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.

Robust banded protoxylem pattern formation through microtubule-based directional ROP diffusion restriction

“…We start with two simple reaction-diffusion models for small GTPase-based membrane patterning that can generate coexisting spots, stripes, and gaps [6]. Both models are adaptations of the wave pinning model from [41], with the addition of either protein turnover (WPT model; see Fig.…”

“…Both models are adaptations of the wave pinning model from [41], with the addition of either protein turnover (WPT model; see Fig. 1D) or negative feedback through GAP activation (WPGAP model) to prevent accumulation of all active ROP into a single cluster (see [6] for a mechanistic explanation). The models assume that active 110 ROP is exclusively membrane bound and inactive ROP is exclusively cytosolic.…”

“…Smaller square domains (95x95 or 63x63) with fully 150 periodic boundary conditions were used for investigating the orientation mechanism. Unless stated otherwise, simulations were initiated at the homogeneous steady state (see [6]) with a small amount of noise added to each integration pixel. To ensure numerical accuracy, small scale tests were performed using 155 reproducible perturbations as described by [43] to determine the optimal time step and pixel size.…”

“…1A). Since ROP involvement has also been indicated in protoxylem differentiation [15] and the same effectors (MIDD1, Kinesin13A) are ex- 25 pressed during protoxylem development [16,17], patterning of [6]. pattern harder to obtain with a reaction-diffusion mechanism.…”

“…We used identical values for the parameters for the reaction parts and the unrestricted diffusion coefficients as in [6]. We have previously performed extensive bifurcation analyses 135 of these models [6] to locate parameter regimes where spontaneous patterning can occur from a homogeneous state (socalled Turing regimes). This analysis directed us to relevant parameter sets that remained useful in the case of anisotropic diffusion.…”