Small GTPase patterning: How to stabilise cluster coexistence

Abstract Many biological processes have to occur at specific locations on the cell membrane. These locations are often specified by the localised activity of small GTPase proteins. Some processes require the formation of a single cluster of active GTPase, also called unipolar polarisation (here “polarisation”), whereas others need multiple coexisting clusters. Moreover, sometimes the pattern of GTPase clusters is dynamically regulated after its formation. This raises the question how the same interacting protein components can produce such a rich variety of naturally occurring patterns. Most currently used models for GTPase-based patterning inherently yield polarisation. Such models may at best yield transient coexistence of at most a few clusters, and hence fail to explain several important biological phenomena. These existing models are all based on mass conservation of total GTPase and some form of direct or indirect positive feedback. Here, we show that either of two biologically plausible modifications can yield stable coexistence: including explicit GTPase turnover, i.e., breaking mass conservation, or negative feedback by activation of an inhibitor like a GAP. Since we start from two different polarising models our findings seem independent of the precise self-activation mechanism. By studying the net GTPase flows among clusters, we provide insight into how these mechanisms operate. Our coexistence models also allow for dynamical regulation of the final pattern, which we illustrate with examples of pollen tube growth and the branching of fungal hyphae. Together, these results provide a better understanding of how cells can tune a single system to generate a wide variety of biologically relevant patterns. Author summary Where to form a bud? Where to reinforce the cell wall? In which direction to move? These are all important decisions a cell may have to make. Proper patterning of the cell membrane is a critical part of such decisions. These patterns are often specified by the local activity of proteins called small GTPases. Mathematical models have been an important tool in understanding the mechanisms behind small GTPase-based patterning. Most of these models, however, only allow for the formation of a single cluster of active GTPase and thus cannot explain patterns of multiple coexisting GTPase clusters. A previously proposed mechanism for such coexistence can only explain a temporary, unstable coexistence, and fails to explain several key biological phenomena. In this manuscript, we investigate two mechanisms that can produce patterns of many stably coexisting GTPase clusters. Using a combination of modelling techniques, we show why these mechanisms work. We also show that these mechanisms allow for the addition of new clusters to an existing pattern, as is observed for example during the branching of fungal hyphae. With our results, we now have handles to explain the full range of naturally occurring small GTPase patterns.