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Estimation of population effects in synchronized budding yeast experiments Antti Niemist¨oa , Tommi Ahoa,b , Henna Thesleffb , Mikko Tiainenb , Kalle Marjanena , Marja-Leena Linnea , and Olli Yli-Harjaa a Tampere

University of Technology, Institute of Signal Processing, P.O. Box 553, FIN-33101, Tampere, Finland b MediCel Ltd., Haartmaninkatu 8, FIN-00290, Helsinki, Finland ABSTRACT

An approach for estimating the distribution of a synchronized budding yeast (Saccharomyces cerevisiae) cell population is discussed. This involves estimation of the phase of the cell cycle for each cell. The approach is based on counting the number of buds of different sizes in budding yeast images. An image processing procedure is presented for the bud-counting task. The procedure employs clustering of the local mean-variance space for segmentation of the images. The subsequent bud-detection step is based on an object separation method which utilizes the chain code representation of objects as well as labeling of connected components. The procedure is tested with microscopic images that were obtained in a time-series experiment of a synchronized budding yeast cell population. The use of the distribution estimate of the cell population for inverse filtering of signals that are obtained in time-series microarray measurements is discussed as well. Keywords: budding yeast, cell cycle, synchronization, microarray, time-series, object separation, inverse filtering

1. INTRODUCTION The microarray technique, introduced in 1995, has spawned a new paradigm in molecular biology and biomedical sciences.1–3 It is presently the most advanced technique for measuring and monitoring gene expression levels of thousands of genes in parallel. Gene expression is an important factor determining the state of a cell, and accurate measurements of gene expression levels are thus needed. The goals of different microarray studies are various. For example, many microarray studies aim at profiling or classifying genes. In such studies the goal can be, e.g., to identify genes that are involved in specific types of cancer.4–6 Typically comparisons are made between two different types of tissue (e.g. healthy and cancerous) without paying attention to the time dimension. However, while these studies are of great clinical importance, some of the recent studies have concentrated on the dynamic modeling of genetic networks. In such studies, it is required that the gene expression levels of specific genes are observed as a time-series with a relatively short sampling interval over a relatively long period of time.7, 8 This can be achieved by time-series microarray measurements. The purpose of this paper is to develop an image processing procedure which can be used in connection with time-series microarray measurements of cell cycle dependent signals. These signals are sequences of gene expression levels of cell cycle regulated genes. In mathematical terms, cell cycle regulation means that the expression profile of a particular gene is periodic and the length of the period is equal to the length of the cell cycle. When cell cycle dependent signals are measured, the cell population is set in synchrony by using, e.g., chemical treatments (see, e.g., Ref. 9). To understand synchrony, we must first define a concept called cell cycle. One definition is that a cell cycle is a series of events which enable a cell to grow and to divide into parent and daughter cells that contain the same genetic material. Ideally, in a synchronized cell population all cells are exactly in the same phase of the cell cycle, and the distribution of the cell population is in signal processing terms an impulse.10 Further author information: A.N.: E-mail: antti.niemisto@tut.fi ___________________________ Copyright 2003 SPIE and IS&T. This paper was published in Image Processing: Algorithms and Systems II, Proceedings of SPIE, vol. 5014, and is made available as an electronic reprint with permission of SPIE and IS&T. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.

number of cells

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1

phase of the cell cycle

Figure 1. The distributions of two hypothetical cell populations. The distribution on the left (solid line) is of a relatively synchronous cell population, whereas the distribution on the right (dashed line) is of a relatively asynchronous population.

At present, microarray measurements cannot be done using a single cell, and synchrony of the cell population is therefore required. Instead, typically a sample that contains millions of cells is required. Since each cell has an effect on the measured gene expression levels, an asynchronous population leads to a blurred measurement when a cell cycle dependent signal is measured. Therefore, the whole population should be in the same phase of the cell cycle. For biological reasons, however, synchrony is lost over time, i.e., the cells gradually distribute themselves into different cell cycle phases. The resulting spreading of the distribution is illustrated in Fig. 1. The unavoidable asynchrony of the cell population thus results in that the measured gene expression levels are in fact some mean values of the true values of neighboring cell cycle phases. However, in the case of a relatively synchronous population this effect can be modeled by convolution. Moreover, if the distribution of the cell population can be estimated, the blurring effect of convolution can be inverted to obtain an estimate of the true signal that would have been obtained in a hypothetical perfectly synchronized experiment. Naturally, the better the estimate of the distribution, the better the estimate of the true signal.11 In the case of the budding yeast Saccharomyces cerevisiae there are several synchronization methods.12 For this paper, an experiment in which α factor-based synchronization was used to synchronize a budding yeast cell population was carried out. In this time-series experiment a budding yeast cell population was imaged with the sampling interval of 2 minutes. The complete description of the experiment as well as a brief description of the α factor-based synchronization method can be found in Appendix A. More information on synchronization methods and on experiments with cell cycle regulated genes in the case of yeast can be found in, e.g., Ref. 9. One way of estimating the distribution of a budding yeast cell population is to use bud-counting data to estimate the phase of the cell cycle. Here it suffices to say that a bud is a visible starting point of cell division, and a more exact definition will be given in the sequel. To be able to make the estimate, microscopic images of a budding yeast cell population must be obtained in a time-series experiment such as the one described in Appendix A. The estimate of the distribution can then be made on the basis of information on bud sizes in each image. The underlying idea is that cells that have a bud of the same size are in the same phase of the cell cycle. Thus, if the microscopic images are obtained in parallel with a time-series microarray measurement, the distribution of the cell population can be estimated. This estimate can then be used for inversion of the effects of convolution in the signals that are obtained in the microarray experiment. Two bud-counting approaches as well as the use of the obtained distribution for inversion of the convolution are discussed in more detail in Section 2. Because the amount of budding yeast images for which bud-counting data are needed is large in a typical time-series microarray measurement, an automatic bud-counting procedure is needed. Such a procedure as well as real image processing results on experimental images are presented in Section 3. The first step of the procedure is the segmentation step in which the yeast cells are separated from the background. This is based on the calculation of the local mean and the local variance, or more precisely, on clustering of the resulting two-dimensional mean-variance space. An object separation method that is based on the chain code representation of objects and on labeling of connected components is subsequently utilized for separating buds from their parent cells, after which the bud-counting task is relatively easy. Finally, some concluding remarks are given in Section 4.

Figure 2. The cell cycle of the budding yeast Saccharomyces cerevisiae.

2. ESTIMATION OF THE DISTRIBUTION OF A YEAST CELL POPULATION BY BUD-COUNTING The cell cycle of budding yeast, illustrated in Fig. 2, consists of the four main phases G1, S, G2, and M. A cell that is growing in the G1 phase starts the division process if it enters the S phase. This is determined by gene expression. At the beginning of the S phase a small daughter cell, referred to as a bud, appears on the side of the parent cell. As the parent cell proceeds through the G2 phase and mitosis, the size of the bud grows, and is at its largest at the end of the M phase just before cell division is completed. As a result, both the parent and the daughter cells are in the G1 phase. They contain the same genetic material and are ready to start the division process upon entry into the S phase∗ .10 The size of a bud thus depends on the phase of the cell cycle. Specifically, cells that are in the same phase of the cell cycle have buds of equal sizes, and cells that are in different phases of the cell cycle have buds of different sizes. Therefore, we propose to estimate the distribution of a budding yeast population on the basis of bud sizes. For a review of other estimation methods such as the use of the results from a FACS analysis, see Ref. 11. In a bud-counting approach, one possibility is to count the number of buds of different sizes at one time instant. This can be done by analyzing a single microscopic image taken from a sample of a budding yeast population. The result of this kind of bud-counting is a distribution estimate similar to the ones presented in Fig. 1 with the exception that the obtained estimate of the distribution is, of course, discrete. Since the size of a bud is assumed to be directly proportional to the phase of the cell cycle, the horizontal axis in Fig. 1 can alternatively be labeled “size of the bud”. Each of the four main phases of the cell cycle can last several minutes or longer, and a bud grows significantly in size during, e.g., the S phase. Therefore, the goal is not to merely be able to determine for each cell if it is in the G1, S, G2, or M phase, but rather, the goal is to use a larger number of phase categories. This means that there are more than four bins in the discrete estimate of the distribution. In the case of perfect synchrony of the cell population, the distribution is in signal processing terms an impulse, i.e., the central bin is the only nonzero bin in the distribution. There are a number of problems with the above approach. Obviously, since buds are small and we would like to obtain an accurate estimate of the distribution, it may be difficult to define the classes of buds of different sizes accurately enough. This means that there may not be enough bins in the discrete estimate of the distribution in order for it to be useful. Secondly, in the M phase the growth of the bud is less apparent than in the earlier phases, and in the G1 phase there are no buds at all.10 This means that there are more classes of buds of different sizes in the S and G2 phases than there are in the M and G1 phases, which makes the estimate of the phase less useful. In principle, the fact that daughter cells grow in size during the G1 phase could be used to ∗ After cell division, the daughter cell is smaller than the parent cell. The daughter cell is therefore ready to enter the S phase somewhat later than the parent cell. This is one of the reasons why a synchronized budding yeast cell population loses synchrony over time.

number of cells

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Figure 3. The time-distribution of a hypothetical cell population.

compensate for the fact that there are no buds in the G1 phase.10 In practice, however, this growth may not be noticeable by a bright field light microscope. An alternative approach for estimating the distribution of the cell population is to monitor how the number of buds of a certain size varies in time, i.e., in images obtained at different time instances. Of course, the number of cells that are analyzed at each time instant must be calculated as well. This means that we count the relative amount of cells that are in a certain phase of the cell cycle at each time instant of the time-series. The result is a time-distribution such as that in Fig. 3. Since the samples of the cell population for which bud-counting is done are taken at discrete time instances, the estimate of the distribution is discrete. For example, in Fig. 3 the time domain consists of 41 discrete time instances. In the ideal case, i.e. in the case of perfect synchrony, the distribution would here too be an impulse. The estimation method assumes that the distribution of the cell population remains constant during the time domain of the estimated distribution. This imposes strict biological requirements on the experiment in which microscopic budding yeast images are obtained and sets an upper limit for the length of the time domain of the estimated distribution. Moreover, a large number of cells must be imaged at each time instant in order for the estimate of the distribution to be statistically meaningful. As explained in the Introduction, in the case of an asynchronous population, microarray time-series measurements of gene expressions of cell cycle regulated genes lead to that the measured signals are blurred versions of the true signals. However, if the population is not totally asynchronous, the blurring effect can be modeled by convolution. An estimate of the distribution of the cell population, such as the ones described above, can then be used for inversion of the blurring effect. An approach based on inverse filtering with a Wiener filter as well as a regression-type approach have been proposed for this task.11 Naturally, the accuracy of the estimate of the distribution is crucial. In the next section, an image processing procedure for obtaining such an accurate estimate is presented.

3. COUNTING THE NUMBER OF BUDS The image processing procedure for counting the number of buds was developed for the images that were obtained in the budding yeast experiment that is described in Appendix A. The green component† of one of these images is presented in Fig. 4. In the image, the cell membranes are clearly visible as circular or elliptic regions that are darker than most of the background. It is seen that there is a relatively large number of yeast cells, some of which have buds. The bud-sizes vary quite heavily, which is an indication that the cell population is not in perfect synchrony. In fact, the image was obtained at the time instant 280 minutes, i.e., it is the last image that was obtained in the experiment. More details on the imaging process can be found in Appendix A. In estimating the distribution of the cell population we are only interested in the relative numbers of cells in different phases of the cell cycle. Specifically, we do not need to know the real percentage of buds versus parent cells. Therefore, we can ignore several biasing effects, such as the three-dimensional orientation of the samples (a bud may be hidden behind the parent cell), that otherwise could have a significant impact. †

There are actually two green components since the used camera has a Bayer matrix. We use one of them.

Figure 4. The green component of a microscopic image of a budding yeast cell population. The size of the image is 1388 × 1037 pixels. The image was obtained in the experiment described in Appendix A at the time instant 280 minutes.

3.1. Segmentation The first task is segmentation of the images to separate the cell membranes from the background. This requires that the cells are focused relatively well. However, since the yeast cells grow loose in a solution, the scene that is imaged by the microscope is three-dimensional, and there are generally some cells that are not well in focus. In fact, there may be cells in the scene that are not at all visible in the image because of being in a different focal plane. Therefore, the goal is to detect cells that are focused relatively well and to completely ignore cells that are in poor focus. First, the effect of uneven lighting is removed from the image with a polynomial fit that also subtracts the mean of the image. After this, the estimates of the local mean and the local variance are computed. This can be done efficiently with the two-dimensional convolution. The local mean is computed with µX = x(m1 , m2 ) ∗ h(n1 , n2 ),

(1)

where x(m1 , m2 ) is an image, h(n1 , n2 ) is an M × N convolution kernel having equal weights that add up to one, and ∗ denotes the two-dimensional convolution. In our case the size of the convolution kernel is 5 × 5. The computation of the quadratic mean is done similarly with a 5 × 5 kernel, that is, Ψ2X = x(m1 , m2 )2 ∗ h(n1 , n2 ).

(2)

Finally, the local variance can be calculated by using (1) and (2) in the well-known formula 2 σX = E[(X − µX )2 ] = Ψ2X − µ2X ,

(3)

where X refers to the value of a pixel from the image x(m1 , m2 ) and the operator E[·] denotes expectation. The resulting local mean and variance images are used to form a two-dimensional histogram. The core of the segmentation method is the subsequent clustering of the two-dimensional mean-variance space. The clustering is based on two assumptions. The first assumption is that the cell membranes are darker than their neighborhoods on average. The second assumption is that if a cell is in focus, the variance of its neighborhood is high. In other words, cells that are well in focus have sharper edges than defocused ones, and therefore the variance of a cell neighborhood is in general higher than the variance of the background of the image.

Figure 5. The segmentation result of the image in Fig. 4 showing the inner and outer boundaries of the cell membranes.

A binary image is formed from the original image based on the clustering of the local mean-variance space. The result is an image in which the cell membranes are shown as white pixels and the background is black. The segmentation procedure is completed by filling the remaining holes in the cell membranes and removing all small objects. The assumption is that objects that are very small are not cells but result from artefacts in the original image. The removal is done by labeling the connected components (see, e.g., Ref. 13) after which it is easy to determine the sizes of each object and remove them if necessary. The holes are filled by the morphological closing operation with a circular structuring element inside a 11 × 11 square. Finally, the inner and outer boundaries of the cell membranes are detected. Because the source image is a binary image, most edge detectors can be used for this task. Here we choose to calculate, for each pixel, the distance between the pixel and the nearest nonzero pixel. The pixels for which this distance is equal to one are boundary pixels of the cell membrane. The result of the whole segmentation procedure for the image in Fig. 4 is shown in Fig. 5. For purposes of visualization, that is, in order for the boundaries to be clearly visible, the figure presents a dilated version of the true segmentation result.

3.2. Bud-Separation It can be seen from Fig. 5 that the inner boundary of the cell membrane can be used for detection of small buds. Specifically, in most cases a small bud remains connected to the parent cell, and there is bridge-like connection between the parent cell and the bud. A particularly good example is shown in Fig. 6, which shows a part of the image in Fig. 4 at different image processing stages (see below). On the other hand, the inner boundaries of larger buds are usually disconnected from the inner boundaries of the parent cell. The same often applies to cells that are clustered in the image, i.e., to cells whose boundaries are connected to each other in the segmentation result. It is therefore often difficult to distinguish between large buds and cells that are connected to other cells. However, small buds that are separated from the parent cell in the segmentation result can be detected based on the sizes and numbers of objects (inner boundaries of a cell membrane) that are inside the outer boundary of a cell membrane. The sizes and numbers can be obtained by employing labeling of connected components. The detection of small buds is thus a more feasible task than the detection of buds of all sizes. This leads to an image processing procedure that is suitable for the latter estimation approach described in Section 2, in which the estimate of the distribution is based on the determination of how the number of buds of a certain small size varies in time. However, only the image processing procedure is discussed here, and the time-series analysis is left as part of future work.

(a)

(b)

(c)

(d)

Figure 6. A part of the image in Fig. 4 at different image processing stages. The upper left corner is at (x, y) = (609, 383) and the size of the image is 86 × 105. (a) original image; (b) segmentation result; (c) result after removing the outer boundary and filling the remaining inner boundary; (d) bud-separation result.

Figure 7. The image in Fig. 5 after removing objects that touch the edges and filling the objects according to the inner boundary of the cell membrane.

First, all objects (cell membranes) that touch the edges of the image are removed from the image, because it is not realistic to estimate the sizes of objects that are not completely seen in the image. Then, all outer boundaries of the cell membranes are removed. Since there are now no objects touching the edges of the image, a simple flood-fill can be performed, e.g., from the pixel at the upper left corner. Then, the outer boundaries can be removed by simply removing the object that touches the edges of the image. At this point inner boundaries that were originally inside an outer boundaries that touched the edges of the image are outer boundaries and thus their removal is guaranteed as well. Moreover, some objects that are not in good focus in the original image only have a horseshoe-like outer boundary with no inner boundary, and thus they are removed here, too. One example of this can be seen near the upper left corner of the image in Fig. 4. Before the actual bud-separation phase, the objects are filled to obtain the image in Fig. 7. This is based on a labeling of the connected components of the complement image. In the labeled image, the component that touches the edges of the image corresponds to the background and all the other components correspond to cell regions that need to be filled in the original image. The filling is then done according to the labels of the connected components.

Figure 8. The image in Fig. 7 after bud-separation.

Bud-separation is done with a modification of the object separation method that has been proposed by Balthasar et al.14 The method is based on two criteria of the objects. The first one is a compactness measure c=

4πA , p2

(4)

where A is the area of an object and p is the length of its boundary line, i.e., its perimeter. Both of these can be measured in pixels, but note that c is a dimensionless quantity. The compactness can be computed efficiently using the chain code representation of objects (see, e.g., Ref. 13). Objects that have a low compactness are candidates for objects that represent cells that have a small bud. The second criterion is calculated in the case of bud-separation only for objects for which c < 0.6. It is given by r = max

lb (x1 , x2 )

x1 ,x2 ∈B ld (x1 , x2 )

,

(5)

where x1 = (x1 , y1 ) and x2 = (x2 , y2 ) are the coordinates of two points on the boundary of the object, B is the set of boundary coordinates, lb is the distance between the points along the boundary of the object, and ld is the length of the direct line between the points, i.e., the Euclidean distance between the points. In the case of bud-separation, a cutline is drawn between the corresponding boundary coordinates if r > 3.5. The threshold values of c and r were obtained in iterative tests with different threshold values. The result of applying the object separation method to the image of Fig. 7 is shown in Fig. 8. For visualization purposes, the cutlines are drawn with the thickness of five pixels. However, calculations of bud-sizes are done with images in which the thickness of the cutline is one pixel (see Fig. 6 (d)). It can be seen from the image that all small buds are detected and separated from their parent cells. Moreover, there are no false separations, i.e., all cutlines are located between a bud and a parent cell. For this image, our procedure produces the following bud-counts: the number of cells with a bud whose size is at most 400 pixels is 1 and the number of cells with a bud whose size is larger than 400 pixels and at most 800 pixels is 7. These bud-counts are in agreement with the results that can be obtained by visual inspection of the focused cells of the image in Fig. 4. The steps of the bud-separation procedure for one cell taken from Fig. 4 are illustrated by the images in Fig. 6, in which the details are more clearly visible.

Figure 9. The green component of a microscopic image of a budding yeast cell population. The size of the image is 1388 × 1037 pixels. The image was obtained in the experiment described in Appendix A at the time instant 252 minutes.

As the number of cells in the images generally varies, the total number of cells must be determined as well to be able to calculate the relative amount of buds in the budding yeast images. The procedure is similar to the bud-counting procedure. The main difference is that the outer boundaries of the cell membranes are utilized instead of the inner boundaries. Because the cells can be clustered, the object separation method must be applied as well. Due to the limited space, we do not present any images related to cell-counting, but merely state that good results can be obtained with c < 0.45 and r > 3.5 as the criteria in the object separation method. Finally, we present the bud-counting results for another microscopic budding yeast image from the experiment described in Appendix A. This image was obtained at the time instant 252 minutes and its green component is shown in Fig. 9. It can be seen that this image contains some cells that are not focused well, but are still partially visible. However, as can be seen from the final bud-separation result in Fig. 10, these defocused cells are completely ignored by the bud-counting procedure. For this image, the following bud-counts are obtained: the number of cells with a bud whose size is at most 400 pixels is 3 and the number of cells with a bud whose size is larger than 400 pixels and at most 800 pixels is 5.

4. CONCLUSIONS A method for estimating the distribution of a budding yeast cell population was discussed. The method is based on counting the number of buds of a certain size in microscopic images of the cell population. The estimate of the distribution is thus an estimate of the number of cells that are in a selected phase of the cell cycle at each time instant. A good choice is to count small buds that correspond to cells that are at the beginning of the S phase of the cell cycle, and an image processing procedure was developed for this case. If a FACS analysis is done for the same samples for which microscopic imaging is done, the results of FACS analysis can be used to make another estimate of the distribution, and the two estimates can be compared. The image processing procedure was tested with microscopic budding yeast images. The results indicate that the procedure provides good bud-counting results if the yeast cells are focused relatively well. However, since yeast cells are grown in a cell suspension and not, e.g., on the bottom of a petri dish, the focusing situation may not always be as good as it is in the images that were presented in this paper. Therefore, the robustness of the procedure in different focusing situations must be verified before it can be applied for a time-series analysis of

Figure 10. The final bud-separation result for the image in Fig. 9.

budding yeast images. On the other hand, one can attempt to improve the imaging process in which budding yeast images are produced to obtain images with good focus at all time instances. Moreover, the number of cells that are imaged at each time instant should be high in order for the bud-counting results to be statistically meaningful. The use of the bud-counting procedure for obtaining an estimate of the distribution of the yeast cell population is left as part of future work.

APPENDIX A. AN EXPERIMENT FOR PRODUCING BUDDING YEAST DATA In this experiment budding yeast cells which were synchronized with α factor were imaged. In addition, FACS analysis was performed for some of the samples.

A.1. Alpha Factor-Based Synchronization Yeast Saccharomyces cerevisiae cells may grow and multiply as haploids or diploids. Haploid yeast cells are either MATa or MATα cells, and haploid cells of different types may fuse together to form a diploid cell. When cells grow as haploids, they convert their type every time they divide, i.e., MATa cells become MATα cells and MATα cells become MATa cells. An important part of this process called mating-type conversion is a site-specific cleavage in the MAT-locus that is performed by HO endonuclease. MATa cells of HO mutated yeast strain cannot convert to MATα cells, and if there are no MATα cells in the population, the cells cannot fuse to form diploid cells. Mating (fusion) of α and a cells is induced by pheromones. MATa haploid cells secrete a pheromone called a factor and MATα haploid cells secrete a pheromone called α factor. When the receptors of a MATa cell recognize the presence of α factor, the cell growth stops in the G1 phase of the cell cycle and the MATa cell starts waiting for fusion with a MATα cell. Thus, α factor synchronization is based on an artificial introduction of α pheromone to a cell population of MATa cells which are HO mutated. After the cells are released from the resulting α factor arrest, they grow again as haploids but now in synchrony. The genotype of the yeast strain that was used in the experiment was MATa (BY4741; MATa; his3D1; leu2D0; met15D0; ura3D0; YIL015w::kanMX4). The overnight grown culture was refreshed to an OD600 of 0.6 and then grown to an OD600 of 0.8 in YEP 20 g/l glucose in 2 hours and 15 minutes. The growth took place at +30◦ C in ten 250 ml bottles, each containing 150 ml medium. During growth the bottles were shaken at a rate

of 200 rpm. At OD 0.8, the pH was adjusted to 4 with 1 M HCl. After the adjustment, α factor (Nova Biochem, Switzerland, prod. no. 05-23-5300, batch no. A18684) was added to a concentration of 1 µM to each bottle and the shaking was continued. After 60 minutes, the medium and α factor were removed by centrifuging the cells at 5000 rpm for 10 minutes at the working temperature +4◦ C (Beckman Coulter Allegra 25R centrifuge). The cells were resuspended in approximately 10 ml fresh and cold YEP glucose and then inoculated to 1.5 liters YEP glucose in order to let them grow without α factor arrest. The initial OD600 was 0.8. During the subsequent sampling the cells grew in a fermentor (Braun Biostat CT-DCU 3). The temperature was kept at +30◦ C, pH at 5.5, and the medium was agitated at a rate of 1000 rpm. A 1 ml sample was taken from the fermentor every 2 minutes for 280 minutes in total.

A.2. Microscope Imaging Microscope imaging was performed for all the 140 samples that were taken from the fermentor. 15 µl of each sample was pipetted on a 1 mm microscope slide and each sample was covered with a #1.5 cover glass. Three different fragments were then imaged for each sample. Imaging was performed with an upright bright field light microscope (Olympus BX51). An achromatic condenser with the numerical aperture adjusted to 0.4 and a 100x Universal Plan Fluorite oil immersion objective with 1.3 numerical aperture were used (Olympus UPLFL 100x OP). The light source was a 100 W Tungsten Halogen bulb. The immersion oil had a refractive index of 1.515 − 1.517 and was pipetted onto each sample slide at the microscope. The magnification of the camera adapter was 0.5 leading to the overall 50 times magnification (Olympus U-TV 0.5x). The camera had a 1.5 million pixels CCD and a color filter array (Olympus DP-50). The used exposure time was 1/25 s. Exact information on the size of each pixel was not available, but it can be estimated to be around 5 × 5 µm. The images were saved in an uncompressed tiff-format with the image size 2776 × 2074 pixels. In the images the diameter of a full-grown yeast cell is approximately 100 pixels. The software that was used for imaging included Pixera Corporation Viewfinder 1.0 and Pixera Corporation Studiolite 1.0 running under Microsoft Windows 2000 (SP3) on an AMD Thunderbird 1.3 GHz PC with 1280 Mb of memory. These software performed the color interpolation required in using a CCD camera with a color filter array.

A.3. FACS Analysis The FACS analysis was performed for every third sample that was taken from the fermentor (starting from the second sample), i.e., every 6 minutes. The samples were chilled on ice immediately after harvesting. Cell dublets were separated by sonicating the samples 3 times for 30 seconds with output power 40 W (Branson Sonifier 450). In the last 11 samples the sonication times were increased while the output power remained the same. After sonicating, the cells were removed from the medium by centrifuging them at 13000 rpm for 2 minutes at the working temperature +4◦ C (Eppendorf Centrifuge 5415R). The supernatant was then discarded, and cells were fixed by gently shaking them in 1 ml of 70% ethanol for one hour. After five days of preservation at +4◦ C, the fixed cells were centrifuged at 13000 rpm for 5 minutes at room temperature. They were washed with 35% ethanol, centrifuged again, washed with water, and centrifuged again. Then, the cells were suspended to 0.5 ml of 2 mg/ml ribonuclease A solution (50 mM Tris-HCl, pH 7.5). They were incubated by gently shaking the solution for 1.5 hours at room temperature. Next, the cells were spun down with the centrifuge and suspended to 0.5 mg/ml of pepsine media (55 mM HCl). They were then incubated for 1.5 hours at room temperature in the same way as was done for the ribonuclease A solution. Then, the cells were centrifuged down and suspended to 0.5 ml of propidium iodide media (180 mM NaCl, 70 mM MgCl2, 100 mM tris, 75 µM propidium iodide). They were incubated by slowly shaking the solution at room temperature for 1 hour to stain the DNA. Finally, the DNA contents of the cells were estimated with a FACS analysis (Becton-Dickinson FACS Calibur).

A.4. Summary of Obtained Data The data were obtained from three different sources. Firstly, 140 readings of oxygen and carbondioxide concentrations along with the respective pH values were obtained from the fermentor at 2 minute intervals. Secondly, three times 140 images of yeast cells were obtained from the microscope (also at 2 minute intervals). Some of the images are not focused perfectly, and as a result, generally 1–2 images are successful for each sample. Each image contains approximately 5–15 cells, although some variation exists. Finally, the FACS analysis produced 5 results with 15 minute intervals during the α factor arrest and 47 results with six minute intervals after the α factor arrest. Each FACS result gives the DNA content of 20000 cells.

ACKNOWLEDGMENTS The support of TEKES and MediCel Ltd. is acknowledged. We would also like to thank Juha-Pekka Pitk¨ anen (M.Sc.), Daniel Nicorici (M.Sc.), Jari Niemi (M.Sc.), and Petri Vesanen for their help in the experiment in which the budding yeast data that are used in this paper was produced.

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