Beyond Symmetry Breaking: Competition and Negative Feedback in GTPase regulation

Summary

Cortical domains are often specified by the local accumulation of active GTPases. Such domains can arise through spontaneous symmetry breaking, suggesting that GTPase accumulation occurs via positive feedback. Here, we focus on recent advances in fungal and plant cell models, where new work suggests that polarity-controlling GTPases develop only one “front” because GTPase clusters engage in a winner-takes-all competition. However, in some circumstances two or more GTPase domains can co-exist, and the basis for the switch from competition to coexistence remains an open question. Polarity GTPases can undergo oscillatory clustering and dispersal, suggesting that these systems contain negative feedback. Negative feedback may prevent polarity clusters from spreading too far, regulate the balance between competition and co-existence, and provide directional flexibility for cells tracking gradients.

Positive feedback enables accumulation of active GTPases in cortical domains

Complex cell behaviors often involve the specification of distinct cortical domains. A prominent and well-studied example involves specification of a cell’s “front” during polarity establishment, which occurs by locally concentrating the active, GTP-bound form of a GTPase (Cdc42, Rac, or Rop) at a patch of the plasma membrane [1, 2]. Other cortical patterning events, such as the generation of alternating lobes and indentations in leaf pavement cells [3], involve specification of multiple GTPase-enriched domains. Recent studies have begun to elucidate the principles involved in generating such domains.

The GTPases are associated with membranes via prenylation, and their nucleotide status is regulated by factors that promote GTP loading (GEFs) or GTP hydrolysis (GAPs)(Box 1). GTP-bound forms interact with a variety of “effector” proteins to control local cytoskeletal organization, vesicle trafficking, and other processes. For example, a concentrated patch of GTP-Cdc42 at the bud site in the yeast Saccharomyces cerevisiae promotes local actin filament nucleation by regulating formins [4, 5] and local secretory vesicle fusion by regulating the exocyst [6, 7], leading to polarized growth.

Text Box 1. Positive feedback via GEF-effector complexes.

GTPases switch between inactive GDP-bound forms (blue) and active GTP-bound forms (red) in a manner regulated by guanine nucleotide exchange factors (GEFs) and GTPase-activating proteins (GAPs). Effector proteins recognize the GTP-bound form. In budding yeast, the scaffold protein Bem1 binds both an effector and a GEF, forming a cytoplasmic three-way complex that can promote positive feedback as follows: By binding to the effector, an active GTPase at the membrane can recruit a GEF-effector complex from the cytoplasm. Diffusion of cytoplasmic proteins is much faster than that of proteins in the plasma membrane, so the GEF-effector complex is effectively immobilized for as long as it remains bound. During this time the GEF promotes GTP-loading of the inactive GTPases in its vicinity, thereby creating a cluster of active GTPases. These in turn recruit more GEF-effector complexes, until such complexes become depleted from the cytoplasm. GAPs continuously convert the active GTPases back to their GDP-bound forms. In the center of the cluster, the high concentration of GEF-effector complexes would rapidly re-activate these GTPases (and any others being delivered to the cluster). Similarly, dissociation would constantly return bound GEF-effector complexes to the cytoplasm, but the high concentration of active GTPases would re-recruit more complexes, generating a dynamic, self-renewing cluster.

Figure I.

Positive feedback via GEF-effector complexes

Assembly of cortical GTPase domains is often triggered by localized cues, but such domains can also arise spontaneously at random locations in the absence of cues. Spontaneous domain assembly is called symmetry breaking [1, 2]. To explain how GTPases might cluster at a random location, theoretical studies posited that stochastic fluctuations in the concentration of key factors along an initially homogeneous cell cortex could be amplified by positive feedback [8, 9]. Positive feedback can promote domain assembly by recruiting more GTPases to sites that already have some GTPase.

The mechanistic basis for positive feedback is unclear in many systems, but in S. cerevisiae it involves linking a Cdc42 GEF to a Cdc42 effector [1, 10]. Similar GEF-effector complexes are found in many other cells [11, 12]. Because cells often contain more GEFs and effectors than they do GTPases, GEF-effector linkages have been proposed to allow particular GEFs to “channel” the GTPase to specific effectors [13]. However, in S. cerevisiae there is only one Cdc42-directed GEF, and the linkage is proposed to play a different role. The GEF-effector complex can bind to pre-existing GTP-Cdc42 via the effector, and then activate neighboring GDP-Cdc42 via the GEF, thereby “growing” a cluster of active GTP-Cdc42 at the membrane (Box 1). Thus, GEF-effector complexes may provide a common mechanism for positive feedback.

In addition to positive feedback, theoretical analyses have highlighted the critical role of diffusion in symmetry breaking. “Turing”-like systems consider two interacting molecular species that diffuse at different rates: an “activator” and an “inhibitor”. The slowly diffusing activator promotes its own synthesis, so that a local cluster of activator will acquire more activator, which only gradually diffuses away. At the same time, the activator induces synthesis of an inhibitor that antagonizes generation of more activator. The inhibitor diffuses more rapidly than the activator, and suppresses formation of new activator clusters in the vicinity of an existing cluster. Similar behavior also arises if one considers a rapidly diffusing “substrate” that is consumed upon activator synthesis. In this case, depletion of the substrate replaces the inhibitor as a mechanism to prevent formation of nearby clusters. Such simple two-component models yield periodic patterns in which cortical activator-rich domains are evenly spaced [14, 15].

The molecular analyses of GTPase domain formation are broadly consistent with the earlier theoretical work on Turing systems. For example, GTP-Cdc42 in yeast can be considered a Turing-type activator: it diffuses very slowly in the yeast plasma membrane and it promotes local accumulation (“synthesis”) of more GTP-Cdc42 [1]. The GEF-effector complex has characteristics of a Turing-type substrate: it diffuses rapidly in the cytoplasm, from which it is depleted (“consumed”) due to recruitment to the growing GTP-Cdc42 cluster. However, recent studies indicate that the rules for GTPase domain formation may be more complex than predicted by Turing models. In this review, we highlight recent findings that seek to explain how cells decide how many GTPase domains will form in specific situations.

Making one and only one front: winner-takes-all competition

In principle, positive feedback could lead to the simultaneous growth of several GTPase domains. However, when most cells (including yeasts) polarize, they generate only one front. Why is only one polarity domain established? The number of domains generated by Turing models depends on the size of the cell: small cells generate only one domain (if the cell is smaller than the characteristic spacing between domains), while larger cells generate more [14]. However, other computational models predict that there will be a “winner-takes-all” competition between GTPase clusters no matter how large the cell [16, 17]. A key feature of such models is that larger clusters have a competitive advantage in recruiting and retaining cytoplasmic polarity factors (like the GEF-effector complexes in yeast), so that the largest cluster wins. Imaging polarity establishment at high resolution in S. cerevisiae revealed that many cells did initially grow more than one small cluster of Cdc42 [18]. Subsequently, however, one cluster grew while the others shrank, leaving a single large domain just 2 minutes later (Fig. 1A). This behavior strongly suggests that the clusters compete with each other. Moreover, experimental manipulations intended to increase the abundance of GEF-effector complexes yielded slower competition between Cdc42 clusters in yeast [18, 19]. The direct observation of multi-cluster intermediates supports the models in which cluster competition assures that cells make only one front.

Figure 1. Competition and co-existence among GTPase clusters.

A) In S. cerevisiae cells breaking symmetry, clusters of Cdc42 compete until a single winner emerges. B) In S. pombe, initial symmetry breaking is followed by stereotypical cycles of old-end growth and NETO (new end take-off) leading to bipolar growth. C) In A. gossypii, initial symmetry breaking is followed by hyphal branching (not shown) and then apical branching that involves the splitting of one Cdc42 cluster into two. D) In A. thaliana, heterologous expression of the xylem-specific GTPase Rop11 and its GEF and GAP in nonxylem plant cell types leads to formation of multiple dispersed clusters containing Rop11-GTP and its GEF (left). In leaf pavement cells, mutually inhibitory clusters of Rop2/Rop4 and Rop6 GTPases establish zones of growth versus indentation (right).

From one site to two

Homologs of the polarity establishment proteins identified in S. cerevisiae are important in all fungi studied to date. However, whereas polar growth in budding yeasts is always restricted to one site, other fungi can develop two or more growth zones, each with its own GTPase domain (Fig. 1B, C). If the polarity system involves competition, then how do cells transition from one to two (or more) domains?

The cylindrical fission yeast Schizosaccharomyces pombe is a case in point. As in S. cerevisiae, depolarized S. pombe cells (spores or regenerating spheroplasts) break symmetry and develop a single Cdc42-enriched site that initiates polar growth (Fig. 1B)[20]. Subsequent vegetative growth follows a stereotyped pattern: after cell division, there is a period of unipolar growth at the “old” end (opposite the “new” end created upon cell division), followed by a period of bipolar growth at both ends [21]. The transition from one to two growth zones is called “new end take-off” or NETO. This behavior suggested that NETO might be triggered by a time- or size-dependent cue. One possibility, suggested by Turing models [14], is that the diffusion properties of the polarity factors (GTPases and their regulators) set a length scale such that small cells develop a single Cdc42 domain while larger cells develop two. However, there are some intriguing mutants that argue against such models. Cells lacking the Cdc42 GAP Rga4 [22] or the formin For3 [23] divide to produce equal-sized daughters that progress through the cell cycle normally, yet one daughter grows at only one end (no NETO) while the other daughter grows at both ends from the beginning (premature NETO). What determines growth at one end versus two ends?

An appealingly simple idea to explain NETO starts with positive feedback and competition, but adds a key new ingredient: saturation [24–26]. S. pombe cells contain several “tip factors” that are present at both tips, regardless of whether the tip is actively growing. Assuming that one or more such factors promote local Cdc42 recruitment via positive feedback, both tips would recruit Cdc42 and its regulators until a limiting cytoplasmic factor becomes depleted. At this point, the tips compete with each other. If tip factors are present in excess relative to the limiting cytoplasmic factor, competition would proceed until one tip (perhaps endowed with a slight starting advantage) wins. But as levels of the cytoplasmic factor rise in parallel with cell growth, the winning tip may saturate, allowing cytoplasmic factor concentrations to rise and the other tip to recruit Cdc42. Thus, the system proceeds from a monopolar to a bipolar pattern as the cytoplasmic factor levels rise. A key assumption is that unlike Cdc42 or the cytoplasmic factors, the levels of tip factors are constant and do not rise during cell growth, enabling saturation. Therefore, during cell division the tip factor levels would have to double to accommodate the doubling in the number of tips.

Mathematical modeling indicates that with suitable positive feedback and saturation, this system proceeds from monopolar to bipolar via a bistable intermediate in which either monopolar or bipolar solutions are attainable [24–26]. In the bistable regime, small differences in the starting conditions (e.g. relative Cdc42 levels) at the two tips would allow the daughter cells to exhibit either monopolar or bipolar growth just after cell division, which could explain the rga4 or for3 mutants discussed above. Although many tip-localized factors have been identified, it remains to be seen whether any of them act in the manner proposed by these models.

Transition from one to two or more growth zones is also common in filamentous fungi like Ashbya gossypii, which grows from needle-shaped spores to form extended multinucleated mycelia. Following spore germination, symmetry breaking creates a single growth site (Fig. 1C). As hyphae grow, they initiate new polarity sites in the shafts that become side branches. Every time a new branch is initiated, the tip growth rate transiently slows [27], suggesting that new and pre-existing sites may transiently compete, although the long distance between the tip and the lateral branch site may make competition ineffective in this case. However, later in development the tip polarity site splits in two, leading to adjacent “apical” branches [27](Fig. 1C). How does a single polarity domain split? Why don’t the daughter domains compete with each other? As they are immediately adjacent, why don’t the domains merge? We return to these questions below.

Many co-existing cortical domains

In several plant cell types, patterned cell wall structures are formed in a manner involving multiple, dispersed GTPase domains in a single cell. A striking study showed that when a xylem-specific GTPase, Rop11, is expressed together with its GEF and GAP in nonxylem cells (where these factors are not normally present), it spontaneously assembles into multiple cortical clusters [28](Fig. 1D). Clustering requires all three proteins to be co-expressed: in the absence of either regulator, Rop11 is uniformly distributed in the plasma membrane. Rop11 and its GEF colocalize in clusters, suggesting the presence of a Rop11-GEF positive feedback process. However, these clusters co-exist instead of competing to yield a single winner.

Another example in which multiple GTPase domains co-exist is provided by leaf epidermal cells that grow to form jigsaw-like patterns in which a bulge growing from one cell is matched to an indentation in the neighboring cell. Starting from smooth initial cell contours, these cells generate alternating cortical domains enriched in GTP-Rop2/Rop4 or GTP-Rop6 [2](Fig. 1D). Rop2/Rop4 harnesses actin to promote bulging, while Rop6 harnesses microtubules to restrain growth and allow indentation [3]. The alternating pattern is established by mutual inhibition between Rop2/Rop4 and Rop6 domains [3], and by auxin-mediated communication between neighboring cells [29]. Mutual inhibition can explain why the Rop2/Rop4 and Rop6 domains don’t overlap, but why are there several interspersed domains, rather than (for example) one large domain of each GTPase? Similarly, what prevents the Rop11 clusters from competing, or merging into a single larger cluster? Answering these questions poses challenge for computational biologists: are there general rules embedded in the architecture of positive feedback pathways that make some GTPase domains cut-throat competitors while others enjoy a peaceful coexistence? The answer to that question may depend on the presence of negative feedback, discussed further below.

Oscillatory clustering of GTPases

Even when there is no competitor domain in sight, GTPase domains sometimes disappear. In budding yeast cells breaking symmetry, the winning Cdc42 cluster to emerge from rapid competition then disperses and re-forms in an oscillatory manner [18](Fig. 2A). In fission yeast cells undergoing bipolar growth after NETO, Cdc42 accumulates at one tip, then disperses from that tip while simultaneously accumulating at the other tip in an oscillatory manner [26](Fig. 2B). In plants, the GTPase Rop1 undergoes oscillatory accumulation and dispersal at the tips of growing pollen tubes [30](Fig. 2C). Oscillatory behaviors in biological systems are thought to require the presence of a delayed negative feedback loop, so that initial activation triggers subsequent inactivation [31]. Thus, these observations suggest that clustered polarity GTPases may trigger their own dispersal via some form of negative feedback.

Figure 2. Oscillatory GTPase clustering and dispersal indicates presence of negative feedback.

A) In S. cerevisiae cells breaking symmetry, the Cdc42 cluster that wins the competition goes on to partially disperse and reform. B) In S. pombe after NETO, Cdc42 alternately clusters and disperses in an anticorrelated manner at each tip. C) In pollen tubes, Rop1 clusters and disperses in an oscillatory manner. Clustering precedes (and probably causes) each growth spurt.

What role does oscillatory clustering play in each of these systems? During pollen tube growth, both Rop1 tip concentration and the rate of tip growth oscillate with similar periodicity [30](Fig. 2C). Growth rate peaks about 18 seconds after the peak of Rop1 concentration in every cycle. Interestingly, faster overall tip growth is correlated with a shorter period of oscillation, perhaps suggesting that fast oscillations can somehow enable more rapid cell expansion [32]. In fission yeast (Fig. 2B), oscillatory Cdc42 accumulation (albeit with lower amplitude) is observed at the old end prior to NETO, perhaps suggesting that oscillation could allow the new end to have earlier access to Cdc42, promoting the switch from monopolar to bipolar growth [26].

In budding yeast (Fig. 2A), it is not intuitively obvious why oscillation would be beneficial. Moreover, oscillations were markedly dampened when cells were exposed to mild stress during imaging (e.g. small increases in light exposure or temperature), even though these conditions did not overtly affect polarization efficiency [18]. Similarly, oscillations were only apparent in about 50% of fission yeast cells [26]. Even in pollen, rapid polar growth can proceed without oscillations: Lilly pollen tubes grow in a consistent manner until they reach a length of 1 mm, and only then do they begin to oscillate, with no dramatic change in average growth rate [33]. These observations suggest that oscillation might simply be a byproduct of negative feedback that is present in these systems for other reasons.

Roles of negative feedback: robustness and competition

What benefit might be conferred by the presence of negative feedback in polarity pathways? One attractive role for negative feedback is to buffer the system against fluctuations in polarity protein concentration. The presence of positive feedback creates the potential for uncontrolled spreading of the GTPase-enriched domain. Depletion of limiting factors could restrain a growing cluster, but mathematical modeling indicates that this restraint is fragile. Addition of negative feedback to the model makes it much more robust, able to retain a limited GTPase domain over a wide range of parameters [18]. Although extreme overexpression of polarity factors can be lethal [34], moderate (~10-fold) overexpression is well-tolerated in both S. cerevisiae [18] and S. pombe [35]. The ability of these cells to retain polarity even when GTPases or their regulators are overexpressed is consistent with the idea that negative feedback restrains undue spreading of the polarized domain.

In addition to making polarity circuits more robust, negative feedback could significantly change the dynamics of competition [18]. During winner-takes-all competition, the losing GTPase cluster must be dismantled, and in budding yeast cells this process is unexpectedly rapid. By restraining the growth of polarity domains, negative feedback may accelerate the disappearance of the losing cluster. However, mathematical modeling reveals an additional, unexpected effect of negative feedback: as concentrations of polarity factors increase and clusters grow larger, it is possible to enter a regime in which very large clusters trigger enough negative feedback to become self-defeating. In that event, smaller clusters could gain the upper hand in the competition, until they in turn grow very large. At least in theory, these dynamics would resolve to a situation with two equal clusters in which neither can outdo the other [18]. It is attractive to speculate that this feature may explain the apical branching of fungal hyphae discussed above (Fig. 1C). As the hypha grows and accumulates polarity factors, the system may transition from a regime where GTPase clusters compete (yielding one winner) to a regime where they equalize (splitting to form two clusters).

Another role for negative feedback could be to allow repositioning of the polarity cluster. In a subset of S. cerevisiae cells preparing to bud, the initial Cdc42 cluster disappeared and a new cluster formed elsewhere (a phenomenon termed “relocation”)[18]. Relocation may be advantageous for cells that need to grow towards specific targets, like pollen tubes in search of ova or yeast cells in search of mating partners. Intriguingly, recent studies suggest that polarity site relocation is important for partner selection in both S. cerevisiae [36] and S. pombe [37].

To definitively assess the role played by negative feedback, it will be necessary to determine the mechanism(s) of negative feedback and develop tools to short-circuit such feedback in cells.

Mechanistic basis for negative feedback

Negative feedback does not simply reflect the presence of negative regulators (like GAPs) that are constitutively present: rather, accumulation of an active GTPase must induce its own inactivation and/or dispersal. In principle, this might occur via GTPase-mediated stimulation of GAP activity, or inhibition of GEF activity, but neither of these mechanisms has yet been documented. A different, appealingly simple, negative feedback mechanism emerges from considering the cell biology that underlies polar growth. As mentioned above, active GTPases are thought to promote formation of actin filaments that deliver secretory vesicles to the GTPase domain, where concentrated GTPase facilitates exocytic vesicle fusion. Imaging of both GTPases and their activators in fungal and plant systems indicates that these factors are more concentrated at the cortical plasma membrane than they are on secretory vesicles [30, 38–40](Fig. 3A). Thus, fusion of the secretory vesicles (driving polar growth) would dilute the GTPases [41], potentially constituting a negative feedback loop.

Figure 3. Potential negative feedback pathways and their effects.

A) Fungal hyphae (left) and pollen tubes (right) display concentrated GTPases at the tip plasma membrane. Large vesicle clusters (spitzenkörpers or inverted cones) are not enriched for the GTPases, implying that fusion of the vesicles to the plasma membrane would dilute the GTPases. B) In pollen tubes, the Rop1-GAP, Ren1, is concentrated on vesicles. Thus, vesicle fusion would not only dilute but also inactivate Rop1, providing strong negative feedback. C) In S. cerevisiae, stochastic off-center delivery of vesicles may nudge the Cdc42 cluster away from the vesicle fusion site, promoting wandering of the polarity site in cells tracking pheromone gradients. D) In U. maydis, Rac-GTP activates the effector kinase Cla4 to phosphorylate the Rac-GEF, promoting its degradation.

The magnitude of the dilution effect depends on the amount of membrane traffic and the rapidity with which the polarity factors are re-recruited to the tip from the cytoplasm. In the budding yeast system, membrane traffic is modest and computational simulations suggest that the dilution effect of vesicle traffic, though real, would be small [42]. However, given the 50–1000-fold faster tip growth rates in hyphae and pollen tubes, dilution by vesicle fusion may become highly significant. A growth surge mediated by a bolus of new membrane addition could dilute the GTPase, slowing local exocytosis until positive feedback builds the GTPase concentration back up and triggers another growth surge. Intriguingly, a Rop1-directed GAP is concentrated on vesicles in pollen tubes [39], suggesting that in addition to diluting Rop1, vesicle fusion would tend to inactivate the remaining Rop1, enhancing negative feedback (Fig. 3B).

Thus far, there is little evidence that GAPs are concentrated on vesicles in S. cerevisiae, although vesicle-mediated GAP delivery could provide negative feedback in that system as well [43]. Recent work on cells preparing to mate suggests that vesicle delivery does have a significant polarity-perturbing effect [36]. Due to the small numbers of actin cables in this system, stochastic delivery of off-center vesicles can reduce polarity factor concentration on one side of the polarity patch and nudge the patch centroid aside (Fig. 3C). Rather than oscillation, this causes the polarity site to wander around the cell cortex. In yeast cells seeking prospective mates by sensing peptide pheromones, such wandering may help the cells to track shallow pheromone gradients [36].

Actin-mediated delivery of polarity-perturbing membrane cannot be the only mechanism of negative feedback, because oscillatory clustering of Cdc42 in budding yeast or Rop1 in pollen tubes continued even following actin depolymerization [18, 30]. Thus, additional actin-independent sources of negative feedback must be present. Oscillatory growth of pollen tubes is accompanied by periodic changes in tip Ca⁺⁺ levels, which may participate in negative feedback (reviewed in [44]). Another potential negative feedback mechanism is suggested by findings from the basidiomycete Ustilago maydis. In that system, a GTPase effector (Cla4) phosphorylates the GEF, triggering its degradation and hence a reduction in GTPase activity [45](Fig. 3D). Cla4-mediated phosphorylation of the GEF also occurs in both S. cerevisiae [46, 47] and S. pombe [11], although that is not accompanied by GEF degradation in those systems. In S. cerevisiae, the GEF is phosphorylated at over 35 sites, but the role of that phosphorylation remains mysterious [48]. Thus, additional mechanisms of negative feedback remain to be elucidated.

Concluding remarks

Recent studies on the behavior of the GTPases that specify cortical domains in fungi and plant systems suggest that GTPase regulatory pathways contain built-in positive feedback and negative feedback loops. The interplay between these features can produce multiple outcomes, including competition between GTPase clusters, mutual inhibition, and co-existence. Negative feedback provides further potential for oscillation, robustness, and exploratory behaviors. Symmetry breaking, mutual inhibition between GTPase domains [49], and oscillatory formation and dispersal of GTPase domains [50] have also been documented in mammalian cells, suggesting that they contain similar feedback loops. Mathematical modeling has proven valuable in suggesting plausible roles for these circuit elements, but the mechanisms of positive and negative feedback remain to be definitively established in most systems, and this is critical to allow testing of their proposed functions.

Highlights.

• Positive feedback enables formation of cortical domains enriched in GTPases

• Competition between polarity GTPase domains assures a single winner

• In other cases, co-existing domains indicate an absence of competition

• Oscillation of GTPase levels within domains suggests presence of negative feedback

• Negative feedback could confer robustness and influence competition