1
Short title: 1
Actin-Based Vesicle Focusing Sustains Tip Growth 2
3
Jeffrey P. Bibeau1† , James L. Kingsley2†, Fabienne Furt1, Erkan Tüzel2*, Luis 4
Vidali1* 5
† Co-first authors 6
* Co-corresponding authors 7
8
Long title: 9
F-Actin Meditated Focusing of Vesicles at the Cell Tip Is Essential for Polarized 10 Growth 11 12
1 Worcester Polytechnic Institute, Department of Biology & Biotechnology 13
2 Worcester Polytechnic Institute, Department of Physics 14
15
Summary sentence: 16
Quantitative analysis and modeling of vesicle diffusion shows that polarized cell 17 growth rates are sustained by actin-based vesicle clustering at the tip. 18 19
20 Author Contributions: 21 22 J.P.B. performed experiments and differential equation modeling of cell growth 23
and wrote the article with contribution from all authors. J.L.K. created the FRAP 24
model and provided assistance on differential equation modeling of cell growth. 25
F.F. generated cell lines. E.T. supervised modeling and complemented writing. 26
L.V. designed and supervised experiments, and complemented writing. 27
28
Financial Support: 29
This work was supported by National Science Foundation CBET 1309933 to ET 30
and NSF-MCB 1253444 to LV. 31
32
Plant Physiology Preview. Published on October 2, 2017, as DOI:10.1104/pp.17.00753
Copyright 2017 by the American Society of Plant Biologists
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2
33
Abstract 34 35 Filamentous actin has been shown to be essential for tip growth in an array of 36
plant models, including Physcomitrella patens. One hypothesis is that diffusion 37
can transport secretory vesicles, while actin plays a regulatory role during 38
secretion. Alternatively, it is possible that actin-based transport is necessary to 39
overcome vesicle transport limitations to sustain secretion. Therefore, a 40
quantitative analysis of diffusion, secretion kinetics and geometry is necessary to 41
clarify the role of actin in polarized growth. Using FRAP analysis, we first show 42
that secretory vesicles move toward and accumulate at the tip in an actin-43
dependent manner. We then depolymerized F-actin to decouple vesicle diffusion 44
from actin-mediated transport, and measured the diffusion coefficient and 45
concentration of vesicles. Using these values, we constructed a theoretical 46
diffusion-based model for growth, demonstrating that with fast-enough vesicle 47
fusion kinetics, diffusion could support normal cell growth rates. We further 48
refined our model to explore how experimentally-extrapolated vesicle fusion 49
kinetics and the size of the secretion zone limit diffusion-based growth. This 50
model predicts that diffusion-mediated growth is dependent on the size of the 51
region of exocytosis at the tip, and that diffusion-based growth would be 52
significantly slower than normal cell growth. To further explore the size of the 53
secretion zone, we used a cell wall-degradation enzyme cocktail, and determined 54
that the secretion zone is smaller than 6 𝜇𝑚 in diameter at the tip. Taken together 55
our results highlight the requirement for active transport in polarized growth and 56
provide important insight into vesicle secretion during tip growth. 57
58
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Introduction 59
60 Precise regulation of exocytosis is essential to maintain polarized cell growth in a 61
variety of plant systems. Cell polarized growth, or tip growth, is a process by 62
which a cell grows in a unidirectional manner and is found ubiquitously 63
throughout the plant kingdom (Hepler et al., 2001). Pollen tubes, root hairs, and 64
moss protonemal cells have all emerged as models for this process (Hepler et 65
al., 2001; Menand et al., 2007). To achieve polar expansion in the presence of 66
uniform turgor pressure, these cells must spatially regulate the extensibility of the 67
cell wall (Winship et al., 2010; Hepler et al., 2013). This is achieved through the 68
polarized exocytosis of various cell wall materials and loosening enzymes (Rojas 69
et al., 2011). 70
How plant cells establish spatially directed exocytosis during polarized 71
growth has been the focus of a number of studies in the past decade (Cardenas 72
et al., 2008; McKenna et al., 2009; Moscatelli et al., 2012). Many of these efforts 73
have heavily implicated the cytoskeleton as a key player in exocytosis. Evidence 74
suggests that myosin XI transports vesicle containing cell wall materials via 75
filamentous actin (F-actin) to the growing tip of the cell (Vidali et al., 2010; 76
Madison and Nebenfuhr, 2013; Madison et al., 2015). In pollen tubes, a cortical 77
actin fringe several microns behind the cell tip has been shown to be essential in 78
polarized growth (Vidali et al., 2001; Lovy-Wheeler et al., 2005; Vidali et al., 79
2009). Rounds et al. have shown that the presence of this fringe is necessary for 80
the focusing of apical pectin deposition (Rounds et al., 2014). However, work 81
with FM dyes supports the hypothesis that exocytosis happens along an annulus 82
behind the cell tip (Bove et al., 2008; Zonia and Munnik, 2008). In moss 83
protonemal cells, the actin cytoskeleton concentrates at the extreme cell apex 84
(Vidali et al., 2009). At this extreme apex, vesicle fluctuations have been shown 85
to predict F-actin fluctuations (Furt et al., 2013). Furthermore Myosin XI, which is 86
essential for tip growth (Vidali et al., 2010), can also anticipate actin fluctuations 87
(Furt et al., 2013). ROP GTPases, which have been thought to initiate tip growth 88
(Lee and Yang, 2008), have been shown to influence apical filamentous actin 89
dynamics and concentrations (Burkart et al., 2015). 90
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Significant work has been done to probe the molecular players involved in 91
cytoskeletal mediated exocytosis, however, there is a growing need to 92
demonstrate a mechanistic link between F-actin and polarized growth (Rounds 93
and Bezanilla, 2013). Although the actin fringe has been modeled in pollen tubes 94
(Sanati Nezhad et al., 2014), to the best of our knowledge, the role of apical F-95
actin in other, slower polar growth systems, is yet to be examined. What are the 96
physical limitations an active transport system like the actin cytoskeleton must 97
overcome to facilitate vesicle exocytosis and sustain polarized growth? Vesicle 98
concentrations and diffusion coefficients, exocytic reaction kinetics, cell growth 99
rates, and the size of the active region of exocytosis, all place specific limitations 100
on the actin-based transport system. Quantifying these fundamental 101
requirements will provide key insight into understanding the requirement for 102
transport in this system. 103
Without a quantitative assessment of the potential physical limitations 104
outlined above, we can hypothesize several functions for the actin cytoskeleton. 105
For example, it could serve as a means to overcome slow vesicle diffusion 106
limitations to drive exocytosis. The actin cytoskeleton could also function to 107
surpass slow reaction kinetics associated with vesicle fusion events on the 108
plasma membrane. It is also possible that exocytosis is confined to a relatively 109
small area on the plasma membrane; the actin cytoskeleton could then function 110
as a means to focus vesicles to this small exotic zone. Finally, it also remains a 111
possibility that F-actin active transport is not required to sustain polarized growth. 112
To better understand how F-actin influences vesicle transport, we 113
fluorescently labeled the v-SNARE, VAMP72 (Sanderfoot, 2007) in the moss 114
Physcomitrella patens (Vidali and Bezanilla, 2012). P. patens was chosen here 115
because it does not exhibit large organelle cytoplasmic streaming (Shimmen, 116
2007) which can complicate the analysis of vesicle transport (Furt et al., 2012). 117
Instead, P. patens only exhibits two modes of vesicle transport, namely diffusion 118
and active transport along the cytoskeleton. We visualized these modes of 119
transport, and performed Fluorescence Recovery After Photobleaching (McNally, 120
2008; Loren et al., 2015), FRAP, during polarized growth. To probe the utility of 121
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actin-mediated active transport we used the small molecule inhibitor latrunculin B 122
to depolymerize actin and uncouple vesicle diffusion from active transport. With 123
FRAP, and Number and Brightness analysis (Digman et al., 2008; Loren et al., 124
2015)(Kingsley, Bibeau et al., see attached supporting manuscript), we 125
measured vesicle diffusion rates and concentrations, respectively. We then 126
developed a diffusion-limited analytical model, and numerically solved it using 127
these parameters, as well as previously measured cellular growth rates (Furt et 128
al., 2013). Using this model, we quantitatively explored the limiting factors 129
associated with cell growth, and used enzymatic digestions of the cell wall to 130
further constrain the model. 131
132
Results 133
Depolymerization of Actin Stops Cell Growth in Minutes 134 135 Previous evidence in plants suggests that actin filaments are essential for 136
polarized growth (Vidali et al., 2001). It remains unclear, however, if removal of 137
the actin cytoskeleton immediately abolishes growth, or if some growth, 138
supported by diffusion, continues to happen once actin is removed. To address 139
this question, we treated growing protonemal cells with the actin monomer 140
sequestering agent latrunculin B to depolymerize the actin filaments (Vidali et al., 141
2001; Vidali et al., 2009). To visualize vesicle accumulation, we used a cell line 142
expressing 3mEGFP-VAMP72 (Furt et al., 2013). Following latrunculin B 143
treatment, we could not detect any tip growth (Fig. 1A), which is consistent with 144
previous work (Vidali et al., 2001; Vidali et al., 2009). Treatment also abolished 145
tip localization of VAMP72-vesicles (Fig. 1B) and produced an intensity gradient 146
that decreased toward the cell tip (Fig. 1C). Vehicle-treated controls grew at 147
5.5 ± 0.4 𝑛𝑚/𝑠, which is within the range of previously measured growth rates 148
(Furt et al., 2013). Since latrunculin B arrests growth, we concluded that cell 149
growth could not continue without filamentous actin. 150
Vesicles Exhibit Active Transport at the Cell Tip 151
Since the depolymerization of filamentous actin immediately blocks growth, we 152
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sought to determine if actin plays a role in vesicle transport at the cell tip. To this 153
aim, we performed fluorescence recovery after photobleaching experiments on a 154
cell line expressing the vesicle marker 3mCherry-VAMP72 (Furt et al., 2013) at 155
the cell tip (Fig. 2A), and a region distal to the tip, subsequently referred to as the 156
shank. We chose this cell line because we found that 3mCherry is more sensitive 157
to photobleaching than 3mEGFP. To better understand the differences in 158
molecular flux at the tip and the shank, fluorescence recoveries were corrected 159
for acquisition photobleaching (Supplementary Data, Fig. S1) and normalized to 160
the mean prebleach shank intensity. Since VAMP72-vesicles localize to the cell 161
tip (Fig. 2B, and Supplementary Data Fig. S2) --likely through myosin binding to 162
actin, we expected a reduction in the recovery after photobleaching of vesicles at 163
the cell tip. Instead VAMP72-vesicles exhibited a faster exchange of particles at 164
the tip than the shank (Fig. 2A), demonstrating that the accumulation of vesicles 165
at the cell tip is not simply due to static capture. This indicates that there is a 166
stream of active transport at the cell tip that is faster than the recovery at the 167
shank. 168
To better understand the directionality of this fast active transport, we 169
recorded the movement of VAMP72-vesicles after photobleaching. After 170
averaging several fluorescent recoveries we found that these vesicles moved 171
along the cell cortex toward the tip of the cell (Fig. 2B and Supplementary Data 172
Movie 1). We further quantified this directional recovery by measuring the 173
fluorescence intensity along the perimeter of the photobleaching region of 174
interest (Fig. 2B). At early times (∆𝑡1 = 0.7 − 1.6 𝑠) after photobleaching we 175
found that the maximum fluorescence intensity was cortical but moving toward 176
the cell tip (Fig. 2B and C and Supplementary Data Movie 1). Finally, at longer 177
time intervals (∆𝑡2 = 20 – 40 𝑠) VAMP72-vesicles became localized to the cell 178
tip (Fig. 2B and 2D, and Supplementary Data Movie 1). Since these vesicles 179
exhibited an increased flux at the cell tip when compared to the shank, and 180
because the vesicles recovered along the cell cortex toward the tip, we conclude 181
that active transport drives a significant portion of the movement of VAMP72 182
labeled vesicles. 183
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Vesicles Undergo Diffusion when Uncoupled from Actin 184
To determine if active vesicle transport is actin dependent, and to quantify vesicle 185
diffusion, we uncoupled vesicle diffusion from actin-mediated transport with the 186
actin depolymerizing agent latrunculin. This treatment abolishes the tip 187
localization of VAMP72-vesicles (Fig. 1 and Supplementary Data Fig. S2), 188
suggesting that untreated VAMP72 labeled vesicles exhibit active transport in an 189
actin dependent manner. To accurately quantify vesicle diffusion, we performed 190
photobleaching at the cell tip and shank, and, as done in the previous section, 191
performed corrections on the recovery curves to remove the effects of acquisition 192
photobleaching and reversible photoswitching (Supplementary Data Fig. S1). 193
Fluorescence recovery curves for the two specific locations were normalized to 194
their respective prebleach intensities. Following photobleaching, the cell tip 195
exhibited a reduced fluorescence recovery rate when compared to the cell shank 196
(Fig. 3A). Because photobleaching at the cell tip was close to the cell membrane, 197
we expected the diffusion based recovery at the tip to be limited by this 198
boundary, and as a consequence slower. This is not the case at the cell shank 199
where fluorescence recovery can happen from all directions. To accurately 200
determine the diffusion coefficient, we used a particle-based computational 201
model of FRAP that incorporates the properties of our confocal imaging system, 202
the three-dimensional moss cell shape, and the thermal fluctuations of the 203
fluorophore (Kingsley, Bibeau et al., see attached supporting manuscript). 204
To reduce the number of free parameters in this FRAP model, we 205
experimentally measured the point spread function of our confocal system, and 206
the bleaching width of the confocal laser (Supplementary Data Fig. S3). The 207
FRAP model recovery curves were also corrected for reversible photobleaching 208
to better match experimental results (see Materials and Methods). The two 209
remaining open parameters in our model were the diffusion coefficient and the 210
photobleaching proportionality constant that relates laser intensity to the number 211
of fluorophores bleached. After generating simulations for an array of these two 212
parameters, we employed a fitting routine to determine the best-fit parameters 213
(see Materials and Methods). This analysis showed that a single diffusion 214
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8
coefficient ( 𝐷 = 0.29 ± 0.14 𝜇𝑚2𝑠−1 ) was sufficient to account for the 215
fluorescence recovery seen both at the tip and the shank. 216
To further demonstrate that our best-fit particle-based simulation results 217
accurately represents the motion of VAPM72-vesicles in vivo, we compared the 218
directional fluorescence recovery of the best-fit particle-based simulation (without 219
the reversibly photobleached fraction) to the experimental fluorescence recovery. 220
At early times of fluorescence recovery, an intensity gradient was present within 221
the photobleached regions for both the experiments and simulations (Fig. 3B, 222
and Supplementary Data Movie 2) following limited volume corrections (Fig. S4). 223
The gradient decayed toward the cell tip (Fig. 3C) and flattened at long times 224
(Fig. 3D), which suggests that the cell boundary restricts the spatial recovery of 225
VAMP72-vesicles. This gradient was also observed in our simulations of FRAP at 226
the cell tip (Fig. 3E and 3F), but not at the cell shank (Supplementary Data Fig. 227
S5). This indicates that vesicle recovery at the cell tip is influenced by its position 228
next to the apical plasma membrane, such that material cannot flow in or 229
exchange in all directions. Importantly, this recovery closely matches a diffusion 230
model (Fig. 3E and 3F), further supporting our claim that VAMP72-vesicles 231
exhibit diffusion. 232
Analytical Modeling Demonstrates Cell Growth Is not Entirely Diffusion 233 Limited 234
To determine if diffusion alone can supply enough vesicles to the growing cell 235
edge to sustain polarized growth in P. patens, we initially created a simple 236
analytical model of diffusion-based cell growth in the absence of the actin 237
cytoskeleton. To build this model, we first determined the number of vesicle 238
fusion events per second, 𝜙, needed to support normal cell growth (Bove et al., 239
2008). We assumed that P. patens is cylindrical in shape at the shank with an 240
outer cell radius of 𝑅𝑜 ~ 6 𝜇𝑚, and a wall thickness 𝑑 ~ 250 𝑛𝑚 (Martin et al., 241
2009). As the cell grows, the wall maintains its outer radius Ro and thickness d, 242
and elongates at a rate of �̇�𝑔 = 5.5 ± 0.4 𝑛𝑚/𝑠. The wall volume per second, 𝑉�̇�, 243
needed to sustain this growth can be written as, 244
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�̇�𝑤 ≡ 𝑑𝑉𝑤/𝑑𝑡 = �̇�𝑔𝜋[𝑅02 − (𝑅0 − 𝑑)2] . (1) 245
Assuming that the cell wall materials within a vesicle do not change in volume 246
once they are incorporated into the wall, the number of vesicle fusion events 247
needed to support growth can be written as, 248
𝜙 =�̇�𝑤
𝑉v . (2) 249
Here 𝜙 is the number of vesicle fusion events as introduced above, and 𝑉v is the 250
volume of a vesicle. This assumption is supported by electron micrographs in 251
pollen tubes that show that the electron densities of vesicles and the cell wall are 252
similar (Lancelle and Hepler, 1992; Derksen et al., 1995). Assuming that 253
secretory vesicles are spherical in shape with a radius of a 40 nm (Lancelle and 254
Hepler, 1992), one can calculate that 𝑉v ~ 2.68 × 10−4 𝜇𝑚3 and 255
�̇�𝑤 ~ 0.051 𝜇𝑚3𝑠−1, and therefore, the vesicle fusion rate for a growing cell is 256
𝜙 ~ 189 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠/𝑠. 257
To relate observed vesicle diffusion to this calculated vesicle fusion rate, 258
we modeled the growing cell as a cylinder with an absorbable boundary at one 259
face of the cylinder. This model is equivalent in principle to latrunculin B treated 260
cells, in which diffusion alone must support growth. Here the cylinder is oriented 261
so that the tip is positioned at 𝑥 = 0 and the back end of the cylinder is at 𝑥 = 𝐿 262
(Fig. 4A and 4B). The cylinder contains a population of vesicles with a spatial 263
concentration that can be written as 𝑐(𝑥, 𝑡) . In wild type P.patens polarized 264
growth, we determined that large organelles such as chloroplasts and the 265
vacuole remain at a distance 𝐿 = 16 ± 1.4 𝜇𝑚 behind the growing tip. The 266
presence of these large organelles allows us to make two important 267
simplifications. First, the constant distance from these organelles to the tip makes 268
it reasonable to model the growing tip of the cell as a cylinder of constant size. 269
Second, we assume these organelles act as a reflective boundary (at 𝑥 = 𝐿) and 270
block the flux of vesicles through this edge, 𝑐′(𝐿, 𝑡) = 0. 271
At the opposite edge of the cylinder (at 𝑥 = 0), we assume perfect vesicle 272
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absorbability (e.g. infinite on-rate), simulating a possible maximum limit for 273
growth rate. This assumption of infinite on-rate (or presumably unlimited supply 274
of receptors) uncouples vesicle diffusion limitations from receptor-mediated 275
vesicle-membrane fusion limitations by assuming that vesicles instantly fuse 276
upon contact with this face of the cylinder. This is represented by the vesicle 277
concentration at the extreme edge being zero, i.e. 𝑐(0, 𝑡) = 0. To model vesicle 278
production, we assume a spatially homogenous production rate 𝑄. We impose 279
this uniform production rate because of the almost uniform distribution of Golgi 280
bodies in the cell (Furt et al., 2012). We can then express the concentration of 281
vesicles 𝑐(𝑥, 𝑡) as a time-dependent diffusion equation with a constant production 282
rate 𝑄, i.e., 283
𝜕𝑐(𝑥,𝑡)
𝜕𝑡= 𝛻 ⋅ [𝐷(𝑥)𝛻𝑐(𝑥, 𝑡)] + 𝑄 . (3) 284
Here 𝛻𝑐(𝑥, 𝑡) represents the vesicle concentration gradient. At steady state 285
growth, we can take 𝜕𝑐(𝑥, 𝑡) 𝜕𝑡⁄ = 0 . Assuming homogeneous diffusion (𝐷 =286
𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡) , the radial symmetry of the cell lets us define the concentration 287
throughout the cell as dependent only on the linear position x. This produces a 288
general solution for c(x) of the form 289
𝑐(𝑥) = − (𝑄
2𝐷) 𝑥2 + 𝐾1𝑥 + 𝐾2 , (4) 290
where 𝐾1 and 𝐾2 are constants determined by the boundary conditions. Solving 291
for the two boundary conditions ( 𝑐(0) = 0 and 𝑐′(𝐿) = 0 ) produces a profile 292
dependent on the vesicle production rate 𝑄 such that 293
𝑐(𝑥) = − (𝑄
2𝐷) 𝑥2 + (
𝑄𝐿
𝐷) 𝑥 . (5) 294
There is an additional constraint that fixes the value of 𝑄—this steady state 295
condition requires that the concentration of vesicles at the cell shank 𝑐(𝐿) is 296
equal to a predetermined concentration 𝑐𝐿 . This constraint produces an 297
expression for 𝑄, namely, 298
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𝑄 = 2𝐷𝑐𝐿/𝐿2. (6) 299
During steady state growth, the vesicle production rate 𝑄 must match the number 300
of vesicle fusion events 𝜙 such that, 301
𝜙 = 𝑄𝐿𝜋𝑅2 . (7) 302
Here, 𝑅 is the radius of the growing cylinder. This expression allows us to 303
determine the number of vesicle fusion events for any given 𝑐𝐿, 𝐷, 𝑅 and 𝐿, and 304
the values used for these four parameters are listed in Table I. Diffusion 305
coefficient, 𝐷, was measured as described in the previous section with FRAP 306
analysis (also see attached supporting manuscript) . To determine 𝑐𝐿, we used 307
our confocal particle-based simulation (see attached supporting manuscript 308
companion manuscript) to produce a range of potential concentrations, and 309
found that resolving individual particles becomes impossible at concentrations 310
above 10 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠/𝜇𝑚3 (Fig. 4C). Since we cannot resolve individual particles 311
experimentally, we let this be the lower bound estimate for 𝑐𝐿. Finally, we can 312
relate the vesicle fusion rate predicted by our analytical model in Eq. (7) to the 313
observed vesicle fusion rate calculated using Eq. (2). 314
For the range of possible values of cL, the model predicts two consistent 315
effects that influence cell growth. First, there is a parabolic reduction in vesicle 316
concentration from the shank out toward the growing tip (Fig. 4D). Additionally, 317
we find a linear relationship between cell growth rates and cL. At the lower bound 318
vesicle concentration 𝑐𝐿 = 10 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠/𝜇𝑚 3, the predicted vesicle fusion rate 319
is 𝜙 = 41 ± 20 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠/𝑠 and the corresponding cell growth rate is 1.2 ±320
0.6 𝑛𝑚/𝑠 (Fig. 4E and 4F). At the upper bound vesicle concentration 𝑐𝐿 =321
100 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠/𝜇𝑚3, 𝜙 = 410 ± 201 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠/𝑠 and the growth rate is 12 ± 6 𝑛𝑚/𝑠. 322
The confidence bounds for these estimates are the result of lower and upper 323
bound estimates for the vesicle diffusion coefficient (see Materials and Methods). 324
This growth rate indicates that diffusion cannot sustain cell growth at our 325
estimated lower bound vesicle concentrations (Fig. 4E) but, can easily support 326
growth at our upper bound estimate (Fig. 4F). 327
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This means that diffusion limitations at the growing cell edge may not 328
serve as the only reason why these cells stop growing. Interestingly this implies 329
that under idealized vesicle fusion and vesicle concentrations, diffusion could 330
support cell growth. Additional factors such as membrane-vesicle fusion kinetics, 331
small active exocytic regions, and the three-dimensional cell geometry may also 332
prevent latrunculin B treated cells from growing. 333
334 Vesicle Concentrations Yield an Estimate of Vesicle Fusion Kinetics 335 336 To explore the additional factors that may limit cell growth and better determine 337
the concentration of VAMP72 labeled vesicles during latrunculin B treatment, we 338
used Numbers and Brightness (N&B) analysis (Digman et al., 2008). In N&B 339
analysis, the mean and variance of a fluorophore’s intensity fluctuations are used 340
to determine the concentration of molecules in solution. The foundation of this 341
analysis is the assumption that molecule number fluctuations in a given volume 342
are Poisson distributed—which holds true for a freely diffusing population of 343
vesicles (Digman et al., 2008). Since the mean and variance of a Poisson 344
distribution are equal, it is possible to algebraically solve for the brightness of a 345
fluorophore even in the presence of detector shot noise (Digman et al., 2008). 346
Using this analysis, we found that the vesicle concentrations of latrunculin B 347
treated cells were 39 ± 6 and 38 ± 2 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠/𝜇𝑚3 at the tip and shank, 348
respectively (See Materials and Methods for more details). No statistically 349
significant difference in concentrations were found at the tip and shank (𝑝 −350
𝑣𝑎𝑙𝑢𝑒 = 0.8349, 𝑛 = 6 ). At these vesicle concentrations the analytical model 351
predicts growth at 5 ± 2.9 𝑛𝑚/𝑠, similar to normal growth. 352
Since diffusion-based growth with ideal vesicle fusion kinetics is enough to 353
support cell growth, we sought to estimate the true kinetics of vesicle membrane 354
fusion during exocytosis. Docking and fusion of exocytic vesicles is a multistep 355
process mediated by protein complexes such as the Exocyst (Kulich et al., 2010; 356
Bloch et al., 2016) and the SNARE complex (Lipka et al., 2007; El Kasmi et al., 357
2013); which we simplify by assuming VAMP72-vesicles interact with one type of 358
receptor on the plasma membrane at the cell tip. We also assume that this type 359
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13
of receptor has one reaction rate, and facilitates the integration of vesicles into 360
the plasma membrane. This allows us to write the flux equation through the 361
plasma membrane as follows (Phillips, 2013), 362
363
𝜙 = 𝑚𝐾𝑜𝑛𝑐(0) . (8) 364
365
Here m is the total number of receptors on the plasma membrane at the cell tip, 366
Kon is the binding reaction rate between vesicles and the receptors, and 𝜙 is the 367
measured number of vesicle fusion events per second (as previously defined 368
with Eq. (2)). As a first approximation, and for the most parsimonious case, we 369
assume that 𝑚𝐾𝑜𝑛 is constant during growth. Since the intensity of vesicles at 370
the very cell tip, 𝑐(0), for growing cells is roughly two-fold higher than 𝑐(0) for 371
latrunculin B treated cells (Supplementary Data Fig. S2), we can solve Eq. (8) to 372
get 𝑚𝐾𝑜𝑛 ~ 2.5 𝑠−1𝜇𝑚3. 373
374 Refined Diffusion Model Illustrates the Requirement for F-actin in Polarized 375 Growth 376 377 With relevant vesicle concentrations and fusion kinetics known, we then built a 378
more comprehensive model to determine the physiological conditions under 379
which diffusion could or could not sustain cell growth, and developed an insight 380
into the limiting factors in polarized growth from a vesicle trafficking perspective. 381
To this end, we created a diffusion-based growth model without the actin 382
cytoskeleton. To incorporate a more realistic geometry of the growing moss cell 383
tip, we used the finite element analysis modeling software Comsol Multiphysics 384
(Comsol Inc, Stockholm, Sweden) to solve Eq. (3) within the moss geometry for 385
biologically relevant boundary conditions. We used impermeable (reflective) 386
boundary conditions for most of the plasma membrane, except for the active 387
region of exocytosis at the cell tip, where the 𝑚 receptors were concentrated. In 388
this region we used Eq. (8) as a boundary condition to simulate diffusion-389
mediated exocytosis. Since the size of the zone of vesicle exocytosis is 390
unknown, we simulated four different discrete exocytic zones, centered at the cell 391
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14
apex, with diameters Ω = 1, 2, 4, and 10 𝜇𝑚 (Fig. 5A). To satisfy Eq. (8), each of 392
the four simulated exocytic zones maintained the same total number of 393
receptors, 𝑚, but at different densities. Although it has been previously shown 394
that vesicle exocytic zones may have a monotonically increasing 𝑚𝐾𝑜𝑛 focused 395
at the tip (Campàs and Mahadevan, 2009), we simulate Ω with a constant 𝑚𝐾𝑜𝑛 396
to establish the effective length scales for the exocytic zone. 397
To achieve growth rates similar to a wild type cell, our model predicts that 398
a cell growing by diffusion would have to maintain vesicle concentrations at the 399
shank much greater than those observed experimentally. Specifically, these 400
concentrations range between ~125 and ~477 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠/𝜇𝑚3 at the cell shank, 𝑐𝐿 , 401
while our experimentally measured shank concentration is 38 ± 2 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠/𝜇𝑚3. 402
Based on the size of the exocytosis zone we found that these concentrations 403
exhibited different gradients as they approached the cell tip. Large exocytic 404
zones produced concentration gradients that fell slowly as they approached the 405
cell tip, while smaller zones produced concentration gradients that rapidly fell as 406
they approached the cell tip (Fig. 5B and 5C). We also found that larger exocytic 407
zones could support cell growth at lower vesicle concentrations than smaller 408
exocytic zones. This means that a cell with larger exocytic zones could grow 409
more quickly than a cell with a smaller exocytic zone, if both cells had the same 410
steady state vesicle concentrations. For large exocytic regions and 411
experimentally measured vesicle concentrations, diffusion alone could lead to 412
cell growth rates slightly slower than 2 𝑛𝑚/𝑠 (Fig. 5E). Smaller exocytic regions 413
at experimentally relevant vesicle concentrations produced growth rates slower 414
than 1 𝑛𝑚/𝑠 (Fig. 5E). Although actin could serve other functions associated with 415
growth, our results demonstrate that there is a specific requirement for active 416
transport to sustain cell growth, and that this need is dependent of the size of the 417
exocytic zone. 418
419 Wall Extensibility is Weakest at the Cell Tip 420 421 In order to constrain our diffusion model with an experimentally relevant secretion 422
size, we examined the material properties of the cell wall. To probe these 423
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15
properties during polarized growth, we used the enzyme cocktail driselase, which 424
enzymatically degrades the wall. When exposed to driselase, we found that the 425
wall of the tip-growing cells would begin to extrude and eventually fail (Fig. 6A). 426
Following treatment extrusion and failure was observed within minutes. We found 427
that the average size of the extruded region was approximately 5.8 ± 0.5 µ𝑚 in 428
diameter (Fig. 6B), and its center was within 3 µ𝑚 from the center of the cell (Fig. 429
6C). Assuming degradation happens uniformly, this indicates that the cell wall is 430
most extensible at the cell tip. Due to the fact that exocytosis mediates wall 431
extensibility, we inferred that exocytosis likely takes place within a region smaller 432
than 5.8 µ𝑚 in diameter. This upper limit illustrates that without F-actin, diffusion-433
based cell growth could never achieve growth rates greater than 2 𝑛𝑚/𝑠 (Fig 6D 434
and 6E), which is significantly less than 5.5 ± 0.4 𝑛𝑚/𝑠 observed 435
experimentally. 436
437
Discussion and Conclusion 438 439 This work demonstrates that in moss protonemata actin drives vesicle transport, 440
and shows quantitatively that this transport is necessary to sustain normal cell 441
growth. Specifically, the experimentally measured vesicle diffusion coefficient, 442
vesicle concentrations, membrane reaction kinetics, and size of the exocytosis 443
region collectively impose enough limitations on diffusion based growth to require 444
an active transport system in polarized secretion, Fig 7. 445
While it is well-known that filamentous actin is necessary for polarized 446
growth, here we showed that latrunculin B treatments halt tip growth within 2 447
minutes, indicating an immediate reliance on actin. We then showed with FRAP 448
that VAMP72 labeled vesicles are transported cortically to the cell apex in an 449
actin-dependent manner. Nevertheless, this FRAP analysis is limited in that it 450
does not have the spatiotemporal resolution to infer additional modes of vesicle 451
dynamics, such as transport to the plasma membrane and/or endocytic vesicle 452
resupply. 453
Depolymerizing the actin cytoskeleton with latrunculin B, reduced the 454
number of modes of vesicles dynamics, and allowed us to use FRAP to measure 455
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16
the vesicle diffusion coefficient (~ 0.29 𝜇𝑚2𝑠−1 ). While we assumed that the 456
VAMP72 fluorescent marker exclusively labeled secretory vesicles, it remains a 457
possibility that the marker could have labeled a small fraction of the Golgi or ER. 458
However, our Numbers and Brightness (N&B) analysis shows that the vast 459
majority of pixels in the images have a brightness distribution consistent with the 460
marker labeling a single species (Supplement Data Fig. S6). In addition, 461
fluorescence labeling of the ER and Golgi (Furt et al., 2012) did not match the 462
fluorescence intensity distribution found with VAMP72. Furthermore, the vesicle 463
diffusion coefficient we measured is in agreement with previously measured 464
pollen tube vesicle diffusion coefficients (Bove et al., 2008; Kroeger et al., 2009), 465
and measurements of the viscosity of the moss cytoplasm (Kingsley, Bibeau et 466
al., see attached supporting manuscript). 467
Our quantitative estimate of the vesicle diffusion coefficient, the number of 468
vesicles (through N&B analysis of VAMP72), and the kinetics of vesicle fusion 469
(𝑚𝐾𝑜𝑛 ) allowed us to build a model to describe diffusion-based growth with 470
relevant parameters from moss. While the variability in number of VAMP72 471
molecules on a vesicle can contribute to the observed intensity fluctuations, we 472
considered this effect to be negligible since our measured concentration of 473
vesicles is in agreement with EM estimates (Mccauley and Hepler, 1992). We 474
used this concentration to solve the flux equation at the cell tip, and determined 475
an estimate for the kinetics of vesicle fusion, 𝑚𝐾𝑜𝑛. To explore how the reaction 476
kinetics observed during normal cell growth limit diffusion based cell growth, we 477
assumed 𝑚𝐾𝑜𝑛 is constant and independent of the presence of F-actin. With 478
these parameters used as inputs, we built and solved a comprehensive model of 479
diffusion-based cell growth in a realistic moss geometry. It is important to note 480
that this model is a theoretical proof used to illustrate limitations that highlight the 481
importance of F-actin, and is not expected to match the physiological conditions 482
in latrunculin B treated cells. Nevertheless, our results predict that diffusion-483
based transport is slower than normal cell growth and heavily dependent on the 484
size of the active region of exocytosis. 485
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17
Finally with driselase treatments, we found that the effective length scale 486
for the region of greatest extensibility (maximum secretion) was on the order of a 487
few microns and located at the cell tip. This analysis holds as long the cell wall 488
extruded because of an increased extensibility, and not because of increased 489
stresses resulting from the intrinsic geometry of the cell. Based on the shape of 490
the cell wall, and the assumption that the cell wall is a thin sheet, one can show 491
that the maximum stresses on the cell wall are not at the regions of rupture 492
(Campàs and Mahadevan, 2009). For thin walled shells under uniform pressure, 493
it has been shown that the curvature of the cell wall is inversely proportional to 494
stress (Campàs and Mahadevan, 2009). Since the shank of the cell is less 495
curved than the tip, greater stresses are predicted at the shank; therefore the 496
observed cell rupture is most likely a result of increased extensibility at the tip. 497
Additionally, these measurements for the size of the exocytic zone are consistent 498
with the localization of myosin XI at the cell tip (Vidali et al., 2010). 499
Although we built a tip-growth model that quantitatively highlights the 500
necessity for an active transport mechanism in polarized growth, we cannot rule 501
out the possibility that other factors could limit polarized growth. For example, 502
the F-actin could be necessary for maintaining the active region of exocytosis. 503
Specifically, F-actin could facilitate the transport and polarization of the receptors 504
required in vesicle fusion. However, elucidating such potential limitations is left 505
for future work. Importantly, we have shown and quantified specific reasons why 506
active transport is necessary in polarized growth. These analyses and modeling 507
approaches are likely to apply to other tip growth systems in plants such as root 508
hairs and pollen tubes. 509
510
Materials and Methods 511 512 Measuring Moss Growth Rates 513 514 The moss cell line used for measuring growth rates was 3mEGFP-VAMP72, and 515
was transformed as done in (Furt et al., 2013) the gene used corresponds to 516
accession number Pp3c4_13580V3.1 (Phytozome 12). Moss samples were 517
cultured using the protocol described previously (Vidali et al., 2007). Microscope 518
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18
samples were prepared as described previously (Furt et al., 2013). To stop 519
growth, liquid medium (PpNO3) with 200μL of 5 μM of latrunculin B was pipetted 520
directly on top of the growing cells. Samples were imaged on a Leica TCS SP5 521
confocal microscope with a 63X objective and a numerical aperture of 1.4. The 522
argon laser was set to 25% power and the 488 𝑛𝑚 laser line was set to 10% 523
power. The emission bandwidth was set between 499 − 546 𝑛𝑚, and a hybrid 524
detector was used to acquire images. Kymographs and growth rates were 525
constructed using ImageJ. 526
Experimental FRAP Acquisition, Processing, and Analysis 527 528 The moss cell line used for FRAP was a 3mCherry-VAMP72 3mEGFP-myosin 529
XIa double line previously published by (Furt et al., 2013). Moss samples were 530
cultured using the protocol described previously (Kingsley, Bibeau et al., see 531
attached supporting manuscript). Samples were prepared in QR-43C chambers 532
(Warner Instruments) and perfused with 5 μM latrunculin B. Samples were 533
imaged on a Leica TCS SP5 scanning confocal microscope using the Leica 534
FRAP wizard. A 63𝑋 objective with a 1.4 numerical aperture was used. The 535
pinhole was set to 2 airy disks and the camera zoom was 9. To visualize the 536
3mCherry-VAMP72 cell line developed in (Furt et al., 2013), the DPSS 537
561 𝑛𝑚 laser was turned on and the 561 𝑛𝑚 laser line was set to 10%. The laser 538
scanning speed was set to 1400 𝐻𝑧 with the bi-directional scanning. The 539
emission bandwidth for 3mCherry was set between 574 and 646 𝑛𝑚 . Images 540
were acquired at 256 × 256 pixel resolution, with a bit depth of 12 bits. 541
Following image acquisition, images were subjected to several processing 542
steps. First experimental TIFF stacks were analyzed with an ImageJ macro that 543
tracked the photobleaching Region Of Interest (ROI), performed background 544
subtraction, and normalized the mean ROI to pre-bleach ROI intensities. Image 545
acquisition photobleaching was measured by tracking fluorescence intensity over 546
time while imaging cells at the same sampling rate used during FRAP 547
experiments. This fluorescence time trace was fit to a piecewise exponential. To 548
correct for acquisition photobleaching and reversible photobleaching, normalized 549
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19
FRAP experimental ROI intensities were divided by this piecewise exponential 550
(Supplementary Data Fig. S1). All untreated curves were normalized to the mean 551
pre-bleach shank intensity to illustrate changes in fluorescence intensity relative 552
to the shank vesicle concentration. Recovery curves from latrunculin B treated 553
cells, at the tip and shank, were normalized to their mean pre-bleach intensities 554
at their respective locations. 555
For spatial analysis of fluorescence recovery, experimental images were 556
analyzed as follows. First an image cropping macro was used to extract FRAP 557
ROIs. Cropped ROIs were then normalized to the mean of the pre-bleach ROIs 558
and averaged across experimental replicates. To correct for the limited 559
accessible volume at the cell tip, we fit an exponential decay to a line scan 560
through the cropped prebleach ROIs. We then divided each ROI during 561
fluorescence recovery by this exponential decay (Supplementary Data Fig. S5). 562
For more details on experimental FRAP acquisition and processing see, 563
(Kingsley, Bibeau et al., see attached supporting manuscript). 564
After ROI processing, we spatially sub-sampled the ROIs with an angular 565
sector that was rotated 360 degrees about the ROI (Fig. 2B and 3B). To reduce 566
noise, we averaged about the horizontal axis of the ROI; this produced an 567
intensity profile from 0 − 180 degrees. 568
569 Measuring Confocal Imaging and FRAP Parameters 570 571 Since our particle-based FRAP simulation considers the imaging and 572
photobleaching properties of the confocal microscope, we measured the Point 573
Spread Function (PSF) of our imaging system, and the photobleaching properties 574
of 3mCherry-VAMP72 (Kingsley, Bibeau et al., see attached supporting 575
manuscript). for more details on the simulation inputs and parameter estimates). 576
To determine the PSF of our imaging system, we used the PS-Speck Microscope 577
Point Source Kit P7220 (Invirtogen). Bead images (Supplementary Data Fig. 578
S3A and S3B) were deconvolved with a box car function equal to the width of the 579
bead. This ensured that the experimental images represented a true point 580
source. The deconvolved PSF was then fit to a three-dimensional squared 581
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20
Gaussian beam (Supplementary Data Fig. S3A and S3B) and used for imaging in 582
the simulation (Kingsley, Bibeau et al., see attached supporting manuscript). . 583
Based on these fits, we found that the minimum beam width, 𝑤0 , and the 584
Rayleigh range, 𝑧𝑅, were 520 and 500 𝑛𝑚, respectively. 585
To measure the photobleaching properties of the beam, we fixed cells 586
expressing 3mCherry-VAMP72 with formaldehyde (Fritzsche and Charras, 587
2015). For fixation, a solution of 100 𝑚𝑀 HEPES with 2% formaldehyde at pH 7, 588
was perfused into QR-43C chambers (Warner Instruments) for 30 minutes (Vidali 589
et al., 2007). Fixed cells were subjected to a 1 × 6 𝜇𝑚 rectangular 590
photobleaching region of interest (Supplementary Data Fig. S1C, solid white 591
rectangle) and imaged in the same plane as the photobleach. A rectangular ROI 592
was chosen because it is composed of confocal scans of equal length; which 593
permits fluorescence averaging along the long axis of the rectangle. A line scan 594
was created by collapsing a 4 × 8 𝜇𝑚 rectangular region including the 595
photobleached ROI (Supplementary Data Fig. S1B, dashed yellow rectangle) into 596
a one-dimensional profile. After photobleaching, we fit the photobleaching 597
function described by (Kingsley, Bibeau et al., see attached supporting 598
manuscript) to the line scan. This function characterizes the horizontal line scan 599
of a Gaussian beam as it photobleaches across a fixed distance. As shown 600
previously (Braeckmans et al., 2006), we found that the photobleaching 601
Gaussian beam waist was two-fold larger than the imaging beam waist at 602
920 𝑛𝑚. This fit also yielded a photobleaching proportionality constant, which 603
was used as a starting point in fluorescence recovery fitting routines to measure 604
VAMP-72 vesicle diffusion. For more details on simulating confocal 605
photobleaching see, (Kingsley, Bibeau et al., see attached supporting 606
manuscript) and for general use we developed a Digital Confocal Microscopy 607
Suite (DCMS), which can be found at 608
http://tuzelgroup.wpi.edu/desktop/research/software/dcms/. 609
610
FRAP Parameter Minimization 611 612 To determine the simulation parameters that best characterize the recovery 613
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21
curves for VAMP72-vesicles in latrunculin B treated cells, a minimization routine 614
was used similar to the one by (Kingsley, Bibeau et al., see attached supporting 615
manuscript). Averaged experimental recovery curves 𝑅𝑒𝑥𝑝(𝑡) at the tip and shank 616
were characterized into classes 𝑅𝑇𝑒𝑥𝑝
(𝑡) and 𝑅𝑆𝑒𝑥𝑝(𝑡), respectively. Averaged 617
simulation recovery curves were characterized in the same way to produce 618
𝑅𝑇𝑠𝑖𝑚(𝑡) and 𝑅𝑆
𝑠𝑖𝑚(𝑡) . These two classes of simulation recovery curves were 619
generated in a two-dimensional parameter space for the parameters 𝐷 and 𝐾, 620
where a range of each parameter was simulated ( 𝐷 = 0.1 − 0.5 𝜇𝑚2𝑠−1 and 621
𝐾 = 0.01 − 0.03 ). Here 𝐷 is the diffusion coefficient and 𝐾 is the bleaching 622
proportionality coefficient. The bleaching proportionality coefficient 𝐾 measured 623
during fixation was used only as a reference in generating the range for possible 624
values of 𝐾. This was done because formaldehyde treatment was found to affect 625
fluorophore bleaching properties at the concentrations used. Unlike the approach 626
from Kingsley, Bibeau et al., (see attached supporting manuscript) only two 627
parameters were used here because the photobleaching width, w0, was 628
measured with formaldehyde treated cells. The recovery curve for each 629
parameter pair was stored in a Matlab (MathWorks, Natick, MA) data structure. 630
Best fit simulation parameters for the averaged experimental recovery profiles at 631
the tip, 𝑅𝑇𝑒𝑥𝑝
(𝑡), and shank, 𝑅𝑆𝑒𝑥𝑝(𝑡),, were found by reducing the sum of squared 632
differences between the curves. Averaged tip and shank recovery curves can be 633
represented as 𝑅𝑇𝑠𝑖𝑚(𝑡)𝐷,𝐾,𝑤0
and 𝑅𝑆𝑠𝑖𝑚(𝑡)𝐷,𝐾,𝑤0
, respectively. 634
To account for reversible bleaching we imposed a correction on all 635
simulated recovery curves (Sinnecker et al., 2005; Mueller et al., 2012; Morisaki 636
and McNally, 2014) (Kingsley, Bibeau et al., see attached supporting 637
manuscript). During intentional photobleaching, some fraction of the bleached 638
molecules, 𝛼, convert back to an unbleached state at a given rate, 𝑅(𝑡). We used 639
𝛼 and 𝑅(𝑡) that were previously measured for mCherry. Then using the 640
relationship previously devised,𝐼𝑀(𝑡) = 𝐼𝐹𝑅𝐴𝑃(𝑡) + 𝛼𝑅(𝑡)𝐼𝐹𝐿𝐴𝑃(𝑡), we corrected the 641
simulated recovery curves (Mueller et al., 2012). Here 𝐼𝑀(𝑡) is the resultant 642
fluorescence recovery that incorporates reversible bleaching, 𝐼𝐹𝑅𝐴𝑃(𝑡) represents 643
the fraction of the fluorescent recovery due to movement of unbleached 644
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22
fluorophores and 𝐼𝐹𝐿𝐴𝑃(𝑡) represents the motion of the reversibly photobleached 645
molecules. After correction the averaged simulation tip and shank recoveries 646
become, 𝑅𝑇𝑠𝑖𝑚(𝑡)𝐷,𝐾,𝑤0
𝑟𝑒𝑣 and 𝑅𝑆𝑠𝑖𝑚(𝑡)𝐷,𝐾,𝑤0
𝑟𝑒𝑣 , respectively, where the superscript 𝑟𝑒𝑣 647
indicates reversible bleaching correction. Following this correction, best fit 648
diffusion coefficients for VAMP72-vesicle experiments, were found with the 649
following argument minimization, 650
651
𝑎𝑟𝑔𝑚𝑖𝑛𝐷𝑣,𝐾𝑡,𝐾𝑠[∑ (𝑅𝑇
𝑒𝑥𝑝(𝑡) −𝑡>0 𝑅𝑇𝑠𝑖𝑚(𝑡)𝐷𝑣,𝐾𝑡
𝑟𝑒𝑣 )2 + ∑ (𝑅𝑆𝑒𝑥𝑝(𝑡) − 𝑅𝑆
𝑠𝑖𝑚(𝑡)𝐷𝑣,𝐾𝑠
𝑟𝑒𝑣 )2𝑡>0 ] (9) 652
653
In this minimization, experimental recoveries at the cell tip and shank were 654
compared to their corresponding simulations to find the parameters 𝐷𝑣, 𝐾𝑡, and 655
𝐾𝑠. Here, the subscript 𝑣 denotes VAMP72-vesicles. As shown in Eq. (9), the 656
diffusion coefficient 𝐷𝑣 was shared between the tip and shank. To improve the 657
argument minimization, two unshared bleaching proportionality coefficients were 658
used at the tip 𝐾𝑡 and shank 𝐾𝑠 (Kingsley, Bibeau et al., see attached supporting 659
manuscript). Although using two unshared bleaching probabilities improves the 660
argument minimization, a shared bleached probability for the tip and shank did 661
not appreciably change the mean value of our measured diffusion coefficient, 662
𝐷 = 0.45 ± 0.04 𝜇𝑚2𝑠−1 . This measurement has confidence intervals that 663
overlap with the intervals of our VAMP72-vesicles diffusion coefficient ( 𝐷 =664
0.29 ± 0.14 𝜇𝑚2𝑠−1) and does not change our conclusions. Similarly, we found 665
that the ignoring reversible photobleaching would have had little impact on our 666
measured diffusion coefficient (𝐷 = 0.32 ± 0.18 𝜇𝑚2𝑠−1). 667
To determine the error associated with the measured parameters, we 668
used the Monte Carlo simulation as described in detail in (Kingsley, Bibeau et al., 669
see attached supporting manuscript)(Motulsky and Christopoulos, 2004). In brief, 670
we generated new experimental and simulated recovery curves via Monte Carlo 671
simulation by sampling from a normal distribution for each condition. The mean 672
and standard deviations of this normal distribution were taken from the mean and 673
standard deviations of each point in the corresponding recovery curve. We then 674
performed the argument minimization described in Eq. (9) on the newly 675
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23
generated curves to find new values for the parameters, 𝐷𝑣, 𝐾𝑡, and 𝐾𝑠. We then 676
repeated this process to produce a distribution of these parameters. We used 677
two standard deviations from each distribution to represent the error of our 678
measured parameters such that, 𝐷𝑣 = 0.29 ± 0.24 𝜇𝑚2𝑠−1 , 𝐾𝑡 = 0.02 ±679
0.004,𝐾𝑠 = 0.0125 ± 0.004. 680
681 Comsol Cell Growth Model 682 683 Cell growth models were generated using the Comsol Multiphysics (Comsol Inc, 684
Stockholm, Sweden) modeling software using the “three-dimensional transport of 685
dilute species” interface with one species. To achieve the steady state solution of 686
our growth model, the “stationary study” option was selected. We model the cell 687
as a cylinder of length 10 𝜇𝑚 and radius 6 𝜇𝑚 , capped by a hemisphere. To 688
simulate the active region of exocytosis, we induced a flux, consistent with Eq. 689
(8), through the cell membrane at the cell tip. To simulate the uniform production 690
of vesicles, we imposed a homogenous reaction rate. All simulations were run 691
with a mesh setting of “extremely fine” in the software. To determine the 692
concentration profiles required to maintain wild type growth, for the various 693
secretion sizes, we set the production term to match the desired growth rate. We 694
then modified this production term to match the experimentally measured shank 695
concentrations and reported the growth rate. Vesicle concentration profiles were 696
then exported as text files, and visualized in Matlab. 697
Brightness and Numbers Analysis 698 699 Moss cultures and microscope samples were prepared as described in 700
measuring moss growth rates. Samples were imaged on a Leica TCS SP5 701
confocal microscope with a 63 × objective with a numerical aperture of 1.4. The 702
argon laser was set to 25% power and the 488 𝑛𝑚 laser line was set to 20% 703
power. The emission bandwidth was set between 499 − 546 𝑛𝑚 and a hybrid 704
detector in photon counting mode was used. Images were scanned at 700 𝐻𝑧. 705
Six latrunculin B-treated cells were imaged at both the shank and the cell tip 706
within a 6 × 6 𝜇𝑚 area, and a pixel resolution of 512 × 512. Image stacks were 707
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24
analyzed in Matlab (MathWorks, Natick, MA) as previously described (Digman et 708
al., 2008). 709
To conduct our analysis, we collected confocal image time series at the tip 710
and shank of latrunculin B treated cells expressing 3mEGFP-VAMP72 711
(Supplemental Data Fig. S5A). We assumed that all the VAMP72s on a vesicle 712
equally contribute to the brightness of a vesicle because the size of a vesicle is 713
consistent with a diffraction limited spot (Lancelle and Hepler, 1992). To ensure 714
that detector shot noise and VAMP72-vesicle number fluctuations were the 715
primary contributors to intensity fluctuations, all images were acquired with a 716
hybrid detector in photon counting mode (Dalal et al., 2008; Digman et al., 2008). 717
The intensity fluctuations over time for each pixel were calculated and used to 718
determine the brightness and number of molecules within each pixel 719
(Supplemental Data Fig. S5B). We then manually filtered the pixels by their 720
apparent brightness and intensity. This was done to remove background pixels 721
and anomalously bright pixels (with brightness value 𝐵 > 2) (Supplemental Data 722
Fig. S5C). To convert the number of molecules within a given pixel to a 723
concentration, the number of molecules must be divided by the volume of the 724
Point Spread Function (PSF). To obtain the apparent volume of the PSF, we 725
used our particle-based confocal simulation (Kingsley, Bibeau et al., see 726
attached supporting manuscript). with our measured PSF beam width and 727
Rayleigh range as input parameters. These parameters were measured in the 728
same way as 3mCherry(Supplementary Data Fig. S3). With the particle-based 729
confocal simulation we then generated an array of vesicle concentrations, and 730
used a calibration curve to convert the number of molecules per pixel to the 731
known concentrations (Supplemental Data Fig. S5D). From the calibration curve, 732
we were able to determine the volume of our PSF given our measured 733
experimental parameters. This PSF volume was within 20% error of theoretical 734
PSF volumes (Moens et al., 2011). 735
736
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25
Driselase Treatment on the Cell Wall 737
Moss cultures were prepared as described in measuring moss growth rates. 738
Microscope preparations were made on the bottom of 60X15 mm petri dishes. 10 739
ml of PPN03 with 1% agar was pipetted into the dish. Six 1 ml pipette tips were 740
placed face up onto the dish. Once solidified, the pipette tips were removed and 741
50 𝜇𝐿 of PPN03 with 1% agar was pipetted into the newly made holes. A single 742
moss colony was then placed into one of the holes. Then a 200 𝜇𝐿 solution of 8% 743
mannitol and 2% driselase was pipetted into the hole. The cells were imaged 744
using a Zeiss Axio Observer inverted microscope with a 20 × objective. Images 745
were acquired with a Photometrics Cool Snap Camera with the Pixelfly software. 746
Images were taken every 0.1 seconds. 747
Images were analyzed with Matlab (MathWorks, Natick, MA). Cell edges 748
were detected using the canny edge detection algorithm with the function edge. 749
Rupture points and positions were found manually by selecting points on the 750
image. Polynomial fitting was used to estimate relevant arc lengths. 751
752
Supplemental Figure 1. Image acquisition photobleaching/reversible 753
photoswitching and correction. 754
Supplemental Figure 2. Latrunculin B abolishes tip localization of VAMP72-755
vesciles. 756
Supplemental Figure 3. Point Spread Function (PSF) for imaging and 757
photobleaching. 758
Supplemental Figure 4. VAMP72-vesicle accessible volume correction. 759
Supplemental Figure 5. Spatial fluorescence recovery of VAMP72-vesicles at 760
the cell shank. 761
Supplemental Figure 6. Brightness and numbers analysis reveals vesicle 762
concentrations. 763
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26
Supplemental Movie 1. Analysis of spatial recovery of VAMP72-vesicles at the 764
cell tip. 765
Supplemental Movie 2. Analysis of spatial recovery of VAMP72-veislces at the 766
cell tip of latrunculin B treated cell. 767
768
769
Supplemental Movie 1. Analysis of spatial recovery of VAMP72-vesicles at the 770
cell tip. Cropped and frame averaged photobleaching ROI at the cell tip for 771
3mCherry-VAMP72-vesicles( left). Angular intensity profile of VAMP72-vesicles 772
at the cell tip (right). n = 10; ROI is 4 μm in diameter. Mean subtracted image 773
intensity denoted with rainbow lookup table. 774
Supplemental Movie 2. Analysis of spatial recovery of VAMP72-veislces at the 775
cell tip of latrunculin B treated cell. Cropped and frame averaged photobleaching 776
ROI at the cell tip for latrunculin B treated (left) 3mCherrry-VAMP72-vesicles. 777
Angular intensity profile of VAMP72-vesicles at the cell tip following latrunculin B 778
treatment (right). n = 8; ROI is 4 μm in diameter. Mean subtracted image intensity 779
denoted with rainbow lookup table. 780
781 Acknowledgements 782
We thank Leica Microsystems GmbH for technical guidance, and all members of 783
the Vidali and Tüzel labs for helpful discussions, especially Iman Mousavi. This 784
work was supported by National Science Foundation CBET 1309933 to ET, and 785
NSF-MCB 1253444 to LV. ET and LV also acknowledge support from Worcester 786
Polytechnic Institute Startup Funds. JK acknowledges support from the WPI 787
Alden Fellowship. 788
789
790
791
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27
792
Table 1 Analytical Model Parameters 793 794 Parameter Value Source
Diffusion Coefficient, 𝐷 0.29 ± 0.14 𝜇𝑚2𝑠−1 Measured with FRAP
Cylinder length, 𝐿 16 ± 1.4 𝜇𝑚 Measured from microscope images (n=8)
Cylinder Radius, 𝑅 6 ± 0.2 𝜇𝑚 Measured from microscope images (n=8)
Concentration at 𝑐(𝐿), 𝑐𝐿 10 − 100 𝑣𝑒𝑠/𝜇𝑚3 Estimated from Figure 1B
795 796 797
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28
Figure Legends 798 799 Figure 1. Latruculin B stops growth. A) Representative kymographic analysis of 800
caulonemal cells expressing 3mEGFP-VAMP72 vesicles before (top) and after 801
(bottom) vehicle (left) or 5 𝜇𝑀 latrunculin B treatment (right). Black vertical arrow 802
indicates vertical time axis. Horizontal arrow denotes treatment time. White 803
space between top and bottom figures represents the approximate time 804
necessary to apply the treatment to the culture. Dotted white box indicates region 805
for line scan. B) Representative cells before (top) and after (bottom) latrunculin B 806
treatment. Scale bar is 5 𝜇𝑚. C) Measured intensity gradient for latrunculin B 807
treated cells. Measurement was taken from the white dotted box in (B) for each 808
measured cell. (error bars indicate standard error, and 𝑛 = 4) 809
810
Figure 2. VAMP72-vesicle dynamics during polarized growth. A) Fluorescence 811
recovery of 3mCherry-VAMP72-vesicles at the cell shank (green circles) and cell 812
tip (black squares). 𝑛 = 8 and 10, respectively (error bars indicate standard 813
deviation). B) Cropped and frame averaged photobleaching ROI at the cell tip for 814
3mCherry-VAMP72-vesicles (top) and simulation (bottom) n = 8 and 50, 815
respectively. Image intensity denoted with rainbow lookup table; ∆𝑡1 = 0.7 −816
1.6 𝑠 and ∆𝑡2 = 20 − 40 𝑠. White arrows mark direction of recovery(left). White 817
circle and arrow denotes how the perimeter of the ROI was measured (right). C-818
D) Intensity profiles of 3mcherry-VAMP72 along the ROI perimeter at the cell tip 819
during the time intervals ∆𝑡1 = 0.7 − 1.6 𝑠 (C) and ∆𝑡2 = 20 − 40 𝑠 (D) 820
(𝑛 = 10, error bars indicate standard error). 821
822
Figure 3. Latrunculin B treated VAMP72-vesicle dynamics. A) Fluorescence 823
recovery of latrunculin B treated 3mCherry-VAMP72-vesicles at the cell shank 824
(green circles) and cell tip (black squares) with corresponding best fit simulation 825
results (red). 𝑛 = 6 and 8, respectively (error bars indicate standard deviation). 826
B) Cropped and frame averaged photobleaching ROI at the cell tip for latrunculin 827
B treated 3mCherry-VAMP72-vesicles (top) and simulation (bottom) 𝑛 =828
8 𝑎𝑛𝑑 50, respectively. Image intensity denoted with rainbow lookup table; 829
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29
∆𝑡1 = 0.8 − 2.5 𝑠 and ∆𝑡2 = 20 − 40 𝑠. White arrows mark direction of recovery 830
(left). White circle and arrow denote how the perimeter of the ROI was measured 831
(right). C-F) Intensity profiles of latrunculin B treated VAMP72 along the ROI 832
perimeter at the cell tip during the time intervals ∆𝑡1 = 0.8 − 2.5 𝑠 (C) and 833
∆𝑡2 = 20 − 40 𝑠 (D) with corresponding simulations in red (E and F) (𝑛 = 8, 834
error bars indicate standard error). 835
836
Figure 4. Differential equation model of diffusive cell growth with idealized 837
geometry. A) Diagram of the cylindrical approximation of the moss geometry. 838
Green circles represent vesicles. Red boundaries are reflective boundaries and 839
green boundary is perfectly absorbable. B) Representative bright field image of 840
growing cell with cylindrical approximation of analytical model in red. Scale bar is 841
5 𝜇𝑚. C) Simulated 3mEGFP-VAMP72-vesicles with 𝑐𝐿 = 10 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠/𝜇𝑚3. 842
Scale bar is 4 𝜇𝑚. D) Normalized concentration profile for the solution of the 843
analytical model, Eqs. (3)-(7). E+F) Growth rates for the analytical model, Eqs. 844
(3)-(7), solved for 𝑐𝐿 = 10 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠/𝜇𝑚3 (E) and 𝑐𝐿 = 100 𝑣𝑒𝑠𝑖𝑐𝑙𝑒𝑠/𝜇𝑚3 (F). 845
Model error bars represent predicted growth rates within 95% confidence 846
intervals, with 𝐷 = 0.15 𝜇𝑚2𝑠−1 and 𝐷 = 0.43 𝜇𝑚2𝑠−1, respectively. Wild type 847
error bars represent 95% confidence intervals, 𝑛 = 4. 848
849 Figure 5. Differential equation model of diffusive growth with moss cell geometry. 850
A) Plasma membrane with the active area of exocytosis marked in red. Black line 851
indicates reflective boundary. Dashed line indicates the exocytosis region 852
diameter 𝛺. B) Model predicted steady-state vesicle concentration profile 853
necessary to sustain wild type cell growth. Color table indicates concentration 854
gradients with high concentrations as warm colors and low concentrations as 855
cool colors. C+D) Normalized (C) and unormalized(D) concentration profiles from 856
(B) necessary to sustain wild type cell growth. (B). E) Comsol model predicted 857
growth rates for experimentally measured shank concentrations for 𝛺 = 10,4,2, 858
and 1 𝜇𝑚 from left to right. Model error bars represent predicted growth rates for 859
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30
𝐷 = 0.15 and 𝐷 = 0.43 𝜇𝑚2𝑠−1, respectively. Wild type error bars represent 860
standard error of the mean, 𝑛 = 4. 861
862
Figure 6. Driselase reveals cell wall extensibility. A) Representative time series 863
of cell wall rupture following exposure to driselase. Cell perimeter is highlighted in 864
blue. Green circles mark the end points of the rupture arc length. Black circles 865
mark the cell tip. Red circle shows maximally deflected rupture potion. Red star 866
shows the projected rupture position. Scale bar is 5𝜇𝑚. Dashed line indicates the 867
rupture diameter 𝛺. B) Cumulative frequency of rupture diameter 𝛺. Insert 868
displays a box plot of the rupture diameter. Median is marked in red, the quartiles 869
are marked in blue, and the minimum and maximums are in black. Red dot is the 870
mean. C) Location of cell rupture along the edge. Blue dots indicate the cell 871
boundary. Red stars indicate region of rupture. (𝑛 = 17). D) Comsol model 872
predicted concentration profile, necessary to sustain wild type cell growth, for 873
𝛺 = 5.8 𝜇𝑚. E) Comsol model predicted growth rate for experimentally measured 874
shank concentrations and 𝛺 = 5.8 𝜇𝑚 , compared to wild type growth rate. Model 875
error bars represent predicted growth rates for 𝐷 = 0.15 and 𝐷 = 0.43 𝜇𝑚2𝑠−1, 876
respectively. Wild type error bars represent standard error of the mean, 𝑛 = 4. 877
878
Figure 7. F-actin must overcome the limiting factors in polarized cell growth. A) 879
Illustration of limiting factors in cell growth. Without F-actin, our measured 880
vesicle diffusion, vesicle concentrations, reaction kinetics (𝑚𝐾𝑜𝑛), and the active 881
secretion zone size would result in a significantly slower polarized growth. B) 882
With F-actin the cell can overcome these measured limitations and sustain cell 883
growth. 884
885
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31
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4 μm"
2 m
in"
Tim
e"
Latrunculin B "Vehicle"
Before Treatment" Before Treatment"A)
B) C)
Befo
re"
LatB"
Figure 1. Latruculin B stops growth. A) Representative kymographic analysis of caulonemal cells expressing3mEGFP-VAMP72 vesicles before (top) and after (bottom) vehicle (left) or 5 μM latrunculin B treatment(right). Black vertical arrow indicates vertical time axis. Horizontal arrow denotes treatment time.White spacebetween top and bottom figures represents the approximate time necessary to apply the treatment to theculture. Dottedwhite box indicates region for line scan. B) Representative cells before (top) andafter (bottom)latrunculin B treatment. Scale bar is 5 μm. C) Measured intensity gradient for latrunculin B treated cells.Measurementwas taken from thewhite dottedbox in (B) for eachmeasured cell. (error bars indicate standarderror, and n = 4)
Figure 2. VAMP72-vesicle dynamics during polarized growth. A) Fluorescence recovery of 3mCherry-VAMP72-vesicles at the cell shank (green circles) and cell tip (black squares). n = 8 and 10, respectively(error bars indicate standard deviation). B) Cropped and frame averaged photobleaching ROI at thecell tip for 3mCherry-VAMP72-vesicles (top) and simulation (bottom) n = 8 and 50, respectively. Imageintensity denoted with rainbow lookup table; ∆t1 = 0.7−1.6 s and ∆t2 = 20−40 s. White arrows markdirection of recovery(left). White circle and arrow denotes how the perimeter of the ROI wasmeasured (right). C-D) Intensity profiles of 3mcherry-VAMP72 along the ROI perimeter at the cell tipduring the time intervals ∆t1 = 0.7 − 1.6 s (C) and ∆t2 = 20 − 40 s (D) (n = 10, error bars indicatestandarderror).
Tip!
0.7-1.6s! 20-40s!
VAM
P !
C)! D)!
Δt1! Δt2!
Δt1! Δt2!
A)! B)!shank! tip!
Figure 3. Latrunculin B treated VAMP72-‐vesicle dynamics. A) Fluorescence recovery of latrunculin B treated 3mCherry-‐VAMP72-‐vesicles at the cell shank (green circles) and cell Dp (black squares) with corresponding best fit simulaDon results (red). n = 6 and 8, respecDvely (error bars indicate standard deviaDon). B) Cropped and frame averaged photobleaching ROI at the cell Dp for latrunculin B treated 3mCherry-‐VAMP72-‐vesicles (top) and simulaDon (boQom) n = 8 and 50, respecDvely. Image intensity denoted with rainbow lookup table; ∆t1 = 0.8−2.5 s and ∆t2 = 20−40 s. White arrows mark direcDon of recovery (leZ). White circle and arrow denote how the perimeter of the ROI was measured (right). C-‐F) Intensity profiles of latrunculin B treated VAMP72 along the ROI perimeter at the cell Dp during the Dme intervals ∆t1 = 0.8 − 2.5 s (C) and ∆t2 = 20 − 40 s (D) with corresponding simulaDons in red (E and F) (n = 8, error bars indicate standard error).
0 10 20 30 40Time (sec)
0.2
0.6
1
1.4
Inte
nsity VA
MP !
SIM!
Tip LatB!
Δt1! Δt2!
A)! B)!
C)! D)!
E)! F)!
Δt1! Δt2!
Δt1! Δt2!
Model wt0
1
2
3
4
5
6
Gro
wth
Rat
e (n
m/s
)
φ
10 ves/µm3
A)
C)
B)C(x)
0 x D)
E) F)
10#ves/μm3#
A)
C)
B)
D)
E) F)
Figure 4. Differen)al equa)on model of diffusive cell growth with idealized geometry. A) Diagram of our cylindrical approxima)on of the moss geometry. Green circles represent vesicles. Red boundaries are reflec)ve boundaries and green boundary is perfectly absorbable. B) Representa)ve bright field image of growing cell with cylindrical approxima)on of analy)cal model in red. Scale bar is 5 μm. C) Simulated 3mEGFP-‐VAMP72-‐vesicles with cL = 10 vesicles/μm3. Scale bar is 4 μm. D) Normalized concentra)on profile for solu)on of the analy)cal model, Eqs. (3)-‐(7). E+F) Growth rates for analy)cal model, Eqs. (3)-‐(7), solved for cL = 10 vesicles/μm3 (E) and cL = 100 vesicles/μm3 (F). Model error bars represent predicted growth rates within 95% confidence intervals, with D = 0.15 μm2s−1 and D = 0.43 μm2s−1, respec)vely. Wild type error bars represent 95% confidence intervals, n=4.
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Figure 5. Differen'al equa'on model of diffusive growth with moss cell geometry. A) Plasma membrane with the ac've area of exocytosis marked in red. Black line indicates reflec've boundary. Dashed line indicates the exocytosis diameter Ω. B) Model predicted steady-‐state vesicle concentra'on profile necessary to sustain wild type cell growth. Color table indicates concentra'on gradient with high concentra'ons as warm colors and low concentra'ons as cool colors. C+D) Normalized (C) and unormalized(D) concentra'on profiles from (B) necessary to sustain wild type cell growth. (B). E) Comsol model predicted growth rates for experimentally measured shank concentra'ons for Ω=10,4,2, and 1 μm from leT to right. Model error bars represent predicted growth rates for D = 0.14 and D = 0.43μm2s−1, respec'vely. Wild type error bars represent standard error of the mean, n=4.
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Figure 6. Driselase reveals cell wall extensibility. A) Representative time series of cell wall rupture followingexposure to driselase. Cell perimeter is highlighted in blue. Green circlesmark the end points of the rupturearc length. Black circles mark the cell tip. Red circle shows maximally defl ected rupture potion. Red starshows the projected rupture position. Scale bar is 5 μm. Dashed line indicates the rupture diameter Ω.B)Cumulative frequency of rupture diameter Ω. Insert displays a box plot of the rupture diameter. Median ismarked in red, the quartiles are marked in blue, and the minimum and maximums are in black. Red dot isthemean. C) Location of cell rupture along the edge. Bluedots indicate the cell boundary. Red stars indicateregion of rupture. (n=17). D) Comsol model predicted concentration profile, necessary to sustain wild typecell growth, for Ω = 5.8 μm . E) Comsol model predicted growth rate for experimentally measured shankconcentrations and Ω= 5.8 μm compared to wild type growth rate. Model error bars represent predictedgrowth rates for D = 0.14 and D =0.43μm2s−1, respectively. Wild type error bars represent standard error ofthe mean, n=4.
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Figure 7. F-‐ac(n must overcome the limi(ng factors in polarized cell growth. A) Illustra(on of limi(ng factors in cell growth. Without F-‐ac(n, our measured vesicle diffusion, vesicle concentra(ons, reac(on kine(cs (mKon), and the ac(ve secre(on zone size would result in a significantly slower polarized growth. B) With F-‐ac(n the cell can overcome these measured limita(ons and drive cell growth.
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