Improvement in model flexibility reveals a minimal signalling pathway that explains T cell responses to pulsatile stimuli

Efforts to develop quantitative models must face a trade-off between interpretability and quantitative accuracy, which often disfavores interpretability. Here we adopt an operational definition of interpretability, specifically that a model is described by an arrow diagram wherein each arrow corresponds to a positive effect or negative effect of one component upon a process, and fewer arrows is more interpretable than more arrows. We then develop a method to add flexibility — and thus accuracy in fitting data — to mathematical models by relaxing functional form assumptions, while constrained by the same arrow diagram and thus the same interpretability. We apply this method to the T cell, where quantitative models are particularly needed, in part because of ongoing efforts to engineer T cells as therapeutics. Recent experiments exposed T cells to pulsatile inputs and measured their frequency response, and found several nonlinear frequency responses: high-pass, low-pass, band-pass, and band-stop. Using our modeling approach with enhanced flexibility, we show that a simple signaling model quantitatively captures the frequency response of CD69 surface expression, one of the correlates of T cells activation, with accuracy within the experimental inter-replicate standard error of the mean. Specific qualitative behaviors map to specific parts of the arrow diagram: Band-pass behavior can be explained by refractory de-sensitizing circuit (we refer to this as “first-aid icing a wound”). Band-stop behavior can be explained by removal-inhibition (we refer to this as “roommate interrupts my studying”). Apparent low-pass emerges naturally when total stimulation time is constant. Taken together, our results demonstrate the ability to achieve both quantitative prediction and interpretability in understanding cellular dynamics. Simple models may at first appear incapable of explaining complex data, but might indeed be able to by adding this modest flexibility.