S. Campione and S. Haase were supported by funding from the National Science Foundation (DMS-1839288) and the National Institutes of Health (5R01GM126555). Additionally, the authors would like to thank Huarui Zhou (Duke University) for comments on the manuscript and for beta testing the protocol. We also thank Francis Motta (Florida Atlantic University) and Joshua Robinson for their help with the Java code.

1. Collecting cell-cycle phase and experimental data
<ol>
	<li>Synchronize the cells with respect to the cell cycle using the desired synchronization method (e.g., centrifugal elutriation as described in Leman et al.18 or mating pheromone arrest as described in Rosebrock19; both Leman et al.18 and Rosebrock19 also include methods for the release from synchrony). Begin sampling throughout the time series, ens...

Alignment of Synchronized Time-Series Data for Cross-Experiment Comparisons

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This paper presents a method for more accurately and quantitatively assessing data from time-series experiments on synchronized populations of cells. The method utilizes learned parameters from CLOCCS, a Bayesian inference model that uses input cell-cycle phase data, such as budding data and flow-cytometric DNA content data, to parameterize each experiment14,15. CLOCCS uses the input cell-cycle phase data to infer the parameters for each experiment, which are the...

Time-series measurements made on synchronized populations of cells as they progress through the cell cycle is a standard method for investigating the mechanisms that control cell-cycle progression1,2,3,4,5,6,7,8. The ability to make comparisons across synchrony/release time-series experiments is vital to our understanding of these dynamic processes. The use of replicate experiments to corroborate findings can increase the confidence in the reproducibility of the conclusions. Furthermore, comparisons between environmental conditions, across mutants, and even between species can uncover many new insights into cell-cycle regulation. However, interexperimental variability in the recovery from synchrony and in the speed of cell-cycle progression impairs the ability to make time-point-to-time-point comparisons across replicates or between experiments with altered cell-cycle timing. Due to these challenges, replicates are often not included for the full time series (e.g., Spellman et al.4). When replicates for the entire time series are gathered, the data cannot be analyzed in aggregate, but rather a single replicate is used for analysis, and other replicates are often relegated to supplemental figures (e.g., Orlando et al.8). Furthermore, comparisons between experiments with different recovery or cell-cycle progression characteristics are difficult. The measurements of smaller intervals between an event of interest and a cell-cycle landmark (e.g., bud emergence, S-phase entry, or anaphase onset) can help reduce errors if these landmark events are tracked1,2,3,9,10,11,12. However, subtle but important differences may remain undetected or obscured using these ad hoc methods. Finally, single-cell analyses allow for analyzing cell-cycle progression without relying on synchronization or alignment13, though large-scale measurements in single-cell studies can be challenging and costly.
To overcome these difficulties, we developed the Characterizing Loss of Cell Cycle Synchrony (CLOCCS) model to aid the analysis of time-series measurements made on synchronized populations14,15. CLOCCS is a flexible mathematical model that describes the distribution of synchronized cells across cell-cycle phases as they are released from synchrony and progress through the cell cycle. The branching process framework enables the model to account for the asymmetric qualities of mother and daughter cells after division, as observed in S. cerevisiae, while still being useful for organisms that divide by fission, such as S. pombe. The model can take inputs from a diverse set of measurement types to specify the cell-cycle phase. It can ingest budding cell-cycle phase data, which includes measurements of the percent budded cells over time, allowing for the estimation of the number of cells outside of the unbudded G1 phase14,15. The model can also ingest flow cytometric data that measures the DNA content, thus enabling the assessment of landmark transitions from G1 to S, S to G2, and M to G115. Fluorescent morphological markers can also be used to identify the cell-cycle phase. The fluorescent labeling of myosin rings, nuclei, and spindle pole bodies (SPBs) can be used to determine the cell-cycle phase, and these were incorporated into the CLOCCS model11; however, these measurements will not be described in this protocol. Additionally, the septation index was used as an input for modeling data from S. pombe14. Thus, the model can be used for cell-cycle analyses in a variety of organisms and can be further expanded.
CLOCCS is a parametric model that allows for the full Bayesian inference of multiple parameters from the input data (e.g., budding percentage, DNA content). These parameters include the recovery time from synchrony, the length of the cell-cycle period (estimated separately for mother and daughter cells), and the average cell-cycle position of the cells at each time point. These parameters represent the behavior of the average cell in the population, enabling the researcher to map each time point to a cell-cycle position expressed as a lifeline point. The conversion to lifeline points depends on the CLOCCS parameters lambda (&#955;) and mu0 (&#181;0)14,15. The parameter &#955; corresponds to the average cell-cycle period of the mother cells. However, due to the mother-daughter delay14,15, this is not the average cell-cycle period of the full population that includes both the mother and daughter cells. CLOCCS additionally infers the parameter delta (&#948;), which corresponds to the mother-daughter delay and, thus, allows for the calculation of the average cell-cycle period of the full population. Finally, because each experiment begins after release from cell-cycle synchronization, the time required to recover from the synchronization method is represented by the CLOCCS parameter &#181;0. CLOCCS fits a model to the input cell-cycle phase data and then infers these parameters using a random walk Markov chain Monte Carlo algorithm14,15. By mapping multiple experiments to a common cell-cycle lifeline time scale, direct phase-specific comparisons can be made between replicates or experiments where the recovery time or cell-cycle periods are not identical8,14,15.
As synchronized populations lose synchrony at some rate over the course of the time series14,15,16,17, variability in the rate of synchrony loss can also impede quantitative comparisons across experiments. By identifying the location of populations and the variance in their distributions, CLOCCS accounts for differences in rates of synchrony loss. This powerful tool allows for specific and detailed comparisons across experiments, thus providing the ability to directly make relevant comparisons not only between replicates but also between environmental conditions, mutants, and even species that have dramatically different cell-cycle timing14,15.
This paper describes a method using CLOCCS to estimate parameters by fitting data from synchrony/release time-series experiments, map the data to a common lifeline scale, and then make relevant comparisons between replicates or experiments. Lifeline alignment allows for direct phase-specific comparisons across these experiments, which allows for the aggregation and comparison of replicates and for making more relevant comparisons across experiments with different recovery timings and cell-cycle periods.

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>2x PBS</td>
			<td></td>
			<td></td>
			<td>For Fixative Solution. Described in Leman 2014.</td>
		</tr>
		<tr>
			<td>4% formaldehyde</td>
			<td></td>
			<td></td>
			<td>For Fixative Solution.</td>
		</tr>
		<tr>
			<td>100% Ethanol</td>
			<td></td>
			<td></td>
			<td>For flow cytometry fixation. Described in Haase 2002.</td>
		</tr>
		<tr>
			<td>CLOCCS</td>
			<td></td>
			<td></td>
			<td>https://gitlab.com/haase-lab-group/cloccs_alignment.git</td>
		</tr>
		<tr>
			<td>Flow Cytometer</td>
			<td></td>
			<td></td>
			<td>For flow cytometry protocol.</td>
		</tr>
		<tr>
			<td>Git</td>
			<td></td>
			<td></td>
			<td>https://git-scm.com/</td>
		</tr>
		<tr>
			<td>Java 19</td>
			<td></td>
			<td></td>
			<td>https://www.oracle.com/java/technologies/downloads/#java19</td>
		</tr>
		<tr>
			<td>Microscope</td>
			<td></td>
			<td></td>
			<td>For counting cells and buds.</td>
		</tr>
		<tr>
			<td>Miniconda</td>
			<td></td>
			<td></td>
			<td>https://docs.conda.io/en/latest/</td>
		</tr>
		<tr>
			<td>Protease solution</td>
			<td></td>
			<td></td>
			<td>For flow cytometry protocol. Described in Haase 2002.</td>
		</tr>
		<tr>
			<td>RNAse A solution</td>
			<td></td>
			<td></td>
			<td>For flow cytometry protocol. Described in Haase 2002.</td>
		</tr>
		<tr>
			<td>SYTOX Green Nucleic Acid Stain</td>
			<td>Invitrogen</td>
			<td>S7020</td>
			<td>For flow cytometry staining. Described in Haase 2002.</td>
		</tr>
		<tr>
			<td>Tris</td>
			<td></td>
			<td></td>
			<td>pH 7.5</td>
		</tr>
	</tbody>
</table>

alignment of synchronized time-series data using the characterizing loss of cell cycle synchrony model for cross-experiment comparisons

Investigating the cell cycle often depends on synchronizing cell populations to measure various parameters in a time series as the cells traverse the cell cycle. However, even under similar conditions, replicate experiments display differences in the time required to recover from synchrony and to traverse the cell cycle, thus preventing direct comparisons at each time point. The problem of comparing dynamic measurements across experiments is exacerbated in mutant populations or in alternative growth conditions that affect the synchrony recovery time and/or the cell-cycle period. 
We have previously published a parametric mathematical model named Characterizing Loss of Cell Cycle Synchrony (CLOCCS) that monitors how synchronous populations of cells release from synchrony and progress through the cell cycle. The learned parameters from the model can then be used to convert experimental time points from synchronized time-series experiments into a normalized time scale (lifeline points). Rather than representing the elapsed time in minutes from the start of the experiment, the lifeline scale represents the progression from synchrony to cell-cycle entry and then through the phases of the cell cycle. Since lifeline points correspond to the phase of the average cell within the synchronized population, this normalized time scale allows for direct comparisons between experiments, including those with varying periods and recovery times. Furthermore, the model has been used to align cell-cycle experiments between different species (e.g., Saccharomyces cerevisiae and Schizosaccharomyces pombe), thus enabling direct comparison of cell-cycle measurements, which may reveal evolutionary similarities and differences.

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons  

Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

A major challenge of analyzing time-series experiments is that they often differ in the length of recovery from synchrony and the cell cycle period. So measurements from different experiments cannot readily be compared or analyzed in aggregate without alignment. Clocks lifeline alignment is a method for phase specific and biologically relevant comparisons between experiments and for aggregating multiple replicate experiments both of which were previously difficult or impossible.Previously phase specific and biologically relevant comparisons were made by tracking landmark events. However, using these ad hoc methods, subtle but important differences remain undetected. Comparison between time series experiments is particularly difficult between experiments with significant differences in timing such as in mutant populations or growth conditions that affect the synchrony recovery time or the cell cycle period.Clocks lifeline alignment allows for phase specific comparison in these cases. We have used clocks to align time series transcriptomic and proteomic data, which allowed for the direct comparison between the dynamics of the mRNA and the corresponding protein. Furthermore, we align time series experiments across different species, providing critical insights into cell cycle evolutionary changes.

The steps described in the above protocol and in the workflow in Figure 1 were applied to five cell-cycle synchronized time-series experiments to demonstrate two representative comparisons: between replicates with different synchrony methods (mating pheromone and centrifugal elutriation18) and sequencing platforms (RNA-sequencing [RNA-seq] and microarray), as well as across experimental conditions. Multiple experiments were performed with S. cerevisiae,&#160;...

Watch this Scientific Journal Video about Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons at JoVE.com

One challenge of analyzing synchronized time-series experiments is that the experiments often differ in the length of recovery from synchrony and the cell-cycle period. Thus, the measurements from different experiments cannot be analyzed in aggregate or readily compared. Here, we describe a method for aligning experiments to allow for phase-specific comparisons.

Investigating the cell cycle often depends on synchronizing cell populations to measure various parameters in a time series as the cells traverse the cell ...