4. Sample chamber

To trace the cell cycle of fission yeast cells under a microscope, the surrounding temperature and humidity in the sample dish must be kept appropriately. Otherwise, the yeast cells would not divide well. We designed a sample chamber (Figure II-5) that enabled us to keep high humidity and constant temperature for yeast cells. The body of the chamber was made of aluminum. The inside of the chamber was partitioned into inner and outer spaces by a square wall (41 × 41 mm). The water-filled moat surrounded the sample dish and prevented the medium from drying. Two heating bars were inserted into the two holes made at the bottom of the chamber so that the temperature of the chamber was controlled by a PID

9

controller (Vertex, VT7226). The temperature was controlled to be 30 ± 0.5 ^oC at the sample and its surrounding, providing the best growing environments for fission yeast. The chamber was covered by an acrylic plate to make the chamber nearly a closed-system. Tubing for continuous air flow and a thermocouple were introduced through two holes on the cover.

10

Figure II-2. (a) Growth curves of fission yeast cells in YES and PMLU media at 30 ^o C.

(b) Raman spectra of pure YES and PMLU media taken with a 60-s exposure time.

(a) (b)

Figure II-1. A single colony on the YES plate after 3-5 day cultivation at 30 ^o C.

single colony

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Figure II-4. Evaluation of lateral (a) and axial (b) resolution of the laboratory-built confocal Raman microspectrometer. Black dot, observed Raman intensity; red line, best fit to the model function (Equation II-1).

(a) (b)

Figure II-3. Schematic of the laboratory-built confocal Raman microspectrometer used in this work. The apparatus consists of a He-Ne laser for Raman excitation, inverted microscope, imaging spectrometer and charge-coupled device (CCD) detector. To scan the sample and acquire Raman images, we combined a piezoelectric stage with the microscope stage.

12

Figure II-5. Side cross-sectional view (a) and top view (b) of a laboratory-built sample chamber (not to scale).

(a) Side cross-sectional view

(b) Top view

13

Chapter III

Data Analysis

14

III-1. Introduction of univariate and multivariate data analyses

The conventionally employed approach to construct Raman images is based on two dimensionally plotting the area intensity of a Raman band of interest assigned to a specific molecular species. Because this analysis depend on a single variable (i.e., wavenumber), it can be called univariate Raman imaging. The advantages of univariate Raman imaging are easy-to-perform, time-saving, and Raman-band specific. However, Raman spectra of biological samples intrinsically contain very complex and overlapped Raman bands within a spectral region of interest. This fact leads to difficulties in getting a Raman image of a single molecular species without contaminations of other species even when the Raman band looks isolated. As an example, we would like to show how complicated the Raman spectrum of fission yeast is. Figure III-1 is the typical lipid-rich Raman spectrum of a fission yeast cell.

Detailed assignments of the major Raman bands observed in this spectrum are shown in Table III-1. Obviously, the Raman band at 1655 cm^-1 is attributed to both the cis-C=C stretch of lipids and the amide I of proteins. Similarly, the Raman band at 1440 cm^-1 comes from the CH bending of the aliphatic chain of both lipids and proteins. There might still be several different Raman bands underlying the 1655 and 1440 cm^-1 regions and what is worse, many weak Raman bands of lipids, proteins, and other species severely overlap with each other in the 1000-1400 cm^-1 region. Thus, the overestimation of band area may arise due to heavily overlapped spectral information. In fact, only few bands can be assigned unequivocally according to our experience and previous reports [12, 16-19].

To overcome this problem inevitably encountered in analyzing cellular Raman spectra, multivariate data analysis, such as principal component analysis [20-26] (PCA), cluster analysis [21, 22, 26-29] and multivariate curve resolution [20, 22, 25, 30, 31] (MCR, also known as non-negative matrix factorization [32]), has recently been applied to Raman image data. Multivariate data analysis is capable of extracting maximum chemical information from

15

complicated Raman spectra without a priori knowledge about spectral characteristics and analyzes global data set instead of mapping the intensity of an individual band. As a result, we obtain the intrinsic spectrum and concentration distribution of each component. In the present work, we use MCR to analyze our time-lapse Raman spectra of a single living fission yeast cell during its cell cycle.

In what follows, we describe the procedures of univariate and multivariate data analyses in detail.

III-2. Singular value decomposition analysis

In order to provide a better growing environment to yeast cells during cell cycle, it is important to irradiate the sample with sufficiently low laser power and short exposure time.

However, Raman spectra acquired under such experimental conditions (laser power of 1 mW and exposure time of 1.5 s) show poor signal-to-noise ratio (S/N). To practically resolve this dilemma, we performed singular value decomposition (SVD) as a pretreatment for subsequent data analysis. This technique has been successfully used in numerous studies [12, 14, 19, 33-36] to reduce noises in Raman spectra and hence improve the S/N. SVD is a mathematical technique that factorizes an arbitrary 𝑚 × 𝑛 matrix 𝑨 into the product of three matrices as 𝑨 = 𝑼𝑾𝑽^𝑇. Here 𝑼 is an 𝑚 × 𝑛 column-orthonormal matrix, 𝑾 an 𝑛 × 𝑛 diagonal matrix of positive singular values, and 𝑽 an 𝑛 × 𝑛 orthonormal matrix. 𝑼 and 𝑽 represent the spectral and positional matrices, respectively. Only components of 𝑼 and 𝑽 having significantly large singular values were retained to reproduce matrix 𝑨, because other components with much smaller singular values contributed to the original data negligibly and can be regarded as noises. The matrix 𝑨 was then reconstructed by using the components of 𝑼 and 𝑽 associated with large singular values. The number of singular values retained in this reconstruction was typically less than 10. The main criterion for determining how many components were taken into account was whether or not the spectral component of 𝑼

16

corresponding to a particular singular value showed definite Raman features. The SVD was computed in Igor Pro (WaveMetrics) using LAPACK routines. Figure III-2a illustrates how well SVD denoising worked. Space-resolved Raman spectra taken at five different locations in a fission yeast cell are compared before and after the SVD. It is clear that the SVD did good job of dramatically reducing noises. As compared in Figure III-3b, the Raman image constructed for the 1655 cm^-1 band from the raw data (without SVD) is featureless due to noisy spectra, but the image constructed from the SVD-analyzed data shows clear contrast.

III-3. Univariate data analysis

The univariate data analysis simply uses the area intensity calculated under the band contour of a Raman band of interest. The area intensity between the band contour and a baseline connecting the two ends of an interval chosen to include the whole band was calculated (Figure III-3). Here, the selected region was chosen as narrow as possible (< 10 cm^-1) to avoid spectral overlap of unexpected molecular species. Curve fitting was not used for this purpose due to the low S/N with extremely low power and short exposure time in our experiment. The integrated Raman intensities so obtained at every position (XY on the mapping region) were combined to construct a two-dimensional map of the Raman intensity distribution, namely, univariate Raman image of the band.

III-4. Multivariate data analysis

For the multivariate analysis, we performed multivariate curve resolution (MCR) to analyze a four-dimensional data matrix (XY on the image plane (spatial), spectral and temporal dimensions; see Figure III-4) by the software (nmf-11, Pylone) which was developed at Tokyo specifically for spectral imaging applications. To be able to deal with four-dimensional data, we unfolded the four-dimensional data matrix into a two-dimensional

17

array. One dimension should correspond to the spectral dimension (pixel or wavenumber);

thus the non-negative matrix factorization constrains each resolution as an individual component [37]. The other dimensions were merged to be a single dimension. In MCR, given an 𝑚 × 𝑛 non-negative data matrix A, a low-rank approximation of the matrix A is sought for by solving the problem [37, 38]:

𝑨 ≈ 𝑾𝑯 (III − 1) with non-negativity constrains 𝑾 ≥ 𝟎 and 𝑯 ≥ 𝟎. In the present work, 𝑾 is an 𝑚 × 𝑘 matrix whose columns correspond to spectra and 𝑯 is a 𝑘 × 𝑛 matrix whose rows represent spatiotemporal concentration profiles. By reorganizing the 𝑯 matrix, multivariate Raman images can be obtained. The parameter 𝑘, which specifies the number of components that consist of the data, should be given by the user in advance. The most suitable value of 𝑘 was found to be k = 6 in the present case. The optimal solutions of 𝑾 and 𝑯 are obtained by solving alternating least-squares (ALS) problems of equation III-1 so that the Frobenius norm

‖𝑨 − 𝑾𝑯‖_F² is minimized.

Here, we briefly describe the MCR procedure adopted in this work, which consisted of the following steps:

(1). The MCR software requires a two-dimensional matrix as input. Thus, we need to rearrange a four-dimensional matrix which was constructed by the data cube at each measurement time (Figure III-4) into a two-dimensional matrix. Because spectral information is one of our primary concerns, the wavenumber dimension was treated as a single variable.

By doing so, we generated the data matrix 𝑨.

(2). SVD-based initialization [39] was utilized to generate initial guesses for 𝑾 and 𝑯 in this case. Although random initialization is also available in our software, it often results in falling into a local minimum [39]. The number of components was set to be 𝑘 = 6, which yielded the best resolution of polysaccharide, lipid, and protein components.

(3). Additional constraint L1-norm (lasso regression [40]) was further added to ALS

18

optimization of 𝑾 and 𝑯. An L1 penalty term of α² = 0.0095 was added to obtain sparser solutions as

(𝑾^T𝑾 + α²𝑬)𝑯 = 𝑾^T𝑨 (III − 2) and

(𝑯𝑯^T+ α²𝑬)𝑯 = 𝑯𝑨^T (III − 3) where 𝑬 is a 𝑘 × 𝑘 matrix all of whose elements are unity.

(4). Repeat step (3) until ‖𝑨 − 𝑾𝑯‖_F² converges. The number of iteration was to be 4000, ensuring that ‖𝑨 − 𝑾𝑯‖_F² converged to a sufficiently small number.

Last, we discuss how well the matrices 𝑾 and 𝑯 reproduce the matrix 𝑨. For the unfolded data matrix 𝑨 (a 790 × 6885 matrix), we calculated the normalized residual matrix 𝑹 (Figure III-5a) using the following equation:

𝑅𝑖𝑗 = ^{�𝐴𝑖𝑗−(𝑾𝑯)}_𝐴 ^𝑖𝑗�

𝑖𝑗 (III − 4) where 𝑅_𝑖𝑗 represent the normalized residue at row i and column j. Besides horizontal stripes indicating the locations of intense Raman bands, the 2D plot shows no particular distribution pattern and residues seem to be randomly distributed. Figure III-5b shows a histogram of all fitting residues, which are less than 10%. This result indicates that the original data is well reproduced by the present MCR analysis. We also compare a reproduced spectrum with the corresponding original spectrum (SVD-treated) at a randomly selected position (Figure III-5c). The two spectra are almost identical with less than 5% residues.

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Table III-1. Band assignments for Raman spectra of single living S. pombe cells.

Wavenumber (cm^-1) Assignment

1655 cis-C=C stretching of the unsaturated lipid chains Amide I mode of proteins

1602 Not yet assigned. "Raman spectroscopic signature of life"

1440 CH2 scissoring and CH3 degenerate deformation 1340 CH bending of the aliphatic chain of proteins 1301 In-phase CH2 twisting mode

1260 C=C-H in-plane bend of the cis- –CH=CH– linkage Amide III mode of proteins

Ring breathing of the phenylalanine residues 852

783

“Tyrosine doublet” (Fermi resonance of a ring-breathing vibration and the overtone of an out-of-plane ring-bending vibration of the tyrosine residues)

Cytosine vibration and/or −O−P−O− symmetric stretching

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Figure III-1. Typical lipid-rich Raman spectrum of fission yeast cells with 633 nm excitation. Some Raman bands, e.g. at 1655, 1440, 1260, and 1154 cm^-1, show a complicated feature composed of lipids/proteins and other molecular species.

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(a)

Figure III-2. (a) Typical space-resolved Raman spectra of a single living S. pombe cell acquired with an exposure time of 1.5 s and laser power of 1 mW. A–E denote the positions in the cell at which the Raman spectra were recorded. The SVD-treated spectra (right) exhibit much higher S/N than the raw data (left). (b) Raman images for the 1655 cm⁻¹ band constructed from the raw (left) and SVD-analyzed (right) data, respectively. It is clear that SVD analysis makes it possible to construct high-contrast Raman images even with low excitation power and short exposure time.

raw data SVD-analyzed data

raw data

(b) SVD-analyzed data

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(a) (b)

Figure III-3. (a) Baseline connecting two ends for the Raman band at 1655 cm^-1. The blue-shaded area is used as the Raman intensity of this band at a given pixel in the univariate Raman image. (b) Univariate Raman image of the 1655 cm^-1 band. A rainbow color scale displays the highest Raman intensity with red and the lowest with purple.

Figure III-4. Diagrammatic representation of the unfolding of overall four-dimensional spectral data into a two-way array that facilitates multivariate data analysis. X and Y denote positions in the image plane, and denotes the spectral dimension. The three dimensions (two spatial and one temporal dimensions) are combined to be a single dimension.

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(a)

(b) (c)

Figure III-5. (a) 2D plot of the normalized residual matrix 𝑹 (see equation III-4).

(b) Histogram of all fitting residues calculated at all pixels. (c) Comparison of a typical SVD-treated Raman spectrum (blue curve) and the corresponding MCR fitted spectrum (red curve). Also shown is their difference spectrum.

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Chapter IV

Results and Discussion

25

IV-1. Cell cycle of fission yeast cells under the microscope

Figure IV-1 schematically shows the cell cycle of S. pombe. The optical images showing the morphology of the S. pombe cell in each phase during the cycle are those captured in our Raman imaging experiment (see below). The S. pombe cell cycle consists of four different phases called the M (mitosis) phase, G1 (gap-1) phase, S (synthesis) phase, and G2 (gap-2) phase. It is known that S. pombe has a very short G1 phase under normal vegetative conditions.

This fact makes the G1 phase of S. pombe unclear. Thus, we use the notation G1/S for the two indistinguishable phases. In the present work, we randomly chose a single yeast cell that stayed in G2 phase and started an in vivo long-term measurement with the Raman microspectrometer equipped with the laboratory-built chamber (see Chapter II). The time zero is defined as the instance when we put a single colony of S. pombe into PMLU medium. At 1 h, we start to measure a randomly chosen single yeast cell in the sample dish. Once an imaging measurement is done, laser illumination is blocked until a next measurement. We are sure that the cell initially stayed in the G2 phase, because we observe elongation of the cell along the cell polarity axis by a factor of ∼1.2 on going from 1 to 4h, which is a common biological behavior in G2 phase. The cell cycle progresses from G2 to M phases and the cell prepares for a coming cell division in the first four hours (1-4 h). At 6 h, a septum is already formed to segregate the cell into two compartments, indicating that the cell is in the G1/S phase. By 6.5 h, the cell divides completely and splits into two daughter cells. Subsequently, two daughter cells should enter a new cell cycle (G2 phase again). To clearly present the stages in the cell cycle, we also performed experiments using nucleus-labeled fission yeast cells with GFP, but they were not successful. A possible reason for the failure might be that the nucleus-labeled fission yeast cells seem to be more photolabile than unlabeled cells and be strongly affected by laser illumination during the cell cycle.

It is worthy to discuss the behaviors of our selected yeast cell after 6.5 h. We tentatively

26

think that the selected fission yeast cell enter a new cell cycle after the mother cell divided into two daughter cells. They each are supposed to start new cytoplasmic division after 6.5 h.

However, as shown in the optical images of Figure IV-2, the daughter cells exhibit little morphological change, suggesting that the conditions are not favorable for the yeast cells to divide. Singh et al. [41] showed that budding yeast cells cannot sustain even with 400 µW of 632.8-nm laser radiation if it lasts for a long period of time. Thus, we presume that the fission yeast cells divide only once due to 1 mW laser irradiation in our experiments. The fission yeast cells may fall into G0 (gap-0) phase without morphological changes. Even in such a case, changes of molecular compositions are still progressing to overcome the external stress. As discussed in the next section, our results do reveal that the molecular compositions and distributions continuously vary even while there is little morphological change in optical images.

IV-2.Univariate Raman images

Using the univariate analysis described in Chapter III, 10 time-lapse univariate Raman images of a single S. pombe cell during the cell cycle are constructed at the Raman shift of 1655, 1602, 1440, 1340, 1301, 1260, 1154, 1003, 852, and 348 cm^-1 within as narrow as possible selected bands (Figure IV-2). We classify these 10 Raman images into three groups according to their assignments. The three groups are lipids, proteins, and admixtures of lipids, proteins, and other molecular species.

IV-2-1.Group of lipids

Univariate Raman images of lipids include those for the 1440 and 1301 cm^-1 Raman bands. As we discussed in Chapter III, the Raman band at 1440 cm^-1 comes from the CH2

scissoring (1439 cm^-1) and CH3 deformation (1456 cm^-1) of both lipids and proteins. How then can we obtain a Raman image that is solely attributed to lipids? Figure IV-3 shows a pair

27

of lipid-rich and protein-rich Raman spectra of fission yeast cells. The peak position of the CH bend in the protein-rich spectrum (Figure IV-3a) is at 1451 cm^-1, which is different from that in the lipid-rich spectrum, i.e., 1440 cm^-1 (Figure IV-3b). This result is consistent with the fact that proteins have a larger CH3/CH2 ratio than lipids [42]. As long as we carefully choose a narrow region around 1440 cm^-1 for intensity integration (recall Chapter III), we can extract a Raman image of lipids from contaminated bands. Compared to the 1440 cm^-1 Raman band, the 1301 cm^-1 Raman band originates predominantly from CH2 in-phase twist of lipids, so a pure Raman image can be constructed easily.

IV-2-2.Group of proteins

The group of proteins contains the 1003 and 852 cm^-1 Raman bands. Their origins are exclusively proteins. The sharp band at 1003 cm^-1 is assigned to the ring breathing mode of the phenylalanine residue in proteins. The 852 cm^-1 band is one of the tyrosine doublet, which arises from a Fermi resonance between the ring breathing fundamental and the overtone of an out-of-plane ring bending vibration of tyrosine residues [43].

IV-2-3. Group of admixtures of lipids, proteins, and other molecular species

Here we discuss the last group consisting of the 1655, 1340, 1260, and 1154 cm^-1 Raman bands. It is well known that the peak positions of the amide I band (1657 cm^-1) and the C=C stretching of the unsaturated lipid chains (1655 cm^-1) are almost identical [44]. Thus, those severely overlapped Raman bands cannot be easily resolved even by using the same method as for the 1440 cm^-1 Raman bands. The 1340 cm^-1 Raman band is located at a shoulder of a broad band around 1300 cm^-1 which include a lot of complicated species, suggesting that the contributions to the 1340 cm^-1 image are very complicated. The Raman images of the weak band at 1154 cm^-1 may also suffer from large uncertainties. Furthermore, the Raman bands of crystalline sodium polyphosphate at 1162 cm^-1 [17] and the skeletal C-C stretch modes in the

28

1000-1150 cm^-1 region [45] may interfere with the 1154 cm^-1 Raman images.

Despite the spectral contaminations for those complicated bands, we can still separate those admixtures, to some extent, into lipid-dominated and protein-dominated contributions.

The cis-C=C band at 1655 cm^-1 of lipids is usually stronger than the amide I band at 1657 cm^-1 in yeast cells. Thus, the lipid-dominated Raman images at 1655 cm^-1 coincide with other lipids Raman images. However, more green patterns that fill up the entire yeast cell are observed in the Raman images at 1655 cm^-1. It implies that proteins also contribute slightly to the Raman images at 1655 cm^-1. Crystalline sodium polyphosphate is known to appear in yeast cells under conditions of starvation [17]. However, in the present work, the treatment with fresh medium provides sufficient nutrition and prevents the yeast cells from starvation.

The interference from this band should thus be small. Skeletal C-C stretch modes are very broad so that we can remove this contribution by using a well-selected baseline. Thus, the

The interference from this band should thus be small. Skeletal C-C stretch modes are very broad so that we can remove this contribution by using a well-selected baseline. Thus, the