Comparative Autoregressive Moving Average Analysis of Kinetochore Microtubule Dynamics in Yeast

Abstract

To elucidate the regulation of kinetochore microtubules (kMTs) by kinetochore proteins in Saccharomyces cerevisiae, we need tools to characterize and compare stochastic kMT dynamics. Here we show that autoregressive moving average (ARMA) models, combined with a statistical framework for testing the significance of differences between ARMA model parameters, provide a sensitive method for identifying the subtle changes in kMT dynamics associated with kinetochore protein mutations. Applying ARMA analysis to G1 kMT dynamics, we found that 1), kMT dynamics in the kinetochore protein mutants okp1-5 and kip3D are different from those in wild-type, demonstrating the regulation of kMTs by kinetochore proteins; 2), the kinase Ipl1p regulates kMT dynamics also in G1; and 3), the mutant dam1-1 exhibits three different phenotypes, indicating the central role of Dam1p in maintaining the attachment of kMTs and regulating their dynamics. We also confirmed that kMT dynamics vary with temperature, and are most likely differentially regulated at 37°C. Therefore, when elucidating the role of a protein in kMT regulation using a temperature-sensitive mutant, dynamics in the mutant at its nonpermissive temperature must be compared to those in wild-type at the same temperature, not to those in the mutant at its permissive temperature.

Quantitative image analysis identifies pVHL as a key regulator of microtubule dynamic instability

“…MT dynamic instability is an intrinsically stochastic process. Therefore, distributions with hundreds to thousands of values have to be sampled to permit undistorted and significant comparisons between MT behaviors in the presence or absence of pVHL or in association with the expression of different mutants (Jaqaman et al, 2006). To collect unbiased statistics of the dynamics of many MTs, we expressed in both RPE-1 and RCC-4 cells a GFP fusion construct of EB3 and applied a recently developed method for the detection and tracking of EB3-GFP comets ( Fig.…”

Phenotypic clustering of yeast mutants based on kinetochore microtubule dynamics

“…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 þ white noise (WN) variance] and the variance-covariance matrix of the coefficients were estimated using Gaussian likelihood maximization.…”

“…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.…”

“…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.…”

“…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.…”