IFNB1-DDX58 Feedback Loop Cell-to-Cell Variability Figure 6. Phase space trajectories of individual cells in simulations. Each plot follows a single cell at 10 minute intervals, and plots the number of bound receptors vs. the number of IFNB1 messages in that cell at that time point. A. An uninfected cell cannot produce IFNB1 message, and thus exhibits only an increase in the number of bound receptors. B. A late responder cell is characterized by receptors binding before the cell produces IFNB1 messages, and is thus activated only through paracrine signaling. C. An early responder cell produces considerable amounts of IFNB1 message prior to significant receptor binding, suggesting an autocrine activation. The ratio between early and late responders in the simulation is 7:124. D. A cell that shows a late responder trajectory in the simulation without antibodies (solid line), but changes to a trajectory suggesting autocrine activation when the simulation includes antibodies (dashed line). doi:10.1371/journal.pone.0016614.g006 infection, while it is only at 6 hours after infection that the full impact of Jak/Stat pathway induction of DDX58 on IFNB1 production is seen at the cell population level as the latter rises rapidly on average (Figure 1A) with many cells producing a thousand and more copies (Figures 2,4). The model time behavior allows one to connect the very early cellular responses to experimental measurements at 6 and 10 hours that show a large cell-to-cell variability in interferon induction (Figures 2,4), that is consistent with previous results [14,15,16]. The fit to these later time data determines model parameter values, which were then tested by making predictions and comparing them to experiment when interferon diffusion is suppressed. The model shows the right qualitative behavior, which supports the hypothesis that the very early immune response is carried by a small subset of early responder cells. We have thus uncovered in the early immune response another instance where single cell dynamics is different from cell population behavior [17], as has been shown to occur in various systems such as the Xenopus oocytes response to progesterone level [18] and PC12 responses to oxidative stress [19]. In view of the experimental difficulty of measuring reliably small numbers of mRNA, our methodology had to rely on a combination of model simulation and experimental validation, with the model providing the bridge between the presumed existence of early responder cells and the later single cell measurements. One might question some of the simplifying assumptions that went into our model. Firstly, there is the representation in 2 dimensions of 3 dimensional processes. However, since we impose in 2 dimensions average experimental cell distance and diffusion time, we mimic closely in 2 dimensions the temporal 3 dimensional behavior. Thus a crucial aspect of a realistic situation is preserved, despite the fact that in 3 dimensions the number of neighboring cells is larger, which entails that more interferon molecules impinge on a cell’s surface receptors. The latter situation can however be compensated for in 2 dimensions by an increase in the receptor binding probability. Secondly, in terms of intracellular processes we limit ourselves to those mRNA that are actually measured, and that compose the DDX58-IFNB1 feedback loop. PLoS ONE | www.plosone.org 7 February 2011 | Volume 6 | Issue 2 | e16614