Abstract
In biological contexts as diverse as development, apoptosis, and synthetic microbial consortia, collections of cells or subcellular components have been shown to overcome the slow signaling speed of simple diffusion by utilizing diffusive relays, in which the presence of one type of diffusible signaling molecule triggers participation in the emission of the same type of molecule. This collective effect gives rise to fast-traveling diffusive waves. Here, in the context of cell signaling, we show that system dimensionality - the shape of the extracellular medium and the distribution of cells within it - can dramatically affect the wave dynamics, but that these dynamics are insensitive to details of cellular activation. As an example, we show that neutrophil swarming experiments exhibit dynamical signatures consistent with the proposed signaling motif. We further show that cell signaling relays generate much steeper concentration profiles than does simple diffusion, which may facilitate neutrophil chemotaxis.
Highlights
Prototypical diffusive signaling – in which individual cells communicate with neighbors by releasing diffusible molecules into the extracellular medium – is a relatively slow process
For thousands of cells coordinating actions over millimeters, simple diffusive signaling with small molecules (D » 10À10 m2/s) takes hours. These length and times scales are incommensurate with observed behavior in developmental biology (Chang and Ferrell, 2013; Cheng and Ferrell, 2018; Vergassola et al, 2018), immune response (Reategui et al, 2017), and microbial consortia (Parkin and Murray, 2018), in which cells exchanging diffusible molecules coordinate activity over millimeters in tens of minutes
Calculated by solving Equation (2) and approximated in Equation (9) – to a comparable simple diffusion model, such as that pictured in Figure 4B. (In Appendix 10: Simple diffusion model, we present the same comparison for a thin extracellular medium.) As is well-known, a burst-like emission of a diffusible molecule creates shallow, Gaussian concentration profiles away from the source; the same is true for continuous emission of a fixed source
Summary
Prototypical diffusive signaling – in which individual cells communicate with neighbors by releasing diffusible molecules into the extracellular medium – is a relatively slow process. When many cells collectively integrate environmental cues and participate in the signaling, they can propagate diffusive waves with a fixed speed, v, in the asymptotic limit This effect and its analogs have long been studied in the context of excitable media (Keener and Sneyd, 2009; Keener, 1987; Muratov, 2000) and observed in biological phenomena as diverse as natural cell signaling circuits (Noorbakhsh et al, 2015; Palsson and Cox, 1996; Kessler and Levine, 1993; Gelens et al, 2014), synthetic cell signaling circuits (Parkin and Murray, 2018), apoptosis (Cheng and Ferrell, 2018), range expansions (Tanaka et al, 2017; Fisher, 1937; Kolmogorov et al, 1937; Barton and Turelli, 2011; Gandhi et al, 2016; Birzu et al, 2018), and development (Chang and Ferrell, 2013; Vergassola et al, 2018; Muratov and Shvartsman, 2004; Nolet et al, 2020). Small groups of cells can transmit signals more quickly than simple diffusion allows by recruiting the help of their neighbors
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