3.1. Sum of z-Sections and 0.5 µm z-Spacing Yield Practical Quantitative Measurements of Microtubules
Limitations in quantifying fluorescent intensities in living cells include photobleaching and sample movement away from the focus plane. Photobleacing, due to time-dependent exposure to excitation lights, contributes error to the intensity measurement particularly at later time points. Photobleaching can be largely minimized with efficient and sensitive imaging methods, such as the spinning disk confocal microscope coupled to a high quantum yield, high signal-to-noise cooled CCD camera [
20]. Sample movement away from the focus plane, due to the dynamic nature of subcellular structures, also contributes error to the intensity measurement, i.e., intensity fluctuates if an object such as a MT moves away from the focus plane. In theory, performing fast and fine optical z-sectioning through the cell will capture the in focus plane. In practice, there is a sweet spot speed and z-section sampling which should give both low intensity error and high spatial-temporal resolution.
We measured the point spread function (PSF) of our optical set-up and derived the fluorescent intensity errors due to sample movement (see Methods). From the measured PSF, we derived the intensity error due to sample movement out of the focus plane for a 5-µm-thick object sampled at 0.1, 0.2, 0.5, and 1 µm z-spacing. Maximum intensities were observed when an object was in focus. Minimum intensities were observed when an object was exactly half-way between two focused planes. The intensity error increased from 1% at 0.1 µm, to 3.5% at 0.2 µm, to 20% at 0.5 µm, and up to 60% at 1 µm z-spacing (
Figure 1A). We next derived the intensity error of sums of all planes for the different z-spacing. The intensity error due to sample movements decreased to 0% when all frames at each 0.1, 0.2, or 0.5 µm z-spacing were summed (
Figure 1A). Therefore, the sum of all z-planes yields more precise fluorescence quantification.
We next determined the z-spacing as a function of temporal resolution. The percent intensity error follows the function:
where
E is the intensity error (%),
z is the z-spacing (µm), and
IFocus and
IUnfocus are the intensity at the focus and out-of-focus plane. The total number of z-planes in a stack and with that the total acquisition time required to capture a given thickness, decreases with increasing z-spacing as follows:
where
T is total time,
D is the thickness of the sampled object (µm), and
z is the z-spacing (µm). We defined the intersection between the two curves of the functions
E(z) and
T(z) as the optimal imaging condition where intensity error and acquisition time are minimized.
We found that in the context of our microscope set-up, the practical z-spacing is 0.5 µm (
Figure 1A,C), corresponding to 11 optical sections covering 5 µm thickness (fission yeast is 4 µm thick). We conclude that: (1) the smaller the z-spacing, the less intensity error would be generated; (2) the sum of all z-planes at each z-spacing yields an intensity measurement with less error than maximum-projection images; and (3) a z-spacing of 0.5 µm is the practical spacing for quantitative fluorescence measurements. In other words, 0.5 µm z-spacing is the practical choice for which the intensity error is small and the stack acquisition time is short.
We also quantified the photobleaching resulting from long-term imaging (see Methods). The GFP-Atb2 signal decreased from 150 a.u. to 90 a.u., or ~40%, over a period of 30 min (
Figure 1D). The mean intensity of cytoplasmic MTs is ~30 a.u. (see
Figure 2). This indicates a potential counting error of ~2 MTs at the end of 30-min imaging. This error is within the range of spindle signal variation (see
Figure 3 and
Figure 4). In addition, photobleaching of GFP-Atb2 is not expected to affect the MT length measurement.
3.2. Microtubule Fluorescence is a Direct Measurement of Microtubule Number
We imaged wild-type living fission yeast cells expressing GFP-Atb2 at the practical settings for quantitative measurements of microtubules throughout the cell cycle (see
Section 3.1 above). Cells were imaged from the interphase to mitosis transition (G
2 to M) to capture all classes of microtubule structures, i.e., interphase MTs, spindle MTs, astral MTs, and PAA microtubules. A montage of a representative wild-type cell undergoing spindle elongation at mitosis, and the diverse MT structures—interphase, astral, PAA microtubules, and the spindle structure—is shown (
Figure 2A).
The interphase, astral, and PAA microtubules were very dynamic, and showed similar fluorescent intensities. For each cell, we quantified the intensities of the interphase, astral, and PAA microtubule structures (see Methods). Line scans revealed that interphase, astral, and PAA MTs have similar fluorescent signal intensities throughout their long axis (
Figure 2B). While these three different classes of MTs occurred at different times during the cell cycle, they showed similar mean ± standard deviation (s.d.) intensities of 31 ± 12 a.u. (interphase MTs), 35 ± 13 a.u. (astral MTs), and 36 ± 11 a.u. (PAA MTs) (
Figure 2C,D). Because fluorescent intensity is a function of polymer number, our results indicated that interphase, astral, and PAA microtubule bundles all have a similar number of MTs. Further, the intensities of these different classes of MTs were always the lowest intensities observed in the cell, as compared to the spindle intensities, indicating that they represented the smallest, or one fluorescence unit of MT number. We previously reported that interphase and astral MT bundles are organized with their minus ends crosslinked at the cell middle or the spindle pole body (SPB), respectively, by the protein Ase1, and their dynamic distal plus ends interacting with the cell cortex [
28]. In addition, Hoog et al. showed by electron microscopy (EM) that each fission yeast interphase MT bundle is composed of a few distinct MTs [
21]. In particular, the distal plus ends facing opposite cell tips are generally composed of a single MT [
21]. Thus, our MT intensity of ~34 a.u. (the average of interphase, astral, and PAA MT signal) likely represents 1 distinct MT and serves as a calibration for all other MT signals. Each interphase MT, astral MT, and PAA MT structure are thus primarily composed of single MTs crosslinked at their minus ends.
3.3. Spindle Elongation Exhibits 3-Phase Elongation Kinetics and Dynamic Microtubules
We imaged 15 mitotic events. Fission yeast mitosis is remarkably consistent [
14,
28], showing the typical three-phase spindle elongation kinetics, representing pro-metaphase, metaphase-anaphase A, and anaphase B (
Figure 3A). We measured the complete spindle intensity through time. For each time point, the measured MT fluorescent intensity along the spindle length was normalized to the fluorescent unit representing one MT (34 a.u. is the average intensity of the individual interphase, astral, and PAA MTs). The normalization procedure converted absolute MT fluorescent intensities into relative MT numbers along the length of the spindle. For example, for the cell shown in
Figure 2A, at the 6.5 min time point (pro-metaphase), the spindle reached 2 µm in length, and had a maximum intensity of 500 a.u., which when normalized by dividing by 34 a.u. yielded 16 MTs (
Figure 3B). Effectively, all intensities at all spatial-temporal points can be normalized in this way to give relative measurements of MT numbers.
Figure 3A,B illustrates the dynamic changes of spindle MT numbers at different spindle elongation phases. Pro-metaphase was characterized by a growing spindle with bi-modal MT distribution, where the middle region of the bipolar spindle showed a decrease in MT number compared to the regions at the SPBs (
Figure 3B, time = 6.5 min). We interpret this exclusion zone as the zone of MT and chromosome interaction. Meta-anaphase A showed a similar profile of spindle MTs compared to pro-metaphase (
Figure 3B, time = 15 min). However, we began to observe a decreased number of MTs at the spindle pole region. Anaphase B clearly showed the spindle midzone region, which had the highest spindle MT number due to overlapping MTs emanating from opposite spindle pole bodies (SPBs) (
Figure 3B, time = 26 min). Our conversion of fluorescent intensities into MT number, and the subsequent interpretation of MT organization, are only possible with EM foundational work describing the interphase MT and spindle structures of fission yeast [
20,
21,
23].
3.4. Microtubule Number Decreases, but Total Microtubule Polymer Length Remains Constant During Mitosis
We then measured the complete spindle MT number throughout mitosis. During the pro-metaphase (phase 1), ~12 MTs emanated from each SPB at the onset of spindle formation to form the spindle structure. The number of MTs at each SPB increased to the maximum 23 ± 6 at the end of the pro-metaphase (
Figure 4A,D). Microtubule numbers emanating from both SPBs were nearly identical throughout mitosis. During metaphase-anaphase A (phase 2), the spindle MT number began to decrease from the maximum found at the end of prophase to 17 ± 3 at the end of metaphase-anaphase A (
Figure 4A,D).
During anaphase B (phase 3), the number of MTs emanating from the two SPBs continued to decrease. At the moment just before spindle breakdown at the end of anaphase B, there were approximately 4 ± 1 MTs emanating from each SPB (
Figure 4A,D). The MT number found at the spindle midzone follows a similar trend as MTs emanating from the SPBs (
Figure 4B). However, at the start of anaphase, the midzone MT number began to increase compared to the MT number at the SPBs, a clear indication of the overlapping MTs indicative of the midzone (
Figure 4B).
Figure 4D summarizes the number of MTs found in the dynamic spindle of wild-type fission yeast.
Noteworthy, two previous EM studies reconstructed the number and lengths of spindle MTs for wild-type fission yeast with spindle lengths ranging from 1–11 µm [
20,
23]. We overlaid these static data points onto our dynamic measurements and found an exact match to the Ding et al. data (
Figure 4A,B, red dots). However, the Ward et al. data were generally lower than those of Ding et al. and ours (
Figure 4A,B, yellow dots). We conclude that our fluorescent imaging and analysis method has the ability to quantify individual MTs when cross-referenced with EM data, even when the MT number in a bundle is not spatially resolved by optical microscopy. Further, our quantitative fluorescent imaging method extends on current EM methods and enables a direct read out of MT number and distribution in individual living cells with high temporal resolution.
3.5. Tubulin Concentrations in Interphase and Mitotic Cells
What is the αβ-tubulin concentration in a living fission yeast cell? Total tubulin subunits in a cell are composed of the cytoplasmic fraction plus the fraction that has incorporated into the MT polymer. As we now have a method to quantify the polymerized fraction, we should be able to use the fluorescent intensity of the whole cell to derive the soluble fraction, i.e., I
Cell = I
MT + I
Soluble. As fission yeast has a closed mitosis, where the nuclear membrane does not breakdown, the soluble tubulin indicates tubulin not in MT form, in the whole cell irrespective of cytoplasmic or nucleoplasmic localization. We measured the fluorescent intensities I
Cell and I
MT of mitotic wild-type cells as boxed regions around the whole cell and spindle (see Methods). We found that the total fluorescent intensity of the cell, I
Cell, remained constant throughout mitosis during metaphase and anaphase, and the average ratio of cell intensity to spindle intensity, I
Cell/I
MT, was 3.88 ± 0.58, i.e., the total cell has ~4× more total tubulin subunits than that of the spindle alone. Because each spindle has 48 ± 5 µm of total MTs (
Figure 4C), each cell, therefore, has the equivalent of 186 ± 15 µm (3.88 × 48 µm) of MTs. Given that a MT has 13 protofilaments, and each 1 µm of MT has 1625 αβ-tubulin subunits, then each fission yeast cell has 3.0 ± 0.2 × 10
5 αβ-tubulin subunits (186 µm × 1625 subunits/µm) at mitosis. We calculated the average volume of these cells to be 94 ± 13 µm
3 (see Methods). Therefore, the molar concentration of αβ-tubulin, the fission yeast cell during mitosis, is 5.35 ± 0.55 µM, of which three-quarters is soluble tubulin and one-quarter is in the MT polymer in the spindle (
Table 1).
Fission yeast has a characteristic unipolar growth during G
1-S, where cells are relatively short after exiting cytokinesis and septation, and grow at their old end. At G
2, fission yeast switches to bipolar growth, a process termed new-end-take-off (NETO). The length of fission yeast serves as a good indicator of cell cycle stages [
29]. Throughout interphase, fission yeast has an average of 4 ± 1 discrete bundles of MTs, with each bundle having an overlapping medial region [
6,
8,
28,
30]. We measured the average tip-to-tip bundle length to be 5.3 ± 1.6 µm and 8.4 ± 2.9 µm, and the average overlapping region to be 1.0 ± 0.4 µm and 1.2 ± 0.8 µm, for pre- and post-NETO interphase cells, respectively. In a similar fashion to the mitotic cells, we measured the molar concentration of αβ-tubulin, the fission yeast cell during interphase. We found that the total fluorescent intensity of the cells, I
Cell, increased throughout interphase. However, the ratio of cell intensity to MT bundle intensities remained constant throughout G
1-S and G
2, with the average ratio of cell intensity to MT bundle intensities, I
Cell/I
MT, as 2.85 ± 0.80 for G
1-S and 2.96 ± 0.27 for G
2 interphase cells, i.e., the total cell has ~3× more total tubulin subunits than that of the combined interphase MT polymers (
Table 1). By the same reasoning used to calculate tubulin concentrations for mitotic cells, pre-NETO interphase cells have an average MT polymer length of 23 ± 4 µm and post-NETO cells have an average MT polymer length of 41 ± 5 µm. Thus, G
1-S interphase fission yeast cells have 1.06 ± 0.30 × 10
5 αβ-tubulin subunits, and a total tubulin concentration of 4.04 ± 0.24 µM; and G
2 interphase cells have 1.97 ± 0.24 × 10
5 αβ-tubulin subunits and total tubulin concentration of 3.83 ± 0.32 µM. These values are similar to previously reported values using quantitative mass spectrometry [
19,
22]. We conclude that interphase cells maintained a relatively constant molar concentration of tubulin, of which two-thirds is in αβ-tubulin form in the cytoplasm and one-third is in MT polymer form (
Table 1).
We note that our imaging method systematically underestimates the interphase cellular αβ-tubulin concentrations, but not the mitosis cellular tubulin concentrations. Careful EM reconstruction of the fission yeast mitotic spindles showed that all spindle MTs emanated from the SPBs [
20,
23]. As our fluorescence measurement of spindle MTs matched those of EM data from Ding et al. (
Figure 4A,B), our fluorescence measurement for spindle MTs is therefore exact. In contrast, there are satellite-MTOCs that are recruited to the lattice of a pre-existing interphase MT, where they nucleate new short MTs [
31,
32,
33]. In addition, EM tomography of interphase fission yeast MTs also showed short MTs attached to the primary MT [
21]. These findings suggest that our optical method would fail to detect sub-resolution short MTs, i.e., MTs shorter than ~0.3–0.5 µm. Sub-resolution short MTs comprise ~25% of the total MT polymer length at interphase [
21]. This suggests that we may have underestimated the interphase cellular tubulin concentrations by ~33% (25% short MTs /75% long MTs = 33%), i.e., instead of the measured ~4 µM, the correct interphase concentration may be ~5.32 µM (4 µM × 1.33), or equal to our measured mitosis concentration of 5.35 ± 0.55 µM (
Table 1). This implies that the total cellular tubulin concentration remains constant throughout the cell cycle, and the transition from interphase to mitosis sees an up regulation in total MT polymer.