. Cells make discrete jumps between neighbouring lattice sites in directions that are randomly determined from specified discrete probability distributions, which are defined by a small number of parameters. It is shown that the main characteristics of the random motion of T cells as typically observed in vivo can be reproduced by suitable specification of model parameters. The model is computationally highly efficient and provides a suitable engine for a model capable of simulating the full T-cell population of the paracortex.

Figure 1

Mean squared displacement of 4272 cell paths generated with Model N, plotted as a function of time, over 6 hours. After a linear section spanning about 80 minutes the plot begins to flatten as the cell trajectories are limited by the boundary of the modeled region.

Figure 2

Mean squared displacement of 4272 cell paths generated with Model N, plotted as a function of time, together with the line of best fit for t > 5 min. These results were obtained with β = 0.51, ρ = 0.71.

Figure 3

Mean speed contour lines computed from model results generated with 1500 (β, ρ) parameter pairs, showing how the mean speed depends mainly on β. (a) Model N, (b) Model M18, (c) Model M26.

Figure 4

Motility coefficient contour lines computed from model results generated with 1500 (β, ρ) parameter pairs, showing how C_m depends on both β and ρ. (a) Model N, (b) Model M18, (c) Model M26.

Figure 5

2-D projections of 20 T cell trajectories of 75 minutes duration generated with Model N, with β = 0.51, ρ = 0.71. (a) Model N, with β = 0.51, ρ = 0.71, (b) Model M18, with β = 0.41, ρ = 0.76, (c) Model M26, with β = 0.38, ρ = 0.76.

Figure 6

Comparison of turning angle distributions from experimental data (blue) and the model (green). (The experimental data are replotted from Mempel et al., combining data for positive and negative angles.) (a) Model M18. (b) Model M26.

Figure 7

Model N probability-weighted jump vectors for the cases with β = 1.0 and ρ = 0.0, 0.2, 0.4, and 0.6. Since the step lengths are independent of direction, the vector lengths are simply proportional to the probabilities. The dark grey vector in the direction of the previous step has length = 0.1.

Figure 8

A composite ellipsoidal surface, half prolate and half oblate. The probabilities associated with cell jumps are specified such that the probability-weighted step distances are proportional to the distances from the origin to the surface.

Figure 9

Model M18 probability-weighted jump vectors for the cases with β = 1.0 and ρ = 0.0, 0.2, 0.4, and 0.6. The six directions parallel to the axes correspond to a step length of one unit, the other 12 to a step length of √2 units (unit = grid spacing). The dark grey vector in the direction of the previous step has length = 0.1.