Understanding the behavior of T cells in lymphoid tissue as they begin to be primed by antigen-presenting cells is very important since it is a key stage that leads to the detection of antigen and the mounting of an immune response. Progress in this regard has been aided by the recent application of multiphoton microscopy technology (51
) to immunological questions, since this has enabled spatially resolved in vivo imaging of T cells in real time (2
). Among the earliest findings from these studies was that the migratory pattern of T cells (on large length and time scales) exhibited the statistical features characteristic of a random walk (32
). Subsequent computer simulations have suggested that this enables efficient scanning of DCs in LNs (5
). Furthermore, recent experiments suggest that the apparently random (or diffusive) motion may be because T cells follow “tracks” made up of reticular fibers which span the LN in a statistically random manner, and T cells can choose different tracks at the intersections (2
). Other important findings are that chemokines can influence the details of T-cell motility patterns (9
) and that T cells can organize into dynamic “streams” (5
The dynamic characteristics of T-cell migration in LNs varies over time (23
). In CD8+
T cells, the first stage (phase one) of rapid scanning (characterized by random walk statistics) is followed by a second phase wherein T cells make extended contacts with DCs. In this second phase, presumably, T cells are making sustained contacts with DCs that are known to be necessary in vitro for full commitment to activation (e.g., see reference 24
). Therefore, a mechanistic understanding of which factors determine the transition into phase two and how they regulate this decision is crucial. Such an understanding was not available, which was the impetus for this study.
We reasoned that the transition from phase one to phase two results from T-cell signaling stimulated by encounters with cognate DCs. This, in turn, suggested that this transition is strongly influenced by the quantity and quality of antigen. We have studied this hypothesis extensively in silico by systematically varying conditions that determine antigen quantity and quality. Our results are qualitatively consistent with experimental observations (22
), and they provide a mechanistic framework that describes how antigen dose and type impact the ability of T cells to detect antigen and “decide” to make extended contacts with DCs.
Increasing the initial concentration of cognate ligands loaded on DCs or increasing the fraction of cognate DCs reduces the duration of phase one, because both actions lead to a higher propensity for a productive T-cell-DC encounter. If the antigen concentration on DCs and/or the density of cognate DCs exceeds a threshold value, the transition from phase one to phase two occurs very rapidly. This may explain why it is difficult to observe phase-one-type behavior in a system characterized by high doses of high-affinity antigen on the majority of endogenous LN DCs (38
Stability of the pMHC complex itself is also an important variable, with more stably bound peptides resulting in a shorter phase one. This is because unlike the case with in vitro experiments with multiple or single cells or lipid bilayers, a T cell might encounter a DC in the LN several hours after antigen loading (as in the experiments reported in references 23
, and 37
). During this time, peptides are lost from the DC surfaces. The less stable pMHC complex will thus display smaller amounts of cognate ligand, thereby decreasing the probability of productive T-cell-DC encounters.
The power of our theoretical analysis is that it shows that these seemingly unrelated findings emerge from a single conceptual framework. We have identified three important time scales. The first is the characteristic time for T cells to find DCs bearing cognate ligands, which is rather short for conditions that have been studied previously (7
) and by us. Therefore, it is not as important a determinant for the transition from phase-one- to phase-two-type behavior. It is worth remarking, however, that in the early stages of a real infection, the number of DCs bearing a cognate ligand may be smaller than that in in vivo imaging experiments (e.g., ~100 to 300 cognate antigen-bearing DCs are in the draining LN at the time of T-cell adoptive transfer in the experiments of Henrickson, et al. [22
]), and this time scale may become important. It may also become important if an antigen dose is extremely high, in which case the T cells would receive a sufficiently high stimulus from the first cognate DC they encounter. As a result, the time it takes to encounter the first cognate DC dictates the duration of phase one.
An important time scale is the time required for a productive T-cell-DC encounter to occur (τs). Using a mean-field approach, we derived how this time scale is determined by various measures of antigen dose and type. Specifically, we identified the nondimensional ratio of τs and the half-life of the pMHC complex as the composite variable which controls the behavior of the system. Our simulation results for a wide range of values of diverse quantities that reflect antigen dose and quality all collapse onto one master curve when plotted against this ratio. For systems where antigen loss due to peptide dissociation is not important, diverse results scale with τs alone since it is the only relevant time scale.
These results show that differences in T-cell migratory patterns observed upon manipulating different variables (antigen dose, density of DCs bearing cognate ligands, peptide stability, TCR-pMHC binding, etc.) result from how this particular change, combined with all other prevailing conditions, affects the τ/τs ratio. Changing each of these variables changes the balance between two relevant time scales, thereby influencing the way in which migrating T cells interact with and respond to DCs. We hope that these implications of the conceptual framework revealed by our study will help guide future experimentation.
Our computer simulations and experiments reported by Henrickson et al. (22
) both highlight the existence of a sharp threshold in the antigen dose on DCs beyond which the T cell's ability to transition to phase two drastically improves. The value of this threshold concentration is higher for the less stable pMHC ligands and weaker TCR-pMHC binding characteristics (also observed in vitro [40
]). The existence of a threshold is predicated by the fact that dose-response curves characterizing T-cell signaling exhibit a threshold (29
The time scale associated with T-cell-DC encounters is much shorter than the times at which a transition from phase-one- to phase-two-type behavior is observed in the experimental study by Henrickson et al. (22
). This observation, combined with the fact that there is a larger amount of pMHC ligands on cognate DCs at shorter times, led us to suggest that T cells may be able to integrate signals from multiple serial encounters with DCs. This aspect of our study differs from previous studies, such as a recent study by Preston et al. (35
), in which the detection of antigen and activation of T cells are viewed as a transport-limited process, i.e., the T cells commit to activation upon their first encounter with cognate DCs. Signal integration could result from various aspects of the T-cell signaling network that may confer memory. Our calculations show that such memory effects would enable a transition from phase-one- to phase-two-type behavior when it otherwise may not have occurred because of too low an antigen dose on DCs. We believe that in vivo, productive T-cell-cognate DC interactions are stochastic events. The ability to integrate signals from sequential T-cell-DC encounters enhances the sensitivity with which T cells can detect antigen. Furthermore, it may also narrow the distribution of stochastic times at which individual T cells stop, thereby making the transition to phase-two-type behavior appear to be more sharply defined.
It has been suggested that DCs may alter the presentation of pMHC ligands upon serial encounters with T cells, which provides the source of such “memory” (23
). In our current model, this would simply result in a different type of variation of the propensity of a productive T-cell-DC encounter (k
) with time. Thus, it will result in a different value for the ratio of the two important time scales we have identified. Nevertheless, as noted earlier, the results will still depend only on this ratio, and simulations carried out with DCs as the source of memory will also collapse onto the consolidated master curve shown in Fig. . Resolving whether the origin of “memory” lies in the T-cell signaling network and/or pMHC presentation on DCs requires the integration of molecular-signaling models with migration simulations and concomitant experiments. It is expected that the details of the temporal migratory patterns should be different in the two cases, since the dynamical behavior of the T-cell signaling network and enhanced pMHC presentation on DCs (e.g., by clustering ligands) should be very different. Experiments aimed toward resolving this have been described by Henrickson et al. (22
The close connection between T-cell signaling and migration revealed by our studies highlights the need for experimental and computational studies that connect molecular-scale signaling processes to migratory patterns in detail. Multiscale computational models that seamlessly integrate molecular signaling events with T-cell motion are required. Furthermore, the development of efficient computer simulation methods that do not employ a lattice representation of space and can simultaneously incorporate the complexity of signaling is required if all noncognate T cells and DCs are to be included in order to generate models that are quantitatively accurate. Similarly, experimental technologies that can combine the tracking of T-cell motion with the imaging of signaling molecules (as is currently possible in vitro) must be developed. Synergy between such experiments and computational studies will help elucidate how T cells are activated in lymphoid tissues.