We modeled stochastic biochemical reactions between polarity proteins, their diffusion in the cytosol and on the plasma membrane of a spherical in silico cell, together with vesicle trafficking events using time-dependent simulations (see Materials and methods [M&M]). The model contains three modules, interconnected in a polarity factor delivery and recycling circuit: a previously introduced Cdc42 autoamplification module and endo- and exocytosis modules (). Polarization of the Cdc42 module was previously attributed to a Turing-type mechanism. However, when a Cdc42 diffusion rate of 0.036 µm2
is incorporated, as has been measured in vivo, Turing-based models predict significant loss of polarity (Goryachev and Pokhilko, 2008
; Howell et al., 2009
; Savage et al., 2012
). Without excluding the possibility that a Turing-based mechanism may contribute to polarity establishment, we present here an alternative regimen of the same autoamplification module where polarity emerges from a multistable reaction network (M&M; Semplice et al., 2012
). The autoamplification module stimulates exocytosis in two ways. First, active Cdc42-GTP promotes actin polymerization via formin activation, enabling vesicle delivery. Second, the Cdc42 module recruits the exocyst complex, facilitating tethering to the plasma membrane and ensuing SNARE-mediated fusion (Zhang et al., 2001
; Zajac et al., 2005
; France et al., 2006
). Exocytic vesicles are assumed to contain Cdc42, establishing a trafficking-based positive feedback loop, and proteins such as clathrin, seeding the early steps of endocytic vesicle formation (Wedlich-Soldner et al., 2003
; Boyd et al., 2004
; Newpher et al., 2005
). Together, endo- and exocytosis contribute to Cdc42 recycling (Valdez-Taubas and Pelham, 2003
; Marco et al., 2007
). In an initial simplified model, details of the endocytic pathway were neglected; each endocytic event was instantly triggered by endocytic proteins diffusing on the membrane. In 90% of wild-type (WT) in silico cells, Cdc42-GTP polarized to a region on the cortex during the simulation, whereas endo- and exocytic events clustered in and around the Cdc42-GTP pole. The simulated fluorescence of Cdc42-GTP, exocytic, and endocytic events was plotted as a kymograph by drawing a line around the cell cortex (y axis) projected over time (x axis; Fig. S1 A
Schematics illustrating the mathematical model. Shown are the Cdc42 autoamplification module (A), the complete endocytosis module (B), the exocytosis module (C), and a legend for graphics (D).
Disrupting either Cdc42-GTP autoamplification (Fig. S1 A, ii
) or both actin-dependent and -independent Cdc42 recycling mechanisms had drastic effects on polarity establishment (Fig. S1, A [iii
] and C). Moreover, polarity was dependent on the localization of endocytosis relative to the exocytic pole where early endocytic proteins were delivered. Colocalization of endo- and exocytosis within the Cdc42 cluster resulted in severe polarity defects (Fig. S1 B, i
). In our model, restoring the spatial segregation of endo- and exocytic events rescued polarity to almost WT levels (Fig. S1, B [ii
] and C). However, when incorporated into the model proposed by Layton et al. (2011)
, the spatial segregation of endo- and exocytosis was not sufficient to generate a polarized state (unpublished data).
To explore the role of endocytosis in polarity establishment, we modeled a more detailed endocytic pathway, encompassing distinct phases of coat recruitment to early endocytic patches, actin-based vesicle formation, and subsequent scission (Kaksonen et al., 2003
; Weinberg and Drubin, 2012
). In addition to coat proteins, the cargos of this endocytic pathway include Cdc42 and v-SNARES (Valdez-Taubas and Pelham, 2003
; Marco et al., 2007
). The complete model shown schematically in (parameters listed in ) is used in the remainder of this paper.
Model parameters used in this study
As in the simplified model (Fig. S1), Cdc42-GTP polarized within 20 min of starting the simulation (, top; and Video 1
). Meanwhile, exocytosis focused to a vertex, around which endocytic events clustered (, bottom; and Video 2
). These results were robust to individual parameter changes (Fig. S3
Figure 2. Robust polarity establishment involves dynamic changes in endo- and exocytic trafficking systems. (A) Transition of a typical in silico WT cell from nonpolarized to a polarized state. Membrane-bound Cdc42-GTP depolarized over the plasma membrane (top (more ...)
To compare in silico results with in vivo data, endo- and exocytic trafficking compartments were monitored simultaneously in live cells by near-total internal reflection fluorescence microscopy (TIRFM) that facilitated long-term imaging every second for 20 min or more. Many vesicular events were illuminated in the evanescent field by near-TIRFM because post-Golgi secretory vesicles traverse actin cables under the plasma membrane, whereas endocytic sites develop at the plasma membrane (Yu et al., 2011
). Endo- and exocytic vesicles were monitored with actin binding protein Abp1-RFP and the Rab GTPase marker GFP-Sec4, respectively.
Trafficking compartments were spread over the cortex in most unbudded WT cells (, left nonpolarized cell). However, in a minority of cells, they were confined to a polarized cortical region (, right polarized cell), as seen previously (Kilmartin and Adams, 1984
; Layton et al., 2011
). Kymographs of the endo- and exocytic domains were generated as for in silico data, providing a view of membrane trafficking over a narrow region of the entire cortex (). During polarity establishment, and in agreement with our in silico model, an endocytic ring bracketed the constricting exocytic pole ( and Video 3
; McCusker et al., 2012
). The diameter of the endo- and exocytic regions diminished abruptly, both in vivo and in silico ().
The spatial reorganization of endocytosis correlated with a temporal change in the endocytic frequency during polarization (). Endocytic dynamics were analyzed along the time axis of the endocytosis kymograph near the pole, where consecutive endocytic events were observed (M&M). The endocytic signal was differentiated and smoothed to discriminate individual endocytic events from noise (Fig. S2 A
and M&M). In a polarized WT cell, endocytic events within the ring became more regular, displaying a constant frequency and amplitude, in contrast to nonpolarized cells (). The constant amplitude of the differentiated Abp1-RFP signal intensity in polarized WT cells reflected constant quanta of Abp1 molecules being internalized from the endocytic zone (). The time interval between consecutive endocytic events at the same position on the cortex was longer in nonpolarized cells (79 s; SD = 50 s) than in polarized cells (53 s; SD = 28 s). The lower SD of time intervals in polarized cells reflected endocytic events becoming regular, or periodic. The variance of the distribution of time intervals was significantly different between nonpolarized and polarized cells (). These results indicate that during tightening of the exocytic pole, the endocytic system reaches an equilibrium at which a stable, periodic endocytic flux operates. This behavior, also borne out in silico (), appears to be a characteristic signature of the endocytic system in polarized cells.
Figure 3. Robust polarity establishment involves the generation of a specific endocytic signature. (A) Kymograph of a polarizing WT cell expressing GFP-Sec4 and Abp1-RFP markers (left). Endocytic dynamics evolve from a series of discrete random events (left) to (more ...)
The observation that regular endocytic events increased in frequency, encircling the exocytic zone while both domains abruptly constrict, led us to hypothesize that endocytosis may confine or corral the exocytic zone. In this scenario, endocytic corralling could limit the spreading of polarity proteins outside the exocytic zone, stabilizing the polarity axis. Endocytic mutants in which corralling is perturbed might therefore display polarity defects. To test this, in silico simulations were run in which coating of early endocytic vesicles and subsequent loading with Cdc42/v-SNARE were impaired. Under these conditions, endocytic dynamics may resemble a sla2Δ
mutant, the Hip1R (Huntington Interacting Protein 1) homologue in budding yeast (Holtzman et al., 1993
). In these simulations, endocytic events were depolarized over the cortex and exocytic clusters were unstable, consistent with endocytic dynamics contributing to a robust polarity axis (, top; and Video 4
). In sla2Δ
mutants in vivo, the endocytic marker Abp1-RFP was depolarized over the cortex and severe polarity defects were observed (, bottom; and Video 5
; Hervás-Aguilar and Peñalva, 2010
). As predicted in silico, kymographs of trafficking compartments in polarized sla2Δ
cells in vivo showed multiple exocytic foci that often disintegrated over time, consistent with the model that endocytic corralling stabilizes the exocytic pole (, bottom kymograph; and Video 5). The internalization of Abp1-RFP was less efficient in sla2Δ
cells, resulting in longer Abp1-RFP residency times at the cortex (22 ± 12 s) compared with WT cells (9.9 ± 3.6 s; ). Consistently, the patch residency time of RVS167-GFP
, an additional endocytic marker, was also significantly increased in sla2Δ
cells (39.3 ± 36 s) compared with WT cells (5.5 ± 3.5 s; ). The characteristic endocytic signature of polarized WT cells was abolished in sla2Δ
Figure 4. Endocytic cortical corralling is required for robust polarity establishment. The endo- and exocytic vesicles are marked by Abp1-RFP (red) and GFP-Sec4 (cyan), respectively. (A, top) The kymograph of an in silico sla2Δ mutant cell shows depolarized (more ...)
We next tested whether other endocytic mutants display polarity defects. Endocytic vesicle formation occurs sequentially via the recruitment of coat, actomyosin, and scission modules to the incipient endocytic site (Kaksonen et al., 2003
; Weinberg and Drubin, 2012
). We therefore altered in silico endocytic vesicle maturation rates to recapitulate the effect of sla2Δ
, sla1Δ bbc1Δ
, and rvs167Δ rvs161Δ
mutations on endocytic dynamics (M&M). In silico sla2Δ
, sla1Δ bbc1Δ
, and, to a lesser extent, rvs167Δ rvs161Δ
mutants disrupted the endocytic signature, resulting in irregular endocytic events (). These effects were also evident from in vivo analyses: the time interval between endocytic events was longer and irregular in sla2Δ
mutant cells (76 s; SD = 66 s), in contrast to polarized WT cells (53 s; SD = 28 s). Similar defects were observed in sla1Δ bbc1Δ
(111 s; SD = 83 s) and rvs167Δ rvs161Δ
mutants (74 s; SD = 48 s; ).
To study the effect of modifying endocytic dynamics on exocytic polarization, we analyzed the diameter of the exocytic pole in WT and endocytic mutants. As predicted in silico, sla2Δ, sla1Δ bbc1Δ, but also rvs167Δ rvs161Δ mutants displayed wider exocytic poles in vivo (1.88 ± 1.1, 1.92 ± 1.4, and 1.39 ± 0.82 µm, respectively), in contrast to the focused poles in WT cells (0.75 ± 0.17 µm; ). Wider exocytic poles were also observed in additional endocytic mutants including ede1Δ (1.21 ± 0.6 µm) and clc1Δ (2.09 ± 1.4 µm). The wider diameter of the exocytic pole in endocytic mutants was also evident from their respective kymographs (). These results indicate that a focused polarity axis requires endocytosis-based cortical corralling.
Figure 5. Endocytic cortical corralling is required for focused exocytic pole formation. Endo- and exocytic vesicles are marked by Abp1-RFP (red) and GFP-Sec4 (cyan), respectively. (A) In silico and in vivo analyses of the distributions of exocytic cluster size (more ...)
What is the role of endocytosis during polarity establishment? Endocytosis has been proposed to enhance polarization by initiating the recycling of polarity factors (Valdez-Taubas and Pelham, 2003
; Marco et al., 2007
; Slaughter et al., 2009
; Yamamoto et al., 2010
; Orlando et al., 2011
). In contrast, recent modeling studies have predicted polarized endocytosis to be detrimental to polarity (Layton et al., 2011
). To understand how polarized endocytosis contributes to robust polarity, we designed a stochastic mathematical model where trafficking and polarity pathways self-organize. We found that whereas Cdc42-GTP autoamplification drives the clustering of exocytic activity to discrete sites, endocytic corralling ensures the selection of a unique, focused cluster for robust polarity establishment. In agreement with a positive role for endocytosis in polarity, we observed an increased stabilized endocytic frequency within the corralling region as polarization proceeded in vivo, as predicted by in silico simulations. Together with the in silico and in vivo studies in WT and mutant cells, we show the utility of concentrating the cell’s endocytic activity in the corral for maintaining directed exocytosis during robust polarity establishment.