Bioinformatics Advance Access originally published online on May 5, 2007
Bioinformatics 2007 23(13):1666-1673; doi:10.1093/bioinformatics/btm230
Phenotypic clustering of yeast mutants based on kinetochore microtubule dynamics
1Department of Cell Biology, The Scripps Research Institute, 10550 N. Torrey Pines Road, La Jolla, CA 92037 and 2Department of Systems Biology, Harvard Medical School, 200 Longwood Avenue, Boston, MA 02115, USA
*To whom correspondence should be addressed.
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ABSTRACT |
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 TOP ABSTRACT 1 INTRODUCTION2 METHODS AND ALGORITHMS3 RESULTS4 DISCUSSION5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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Motivation: Kinetochores are multiprotein complexes which mediate chromosome attachment to microtubules (MTs) of the mitotic spindle. They regulate MT dynamics during chromosome segregation. Our goal is to identify groups of kinetochore proteins with similar effects on MT dynamics, revealing pathways through which kinetochore proteins transform chemical and mechanical input signals into cues of MT regulation.
Results: We have developed a hierarchical, agglomerative clustering algorithm that groups Saccharomyces cerevisiae strains based on MT-mediated chromosome dynamics measured by high-resolution live cell microscopy. Clustering is based on parameters of autoregressive moving average (ARMA) models of the probed dynamics. We have found that the regulation of wildtype MT dynamics varies with cell cycle and temperature, but not with the chromosome an MT is attached to. By clustering the dynamics of mutants, we discovered that the three genes IPL1, DAM1 and KIP3 co-regulate MT dynamics. Our study establishes the clustering of chromosome and MT dynamics by ARMA descriptors as a sensitive framework for the systematic identification of kinetochore protein subcomplexes and pathways for the regulation of MT dynamics.
Availability: The clustering code, written in MATLAB, can be downloaded from http://lccb.scripps.edu. (‘download’ hyperlink at bottom of website).
Contact: kjaqaman{at}scripps.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
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1 INTRODUCTION |
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TOPABSTRACT1 INTRODUCTION2 METHODS AND ALGORITHMS3 RESULTS4 DISCUSSION5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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The kinetochore is a multiprotein structure that establishes the physical linkage between chromosomes and spindle microtubules (MTs) during mitosis. It comprises more than 70 different proteins (Cheeseman et al., 2002; Chen and Yuan, 2006; De Wulf et al., 2003; Maiato et al., 2004; Meraldi et al., 2006), of which several have been implicated in the regulation of the attached kinetochore MTs (kMTs) (DeLuca et al., 2006; Jaqaman et al., 2006). The regulation of kMT dynamics by the kinetochore is likely an essential part of the process that ensures accurate chromosome segregation. However, very little is known about the pathways among kinetochore proteins that ensure proper control of kMTs, and about the chemical and mechanical signals involved in the regulation.
To reveal the interactions between kinetochore proteins that are important for proper kMT regulation, we are pursuing a quantitative genetics approach using the budding yeast Saccharomyces cerevisiae as a model system. Loss-of-function mutations are introduced into kinetochore proteins and the resulting chromosome movement is determined using 3D live-cell microscopy combined with automated tracking (Dorn et al., 2005; Thomann et al., 2002, 2003). Since chromosome dynamics are stochastic, wildtype (WT) and mutant behavior cannot be compared on a time point by time point basis. Rather, they must be compared indirectly via parameters that capture the properties of the dynamics. In Jaqaman et al. (2006), we established autoregressive moving average (ARMA) model parameters as sensitive descriptors of chromosome and kMT dynamics. Their comparison via statistical hypothesis testing allows the indirect comparison of the measured dynamics and thus the detection of subtle differences between dynamics in WT and in S. cerevisiae strains carrying kinetochore protein mutations. Different ARMA model parameters capture different aspects of the dynamics, and their separate comparison gives insight into which component of the dynamics changes as a result of kinetochore protein mutation.
Here, we advance this analysis by clustering chromosome motion and kMT dynamics based on their ARMA descriptors. This allows us to compare dynamics from large data sets of mutants and identify groups of mutations that lead to similar chromosome and kMT dynamics, a task not achievable by pairwise comparison. We address the critical question whether the clustering of chromosome and kMT dynamics based on ARMA models can be used to derive insight into the functions of and interactions between kinetochore proteins. The quantitative comparison of genotype and phenotype is a key step in assigning protein function: mutants whose phenotypes cluster into a distinct group provide evidence for the joint function of the corresponding proteins in a complex or pathway.
To date, time series clustering in biology has been mostly applied to gene expression data. Gene expression time series exhibit substantial temporal trend, i.e. they are non-stationary, and are generally clustered based on these temporal trends (Bar-Joseph, 2004; Costa et al., 2004). Some clustering approaches explicitly capture temporal trends via parametric models and employ estimated model parameters in the process of clustering (Bar-Joseph et al., 2003; Ramoni et al., 2002; Schliep et al., 2005), while others do not explicitly model the trends but still cluster series based on the similarity of their trends (Eisen et al., 1998). All of these approaches involve steps that treat trend as a deterministic variable over time. In contrast to gene expression, S. cerevisiae chromosome and kMT dynamics are stationary and do not exhibit temporal trends. Their comparison and clustering must solely depend on their ARMA descriptors without explicit reference to the series themselves, ruling out the approaches developed for clustering gene expression time series.
The clustering of stationary stochastic time series based solely on model parameters has been addressed in economics (Liao, 2005). The developed algorithms employed cepstral parameters (Kalpakis et al., 2001; Martin, 2000), autoregressive parameters (Maharaj, 2000; Piccolo, 1990) and moving average parameters (Sarno, 2001). Most of these works used the Euclidean distance between coefficients as a dissimilarity measure between time series. In Maharaj (2000), a hypothesis testing framework was applied to the Mahalanobis distance between autoregressive parameters and the resulting P-values were used as a dissimilarity measure. While these approaches are similar in spirit to our approach, especially the work in Maharaj (2000), none of them employ ARMA model parameters. Thus, they are not applicable to S. cerevisiae chromosome and kMT dynamics.
In this work, we cluster S. cerevisiae chromosome and kMT dynamics based on their ARMA descriptors in three consecutive clustering steps, each step accounting for a different aspect of the dynamics via a specific subset of the ARMA descriptors. Within each step, an agglomerative hierarchical clustering approach is taken. The measure of dissimilarity between dynamics is derived from the P-value of the hypothesis test that compares the relevant subset of ARMA descriptors. The level at which the trees are cut to form distinct groups corresponds to the P-value that indicates significant differences between descriptors (Jaqaman et al., 2006). Although we have developed our algorithm for the specific purpose of clustering yeast mutants based on their chromosome and kMT dynamics, this algorithm is general in design and implementation and can be used to cluster any time series that can be described by ARMA models.
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2 METHODS AND ALGORITHMS |
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TOPABSTRACT1 INTRODUCTION2 METHODS AND ALGORITHMS3 RESULTS4 DISCUSSION5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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2.1 Measurement and ARMA analysis of S. cerevisiae chromosome and kMT dynamics
Chromosome motion relative to the spindle pole body was measured as described in (Dorn et al., 2005; Thomann et al., 2002, 2003). In brief, the spindle pole body (SPB) and centromere (CEN) of chromosome IV or chromosome V were tagged with GFP (He et al., 2000; Robinett et al., 1996; Straight et al., 1996) and imaged in 3D with a sampling rate of 1 Hz. The 3D positions of the tags over time were determined using single particle tracking. The error associated with each positional measurement, expressed as a SD, was calculated by propagating the noise level of the GFP-tag signals in the original image (Dorn et al., 2005). Time-courses of SPB–CEN distance and its SD were calculated from the tag positions and their SDs. The error in SPB–CEN distance ranged from
4 nm to 70 nm, depending on the orientation of the vector in space and the signal-to-noise ratio of the original image. These error values were 10–140% of the average change in SPC–CEN distance in 1 s. In the case of chromosome attachment to kMTs, the SPB–CEN distance was interpreted as the length of the connecting kMT, and its variation over time reflected kMT dynamics (Dorn et al., 2005). Chromosome and kMT dynamics were analyzed by fitting ARMA models to SPB-CEN distance series using the algorithm described in (Jaqaman et al., 2006) [See Supplementary Material for a description of the algorithm and for a discussion of the reasons behind fitting distance series instead of their first difference as done in (Jaqaman et al., 2006)]. In brief, the ARMA descriptors [ARMA coefficients + white noise (WN) variance] and the variance–covariance matrix of the coefficients were estimated using Gaussian likelihood maximization. SPB–CEN distance series from 15 to 30 different cells representing the same condition were used to construct the likelihood, in order to enhance the accuracy of parameter estimation. The algorithm handles series with missing observations and accounts for observational error, as represented by the SPB–CEN distance SD, to get an estimate of the ARMA descriptors that is independent of observational error.
ARMA coefficients and WN variance capture different aspects of chromosome motion. WN variance reflects the confinement radius of a chromosome. In S. cerevisiae, the confinement radius is generally proportional to the speed of chromosome movement relative to the pole (Dorn et al., 2005). Changes in WN variance are thus taken to reflect changes in the overall speed and confinement of a chromosome, which are due to changes in kMT growth and shrinkage speeds and length range in the case of chromosome attachment to a kMT. ARMA coefficients capture the temporal coupling in chromosome motion and kMT dynamics, i.e. what the chromosome or kMT will do next given its current and past states. ARMA coefficients derived from fitting SPB–CEN velocity series as in (Jaqaman et al., 2006) were insensitive to changes in average chromosome poleward and anti-poleward speeds. When applying ARMA models to SPB–CEN distance series, as done in this work, the ARMA coefficients became more sensitive and could capture changes in speeds that did not maintain the ratio of poleward to antipoleward movement rates. In vivo, changes in the temporal coupling of kMT-driven chromosome movement are most likely due to altered regulation of kMT dynamics, for example by kinetochore proteins. Therefore, in this work, changes in the ARMA coefficients of kMT-driven chromosome motion are interpreted as changes in the regulation of kMT dynamics.
2.2 Monothetic clustering of chromosome and kMT dynamics using ARMA descriptors
In order to cluster chromosome and kMT dynamics, a measure of dissimilarity between pairs of conditions was required. We derived this measure from the P-values of the comparison of ARMA descriptors. To distinguish between changes in temporal coupling and changes in confinement radius, we calculated two measures of dissimilarity between the analyzed dynamics, one based on ARMA coefficients and one based on WN variance, respectively.
WT conditions and mutants were grouped in a sequence of three clustering steps, relying on these two measures and building on prior knowledge of possible factors influencing chromosome and kMT dynamics (Fig. 1A):
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Step 1. Separation of conditions with detached chromosomes from conditions with attached chromosomes:
The attachment of chromosomes to kMTs confines their motion and reduces their overall speeds and confinement radii (Dorn et al., 2005). Hence the dynamics of chromosomes attached to MTs have a much smaller WN variance than the dynamics of chromosomes that are detached from MTs [(Jaqaman et al., 2006) and Supplementary Table S1]. The mutant ndc10-1, which carries a mutation in the core kinetochore protein Ndc10p, does not form a kinetochore and hence its chromosomes cannot attach to MTs (Goh and Kilmartin, 1993; Hyman and Sorger, 1995). Thus, ndc10-1 chromosome dynamics provided the phenotype of chromosome detachment: mutants whose WN variances clustered with the WN variance of ndc10-1 were considered to have detached chromosomes, while all others were considered to have attached chromosomes.
Step 2. Distinction of different modes of kMT regulation and chromosome diffusion:
In this step, chromosome and kMT dynamics in the detached and attached groups were clustered based on their ARMA coefficients. In the case of attached chromosomes, differences in the temporal coupling of kMT dynamics between WT and a loss-of-function mutant, as reflected by differences in their ARMA coefficients, were considered to reflect different modes of kMT regulation when the targeted protein was functional (WT) or mutated. Therefore, kMT dynamics with statistically indistinguishable ARMA coefficients were considered to be in the same regulation mode, while dynamics with statistically distinguishable ARMA coefficients were considered to be in different regulation modes (Jaqaman et al., 2006). In the case of detached chromosomes, statistically indistinguishable ARMA coefficients of chromosome dynamics indicated similar chromosome diffusion modes, while significantly different ARMA coefficients indicated different diffusion modes.
Step 3. Identification of phenotypic groups with equivalent dynamics:
In Step 1, we used the WN variance to coarsely separate conditions with detached chromosomes from conditions with attached chromosomes. However, either group might still contain subgroups with significantly different WN variances. Therefore, after clustering conditions into groups with similar ARMA coefficients, we further divided each group based on WN variance. This identified conditions that had equivalent dynamics, i.e. similar ARMA coefficients and WN variance. If kMT dynamics in a group of mutants with attached chromosomes were found to be equivalent, the mutated proteins were considered to be a functional group. These proteins most likely form a pathway or complex that co-regulates kMT dynamics. In the case of mutants with detached chromosomes, equivalent chromosome dynamics assigned the strains to one diffusion group.
The clustering of kMT dynamics in each one of the above steps was achieved via agglomerative hierarchical clustering (Fig. 1B).
One of the major issues in clustering is the decision on the number of groups among which the data are divided (Handl et al., 2005; Jain and Dubes, 1988). Our cutoff criteria (Fig. 1A) were motivated by our prior knowledge and derived from the data. In Step 1, the number of groups was fixed to two: a detached group and an attached group. In Steps 2 and 3, the levels at which the trees were cut to yield different groups corresponded to the P-values indicating significantly different ARMA coefficients and WN variances, respectively. The P-value thresholds, 5 x 10–5 for ARMA coefficients and 1 x 10–12 for WN variance, were obtained via the boot-strapping like method described in Jaqaman et al. (2006). Thus, conditions that fell into the same group had statistically indistinguishable descriptors, while conditions in different groups were significantly different from each other.
2.3 Measure of dissimilarity between chromosome and kMT dynamics
2.3.1 ARMA coefficients
To measure the dissimilarity between dynamics in two groups I and J based on their ARMA coefficients, we defined the distance
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This measure of dissimilarity is always non-negative (with a value of zero only when the two compared objects are identical) and it is symmetric; however, it does not obey the triangle inequality, making it a semimetric. The P-value pcoef in Equation (1) is calculated by comparing the ARMA coefficient vector 
of every individual condition i in group I to the ARMA coefficient vector 
of every individual condition j in group J, i.e. by testing the null hypothesis 
against the alternative hypothesis 
, where
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| (2) |
NI/J is the number of conditions in group I/J. Since the covariance between the ARMA coefficients of models fitted to different data sets is zero, the variance–covariance matrix 
associated with 
is block-diagonal. The entry in 
corresponding to 
is given by 
.
The test-statistic for this comparison is defined as
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Because of the block diagonal structure of 
, Equation (3) simplifies to:
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is the test statistic for comparing condition i in group I to condition j in group J. The test statistic for comparing two individual conditions i and j is a special case of Equation (3) with NI = NJ = 1:
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and 
. If conditions i and j have different ARMA model orders, zero-padding is used to compensate for order mismatch and allow the calculation of 
(Jaqaman et al., 2006).
Under the null hypothesis, the statistic Scoef follows a 
-distribution, where the number of degrees of freedom m is the average (autoregressive order + moving average order) for all pairs compared, rounded to the nearest integer. Thus the P-value pcoef in Equation (1) is given by
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2.3.2 WN variance
To measure the dissimilarity between chromosome dynamics in two groups I and J based on their WN variances, we defined the distance
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| (7) |
Similar to dcoef(I,J), dvar(I,J) is a semimetric. The P-value pvar in Equation (7) is calculated by testing the null hypothesis 
against the alternative hypothesis 
using the test-statistic
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| (8) |
The group variances 
and 
are calculated using
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and 
are the SD and length, respectively, of series i/j in group I/J and 
.
Under the null hypothesis, the statistic Svar follows an 
-distribution with TI and TJ degrees of freedom. Thus the P-value pvar in Equation (7) is given by
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| (10) |
Despite the visual similarity between kMT length series, we have found many pairs of conditions where the ARMA descriptors are very different. In these cases, the test statistics 
and 
exceed the range of values handled by numerical functions used to determine P-values (e.g. MATLAB's cumulative distribution functions). The P-values returned are clipped to zero, yielding dissimilarity measures (Equations 1 and 7) of infinity. This precludes the construction of meaningful trees by hierarchical clustering. Therefore, we developed P-value extrapolation schema for large test statistics, as detailed in Supplementary Material.
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3 RESULTS |
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TOPABSTRACT1 INTRODUCTION2 METHODS AND ALGORITHMS3 RESULTS4 DISCUSSION5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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We analyzed and clustered G1 and metaphase chromosome trajectories obtained from
400 3D live-cell movies of seven S. cerevisiae strains comprising 60 000 time points. The ARMA descriptors of all strains and conditions used in this study are provided in Supplementary Tables S1 (for G1 dynamics) and S2 (for metaphase dynamics). G1 dynamics were best described by ARMA (1,1) or ARMA(2,1) models, while metaphase dynamics required ARMA(1,1) or ARMA(3,3) models.
3.1 Clusters of WT kMT dynamics under different conditions
In order to identify experimental conditions that affect WT kMT dynamics, we grouped kMT dynamics in different phases of the cell cycle (namely G1 and metaphase) and at different temperatures, as well as the dynamics of kMTs attached to different chromosomes (chromosomes IV and V).
Since the chromosomes in all of these conditions are attached to kMTs, we skipped the first clustering step in our algorithm (Fig. 1A) and directly grouped the data according to ARMA coefficients (Fig. 2A). G1 kMT dynamics between 25°C and 34°C, whether obtained by tracking chromosome IV (CEN IV) or V (CEN V), clustered in the same group (group A4). Dynamics at lower and higher temperatures had significantly different ARMA coefficients (groups A2 and A3). On the other hand, kMT dynamics in metaphase (group A1) had ARMA coefficients substantially different from those of G1 dynamics: the measure of dissimilarity between metaphase and G1 was 4.4 x 106, while it was only 12 between the most different G1 dynamics. In the analysis of metaphase dynamics, we distinguished between movies where the sister centromeres were separated [assumed to imply high tension across the spindle (Gardner et al., 2005; Waters et al., 1996)] and movies where the sisters were joint (low tension). Despite the presumably different levels of tension, ARMA coefficients of these two conditions fell into the same group (group A1). Together, these data suggest that the regulation of kMT dynamics, as reflected in their temporal coupling, changes with temperature and cell cycle, but is invariant among chromosomes and independent of sister centromere separation.
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Subsequent clustering based on WN variance further split the group containing G1 kMT dynamics between 25°C and 34°C (Fig. 2B). The dynamics of kMTs attached to chromosome V (group B4) got separated from the dynamics of kMTs attached to chromosome IV (group B5), because of the much larger WN variance in the case of chromosome V (See Supplementary Table S1). This indicated that kMTs attached to chromosome V grew and shrank faster and spanned a larger volume of the nucleus than kMTs attached to chromosome IV. Analysis of the dynamics as in Dorn et al. (2005) yielded growth and shrinkage speed values of
5.0 ± 0.1 µm/min for chromosome V versus 4.2 ± 0.1 µm/min for chromosome IV, and average length SDs, which are proportional to the confinement radius, of 0.11 µm for chromosome V versus 0.08 µm for chromosome IV. The increase in kMT growth and shrinkage speeds and consequently chromosome confinement radius is most likely due to the smaller size of chromosome V (Carle and Olson, 1985) and hence the smaller load it exerts on its kMT (Dogterom and Yurke, 1997).
3.2 Phenotypic clusters among kinetochore protein mutants
To test the ability of our algorithm to identify groups of kinetochore proteins that may form functional complexes for regulating kMT dynamics, we assembled chromosome dynamics data from strains carrying loss-of-function temperature sensitive mutations in the essential genes NDC10, a component of the CBF3 binding complex required for the initial steps of kinetochore assembly (Goh and Kilmartin, 1993; Hyman and Sorger, 1995); OKP1, a component of the COMA complex thought to function as a linker between DNA and MT-binding kinetochore proteins (De Wulf et al., 2003); DAM1, a component of the DASH complex that forms rings around kMTs and is thought to facilitate MT-kinetochore attachment (Miranda et al., 2005; Westermann et al., 2006); STU2, an MT-associated protein; and IPL1, the yeast homolog of the Aurora B kinase. We also examined a strain deleted for the nonessential kinesin KIP3. In all mutants, chromosome dynamics were measured at the non-permissive temperature of 37°C and compared to WT at the same temperature.
First, using the WN variance of chromosome dynamics, we separated strains with detached chromosomes from strains with chromosomes attached to MTs (Fig. 3A). One subset of G1 dam1-1 cells clustered with ndc10-1, our prototype for detached chromosome motion (group A2). This indicated that these G1 dam1-1 cells had their chromosomes detached from MTs. Dynamics in all other strains had WN variances that were significantly smaller than the WN variance of ndc10-1 (group A1). Chromosomes in these strains were considered to be attached to MTs, and we used these mutants to study the regulation of kMT dynamics by kinetochore proteins.
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In the second step, we separately clustered dynamics in the attached and the detached groups based on their ARMA coefficients (Fig. 3B). Chromosome dynamics in the two detached strains were found to have indistinguishable ARMA coefficients (group B5), indicating that detachment due to NDC10 and DAM1 mutation yields the same type of chromosome diffusion. In the attached strains, kMT dynamics got divided into four groups (groups B1–B4), indicating four different modes of regulation of kMT dynamics.
The most interesting group among the attached strains was composed of kMT dynamics in the mutants ipl1-321 (both G1 and metaphase), kip3
(G1) and dam1-1 (one G1 sub-population and metaphase) (group B4). These results imply that the three corresponding proteins co-regulate kMT dynamics. Furthermore, in contrast to WT where the temporal coupling of kMT dynamics changed between G1 and metaphase (Fig. 2A), the temporal coupling of kMT dynamics in ipl1-321 and dam1-1 did not change between the two phases of the cell cycle.
In the third and final step (Fig. 3C), we clustered dynamics in each one of the kMT regulation modes based on their WN variance. With this, metaphase kMT dynamics in ipl1-321 and dam1-1 (group C4) got separated from their G1 counterparts (group C5). The metaphase WN variance was much smaller than the G1 WN variance (Supplementary Tables S1 and S2). Thus, even though the regulation is the same in these two mutants in G1 and metaphase, the overall kMT growth and shrinkage speeds and chromosome confinement radii are smaller in metaphase.
3.3 The emerging clusters are significant and stable
A clustering algorithm, by definition, will find clusters in a data set, even if there are no real underlying groups (Handl et al., 2005; Jain and Dubes, 1988). Thus, it is essential to confirm the significance of the different clusters obtained. Since we use a statistical dissimilarity measure to build the tree and a data-derived significance threshold for cutting it, the clusters emerging from our analysis are inherently significant. Given the noise level of the input chromosome trajectories, kMT dynamics within one cluster are statistically indistinguishable, while kMT dynamics in different groups are significantly different.
Another important aspect of clustering is the stability of the emerging clusters, i.e. their robustness with respect to small perturbations of the data. To ensure the stability of our clustering results, for each data set we (i) generated synthetic ARMA series using the ARMA descriptors of the strains and conditions in that data set and perturbed the synthetic series with noise similar to the experimental measurement noise, (ii) clustered the synthetic series and (iii) compared the clustering results of the synthetic series to the clustering results of the experimental data using the corrected Rand statistic (Hubert and Arabie, 1985; Jain and Dubes, 1988). We repeated the above procedure 200 times for each data set.
For the data set with WT dynamics under different conditions (Fig. 2), we obtained an average corrected Rand statistic of 0.64 at both the ARMA (Fig. 2A) and WN variance (Fig. 2B) levels. For the dataset with the different strains at 37°C (Fig. 3), we obtained an average corrected Rand statistic of 0.74 and 0.75 at the ARMA (Fig. 3B) and WN variance (Fig. 3C) levels, respectively. Corrected Rand statistics above 0.1 are generally considered to indicate stable clustering (Milligan and Cooper, 1986). Therefore, these corrected Rand statistics confirm the stability of the groups of kMT dynamics emerging from our clustering algorithm.
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4 DISCUSSION |
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TOPABSTRACT1 INTRODUCTION2 METHODS AND ALGORITHMS3 RESULTS4 DISCUSSION5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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4.1 The regulation of WT kMT dynamics varies with cell cycle and temperature, but not with chromosome
To elucidate the role of a protein in regulating kMT dynamics, it is critical to exclude external factors that may affect kMT dynamics between experiments and mask the effect of mutants. In our previous studies, we showed that WT kMT dynamics and their regulation change with temperature (Dorn et al., 2005; Jaqaman et al., 2006). In this study, we investigated two additional factors that might vary unperturbed kMT dynamics: cell cycle and the chromosome a kMT is attached to.
As expected, cell cycle phase had an influence on kMT dynamics (Fig. 2, group B1). The ARMA coefficients of metaphase kMT dynamics were very different from the ARMA coefficients of G1 dynamics, implying a different temporal coupling in the two phases. This change in temporal coupling might be due to cell-cycle changes in the regulation of kMT dynamics, or due to the different force regime a kMT experiences in the bipolar metaphase spindle versus the G1 half-spindle. Our observation that metaphase kMT dynamics do not change significantly with sister-centromere separation (Fig. 2, group B1) implies that these metaphase forces are not directly linked to sister-centromere separation as is generally assumed (Gardner et al., 2005; Waters et al., 1996).
WT kMT dynamics tracked by chromosomes IV and V in G1 had the same ARMA coefficients (Fig. 2, group A4), implying that both kinetochores regulate kMT dynamics in the same mode. This provides quantitative evidence supporting the common assumption that all kinetochores are equivalent. Consequently, in our future studies of kinetochore pathways, we can directly compare the ARMA coefficients of mutant kMT dynamics tracked by different chromosomes. This practice will be necessary because some mutations are incompatible with labeling certain chromosomes.
In summary, the proper deduction of kinetochore protein function in regulating kMT dynamics requires the comparison of data sets measured at the same temperature and phase in the cell cycle, but not necessarily from the same chromosome.
4.2 Ipl1p and Dam1p form a functional group with Kip3p and are essential for the cell cycle dependence of kMT dynamics
The most interesting phenotypic groups obtained in our study consist of the mutants ipl1-321 and kip3 and one subpopulation of the mutant dam1-1, which exhibit equivalent dynamics with statistically indistinguishable ARMA coefficients and WN variance in both G1 (Fig. 3, group C5) and metaphase (Fig. 3, group C4). The similarity of these three mutants most likely reflects the phosphorylation chain which has been identified biochemically between Ipl1p and Dam1p (Shang et al., 2003), and between Ipl1p and Kip3p (in vitro study, Chitra Kotwaliwale and Sue Biggins, personal communication). For the first time, we have now collected evidence that these three proteins cooperate also functionally in the regulation of kMTs. Dam1p is part of the DASH complex that forms rings around kMTs (Miranda et al., 2005; Westermann et al., 2006) and is thought to link the kMT to the kinetochore. When Dam1p does not function properly, whether due to direct mutation or due to mutating the upstream kinase Ipl1p, the DASH complex might not mediate proper kMT attachment. This conjecture is supported by our observation that one subpopulation of dam1-1 cells adopts the phenotype of detached chromosomes (Fig. 3, group C6). When the kMT is not attached properly, it might not form the proper contacts with kinetochore proteins that regulate its dynamics, such as Kip3p. Furthermore, inhibiting the function of Dam1p may preclude the formation of a scaffold that holds in place additional kinetochore proteins implicated with the regulation of kMTs, such as Kip3p. Thus, mutating Dam1p and Ipl1p and deleting Kip3p lead to the same misregulation of kMT dynamics. This example demonstrates that the hierarchical clustering of kinetochore protein mutants based on the ARMA descriptors of their kMT dynamics can uncover biologically meaningful connections among kinetochore proteins for the purpose of regulating kMT dynamics.
Our results also implicate two members of this functional group, Ipl1p and Dam1p, in the cell-cycle dependent regulation of kMTs. In contrast to WT cells, the temporal coupling of kMT dynamics in the mutants ipl1-321 and dam1-1 does not change between G1 and metaphase (Fig. 3, group B4). The discrepancy between WT and the two mutants can be a result of the essential role that Ipl1p and Dam1p play in changing kMT regulation between the two phases. Alternatively, the difference in temporal coupling between G1 and metaphase WT cells could originate from the different mechanical configurations of the G1 half-spindle and the bipolar metaphase spindle. The kMT in metaphase experiences forces in response to its polymerization and depolymerization that it does not experience in G1. In ipl1-321 and dam1-1, however, chromosome attachment remains monopolar (He et al., 2001). Thus, kMTs operate under mechanical conditions close to the G1 half-spindle. Consequently, temporal coupling of metaphase dynamics in these two mutants stays close to the temporal coupling of G1 dynamics. We are currently investigating the two possibilities of cell-cycle dependent kMT regulation by ARMA analysis of further monopolar and bipolar configurations where the clustering methods described here will be invaluable to group data into the different pathways.
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5 CONCLUSION |
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TOPABSTRACT1 INTRODUCTION2 METHODS AND ALGORITHMS3 RESULTS4 DISCUSSION5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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We have implemented a hierarchical, agglomerative clustering algorithm that statistically groups S. cerevisiae chromosome and kMT dynamics measured by high-resolution live cell microscopy. The clustering is based on parameters of ARMA models fitted to SPB–CEN distance series. Different parameters reflect different aspects of the dynamics and are thus used in separate clustering steps. In each step, the dissimilarity measure is derived from the P-value of parameter comparison. Groups are formed by cutting the trees at the P-value levels which indicate statistically significant differences between the ARMA descriptors used for the clustering.
We have found that mutants of the genes IPL1, KIP3 and DAM1 form a phenotypic group whose kMT dynamics are significantly different from dynamics in WT. The corresponding three proteins seem to function in a complex that regulates kMT dynamics. We have also found that the regulation of kMT dynamics in WT cells varies with cell-cycle and temperature, but not between chromosomes. Interestingly, the change in the temporal coupling of kMT dynamics between G1 and metaphase disappears in mutants of the proteins Ipl1p and Dam1p.
Our results show that the clustering of chromosome and kMT dynamics based on their ARMA descriptors is a sensitive framework to reveal kinetochore proteins that form a pathway or functional complex for the purpose of regulating kMT dynamics. They demonstrate, for the first time, that systematic readouts of a dynamic cell behavior and subsequent clustering via sensitive parameters allow the grouping of genes in functionally relevant complexes and pathways. No other approach exists to identify functional pathways in a multi-protein complex, where structural analyses are rendered impossible by the size of the complex and biochemical methods are insufficient to reveal the functional consequences of protein–protein interactions.
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ACKNOWLEDGEMENTS |
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TOPABSTRACT1 INTRODUCTION2 METHODS AND ALGORITHMS3 RESULTS4 DISCUSSION5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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This work was supported in part by NIH R01 GM68956 to P.K.S and G.D. K.J. is a Paul Sigler/Agouron Fellow of the Helen Hay Whitney Foundation. J.F.D. is a fellow of the Roche Research Foundation. E.M. is a long-term fellow of the Human Frontier Science Program.
Conflict of Interest: none declared.
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FOOTNOTES |
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The authors wish it to be known that, in their opinion, the first two authors should be regarded as joint first Authors. 
Associate Editor: Martin Bishop
Received on February 17, 2007; revised on April 24, 2007; accepted on April 25, 2007
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REFERENCES |
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TOPABSTRACT1 INTRODUCTION2 METHODS AND ALGORITHMS3 RESULTS4 DISCUSSION5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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