Ignition criteria for trigger waves in cell signaling

TL;DR

This paper derives an analytical expression for the stimulus threshold needed to initiate trigger waves in cell signaling networks, linking it to network parameters and enabling better prediction and design of signaling responses.

Contribution

It provides the first analytic formula for trigger wave ignition thresholds based on realistic Hill-type auto-activation functions in multiple dimensions.

Findings

Trigger wave threshold depends on $K_D$ and Hill coefficient $n$.

The dominant threshold scales as $K_D^{n/(n-1)}$.

The results enable prediction of wave sensitivity from bulk data.

Abstract

To rapidly coordinate collective behaviors in tissues, cells communicate with one another through traveling fronts of signaling activity called trigger waves. The stimulus threshold for wave propagation is a key biological parameter that determines when the system produces a global response to a local stimulus. However, it is unclear how this stimulus threshold is determined by the properties of the underlying signaling network. To address this gap, we studied a model of trigger waves with a realistic Hill-type auto-activation function. We obtained an analytic expression for the wave ignition threshold in 1D and numerical solutions in 2D and 3D. In the limit of high sensitivity, we found that the trigger wave threshold depends on both the effective dissociation constant, $K_D$, and the effective Hill coefficient, $n$, of the positive feedback circuit, with the dominant contribution scaling as $K_D^{n/(n-1)}$ in all dimensions. This result leads to a simple method for predicting the trigger wave ignition threshold from bulk activation data and is potentially of use for developing synthetic trigger wave circuits with desired sensitivities.