Orientation of cell polarity by chemical gradients

Abstract

Accurate decoding of spatial chemical landscapes is critical for many cell functions. Eukaryotic cells decode local chemical gradients to orient growth or movement in productive directions. Recent work on yeast model systems, whose gradient sensing pathways display much less complexity than those in animal cells, has suggested new paradigms for how these very small cells successfully exploit information in noisy and dynamic pheromone gradients to identify their mates. Pheromone receptors regulate a polarity circuit centered on the conserved Rho-family GTPase, Cdc42. The polarity circuit contains both positive and negative feedback pathways, allowing spontaneous symmetry breaking and also polarity site disassembly and relocation. Cdc42 orients the actin cytoskeleton, leading to focused vesicle traffic that promotes movement of the polarity site and also reshapes the cortical distribution of receptors at the cell surface. Here, we review the advances from yeasts and compare with the excitable signaling pathways that have been revealed in chemotactic animal cells.

Introduction

Cell polarity, or the asymmetric organization of cell components along a directional axis, is fundamental for a variety of cell functions. In eukaryotes, a polarized organization of the cytoskeleton enables directed secretion and membrane protrusion, which underlie cell migration and polar growth. Physical and chemical cues can influence the direction of polarization. In this review we focus on how chemical gradients can be decoded by the polarity machinery to facilitate chemotropism (directed polar growth) and chemotaxis (directed cell migration). Chemical gradients are exploited by unicellular organisms to find nutrients and mates, and by cells in multicellular organisms to enable morphogenesis during development, to generate specialized cell-cell contacts, to heal wounds, to detect and destroy pathogens, and to allow successful fertilization (5, 25, 96, 98, 100, 101, 106, 112)

Cell polarity is regulated by an evolutionarily ancient molecular machinery centered on Rho-family GTPases (including Cdc42, Rac, and Rop subfamilies: there are differences between these but in what follows we refer to all simply as “Cdc42” and focus on common aspects)(32, 90, 117). Cdc42 proteins switch between GTP-bound ‘active’ and GDP-bound ‘inactive’ states, in a manner catalyzed by guanine nucleotide exchange factors (GEFs, which switch Cdc42 “ON”) and GTPase activating proteins (GAPs, which switch Cdc42 “OFF”)(Fig. 1A). Cdc42 is prenylated (covalently linked to a hydrophobic lipid), and associates with lipid bilayers. Unpolarized cells have a homogeneous distribution of inactive GDP-Cdc42, and polarity establishment involves the asymmetric accumulation of active GTP-Cdc42 at a region on the cell cortex to generate a cell’s “front” (Fig. 1B). Many cells also generate a specialized “back”, and polarity can be reinforced by mutually inhibitory interactions between “front” and “back” specific factors (119). Active Cdc42 is recognized by proteins called “effectors”, which are recruited to the polarity region and transduce Cdc42 localization into orientation of the cytoskeleton towards the front, leading to growth or migration in that direction.

Fig. 1. Polarity and gradient sensing.

A) Cdc42-related proteins act as molecular switches, turned on by GEFs and off by GAPs. B) Polarity establishment involves switching from a homogeneous distribution of Cdc42 to a polarized distribution with concentrated active Cdc42 defining the cell’s front. C) Chemical signals (Ligand) are sensed by specific G-protein-coupled receptors (GPCR) at the membrane, which cause GTP-loading of Gα and its separation from G Gβγ. The active Gα-GTP and Gβγ go on to influence Cdc42 activation. Gα-GTP can be deactivated by regulators of G-protein signaling (RGS). D) External gradients (blue) influence the location of polarity establishment (top) and can cause relocation of the polarity site (bottom).

Orientation of cell polarity in response to an external chemical gradient requires a machinery to detect and respond to the chemical(s) of interest. In many cases, cells detect chemoattractants using cell-surface G-protein-coupled receptors (GPCRs)(70). Ligand binding allows these receptors to “activate” heterotrimeric G proteins with Gα, Gβ, and Gγ subunits (Fig. 1C). Like Cdc42, the Gα subunit can bind either GDP or GTP. GPCRs catalyze conversion of Gα-GDP to Gα-GTP (analogous to GEF activation of Cdc42), and a family of regulators of G protein signaling (RGS proteins) promote GTP hydrolysis back to Gα-GDP (analogous to GAP inactivation of Cdc42). Also like Cdc42, Gα and Gβ are covalently attached to lipids and bind to membranes. Gα binding to GTP results in unbinding from the Gβγ subunits (which stay together), and that allows the separate Gα and Gβγ to interact with other proteins (Fig. 1C). These interactors regulate Cdc42 activation, thereby connecting chemoattractant sensing to polarization.

To respond to a spatial chemical gradient, a cell must compare concentrations at different locations and then direct growth or migration toward a target. Directional response involves two related but distinct processes, which are often lumped together as “gradient sensing” or “gradient tracking”: (i) an initially unpolarized cell decodes a spatial gradient to orient polarity establishment, and (ii) an already-polarized cell re-orients the direction of the cell front (Fig. 1D). In this review, we focus on advances in yeast model systems that support a polarity-centric view of gradient decoding for chemotropism, and draw parallels to recent insights from studies of chemotaxis. We begin by outlining biophysical models for polarity establishment, and then address how cells orient polarity in response to chemical gradients.

Biophysics of cell polarity

Positive feedback drives polarization

In most cells where it has been examined, polarity establishment does not require a directional cue such as a chemoattractant gradient. This makes sense in terms of cell physiology: a cell needing to find nutrients would do well to polarize and explore its environment even if there is not an obvious nutrient gradient at its current location, and an immune cell sensing an invading pathogen would do well to polarize spontaneously and migrate until it can detect a strong gradient of pathogen-released signal. Polarization in the absence of a directional cue is often called symmetry breaking, and involves positive feedback mechanisms that can amplify small starting asymmetries due to noise. In some systems symmetry breaking can involve forces generated by the cytoskeleton (2, 76, 78, 79, 88), but in this review we focus on biochemical mechanisms. A mechanism of positive feedback with strong support from many lines of evidence in the model yeasts Saccharomyces cerevisiae and Schizosaccharomyces pombe arises from binding interactions that link Cdc42 effectors to Cdc42 GEFs (9, 12, 16, 28, 50, 60, 64, 115) This allows active Cdc42 to recruit GEFs from the cytoplasm to the nascent polarity site (Fig. 2A).

Fig. 2. Models for polarity establishment.

A) Recruitment of GEF to the membrane by active Cdc42 provides positive feedback (green arrow). B) Simplified MCAS model captures key dynamics of polarization. The cytoplasmic (rapidly diffusing) substrate v is interconverted to the membrane-associated (slow diffusing) activator u. C) Symmetry breaking triggered by noise. D) When more than one initial polarity site forms, competition for substrate leads to a single site at steady state.

Theoretical work dating back to the pioneering studies of Turing (1952) and Meinhardt (1972) indicated that systems of two reactants with positive feedback could spontaneously develop spatially patterned concentration profiles from homogeneous starting conditions (37, 109). In addition to positive feedback, pattern formation required differential mobility (diffusion) of the two reactants and a mechanism to limit growth of the polarity site. In the context of cell polarity, the differential mobility arises naturally from the difference in diffusion between proteins at the membrane (<0.1 μm²/s) and in the cytoplasm (>1 μm²/s)(91). Thus, polarity factors accumulating at the membrane diffuse slowly but can recruit more factors from a much larger region of cytoplasm, building up a polarity site. The simplest such models consider a slowly-diffusing “activator” at the membrane, that is generated from a rapidly-diffusing cytoplasmic “substrate” (Fig. 2B)(72). The homogeneous steady state in such systems can be unstable to local perturbation (Turing instability) and evolve to form characteristic patterns (like spots or stripes).

Mass conservation leads to competition between polarity sites

Polarity establishment can occur on a timescale of seconds to minutes, which is rapid relative to the slower processes that synthesize and degrade polarity proteins (47, 114). Moreover, in S. cerevisiae, cells with accumulated stores of Cdc42 can polarize and depolarize normally for many cell cycles after switching off Cdc42 synthesis (38). These observations suggest that synthesis and degradation are not critical to polarity establishment, prompting the development of mass-conserved activator substrate (MCAS) models in which those processes are neglected (Fig. 2B)(39, 42, 55, 77, 85). These models generally include non-linear positive feedback (i.e. n > 1 in Fig. 2B)(19, 39). Some MCAS models exhibit bistability (42, 77), and experimental work has confirmed that the yeast polarity system can exhibit bistability (30).

Mass conservation yields desirable properties for a polarity model. Because accumulation of the activator at a site on the membrane automatically depletes the cytoplasmic pool of the substrate, there is a limit on the growth/spreading of the activator-enriched region. And when there are several regions enriched for the activator, they compete for the shared pool of substrate (Fig. 2C). Competition arises because each patch of activator locally depletes cytoplasmic substrate, and the patch with highest levels of activator recruits substrate faster (Fig. 2D)(20, 42, 85, 116). This sets up a gradient of cytoplasmic substrate towards the strongest patch, siphoning off the activator released from the other patches. Thus, unlike classical Turing models that exhibit a characteristic wavelength between spots or stripes of activator, MCAS models generally develop to yield a single polarity site at steady state, consistent with observations in many cells.

A caveat to the description above is that even if polarity sites in a two-component MCAS system would eventually compete, multiple sites can still co-exist on biologically relevant timescales. This occurs when the amounts of activator at several sites approach a “saturation point”, when cytoplasmic gradients of substrate become very shallow, slowing the timescale of competition (20, 42, 43). Such slow competition can be seen in some yeast mutants (18, 116). In addition, MCAS-style models with more than two components can switch between parameter regimes that yield competition (and hence a single site at steady state) and other regimes that consistently yield multiple equal-strength accumulations of activator at steady state (18, 47, 52). This could be useful for some cell types, like neurons sprouting many neurites, or fungal hyyphae with branching tips, or plant leaf “jigsaw” cells with multiple protrusions (26, 33, 117) However, it would clearly be problematic for a migratory cell to develop more than one stable cell front, as pieces of the cell could migrate away from each other, ripping the cell apart. Thus, for the behaviors considered in this review, it seems likely that polarity systems operate in a “competition” parameter space where Cdc42 (while perhaps exhibiting transient multi-polar configurations) consistently evolves to have a single stable front.

A winner-takes-all behavior similar to that of competition for cytoplasmic substrate can also occur through polarity sites merging to form larger polarity sites (34, 59). This has not been observed in yeasts (18, 47, 116) but may apply in other systems. A reduction in the number of polarity sites from many to one is an example of “coarsening” behavior, which can emerge from various different mechanisms. In neutrophils, elegant experiments suggested that membrane tension was involved in ensuring that cells had a single front (46), and mechanochemical systems involving nonlinear positive feedback can also give rise to coarsening behaviors (40). However, membrane tension may not spread as rapidly as first envisaged (103), and the mechanism that ensures a single front in neutrophils may involve feedback from cell shape or other features on Cdc42 biochemistry (41).

Polarity sites emerging from MCAS models exhibit very stable local concentrations of activator, even though individual molecules of activator dynamically enter and leave the site through diffusion and interconversion. Positive feedback replenishes activator by continuously recruiting more substrate to where the activator is most concentrated. This makes the polarity site location very stable, presenting a problem for a cell that needs to relocate the front. As discussed further below, Cdc42 sites do relocate, and two mechanisms have been proposed to drive such movement: stochastic effects of molecular noise (44, 55, 94) and negative feedback that lowers the local Cdc42 concentration (27, 36, 71).

Polarity establishment oriented by a gradient

The problem of molecular noise

We first consider the problem of orienting initial polarity establishment in response to a chemoattractant gradient (Fig. 1D). In principle, this is straightforward: the chemoattractant gradient would be translated into a gradient of bound receptors at cell surface, and downstream signaling would translate that into an internal gradient of Cdc42 activation, which would kick off polarization up-gradient (Fig. 3A). However, because cells are so small, the difference in chemoattractant concentration between one side of the cell and the other can be minuscule. And because overall attractant concentrations can also be low (often in the nM range), molecular noise due to diffusion and stochastic biochemical interactions can be quite large relative to the gradient signal. Imaging of the chemoattractant cAMP interacting with GPCRs in Dictyostelium discoideum cells revealed large fluctuations in the distribution of bound receptors, with cells often having larger numbers of bound receptors on the down-gradient than the up-gradient side of the cell (75). As fluctuations suffice to initiate polarization by positive feedback, how can cells avoid polarizing in the wrong direction?

Fig. 3. Ratiometric sensing improves gradient detection.

A) With uniformly distributed receptors, a gradient of pheromone (blue) is faithfully translated into a similar gradient of bound receptors, allowing accurate polarization (green). B) Unevenly distributed receptors could mislead a cell: despite higher pheromone concentration at left, there would be more bound receptors at right. Internal dots represent active (green) and inactive (grey) G proteins. C) Mechanism for ratiometric sensing: G protein activation is catalyzed by bound receptor, while inactivation is catalyzed by RGS protein that is recruited to the membrane by unbound receptor. Thus, net activation reflects the ratio of bound to unbound receptor. D) Ratiometric sensing compensates for uneven receptor density, allowing accurate gradient detection. E) Measurement of mean pheromone concentration (Y axis: bound receptors) is noisier in a system that uses ratiometric sensing (blue) than one that directly senses bound receptors (yellow). F) When cells with uniformly distributed receptors are exposed to a pheromone gradient (blue arrows), there is both a gradient of bound receptors (LR) and an inverse gradient of unbound receptors (R). Systems with ratiometric sensing exploit both gradients to generate steeper internal active G protein gradients (green dots) than those with non-ratiometric sensing. Internal arrows indicate resultant vectors from positions of all active G proteins. G) The magnitude of the resultant vector of active G protein is greater in systems with ratiometric sensing (blue) compared to non-ratiometric sensing (yellow), leading to reduced noise in directional sensing (variability in angle between resultant vector and external gradient).

Because stochastic interactions occur with no directional preference, a time-averaging strategy could in principle extract an accurate directional signal from the noise, no matter how shallow the gradient. The longer the averaging interval, the better the noise-suppression. However, there are limits to the ability of cells to apply this strategy. For small cells suspended in liquid, thermal rotation limits the time for which the cell can maintain a stable coordinate system (10). For stationary cells, diffusion of bound receptors degrades the spatial information that they provide about the binding location (63). And for any time-averaging system, the molecular mechanism of averaging may itself introduce further noise. For example, the protein that connects the GPCR to Cdc42 activation in yeast (Far1) is present at only a few hundred copies per cell (108), potentially introducing noise during the transfer of chemical information.

Several theoretical studies have considered physical limitations on the accuracy with which cells can use receptors to detect the direction of a gradient (10, 11, 29, 48, 63, 95), but it is not entirely straightforward to pose this problem in a manner that reflects the biological context. For example, some studies address how well a spherical cell with uniform surface receptor density would be able to distinguish whether the up-gradient half of the cell had more bound receptors than the down-gradient half (10, 95). However, this assumes that the cell “knows” the axis along which the front/back comparison should be made. Other studies have analyzed the variability in the direction of a resultant vector taking into account the distribution of all bound receptors on the cell surface (29, 48, 63). But what if the cell is not spherical? And what if the receptors are not uniformly distributed? These realistic scenarios would seem to require a cell to “know” the spatial distribution of its receptors in order to accurately decode an external gradient. Recent work on pheromone gradient sensing by mating yeast (S. cerevisiae) suggests a mechanism by which cells tackle this problem.

Ratiometric sensing by GPCRs improves signal:noise

Pheromones are secreted by yeast cells of each mating type (sex) and recognized by GPCRs on cells of the opposite mating type (3)(Fig. 1C). The asexual budding mode of replication involves cytokinesis at the mother-bud neck, and GPCRs are often enriched around the neck region during division. Because yeast GPCRs diffuse very slowly (0.0005 μm²/s), new-born daughter cells retain an uneven receptor density, with (on average) 3-fold higher density at one pole than the other (45). This raises an obvious conundrum, in that an external pheromone gradient (whose direction is uncorrelated with the receiving cell’s receptor asymmetry) would not be faithfully translated into a gradient of bound receptors (Fig. 3B). How, then, can yeast cells accurately orient towards their partners?

The answer appears to be that yeast cells respond not to the distribution of bound receptors, but rather to the distribution of the ratio of bound to unbound receptors (ratiometric sensing) (15). This ratio should reflect the local pheromone concentration regardless of variations in the local receptor density. A molecular mechanism for ratiometric sensing depends on the RGS protein (Fig. 1C). The output of GPCR signaling is the local concentration of activated G protein (Gα-GTP and Gβγ), which depends on the counteracting reactions catalyzed by pheromone-bound GPCR (activation) and by RGS (inactivation). In yeast, the Sst2 RGS binds to inactive (unphosphorylated) GPCRs (7, 45) (Fig. 3C). This interaction reversibly recruits Sst2 from the cytoplasm to the membrane, so the local density of Sst2 reflects the local density of inactive GPCR. Therefore, in regions of high receptor density both the activation and deactivation rates are increased as compared to regions of low receptor density. As a result, the level of active G protein reflects the ratio of active to inactive GPCR (15, 45) (Fig. 3D).

Several results support the ratiometric sensing hypothesis (45). Most strikingly, the accuracy with which initial polarity establishment occurs toward a mating partner in yeast is greatly reduced by manipulations that distribute the RGS evenly around the plasma membrane (avoiding the enrichment of RGS at sites with high receptor density). In mutants with evenly distributed RGS, initial polarization is usually directed towards sites with high receptor density, and the accuracy of initial polarity establishment can be restored by manipulations that also distribute the GPCRs evenly around the plasma membrane. Thus, ratiometric sensing by GPCRs provides a strategy to decode external gradients that can compensate for uneven receptor density.

One potential drawback of ratiometric sensing is that it increases fluctuations in the global concentration of active G protein. This is because fluctuations that transiently increase the number of active receptors at the cell surface also decrease the number of inactive receptors, and thereby simultaneously effect both the activation and deactivation rates of the G protein. Thus, ratiometric systems are noisier (less accurate) at measuring average concentrations (Fig. 3E). Despite this, ratiometric sensing can reduce noise when detecting the direction of a gradient even when the receptor distribution is uniform (45). This is because the G protein activity reflects the product of two gradients: a gradient of active receptor and a mirror-image gradient of inactive receptor (Fig. 3F). The ratio amplifies the difference in active G protein between the up-gradient and down-gradient sides of the cell, thereby increasing the directional signal (Fig 3F). This effect increases the magnitude of the gradient of active G protein (Fig 3G, top), and decreases the variability in the direction of the G protein gradient (Fig 3G, bottom).

Re-orientation of polarity to track a gradient

If cells do not establish polarity in the right direction, they need a mechanism to correct the orientation of the front. Moreover, cells that are chasing a moving target need a way of re-orienting an already polarized front. Studies of different systems have highlighted two main strategies to re-orient: (i) cells can dismantle the original polarity site and polarize again, or (ii) cells appear to move the polarity site. In both cases, negative feedback on Cdc42 activity appears likely to play an important role.

Relocating polarity by disassembly and reassembly: Speed dating in fission yeast

The clearest example of the first strategy comes from mating cells of the fission yeast S. pombe. These rodshaped cells proliferate asexually to form dense colonies with cells of both mating types, which enter a mating program when starved of nutrients (Fig. 4A). The cells are not motile, and must polarize towards a partner in order to grow close enough to fuse. Imaging of active Cdc42 revealed that cells entered a “searching” phase in which polarity sites appeared and then disappeared with variable timing (average lifetime 1.5 min) at different locations around the cell surface (Fig. 4B)(8). This search process continued for several hours, until eventually two partners polarized stably towards each other, leading to growth projections that fused to make zygotes. The transient zones of active Cdc42 were somewhat enriched for proteins involved in pheromone secretion as well as pheromone sensing (recall that mating cells sense pheromones from the opposite mating type but not the pheromone that they themselves secrete)(73). These observations led to an attractive hypothesis, called “speed dating”, to explain how the mating partners found each other (67, 73).

Fig. 4. Speed dating in fission yeast.

A) Mating occurs in crowded mixtures of cells of the two mating types (blue and yellow). B) Cells sequentially polarize and depolarize Cdc42 (green), emitting puffs of pheromones locally when polarized. Eventually, assembly of aligned polarity sites leads to sensing of high pheromone levels by receptors and G proteins concentrated at each polarity site, which stabilizes the sites to allow fusion.

Speed dating is based on two central assumptions: (i) much of the cell’s pheromone secretion occurs at the active Cdc42 sites, creating transient but very steep local pheromone gradients; and (ii) pheromone levels are sensed by receptors at the partner’s Cdc42 sites, and sensing of high levels of pheromone serves to stabilize the polarity site, so that Cdc42 persists at a stable location. With these assumptions, the active Cdc42 sites act as coincidence detectors: most sites would secrete local puffs of pheromone and then disassemble, but when partner polarity sites happen to align, each site would detect high levels of pheromone from the nearby partner’s site, and they would both stabilize, leading to mating (Fig. 4B).

Speed dating fundamentally changes the question that a mating cell needs to answer: instead of decoding a potentially shallow and noisy spatial gradient of pheromone to polarize towards the partner, a cell simply needs to determine whether the concentration of pheromone near the polarity site has surpassed some threshold (indicating that a partner’s site is secreting pheromone nearby). This “local sensing” is facilitated by the accumulation of G proteins near the polarity site (the mechanism for this concentrating effect is not yet known)(73). Local sensing enables coincidence detection (stable/strong polarization only when partner’s polarity sites align), which provides a very attractive explanation for how partner cells can find each other even in crowded conditions where the net pheromone gradient from all of the nearby sources may not identify a single partner. However, the validity of the main speed dating assumptions has yet to be rigorously tested in S. pombe. And a fundamental question remains: why does the polarity site disassemble after just a few minutes? It seems likely that this is due to some form of negative feedback, but the molecular nature of that feedback remains to be elucidated.

Turning an existing front: Motile cells

The second strategy to re-orient in a gradient is to “move” the polarity site. Early studies on polarized mammalian neutrophils as well as D. discoideum showed that relocation of a chemoattractant source rarely triggered depolarization and repolarization somewhere else; instead, the front of the cell turned toward the new source (106, 122). Although GPCRs were evenly distributed in those cells (49), receptors at the leading edge had greater influence than those at the back of the cell. Thus, chemoattractant in these systems steers the existing front (58, 65). Similarly, chemotropic growth of axons (107), fungal hyphae (14, 99, 105), and plant pollen tubes (93) involves steering of a polarity site. Because positive feedback acts to maintain the position of the polarity site (rather than move it), simple models of polarity have difficulty making rapid adjustments of the polarity site position in response to gradients (56). However, a local negative feedback loop can destabilize the position and make the system responsive to graded upstream cues (71). And there is ample evidence in motile systems for the presence of multiple negative feedback loops, acting at different levels and with different timescales (25).

Motility is a very complex cell behavior that differs depending on context (e.g. 1D, 2D, or 3D environment, stiffness of substrate) and cell type, and can vary widely in morphology (using lamellipodia, pseudopods, blebs, or other protrusions), mechanism (differing contributions from actomyosin contractility or polymerization-induced protrusion), and velocity (0.2–20 μm/min)(25). Extensive studies in D. discoideum suggest that GPCR-mediated sensing is transmitted via Gβγ to an excitable signaling network involving several Rasrelated GTPases, the signaling lipid PIP₃, multiple kinases including PKBs and TORC2, and other proteins (25). Excitability (including hallmarks like transient adaptive responses to sustained stimuli, refractory periods, and traveling waves of active molecular species) indicates the presence of positive and negative feedback loops. Similar observations have been made in neutrophils, which share a rapid amoeboid locomotion with D. discoideum (120). The signal transduction excitable network impacts the actin cytoskeleton in many ways, producing spontaneous migration and guiding that migration in response to directional cues. Cdc42-related proteins are thought to mediate communication from the signaling network to the actin cytoskeleton, which also displays many potential positive and negative feedback pathways (61) and provides feedback to Cdc42, including through actin-mediated recruitment of GEFs (83).

The large number of partially redundant pathways and feedback loops in the sensing, signaling, and cytoskeletal networks of motile cells has impeded a molecular understanding of how external gradient information is actually translated into directed migration. In contrast, the yeast models represent strippeddown systems with much less redundancy, which has enabled genetic dissection to yield greater insight, as discussed below.

Molecular pathways linking GPCRs to Cdc42 in yeasts

Communication between the pheromone-sensing GPCRs and the Cdc42 polarity system in the budding yeast S. cerevisiae occurs primarily through two very simple pathways. Gβγ activated by the GPCR recruits two scaffold proteins, Ste5 and Far1, from the cytoplasm (17, 81, 92). Ste5 recruitment leads to activation of a MAPK that promotes polarity establishment but does not appear to provide directional information (Fig. 5A). Far1 binds to the Cdc42-directed GEF, so that locations that accumulate free Gβγ preferentially activate Cdc42, providing directional information (Fig. 5B). Mutants that impair binding of Far1 to the GEF (but are otherwise functional) polarize but are completely defective in tracking a pheromone gradient (17, 80, 81, 110).

Fig. 5. Pheromone sensing in budding yeast.

A) Free Gβγ recruits Ste5 from the cytoplasm, leading to activation of a MAPK cascade. B) Free Gβγ recruits Far1 from the cytoplasm, leading to local activation of Cdc42 and polarization of actin by formins (Cdc42 effectors that nucleate actin polymerization). Actin cables then deliver secretory vesicles to the polarity site. C) When cells polarize Cdc42 in the wrong location, the polarity site relocates to align with the partner. In cells with high MAPK activity, relocation involves movement of the polarity sites until the sites become aligned and the cells mate. D) Actin cables that deliver vesicles follow the polarity site as it moves. E) Off-center vesicle delivery perturbs Cdc42 by adding membrane (dilution) and GAPs (inactivation) on one side of the polarity site. Positive feedback is then stronger on the opposite side, and the centroid of the Cdc42 cluster can move persistently away from the actin-mediated vesicle delivery side. F) Directional bias in polarity site movement imparted by pheromone gradient (blue arrow). 1: A polarity site (green: Cdc42 concentration profile) creates a local neighborhood enriched in receptors (yellow: active GPCR concentration profile). 2: A polarity site spontaneously moves to the left (down-gradient: top) or to the right right (upgradient: bottom). 3: As it moves, the polarity site deposits new receptors in its wake. If the site moves down-gradient (top), fewer of the new GPCRs will be activated by pheromone than if the site moves up-gradient (bottom). 4: The activated GPCR gradient is translated into a Cdc42 GEF gradient by the Far1 pathway, biasing movement to return the site towards its earlier position (ping-pong movement). The differences in GPCR activation due to the pheromone gradient lead to a difference in the magnitude of this effect, so that sites that moved down-gradient are strongly biased to return up-gradient (top), while those that moved up-gradient can remain close to the new position.

Pheromone signaling in fission yeast exhibits differences in the molecular pathways linking GPCRs to Cdc42 (67): instead of Gβγ, the signal is transmitted by Gα-GTP, which activates Ras. Ras activates a MAPK cascade (analogous to the Ste5 pathway), and also recruits a GEF for Cdc42 (analogous to the Far1 pathway). Thus, despite molecular differences, the signaling logic is very similar in these distantly related fungi.

The description above suggests that all spatial information is transmitted from GPCR to Cdc42 via a single pathway (Gβγ-Far1-GEF in budding yeast and Gα-GTP-Ras-GEF in fission yeast). This is a useful simplification, but omits a number of molecular connections that seem likely to improve the efficacy of gradient sensing. These include feedback from Gβγ and the RGS to the GPCR (51, 111, 113) and a direct link between Gα-GTP and the active MAPK, which is thought to promote localized phosphorylation of MAPK substrates (1, 24, 31, 68, 74). Because these have more subtle effects and are not as well understood, we will not discuss them further. Instead, we focus on how the simple Far1 pathway can provide a remarkably effective way for cells to orient, re-orient, and lock on to a partner.

Exploratory polarization in budding yeast

Budding yeast use both disassembly/reassembly and movement of the polarity site to relocate the front. Cells of opposite mating type initially polarize using ratiometric sensing (see above), but the direction of polarity establishment is quite error-prone, with 40% or fewer cells orienting towards the eventual mating partner (45, 113). There follows a period of 10–100 min when polarity sites can appear, strengthen, move, and disappear erratically in a process described as “exploratory polarization”, after which the polarity sites of two partners align and stabilize to promote mating (Fig. 5C)(45). This description raises several questions that we will address in turn: What makes a site disappear? How does a polarity site move? And why does movement/disappearance cease once partner cells’ polarity sites reach alignment?

How does the polarity site relocate?

One hypothesis to explain both erratic movement and appearance/disappearance of a polarity site is that these behaviors are a consequence of molecular noise. However, the sites produced by MCAS models are quite stable in the face of noise (87, 94). One way to make them more mobile is to weaken positive feedback: making positive feedback perfectly linear eliminates the Turing instability for a deterministic MCAS model but allows transient clusters of activator to develop in a stochastic model with low molecule numbers, and such clusters appear/disappear and move spontaneously (44, 55). Models with non-linear positive feedback can also produce such behaviors if the abundance of key species is severely limited and the rates of reactions that control molecular dwell times at the polarity site are adjusted (94). The plausibility of these parameter assumptions has yet to be tested experimentally.

Another hypothesis to explain movement is that polarity circuits contain negative feedback pathways that can destabilize the position of the polarity site (71). Budding yeast appear to have at least three separate negative feedback mechanisms. Polarization concentrates the Cdc42 GEF together with Cdc42 effector kinases that can phosphorylate and inhibit the GEF (62). This mechanism can dismantle a strong polarity site and yield polarity oscillations in vegetative cells (47, 62) and perhaps also fission yeast (23), but its role in mating cells has not yet been investigated. A second pathway involves recruitment of Cdc42-directed GAPs to the polarity site by septins (cytoskeletal elements recruited by Cdc42), which may assist in steering the polarity site (57, 84). And a third negative feedback pathway involving the actin cytoskeleton and vesicle traffic has been implicated in polarity site movement in mating cells.

Cells that contain artificially stimulated mating MAPK activity exhibit spontaneous polarity site movement with much less frequent appearance/disappearance, and have been used as a model to dissect the mechanism of movement (36, 69) (Fig. 5C). Imaging revealed that during movement, polarity probes were “chased” by actin-associated and vesicle probes. Actin depolymerization greatly reduced movement, suggesting that movement occurs when actin delivers vesicles to one side of the polarity site, which displaces the Cdc42 away from the vesicle fusion site (Fig. 5D). Computational modeling demonstrated that some movement could arise simply because of the local dilution of polarity factors that occurs when a vesicle fuses and adds membrane to one side of the polarity site (Fig. 5E). However, to quantitatively reproduce the experimentally observed movement required vesicles to do more than just dilute the local polarity factors (36). One possibility is that Cdc42-directed GAPs are delivered by vesicles, yielding a greater perturbation of polarity.

Polarity site movement occurs on timescales (10 minutes) that are long relative to the timescale on which individual polarity proteins reside at the site before returning to the cytoplasm (5 seconds). Thus, movement does not entail displacement of a solid object: instead, it represents a shift in the position of the centroid of a constantly self-renewing cluster of polarity proteins. When vesicle delivery occurs on one side of the site (i.e. off center), Cdc42 activity is reduced on that side, and positive feedback preferentially recruits Cdc42 to the opposite side, “moving” the centroid of the cluster of polarity proteins (Fig. 5E). Polarity site movement is not purely diffusive, and shows persistence in the direction of motion (27, 36, 69). The persistence reflects the stability (on a 1 minute timescale) of the actin cables, which continue to deliver vesicles to the same sites. Persistence is enhanced by actin regulators that focus vesicle delivery to a small portion of the polarity site (36, 69). This system can be modeled as a coupled fast-acting positive feedback and delayed negative feedback through actin/vesicles, with potential to yield wave-like motion (86). However, in mating cells stochastic effects seem to induce frequent changes in the direction of motion.

Directionality of polarity site movement

In the presence of a mating partner, the direction of polarity site movement is biased toward the partner—in other words, the sites perform chemotaxis (35, 113). This is remarkable, for several reasons. First, computational modeling of polarity site movement suggested that polarity sites only respond to the pheromone-bound receptors in their immediate vicinity (a 2 μm diameter zone), which is a very small distance over which to detect a gradient. Second, once a polarity site is present, it acts to concentrate receptors in its vicinity. Because vesicle delivery is focused to the polarity site, new receptors are inserted locally. Older receptors are internalized by endocytosis, clearing them from the cell surface. Thus, as the polarity site moves, it leaves recently-deposited receptors in its wake, generating a receptor distribution that is far more uneven than the starting distribution in unpolarized cells. How can this not distort the pheromone gradient information?

In principle, perfect ratiometric sensing could compensate for the distortion due to uneven receptor density: as vesicle trafficking changes the overall receptor distribution, rapid pheromone binding/unbinding could adjust the local ratio of bound to unbound receptor to yield an accurate picture of the spatial distribution of pheromone. However, pheromone binding/unbinding is quite slow in the yeast system (6, 54, 97, 121), so distortions due to receptor traffic cannot be compensated by faster binding/unbinding. Surprisingly, the very steepness of the receptor gradients surrounding the polarity site may create an opportunity to bias the movement towards a pheromone source. As the site moves stochastically due to vesicle traffic, it makes excursions to regions with steep pheromone-receptor gradients (Fig 5F). These gradients are translated by Far1 into steep gradients of Cdc42 activation, which would promote movement of the polarity site. Simulations produced Cdc42 clusters that “ping-pong” around the receptor-enriched zone (Fig 5F), which can bias net movement up pheromone gradients (35). This bias occurs because random excursions that carry the polarity site up gradient are more strongly reinforced than excursions that move the site down gradient. Consistent with that hypothesis, defects in the Far1 pathway uncouple the direction of polarity site movement from any applied gradient (35).

Recognizing a partner: alignment between polarity sites causes movement to stop

Once chemotactic movement of the polarity site corrects any errors in the initial orientation of polarity establishment, and the polarity sites in partner cells reach alignment, the cells stop further movement (21, 35, 44, 45, 113). How do they know when to stop the search? Experiments in which a wild-type cell was confronted with a partner that secreted its pheromone globally around the surface, rather than locally at the polarity site, showed that the wild-type cell continued to move its polarity site and failed to lock on to the partner (21). Together with other observations, this indicated that local pheromone secretion from the moving polarity site is critical for cells to recognize that alignment has been attained. Local pheromone secretion would lead to higher local pheromone concentrations that decay steeply with distance from the secretion site (21), suggesting two hypotheses for how cells might recognize that they have correctly aligned their polarity sites, involving either a threshold pheromone level or a steep pheromone gradient.

As proposed by the speed dating model in fission yeast, polarity sites may keep moving until they sense a high local concentration of pheromone (the “threshold” hypothesis). In support of this idea, exposure to high levels of synthetic uniform pheromone caused polarity site movement to slow significantly, and this could be recapitulated by genetic manipulations yielding local G protein activation, but not those yielding global G protein activation (69). Reduction of movement required an intact Far1 pathway, suggesting that high local pheromone sensing is translated to high local Cdc42 activation via Far1, and that such activation protects the polarity site from the perturbing effects of vesicle traffic. In addition, high local pheromone yields increased MAPK activation, further strengthening Cdc42 polarization (22, 44, 45).

The second hypothesis is based on the observation that polarity site movement is biased by the pheromone gradients, with steeper gradients causing stronger bias (35). As polarity sites come into alignment, the steepening local pheromone gradients could effectively trap a polarity site in proximity to the partner’s site. The two hypotheses are not mutually exclusive, and it may be that both the absolute pheromone level and local gradient steepness contribute to the cessation of polarity site movement upon alignment. In both cases, it appears critical that pheromone sensing, as well as pheromone secretion, occur locally rather than globally. This provides a rationale for why cells would concentrate their sensing machinery (GPCRs and G proteins) in the vicinity of the polarity site, despite the difficulties this creates for accurate inference of the gradient direction.

In summary, the remarkably simple Far1 pathway linking receptor activation to Cdc42 activation enables mating by three synergistic mechanisms. First, it allows the pheromone landscape to bias the direction of initial polarity establishment, so that polarity sites tend to form near partner cells (45). Second, it allows pheromone gradients to bias the direction of polarity site movement, speeding the search for a partner (35). And third, it allows cells to stop polarity site movement once partner cells are properly aligned (Fig. 5G) (21, 27, 69, 82).

A polarity-centric view of gradient decoding: parallels in chemotactic cells

The work on yeast mating systems has provided significant new insights into how cells decode chemical gradients. The findings center the polarity machinery and the Rho-family GTPase Cdc42 as a crucial intermediary between GPCRs that sense pheromone signals and the actin cytoskeleton that drives vesicle traffic and polar growth (Fig. 6A). The polarity circuit contains a positive feedback loop that enables symmetry breaking as well as competition between polarity sites to ensure that there is only one stable site. Additional negative feedback pathways make the site susceptible to disassembly and relocation. One prominent negative feedback pathway involves orientation of actin cables towards the polarity site and delivery of secretory vesicles that perturb Cdc42 activity and generate polarity site movement. To a large degree, a single pathway linking pheromone-bound GPCRs to Cdc42 activation can explain how gradients are interpreted so as to orient initial polarity establishment and subsequent reorientation. And the same actin-mediated vesicle traffic that causes polarity site movement also ensures local pheromone secretion and local pheromone sensing, which allow cells to employ an exploratory polarization strategy to locate partners even in crowded environments with many sources of pheromone.

Fig. 6. Parallels between gradient decoding in yeast and motile cells.

A) In yeasts, a self-organizing polarity circuit centered on Cdc42 assembles a polarity site via positive feedback, and makes it mobile via negative feedback (R, repressor). Pheromone sensing by GPCRs impacts Cdc42 location primarily by a single pathway that recruits GEF to sites with bound receptors. Cdc42 orients actin cables that deliver vesicles, which both perturb Cdc42 (enhancing mobility) and deliver new receptors (enabling local sensing of pheromone). B) In motile cells, complex excitable signaling and cytoskeletal circuits (F, self-reinforcing “front” factors; R, repressors of F that can create local “refractory” state) generate spontaneous locomotion. GPCR sensing displays adaptation and has been simplified as a Local Excitation/Global Inhibition (LEGI) incoherent feedforward loop (E, excitation factors; I, inhibition factors; RR, response regulators that integrate E and I). A memory module, also simplified as an incoherent feedforward loop (factors as in LEGI), endows cells with directional persistence. C) Generalized roles for positive feedback in generating a polarized front, and for negative feedback in destabilizing the position of the front, enabling relocation to track a gradient.

This polarity-centric view has several parallels to the circuits thought to underlie chemotaxis (Fig. 6B). Motile cells can move spontaneously in the absence of external gradients (4, 13, 118), and external gradients can be converted into internal signals even in immobilized cells (53, 89, 102). Therefore, cells possess independent modules for gradient sensing and motility that are coupled to yield directional motion. Coupling involves an excitable signaling module, with positive and negative feedbacks that may resemble those in the Cdc42 polarity circuit (Fig 6B). Similar excitable networks with both positive and negative feedback loops are inferred from the behavior of the actin cytoskeleton that drives motility. Due to the complexity of these networks, the roles of most individual feedback loops remain to be tested, but we suggest that as in the yeast polarity circuit, a core role for positive feedback is to spatially concentrate regulators to generate a front, while a core role for negative feedback is to destabilize the position of the front so as to make it responsive to external gradients (Fig. 6C).

A fourth module has been inferred from the directional persistence exhibited by motile cells (Fig 6B). Although sometimes called a “polarity” module, the molecular basis for this phenomenological module has not been determined: to avoid confusion we refer to it as a “memory” module. This module is invoked to explain why motile cells turn their pre-existing front to chase a moving source of chemoattractant, rather than initiating a new front (although this can happen in very steep gradients). Both the sensing and memory modules have been suggested to act like incoherent feed-forward loops, involving excitatory (E) and inhibitory (I) species that affect a response regulator (RR)(25). The conceptualization of chemotaxis as an interplay between gradient sensing, signaling, motility, and memory modules brings an appealing simplicity to what is clearly a very complex process.

Given the conservation of many of the key proteins involved (including GPCRs, G proteins, Cdc42 relatives, and actin regulators), it seems likely that the yeast and animal gradient decoding systems evolved from a single ancestral precursor. If so, where does the Cdc42 circuit fit in the chemotaxis modules? Did the polarity module only acquire its central position in the yeast systems (Fig. 6A) after they lost their capacity for motility? Or is it still playing an important role within the complexity of the chemotactic networks (Fig. 6B)?

Several Rho-family GTPases related to Cdc42 are present in and accumulate at the front of motile cells (66, 120). Cdc42 and Rac relatives appear to link signaling proteins to the actin cytoskeleton (25). However, the potential redundancy among these regulators has precluded us from gaining a clear picture of their shared roles in motile cells. The memory module, a potential locus for Cdc42 action, is placed downstream of the cytoskeletal module (Fig. 6B). This assumption is based on experiments implicating actin in many feedback pathways that link to the signaling module (25). However, positive and negative feedback pathways persist even in cells lacking the major actin nucleator Arp2/3 (41) suggesting the presence of actin-independent mechanisms of positive feedback as observed for Cdc42 in yeasts. And signaling components like Ras that accumulate at the cell’s front can remain there for a few minutes even in the absence of polymerized actin, even after a chemoattractant gradient is reversed, providing evidence for an actin-independent molecular memory of the cell’s front (104). We speculate that as in yeasts, a self-organizing polarity system based on Cdc42/Rac is embedded in the excitable signaling networks that connect GPCR-based gradient sensing with directed motion. If so, a polarity-centric view of gradient decoding may unify our understanding of disparate systems.