A Density-Dependent Switch Drives Stochastic Clustering and Polarization of Signaling Molecules

Positive feedback plays a key role in the ability of signaling molecules to form highly localized clusters in the membrane or cytosol of cells. Such clustering can occur in the absence of localizing mechanisms such as pre-existing spatial cues, diffusional barriers, or molecular cross-linking. What prevents positive feedback from amplifying inevitable biological noise when an un-clustered “off” state is desired? And, what limits the spread of clusters when an “on” state is desired? Here, we show that a minimal positive feedback circuit provides the general principle for both suppressing and amplifying noise: below a critical density of signaling molecules, clustering switches off; above this threshold, highly localized clusters are recurrently generated. Clustering occurs only in the stochastic regime, suggesting that finite sizes of molecular populations cannot be ignored in signal transduction networks. The emergence of a dominant cluster for finite numbers of molecules is partly a phenomenon of random sampling, analogous to the fixation or loss of neutral mutations in finite populations. We refer to our model as the “neutral drift polarity model.” Regulating the density of signaling molecules provides a simple mechanism for a positive feedback circuit to robustly switch between clustered and un-clustered states. The intrinsic ability of positive feedback both to create and suppress clustering is a general mechanism that could operate within diverse biological networks to create dynamic spatial organization. Author Summary: A large body of work has focused on the ability of positive feedback in biological networks to create either switches in time (i.e., cells are either in an “on” or an “off” state) or form patterns in space (i.e., spatial organization in cells and tissues). Here, we propose a stochastic “neutral drift polarity model” by which positive feedback alone is sufficient to create switch-like behaviors both in time and space for finite molecule numbers. Our theory predicts that below a critical density of signaling molecules, positive feedback robustly maintains an off state; exceeding this threshold switches on the recurrent emergence of highly localized signaling clusters. Cluster formation requires only this minimal positive feedback circuit, and does not require additional mechanisms such as diffusion barriers, spatial cues, or biochemical inhibitors. This mechanism is general, and could be applied to a variety of cellular signaling systems to create clusters in the membrane, cytosol, or organelles.