Morphogenesis of the fission yeast cell through cell wall expansion

Summary

The shape of walled cells such as fungi, bacteria and plants are determined by the cell wall. Models for cell morphogenesis postulate that the effects of turgor pressure and mechanical properties of the cell wall can explain the shapes of these diverse cell types [1–6]. However, in general, these models await validation through quantitative experiments. Fission yeast Schizosaccharomyces pombe are rod-shaped cells that grow by tip extension and then divide medially through formation of a cell wall septum. Upon cell separation after cytokinesis, the new cell ends adopt a rounded morphology. Here, we show that this shape is generated by a very simple mechanical-based mechanism in which turgor pressure inflates the elastic cell wall in the absence of cell growth. This process is independent of actin and new cell wall synthesis. To model this morphological change, we first estimate the mechanical properties of the cell wall using several approaches. The lateral cell wall behaves as an isotropic elastic material with a Young’s modulus of 50 ± 10 MPa inflated by a turgor pressure estimated to be 1.5 ± 0.2 MPa. Based upon these parameters, we develop a quantitative mechanical-based model for new end formation, which reveals that the cell wall at the new end expands into its characteristic rounded shape in part because it is softer than the mature lateral wall. These studies provide a simple example of how turgor pressure expands the elastic cell wall to generate a particular cell shape.

Graphical abstract

Results and Discussion

Morphogenesis of the new end is likely to be a purely mechanical process

Fission yeast cells serve as an attractive model for eukaryotic morphogenesis because of their highly regular and simple rod-shape and growth patterns [7]. These cells have a capsule-like shape with rounded cell ends, similar to E. coli and many other rod-shaped cells [1]. S. pombe are approximately 4 μm in diameter and grow by tip extension to 14 μm in length before dividing medially [8, 9]. Cells are encased in a fibrillar cell wall that is composed primarily of β-and α-glucans and galactomannan [10, 11]. For cytokinesis, an actin-based contractile ring guides the assembly of a cell wall septum, which is composed of a central primary septum (PS) disc flanked by two secondary septa (SS) [9, 12–15]. Following completion of the septum, the PS and edging are then digested away by endoglucanases for cell separation [16]. During cell separation, the daughter cells snap apart abruptly (“rupture” event), and then the resultant two new ends (NEs) adopt a rounded shape within minutes (Figure 1A and Movie 1). This shape change can be measured by the amount of bulging from original position of flat septum disc (s value in μm; Figure 1A). The s value rises and plateaus to s₁ = 1.43 ± 0.25 μm (n=8 cells) in about 10 min after the rupture (t = 0). While the old end (OE) begins to grow again soon after the rupture, NE does not start to elongate till generally about 40 min later, when cells initiate polarized cell growth at NE in a process known as “new end take off” (NETO).

Figure 1. Shaping of the new end cell wall and septum are independent of actin and wall synthesis.

A) During cell-cell separation, the process starts with a sudden break in the lateral cell wall (−1 to 0 s) followed by formation of a rounded new cell end (0–15 m). Movie 1. The plot shows bulging of the NE wall (as measured by the “s value”) over time. B) Deformation of the septum. In a cell with a complete septum, one of the cellular compartments was lysed by a laser cut to the cell surface (yellow asterisk). The septum forms a curved shape in ≤ 10 ms (within a single frame, arrowhead. See Movie 2.) C) Septum deformation is actin independent. Similar as in B, except one compartment of cells (yellow asterisk) was lysed using physical manipulation (see Supplementary Experimental Procedures). Prior to manipulation, cells were treated with 200 μM LatA (actin inhibitor) or DMSO (control). Cells were stained with blankophor to visualize the deformed septum. D) Cell-cell separation and new end formation are actin independent. Septated cells were treated with 200 μM LatA or DMSO at time 0 and stained with blankophor at 25 min. Brightfield and fluorescence images at indicated time points are shown. E) New end formation and cell separation are independent of wall synthesis. Septated cells were treated with 20 μg/ml caspofungin at time 0, and imaged in bright-field. Scale bars = 4 μm. In this work, all values with errors are MEAN ± SD.

An important unresolved question is whether shaping of the new end is accomplished through active cell wall remodeling that requires actin and polarity factors, or whether it is formed by a mechanical process [13, 14]. An initial indication that the rounded shape might be formed through a purely mechanical process was seen in laser microsurgery experiments [17]. In cells with a complete septum, we cut the lateral cell wall in one of the cellular compartments (Figure 1B and Movie 2). The cut compartment shrank and extruded cellular contents, while the other cellular compartment stayed intact. Interestingly, the septum bulged out towards the lysed part of the cell to form a rounded shape similar to that of a NE. Time-lapse imaging showed that the deformation occurred extremely quickly (in less than 10 ms) with an outward speed > 1μm/sec (3 orders of magnitude faster than the normal rate of cell growth). This shape change occurred similarly in cells treated with the 200 μM Latrunculin A (LatA) (Figure 1C), which leads to rapid depolymerization of all F-actin in minutes and cessation of growth [18–20]. Thus, this bulging of septum is actin independent. Similar deformation of the septum has also been observed in cell wall mutants [13, 14]. These initial observations suggest that the larger turgor pressure in the intact compartment is able to push out the septum cell wall into a curved shape.

We tested whether a similar mechanism shapes the NE during cell separation. We propose that before cell separation, the septum is initially flat because forces from the turgor pressure on both sides balance each other, but when the cells begin to separate, turgor pressure pushes out of the cell wall to form the rounded new cell end. This shape change involves an approximately 65% increase in the surface area at the new end. This increase is due to expansion of the new end cell wall, and not from flow of the lateral cell wall, as indicated by stable position of birthmarks on the cell wall. To test if this process requires actin, we treated septated cells with LatA and followed them by time-lapse imaging. 80% of the cells (n=30) divided and separated, with the NEs forming rounded shapes with similar extent and kinetics as control cells (n=13 cells; Figure 1D). We confirmed that the LatA treatment was effective in inhibiting F-actin and polarized cell growth (Figure S1). We tested the role of wall synthesis by treating septated cells with the β-glucan synthase inhibitor caspofungin [21]. At 20 μg/ml caspofungin, cells exhibit 5x slower tip growth, and many cells lyse. However, most septated cells continued to separate, and those that do formed rounded NEs with a similar extent and time scale as untreated cells (n=12 cells; Figure 1E). Staining with calcofluor and blankophor, which preferentially label newly deposited cell wall [8, 10, 22], further suggest that there is little or no wall growth on the NE during cell separation. These findings support a model in which turgor pressure simply deforms the flat cell wall to a rounded shape without wall growth.

The fission yeast cell wall behaves as an isotropic elastic material

To evaluate cell wall-shaping mechanism(s) in a quantitative manner, we next sought to determine the elastic properties of the cell wall and turgor pressure. To construct a mechanistic model we approximate the fission yeast cells as a capsule-shaped thin elastic shell inflated by internal turgor pressure (Figure 2A). A pressure difference, ΔP, stretches the cell wall to its “natural state”. Without pressure, the tensionless cell wall is in “relaxed state.” We define the expansion ratio in width as $\%R^{\ast }\equiv \frac{R_1-R_0}{R_0}\times 100$ and the expansion ratio in length as $\%L^{\ast }\equiv \frac{L_1-L_0}{L_0}\times 100$. R₁ and R₀ are the radii in natural and relaxed state respectively, and similarly for L₁ and L₀. We assume that cell wall is an elastic material with Young’s modulus Y_r in circumferential direction, Y_l in longitudinal direction, and that Poisson’s ratio is zero in both directions.

Figure 2. Determining the mechanical properties of the cell wall.

A) Model of the fission yeast cell wall as a thin elastic capsule that is inflated by turgor pressure in the natural state (intact cell), and shrinks to a relaxed state when pressure difference is lost. B) Left panel shows a bright-field image of an individual cell before and after lysis by laser microsurgery (Movie 3). Right panel shows a ghost cell (cell wall only). C) Measurement of expansion ratios. Cells were lysed by multiple approaches. Dimensions of individual cells were measured before and after lysis. Top graph shows expansion ratios of cell lengths ( $\%L^{\ast }=\frac{L_1-L_0}{L_0}\times 100$) and widths ( $\%R^{\ast }=\frac{R_1-R_0}{R_0}\times 100$). Bottom graph shows ratios between expansion ratios. For ghosts, the length expansion ratio cannot be measured since the prior geometry of the cells is not known. D) Dimensions of individual cells exposed to various sorbitol concentrations were measured. Graphs show experimental and theoretical osmotic response ratios for length ( $\%L\equiv \frac{L_1-L_0}{L_x}\times 100$) and width ( $\%R\equiv \frac{R_1-R_x}{R_x}\times 100$) where L_x and R_x are dimensions after the shrinkage. β is the water inaccessible volume fraction. E) Ratio between the response ratios. Scale bars = 4 μm.

Crude force balance equations yield the connection between the expansion ratios and the physical parameters of the system as (Suppl. Doc. Section 1):

$$\begin{array}{c}\frac{R_1-R_0}{R_0}\times 100=\%R^{\ast }\cong \frac{\mathrm{\Delta }{PR}_1}{Y_{r}t}\times 100\\ \frac{L_1-L_0}{L_0}\times 100=\%L^{\ast }\cong \frac{\mathrm{\Delta }{PR}_1}{2Y_{l}t}\times 100\end{array}$$

Since the thickness of the wall, t = 0.2 μm, and the radius of the cell, R₁= 1.92 ± 0.07 μm, are known, ΔP/Y_r and ΔP/Y_l can be found if one can measure %R* and %L* experimentally.

To measure these expansion ratios, we devised approaches to release turgor pressure. First, we locally cut the cell wall using laser microsurgery. Time-lapse imaging showed that cells shrink rapidly by approximately 17% in width and 9% in length (see Movie 3 and Figure 2B, left). This corresponds to expansion ratios of 20% ± 5% and 10%±3%, respectively. We also lysed cells by 1) micro-manipulation with a glass needle, 2) dehydration/rehydration and 3) post-osmotic-shock (see Supplemental Experimental Procedures). These approaches all produced similar expansion ratios (Figure 2C). The lysed cells, however, retain intracellular contents that may exert some internal pressure or force onto the cell wall. Therefore, we next isolated cell wall “ghosts” that lack intracellular structures by breaking yeast cells (Figure 2B, right; Figure S2A). Although we could not measure changes in cell length in these broken cell walls, the changes in cell width show that ghosts shrink slightly more than the lysed cells, indicating that the lysed cells still maintain some low level of internal pressure. The corresponding expansion ratio of the width in ghosts is 24% ± 5% (Figure 2C).

A significant outcome of our experiments is that the yeast cell wall is isotropic. For a cylindrical shell, %R*/%L* = 2Y_l/Y_r. If the cell wall has the same stiffness in circumferential and longitudinal directions (i.e. Y_r = Y_l = Y), then %R*/%L* is predicted to be 2. Our experimental measurements produced a ratio very close to 2 (Figure 2C, bottom graph). This behavior is different from that of the E. coli cell wall for instance, in which cell wall fibers are oriented circumferentially and are anisotropic in stiffness [23, 24].

Taking the expansion ratio of the ghosts for the width (24%), we found that

$$\frac{\mathrm{\Delta }P}{Y}=\frac{(\%R^{\ast })t}{R_1}=\frac{1}{40\pm 8}$$

This relationship indicates that the value of Young’s modulus is about 40 times cell turgor pressure (they both carry the same units). Equations stated for %R* and %L* are derived through crude force balance relations. To improve the accuracy of our result, we have included the higher order terms in our formulas by applying a continuum mechanical approach (Suppl. Doc. Section 1), which yields Y/ΔP = 33 ± 8.

Osmotic responses show that fission yeast is inflated by high MPa turgor pressure

Next, to further characterize the mechanical properties of the cells, we measured how cells shrink in different doses of sorbitol in the media (see Supplemental Experimental Procedures). To estimate the turgor pressure, we sought to determine the external molarity, c₀, required to shrink intact cells to the size of their ghosts (i.e, the relaxed wall state); see Figure 2D. Sorbitol shift curves show that on average, c₀ = 1.5M (=1.3 M sorbitol in the growth medium, YE5S). To estimate the pressure from this result, we applied an osmotic theory that takes into account the expansion ratios, the water inaccessible volume and the matrix potential of the solutions (see Suppl. Doc. Section 3). The assumptions of the theory are taken such that it would yield the minimal plausible value for the pressure. We found the turgor pressure (the osmotic pressure difference between inside and outside of the cell) as ΔP = 1.5 ± 0.2 MPa. Given our previous finding that Y/ΔP = 33±8, this yields the Young’s modulus (stiffness) of the cell wall as Y = 50 ± 10 MPa.

The response ratios of cells fit well with the theoretically calculated osmotic responses (Figure 2D). The data suggest a water inaccessible volume fraction of β = 0.22. The ratios between the response ratios (%R%L) in width and length are again close to 2, showing that the cell wall material is isotropic (Figure 2E).

To address a concern that results may be affected by cellular adaptation mechanisms to osmotic changes, we also analyzed gpd1Δ (glycerol-3-phosphate dehydrogenase) mutants, which are deficient in restoring turgor pressure during osmotic shifts [25, 26]. The osmotic response ratios of gpd1Δ mutants (Figure 1D and E) were similar to those of wild type cells.

We also used spheroplast formation as an alternative approach to estimate c₀ because of its importance for application of a reliable osmotic theory. Upon removal of the cell wall, spheroplasts remained intact at external molarities c₀ = 1.2 – 1.7M (Figure S2B-D). This result is consistent with the osmotic shift experiment which showed c₀ ≈1.5 M (Figure 2D).

Mechanical forces can account for the shape of the new end

Having estimated of the properties of the cell wall, we next embarked on testing and analyzing the mechanism for NE formation based upon the effects of turgor pressure on the cell wall. We developed a finite element simulation program based on non-linear continuum mechanics principles. Our algorithm relies upon the deformation of a given surface under a specified force field (or pressure). The surface is discretized with triangular elements, and the elastic energies are calculated through stretch as well as bending terms (Suppl. Doc. Section 2.1). We validated our program by comparisons to known analytic solutions (Suppl. Doc. Sections 2.2–5), and also verified our previous analytic work on expansion ratios (Suppl. Doc. Section 2.6). In simulations, we inflate a closed cylindrical shell (Suppl. Doc. Section 2.7). We assume that before cell separation, the septum is at a relaxed flat geometry, as opposed to the lateral wall, which is expanded under stress; buckling of the septum in sorbitol-treated cells supports this assumption (Figure S3A). We assume that the wall at the NE is also an isotropic material with a constant uniform elasticity and zero Poisson’s ratio, but could have a different thickness and elasticity. The shapes from simulations are dependent on Y/ΔP ratio and therefore are independent of ΔP. Note that we extract Y through Y/ΔP, which is found through experimentally measured parameters. Our simulations successfully yielded the rounded shape of the NE (Figure 3A).

Figure 3. Modeling new end formation.

A) Output of simulations in which turgor pressure causes bulging of the new end cell wall. Simulations are shown in which Y_s (Young’s modulus of SS) is treated as a free parameter while ΔP = 1.5 MPa and Y = 50 MPa. Graph shows the amount of bulging (s₁) plotted as a function of Y_s/Y for measured average SS thickness t_s = 100 nm. B) Simulation of a whole cell at varying values of pressure ΔP where Y = 50 MPa and Y_s = Y/2 = 25 MPa. C) Images of a single cell stained with Lectin-TRITC in intact, lysed, and ghost states, which were generated by successive micromanipulations. D) Averaged NE shapes (from C; n=8 cells) were fitted to an ellipse-rectangle combination and compared to simulation outputs (blue dots). Note that the NE in ghosts does not return to a completely flat geometry (Figure S3B) because of the shrinkage of the lateral cell wall, as also seen in the simulations. The slight discrepancies (maximum error < 0.2 μm) between the ghost profiles could be due to additional structural features between the septum and lateral wall not included in the simulations [12]. Scale bar=1 μm. E) Effect of sorbitol treatment on NE shape. Fully septated cells were treated with 1.3 M sorbitol at 1 or 15 min (arrows) after the time of rupture (t=0). Graph shows curvatures of the OE and NE from “shift at 15 m” experiment and simulations (circles; Figure 3B). F) NE bulging (s values) and cell widths as a function of time after sorbitol treatment. As indicated by their width, cells initially shrink and then re-inflate over 60 min to their original size without tip growth (Figure S3C). G) Relationship between NE bulging and cell width (as an indicator of turgor pressure). Data from experiments in Figure 3C,E or F are plotted and compared to simulation outputs from Figure 3B.

This modeling allowed us to estimate elastic properties of the NE cell wall simply by the extent of its bulging. Published electron micrographs show that the thickness of the secondary septum (t_s = 100 ± 20 nm) is about the half that of the lateral wall (t_s/t ≅ 0.5) [13, 14, 16, 27–31]. In addition, there may be chemical and structural differences between the two types of cell walls [14, 32]. We simulated the NE bulging for varyingvalues of Young’s modulus of the SS (Y_s) by using the values found for ΔP and Y. (Figure 3A). This plot showed that the best fit to the measured s₁ = 1.42 ± 0.15 μm (n=30 cells) is at around Y_s/Y = 0.48; standard deviations in s₁ and t_s measurements yielded error margins of 0.3 < Ys/Y < 0.7. This leads to the conclusion that Y_s ≅ Y/2; cell wall stiffness of the NE is about half of that of the lateral wall (i.e. twice as soft).

Next, we tested the effect of turgor pressure on the shape of the NE in simulations and experiments. In simulations, both cell width and the extent of NE bulging (s value) positively correlate with the increasing pressure (Figure 3B). We then compared these results with effects of altering the turgor pressure in a series of experiments. First, we used micromanipulation to measure the intact, lysed and ghost states of individual cells. Compared to the NEs of intact cells, the NEs of the corresponding ghosts bulged less (smaller s value) and exhibited a flatter shape (as shown by geometric fits with ellipses; Figure 3D and S3B; n=8 cells).

We further tested the effect of turgor pressure experimentally by adding sorbitol to the live, dividing cells (Figure 3E). First we added 1.3 M sorbitol to cells that have just divided (<1 min after rupture). The cells shrank as expected, and the process of cell separation halted with the NEs flat (Figure 3E; middle images). Thus turgor pressure is needed for cell separation and shaping of NE. However, in these experiments, one reason why the NEs are flat could be because the sister cells are still attached by the PS (see below). Hence, in another set of experiments, to eliminate the effects of the PS, we added the sorbitol just after the NEs have adopted a rounded shape (~15 min after rupture; Figure 3E, right images). Upon sorbitol treatment, the shape of the NEs changed from a rounded to a flattened shape. Interestingly, OEs maintained a rounded shape. Curvature decreased at NEs, while it increased at OEs (n=8 cells, bar plot in Figure 3E). These behaviors were as predicted in simulations that assumed that OE wall properties are similar to that of the lateral wall (Figure 3B,E). These findings demonstrate that the two ends of fission yeast cell are mechanically different.

Following the initial shrinkage, the cells in sorbitol gradually re-inflated over 60 min back to normal dimensions (Figure 3E, F). This is likely due to cellular adaptation to osmotic stress, which gradually restores the relative internal pressure [33]. During this recovery period, the width of the cells increased with increasing pressure, without any apparent tip growth (Figure S3C). Thus, these time lapse images allow us to determine the resultant cell morphology over a continuous range of turgor pressure. In Figure 3G we plot s values versus the width of the cells (as the measure of turgor pressure) from the sorbitol shift and the micromanipulation experiments and compared them to simulations; all show a similar, strong positive correlation. The agreement of our simulations with experimental data provides quantitative evidence for the role of turgor pressure in the shaping of NE.

Mechanical forces shape the septum during cell separation and septum bulging

During cell separation, the shape of the NE develops gradually over minutes. An additional factor governing this process is the PS, which acts as an adhesive that holds the sister cells together. The PS is a disc about 50 nm thick (1/4 the thickness of the lateral wall t_p ≅ t/4) [13, 14, 16, 27–31], however its mechanical properties are unknown. After initial rupture, the PS gradually shrinks in diameter (D), and the bulging of the SS (s₄ value) gradually increases as the NE adopts a rounded shape (Figure 4A–C, and Movie 5). In simulations (Suppl. Doc. Section 2.8), we assumed that the PS is mechanically infinitely strong and stiff in the transverse direction (perpendicular to the disc), but could be elastic in the lateral direction (direction along surface) with a uniform and constant Young’s modulus of Y_p. We plotted s₄ as function of D over a range of Y_p values (Figure 4C). The outputs agreed with the experimental data when Y_s = Y/2 and 0 ≤ Y_p ≤ Y. These findings suggest that the PS is an elastic material in the lateral direction with a stiffness < 2Y, and stretches along with the SS during cell separation. In contrast, simulations with Y_s = Y for any value of Y_p failed to fit to experimental data. Thus, these results validate our model further and explain the evolving morphology of NE during cell separation.

Figure 4. Modeling cell separation and septum bulging.

A, B) Images and simulations of cell separation. Experimental images of sister cells stained with blankophor (Movie 5) are compared to outputs from simulations where P = 1.5 MPa and Y = 50 MPa. The PS is assumed to be an elastic disc with Young’s modulus Yp that gradually decreases in diameter, causing the gradual deformation of the SS. Lateral cell wall thickness t ≈ 200 nm, SS thickness t_s ≈ 100 nm and the PS thickness t_p ≈ 50nm. C) Bulging of the SS (s₄) as a function of PS diameter (D). Graph compares experimental data (black dots and red points) with simulations for different values of Y_p and Y_s. The best fits to experimental data are simulations with Y_s = Y/2 and 0 ≤ Y_p ≤ Y. D) The deformation of the whole septum after laser ablation (as in Figure 1B). Inverse image of a blankofluor-stained cell and the output of a simulation. E) Comparison of experiments and simulations for NE formation (s₁) and whole septum deformations (s₅). The whole septum simulations are done with P = 1.5 MPa and Y = 50 MPa; Y_s = Y/2 and Y_p = 0,Y,2Y, and 5Y.

Finally, we applied our simulation to the laser cut experiments of fully septated cells (Figure 1B and 4D), in which the turgor pressure is thought to immediately deform the septum cell wall. In these cells, the deformation of the septum (s₅) was less than the one of the NE in normally dividing cells (s₁) (Figure 4E). We tested whether this shape difference could be explained by the difference between single layered wall of the NE versus the thicker triple-layered wall of the septum. In simulations (Suppl. Doc. Section 2.9), we examined septum deformation at Y_s = Y/2 at different values of Y_p. The case Y_p = Y produced the best fit (Figure 4E) which is consistent with the estimate from cell separation experiments (Figure 4C), providing an independent validation of our results. Thus, our findings using experiments and simulations in a variety of contexts demonstrate that a mechanically-based mechanism based upon turgor pressure and elastic properties of the cell wall can quantitatively account for shaping of the NE.

In summary, we develop a quantitative model for morphogenesis of a rounded cell end in a rod-shaped cell. Our findings suggest that the rounded shape is produced simply by turgor pressure inflating the elastic cell wall, even without cell wall growth. Our measurements of mechanical properties are generally on the same order of magnitude as previous ones in fission yeast and other fungi obtained through a variety of approaches [26, 34, 35]. One advance in this study is in the direct measurements of the relaxed state of the wall that allow us to determine critical parameters needed to apply a reliable osmotic theory. To adopt its rounded shape, the cell wall at the new end is 50% thinner and 50% softer than the lateral wall, and stretches 65% in area. These mechanical properties of the cell wall may explain why cell wall mutants lyse primarily at cell separation [36]. Turgor pressure may not only drive shape changes, but also contribute to the separation of the sister cells and their movement apart. Forces from turgor pressure also contribute to growth and shaping of the growing cell end, but this process is more complex as it involves addition and remodeling of the cell wall [1, 3, 26]. Turgor pressure is also thought to drive cell shape changes in certain plant cells, such as guard cells that regulate the opening and closing of stomatal pores [37]. It will be interesting to examine whether similar mechanically-based mechanisms are responsible for generating the rounded contours of new ends after cytokinesis in other cell types. Our studies illustrate how mechanical as well as molecular agents underlie cellular morphogenesis.