Towards estimating the true duration of dendritic cell interactions with T cells

Abstract

To initiate an adaptive immune response, T cells need to interact with dendritic cells (DCs), and the duration of these interactions plays an important role. In vitro and in vivo experiments have generally tried to estimate the required period of opportunity for T cell stimulation rather than the duration of individual T cell-DC interactions. Since the application of multi-photon microscopy (MPM) to living lymphoid tissues, the interactions between immune cells, as well as the duration thereof, can directly be observed in vivo. Indeed, long-lasting interactions between T cells and DCs were shown to be important for the onset of immune responses. However, because MPM imaging is typically restricted to experiments lasting 1 h, and because T cell-DC conjugates frequently move into and out of the imaged volume, it is difficult to estimate the true duration of interactions from MPM contact data. Here, we present a method to properly make such an estimate of (the average of) the distribution of contact durations. We validate the method by applying it to spatially explicit computer simulations where the true distribution of contact duration is known. Finally, we apply our analysis to a large experimental data set of T-DC contacts, and predict an average contact time of about three hours. However, we identify a mismatch between the experimental data and the model predictions, and investigate possible causes of the mismatch, including minor tissue drift during imaging experiments. We discuss in detail how future experiments can be optimized such that MPM contact data will be minimally affected by these factors.

Figure 1. Relation between contact duration and type of observed event when imaging is time-limited

(a) Cartoon of possible event types for contacts between T cells (red) and DCs (green). Abbreviation codes for these event types are oo, ot, to, or tt (see further explanation in text). (b, c) The event type that is observed depends on the time at which the contact truly started (horizontal axis) relative to the imaging period, which lasts from 0 to T hours. The possible event types also depend on whether the true contact time x is shorter than the imaging period, i.e., x < T (b), or longer than the imaging period, i.e., x > T (c). See text for examples.

Figure 2. Distributions of different event types

(a) An example of a true distribution. Contact time (x) is on the horizontal axis, where imaging time is scaled to T hours. (b–d) Accompanying distributions of expected oo, tt, ot, and to events (see explanation in text). The observed contact time (w) is on the horizontal axis. (d) The distribution of events whose initiation or termination is not observed (ot or to) is built up out of two parts, contributed by interactions lasting shorter (denoted by “A”) or longer (denoted by “B”) than the imaging period.

Figure 3. Possible event types when imaging is limited in both space and time

Cartoon of all possible event types for contacts between T cells (red) and DCs (green). Abbreviation codes for these event types are oo, ot, os, to, tt, ts, so, st, and ss (see further explanation in text). Dashed arrows denote movement of conjugates into or out of the imaged volume, and solid arrows denote the initiation or termination of an interaction.

Figure 4. Estimating the contact duration of simulated data

The sum of two lognormal distributions was fitted to cellular interaction data (excluding entry event data) from spatial simulations using our estimation method (1-hour observation window). (a) The observed distributions (types oo, ot, to, tt, os and ts; see explanation in text) are shown in histograms, along with the maximum likelihood fit (solid lines; filled square in lower rightmost panel). The observed contact time (w′) is on the horizontal axis. (b) The estimated fit (solid line) for the true contact time distribution plotted through a histogram of data from a 100-hour simulation, which approaches the true distribution. The true contact time (x) is on the horizontal axis. The inset shows the fitted distribution (black line) along with fits for 50 random permutations of the simulated data (grey lines). Note the logarithmic scale of the vertical axis. (c) The average contact duration estimated for 1000 random permutations of the simulated data (bootstrap analysis; median of this distribution is 1.45 hours, and the 95% CI is 1.38–1.52 hours) (d) A comparison of the estimated average contact duration (using the event-based approach in upper panel; using the shortcut approach in lower panel) with the true average contact duration. The latter is calculated from the distribution of oo events in 100-hour simulations in which entry and exit is not taken into account. Note that, because the probability of observing these events declines with the duration of the event, to calculate the true average we assign different weights to each event (see main text). Error bars denote 95% CIs (determined with a bootstrap analysis).

Figure 5. Estimating the duration of contacts between T cells and DCs

(a) The estimated distribution of contact duration in the “phase two” data from Henrickson et al. (2008). Fits were made using a gamma distribution (solid line), a lognormal distribution (dotted line), and the sum of two lognormal distributions (dashed line). Note the logarithmic scale of the vertical axis. (b) The experimentally observed distributions (types oo, ot, to, tt, os and ts; see explanation in text) are shown in histograms along with the maximum likelihood fit using the sum of two lognormal distributions (solid lines; filled square in lower rightmost panel). The observed contact time (w′) is on the horizontal axis. (c) Each MPM experiment was categorized according to the observed average of all interactions (0–15 min, 15–30 min, 30–45 min, or 45–60 min). The data points from experiments in each category were combined, and the average true contact duration was estimated by applying our analysis (using a lognormal distribution as a basis). Note that the vertical axis has a logarithmic scale, suggesting an exponential relationship between observed and true contact time.

Figure 6. Deviations between experimental contact data and expectation

(a–d) The frequency of observed initiation (a), termination (b), entry (c), and leaving (d) events combined per time interval of 6 minutes. (e) The number of observed conjugates present at each moment of experimental time. In all panels data from multiple experiments exhibiting phase two behaviour according to the definition by Henrickson et al. (2008) (see main text) are combined.