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

Summary

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.

Abstract

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.

Introduction

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 progression^{1,2,3,4,5,6,7,8}. 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 tracked^{1,2,3,9,10,11,12}. 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 populations^14,15. 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 phase^14,15. 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 (λ) and mu0 (µ₀)^14,15. The parameter λ corresponds to the average cell-cycle period of the mother cells. However, due to the mother-daughter delay^14,15, 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 (δ), 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 µ₀. CLOCCS fits a model to the input cell-cycle phase data and then infers these parameters using a random walk Markov chain Monte Carlo algorithm^14,15. 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 identical^8,14,15.

As synchronized populations lose synchrony at some rate over the course of the time series^14,15,16,17, 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 timing^14,15.

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.

Protocol

1. Collecting cell-cycle phase and experimental data

1. 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, ensuring that the time series is at least two full cell-cycle periods in length, and optimally, collect at least 10 samples per cell cycle. At each time point, collect a sample for cell-cycle phase data (budding or flow cytometry) and a sample for experimental data, as described below.
2. If using budding data as the cell-cycle phase data, collect data on budding for the CLOCCS alignment.
   1. Sample throughout the time series. For each time point, collect cells, and fix them by mixing 200 µL of sonicated cell culture with 200 µL of fixative solution, as described in Leman et al.¹⁸.
   2. For standard budding, count at least 200 cells per time point using a transmitted light microscope with a 40x objective and a hemocytometer. Add the cell sample from step 1.2.1 to the hemocytometer, and dilute if the density prevents counting. Record the number of budded and unbudded cells at each time point. Calculate the percent of budded cells, and plot for each time point in a budding curve.
      NOTE: Other methods of specifying the cell-cycle phase information are available, but these are not described in this protocol. The other methods are described in the CLOCCS readme and in a previous work¹¹.
3. If using flow-cytometric DNA content data as the cell-cycle phase data, collect flow cytometry DNA staining data for the flow-cytometric CLOCCS alignment.
   1. Sample throughout the time series. For each time point, collect cells, and fix them as described in Haase and Reed²⁰.
   2. Stain the DNA, and analyze using standard flow cytometric analysis. A recommended staining protocol for S. cerevisiae is described in Haase and Reed²⁰.
4. Collect associated omics or related experimental data. For standard transcriptomic data, collect as described in Leman et al.¹⁸ and Kelliher et al.^21,22. Ensure that the data are associated with time points containing cell-cycle phase data to allow for downstream alignment. For optimal alignment, ensure that each time point containing experimental data also has phase data associated with it.
   ​NOTE: The experimental data can take many forms. Traditionally, we use the alignment method described for aligning time-series transcriptomic experiments. However, any type of data associated with time points can be aligned (i.e., proteomics²²).

2. Installing the required software

NOTE: This section assumes that Conda, Java 19, and Git are already installed (Table of Materials).

1. Download the CLOCCS_alignment repo by entering the following command into the terminal:
   git clone git clone https://gitlab.com/haase-lab-group/cloccs_alignment.git
2. Create a Conda environment using the conda_req.yml file by entering the following command into the terminal in the folder where the CLOCCS_alignment repo was cloned:
   conda env create -f conda_req.yml

3. Using CLOCCS to parameterize the experiments

1. Double-click on the cloccs_v2023.jar file in the CLOCCS folder in the CLOCCS_alignment repo, and wait for a graphical user interface to open. This screen allows for inputting options for the CLOCCS run and displays the results once run.
2. Input the general settings.
   1. Set Sim Anneal, Burn In, and Iterations by typing in the associated text input boxes. Sim Anneal (simulated annealing) identifies good starting parameter values, Burn In searches for posterior modes, and the final stage allows for all posterior inferences to be drawn. Higher values increase the run-time but also increase the accuracy.
   2. Input the experimental conditions by specifying the temperature in Celsius and the synchronization method using the text box labeled Temperature and the dropdown menu Synchro. Method, respectively.
   3. Optionally configure the advanced settings in the Advanced Settings menu. The advanced settings allow for priors to be set for each of the parameters ("mu0", "sigma0", "sigmav", "lambda", "bud.start", "bud.end").
      NOTE: More information regarding the advanced settings can be found in the readme.txt in the CLOCCS folder of the CLOCCS_alignment repo.
3. Input the settings for use with the budding data.
   1. Choose the appropriate selection from the Model Type dropdown menu. The default option Bud is for standard budding information for budding yeast.
      NOTE: Other more advanced options also exist in the dropdown menu: Mutant for budding information for mutants that undergo multiple budding cycles without division, BudSSLSMR for budding information and additional spindle pole body and myosin ring information, and BudNucDivNeck for budding information and additional dividing and bud neck nuclei information. These advanced options are described in the CLOCCS readme and in previous work^11,14,15.
   2. Import the data using the Data Import panel by typing into the text input boxes or by uploading a file by clicking on the Select File button. The first column specifies the time points. The remaining two columns specify the budding data and can take any of the following options: the number of unbudded cells (No Bud), the number of budded cells (Bud), or the total number of cells (Total).
4. Input the settings for use with the flow cytometric data. For each experiment, run either step 3.3 or step 3.4.
   NOTE: Flow cytometric data and budding data can be used together. Though previously we described running them together¹⁵, for this tool, they must be run independently and then compared.
   1. Convert the .fcs files into the correct CLOCCS input format for flow cytometry by following the instructions in Supplemental File 1 (also found in the CLOCCS_alignment repo as CLOCCS/flow_cytometry_conversion_instructions.txt).
   2. Select the Flow selection from the Model Type dropdown menu.
   3. Import the data using the Data Import panel. Click on Select File, and select the file generated in step 3.4.1.
   4. Select the time points for which a flow cytometric CLOCCS fit should be plotted by selecting the time points in the Times for Fitting box.
5. Once all the inputs have been selected for either budding or flow cytometry, click on the Apply button, and then click on the Sample button at the top of the screen.
6. View the budding curve or flow cytometry plots with the predicted fits by selecting the Predicted Fits tab. This tab opens by default immediately after the previous step.
7. View the parameter histograms for each parameter by selecting the Parameter Histograms tab and then selecting the sub-tab that corresponds to the parameter of interest from the following options: mu0, delta, sigma0, sigmav, lambda, bud.start, bud.end, etc.
8. View the posterior score plot by selecting the Posterior Score tab.
9. View the settings, and further alter them by selecting the Settings tab; view the log of the previous runs by selecting the Log tab.
10. Obtain the CLOCCS parameters from the fit by selecting the Posterior Parameters tab. The resulting table will have the following form: each row consists of a parameter, with the final row being the posterior. The columns consist of the predicted parameter for the mean, the 2.5% lower confidence interval, the 97.5% upper confidence interval, and the acceptance rate.
    1. Record the parameters used for alignment for each experiment: the recovery time from synchrony (µ₀) and the average cell-cycle period of the mother cells (λ).
    2. Calculate the cell-cycle period by calculating the average of the mother cell period (λ) and the daughter cell period (λ + δ), where δ is the daughter-specific delay.
       ​NOTE: Repeat section 3 with all the experiments to be included in the comparisons.

4. Conversion of time points to lifeline points using the Python conversion functions and the CLOCCS parameters

NOTE: Conversion between time points and lifeline points requires two conversion formulas²¹. A Python implementation for conversion and data visualization are available in the CLOCCS_alignment repo and described below.

1. Activate the Conda environment by entering the following command into the terminal: conda activate CLOCCS_alignment
2. Open an interactive Python notebook by typing the following command into the terminal: jupyter notebook
3. Create a new Python notebook in the desired folder.
   NOTE: An example notebook has been included to demonstrate standard use and can be found in Alignment/JOVE_example.ipynb in the CLOCCS_ alignment repo.
4. Import the Python file containing the alignment functions by running the following command in the first cell:
   ​%run path_to_repo/cloccs_alignment/Alignment/utilities.py
   1. Substitute the path to the CLOCCS_alignment repo for path_to_repo.
5. If using budding data as the cell-cycle phase data, import a data frame containing the percent budded at each time point by running the following command in a new cell:
   ​budding_df = pd.read_csv("path_to_folder/budding_filename.tsv", sep ="\t", index_col=0)
   1. Substitute the appropriate file path and filename. If the file is a .csv file, remove sep ="\t"
6. If using budding data as the cell-cycle phase data, align the budding data to a lifeline point time scale by entering the following function into a new cell:
   ​aligned_budding_df = df_conversion_from_parameters(budding_df, timepoints, param_mu0, param_lambda)
   1. For timepoints, substitute a list of the time points to be the index of the budding_df data frame.
   2. For param_mu0 and param_lambda, substitute the learned parameters from the budding CLOCCS run in section 3 for the experiment.
7. If using flow cytometry data, import the flow cytometry data by running the following command in a new cell:
   ​flow_samples = flow_cytometry_import(flow_input_folder)
   1. For flow_input_folder, substitute the appropriate path to the folder containing the flow cytometry .fcs files.
8. If using flow cytometry data, generate a conversion table between the time points and lifeline points for each experiment by typing the following command into a new cell:
   ​flow_converter = convert_tp_to_ll(timepoints, param_mu0, param_lambda)
   1. For timepoints, substitute a list of the time points from the flow cytometry data.
   2. For param_mu0 and param_lambda, substitute the learned parameters from the flow cytometry CLOCCS run in section 3 for the experiment.
9. Import the data frame containing the experimental data into the notebook by running the following command in a new cell:
   ​data_df = pd.read_csv("path_to_folder/exp_data_filename.tsv", sep ="\t", index_col=0)
   1. Substitute the appropriate file path and filename. If the file is a .csv file, remove sep ="\t".
      NOTE: This can be done for any tabular data. The experimental data must simply have the time points as either the columns or the index of the data frame. Example data can be found in the CLOCCS_alignment repo.
10. Align the experimental data to a lifeline point time scale by entering the following function into a new cell:
    ​lifeline_aligned_df = df_conversion_from_parameters(data_df, timepoints, param_mu0, param_lambda, interpolate, lowerll, upperll)
    1. For timepoints, substitute a list of the time points as the index or the columns of the experimental data_df from the previous step.
    2. For param_mu0 and param_lambda, substitute the values obtained in section 3 from CLOCCS.
       NOTE: The parameters can come from any CLOCCS run performed on any of the accepted cell-cycle phase data types.
    3. Optionally, substitute interpolate with True or False, or leave blank (the default is False).
       NOTE: When set to False, the data will not be interpolated. When set to True, the lifeline points will be rounded and interpolated to fill in the values between the lifeline points, such that there is a point per integer in the range of the lifeline points. This allows for better comparison across datasets.
    4. Optionally, substitute lowerll and upperll with None or integer values.
       ​NOTE: When set to None, all of the lifeline points after interpolation are kept. When integers are supplied, this truncates the data so that the lifeline points range from the lowerll to the upperll. This allows for comparison across datasets with a different lowerll or upperll.
11. Download the lifeline-aligned dataset by entering the following command into a new cell: lifeline_aligned_df.to_csv("path_to_desired_location/name_of_file.tsv", sep = "\t")
12. Repeat steps 4.5-4.11 with all the experiments to be included in the comparisons.

5. Comparing budding curves and flow cytometry data

1. Plot the budding curves prior to alignment using the Python utilities function by entering the following command into a new cell:
   ​plot_budding_curves(list_of_budding_curves, list_for_legend = leg_list, point_type = str_type, title = str_title)
   1. Substitute a list containing the data frames of all the desired budding curves for plotting for list_of_budding_curves-[bud_df1, bud_df2, bud_df3].
   2. Substitute a list of the labels for the legend-[Experiment 1, Experiment 2, Mutant] for leg_list if desired. If not, exclude or substitute None.
   3. Substitute time for str_type.
   4. Substitute a string title Comparison Budding Curves for str_title if desired. If not, substitute None, or exclude.
2. Plot the budding curves after alignment using the Python utilities function by following the instructions in step 5.1, but with a list of aligned budding curves substituted for list_of_budding_curves and with lifeline for point_type instead of time.
3. To plot the flow cytometry data, plot the associated data from the .fcs files at the corresponding lifeline points using the converter generated in step 4.8.
4. Convert the lifeline points to the cell-cycle phase by using the converter table (Table 1).
   ​NOTE: This can also be plotted by following the instructions in step 5.1, but with phase for point_type instead of time.

6. Comparing the experimental data

1. Determine the gene list to be plotted in the line graphs based on literature information or the genes of interest for the research.
2. Use the provided plot_linegraph_comparison in the Python utilities file to perform line graph comparisons on the original, aligned, or aligned and interpolated data frame by typing the following command into a new cell:
   ​plot_linegraph_comparison(list_of_dfs, list_for_legend, genelist, point_type = str_type, title = str_title)
   1. Substitute a list of the data frames of the experiments to be compared for list_of_dfs.
      NOTE: The data frames can be unaligned or aligned; however, the corresponding point_type must be input in step 6.2.4.
   2. Substitute a list of the titles for each data frame in the same order as the list of data frames for list_for_legend.
   3. Substitute a list of the gene names (which must be included in the index of the data frames) to be plotted for genelist.
   4. Substitute the point type for str_type. Use lifeline (the default is lifeline point scale) or phase (the cell-cycle phase lifeline scale) for the aligned data frames in step 6.2.1 or time for the unaligned data frames in step 6.2.1.
   5. Substitute an optional string title for str_title.
3. Determine the gene list to be included in the heatmap using the literature or algorithms to determine the top periodic genes.
   NOTE: For proper heatmap comparisons, the data should be aligned, interpolated, and timescale-adjusted in step 6.2; it should have the same starting and ending lifeline value for each experiment.
   1. Run periodicity algorithms to determine the top periodic genes^23,24, or use the desired alternative methods to determine the gene list (i.e., literature results).
   2. Import a .csv or .tsv gene list file into the notebook using the following command in a new cell:
      sort_df = pd.read_csv("path_to_folder/sorting_filename.tsv", sep="\t", index_col=0)
   3. Substitute the appropriate file path and filename. If the file is a .csv file, remove sep="\t".
4. Use the provided function plot_heatmap_comparison in the Python utilities file to perform a heatmap comparison on the aligned, interpolated, and phase-aligned data frame by typing the following command into a new cell:
   ​plot_heatmap_comparison(list_of_dfs, list_for_legend, genelist, title = str_title)
   1. Substitute a list of the aligned data frames of the experiments to be compared for list_of_dfs.
   2. Substitute a list of the titles for each data frame in the same order as the list of data frames for list_for_legend.
   3. Substitute a list of the gene names (which must be included in the index of the data frames) to be plotted for genelist.
   4. Substitute an optional string title for str_title.
      NOTE: The first data frame in the list is the one that will be used for ordering the genes in the heatmap. The genes will be ordered by the maximum in the first period for that data frame, and the same order will be used for the subsequent data frames in the list.

Results

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, and c...

Discussion

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 experiment^14,15. CLOCCS uses the input cell-cycle phase data to infer the parameters for each experiment, which are the...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
2x PBS			For Fixative Solution. Described in Leman 2014.
4% formaldehyde			For Fixative Solution.
100% Ethanol			For flow cytometry fixation. Described in Haase 2002.
CLOCCS			https://gitlab.com/haase-lab-group/cloccs_alignment.git
Flow Cytometer			For flow cytometry protocol.
Git			https://git-scm.com/
Java 19			https://www.oracle.com/java/technologies/downloads/#java19
Microscope			For counting cells and buds.
Miniconda			https://docs.conda.io/en/latest/
Protease solution			For flow cytometry protocol. Described in Haase 2002.
RNAse A solution			For flow cytometry protocol. Described in Haase 2002.
SYTOX Green Nucleic Acid Stain	Invitrogen	S7020	For flow cytometry staining. Described in Haase 2002.
Tris			pH 7.5