Accurate, precise modeling of cell proliferation kinetics from time-lapse imaging and automated image analysis of agar yeast culture arrays

Abstract

Background: Genome-wide mutant strain collections have increased demand for high throughput cellular phenotyping (HTCP). For example, investigators use HTCP to investigate interactions between gene deletion mutations and additional chemical or genetic perturbations by assessing differences in cell proliferation among the collection of 5000 S. cerevisiae gene deletion strains. Such studies have thus far been predominantly qualitative, using agar cell arrays to subjectively score growth differences. Quantitative systems level analysis of gene interactions would be enabled by more precise HTCP methods, such as kinetic analysis of cell proliferation in liquid culture by optical density. However, requirements for processing liquid cultures make them relatively cumbersome and low throughput compared to agar. To improve HTCP performance and advance capabilities for quantifying interactions, YeastXtract software was developed for automated analysis of cell array images.

Results: YeastXtract software was developed for kinetic growth curve analysis of spotted agar cultures. The accuracy and precision for image analysis of agar culture arrays was comparable to OD measurements of liquid cultures. Using YeastXtract, image intensity vs. biomass of spot cultures was linearly correlated over two orders of magnitude. Thus cell proliferation could be measured over about seven generations, including four to five generations of relatively constant exponential phase growth. Spot area normalization reduced the variation in measurements of total growth efficiency. A growth model, based on the logistic function, increased precision and accuracy of maximum specific rate measurements, compared to empirical methods. The logistic function model was also more robust against data sparseness, meaning that less data was required to obtain accurate, precise, quantitative growth phenotypes.

Conclusion: Microbial cultures spotted onto agar media are widely used for genotype-phenotype analysis, however quantitative HTCP methods capable of measuring kinetic growth rates have not been available previously. YeastXtract provides objective, automated, quantitative, image analysis of agar cell culture arrays. Fitting the resulting data to a logistic equation-based growth model yields robust, accurate growth rate information. These methods allow the incorporation of imaging and automated image analysis of cell arrays, grown on solid agar media, into HTCP-driven experimental approaches, such as global, quantitative analysis of gene interaction networks.

Figure 1

An overview of the YeastXtract image analysis algorithm. (a) A limited time series of four replicate cell arrays is shown. The arrays were created from serial 2-fold dilution of a 1:4 dilution of an overnight culture, skipping rows with each dilution and backfilling skipped rows. (b) A time series of one cell array from Panel A is shown at larger magnification. (c) Depiction of the first step of spot detection. A grid is created from the local maximum values after summing row and column pixel intensities over the entire array image (see Materials and Methods). The summed row and column pixel intensities are plotted at the edges of the array. (d) Depiction of the second step of spot detection. A cell containing each spot is defined by the 50 × 50 Pixel square surrounding the grid intersections shown in panel C. Within each cell, the horizontal and vertical diameters of each spot are calculated as the pixel distance between threshold values of summed column and row pixel intensities. An ellipse is drawn around each spot based on the resulting diameters. Spot detection is more precise for darker spots. Hence, the last time point is used for spot detection and those ellipses are used for extracting signal intensities from aligned time series of images of each cell array. (e) After spot detection, the background local to each spot is subtracted and remaining signal intensities are calculated by summing pixel values inside each ellipse. (f) Spot intensities are plotted versus time and used for growth modeling.

Figure 2

Biomass correlates linearly with spot intensity of imaged cultures. An overnight culture was first diluted 1:4 in water and then serially diluted (3:4) in column A of a 96 well plate. All cultures were then 2-fold serial-diluted across each row, and 4 μL of the resulting cell suspension was spotted to agar media. The cell array was imaged 23 hours after spotting and cultures were immediately excised and resuspended in 2 mL of ice-cold water. Biomass was calculated by particle size analysis of each culture resuspension. The data used to generate this figure are in Additional file 2. (a) The numerical output (spot intensity) from YeastXtract is plotted vs. biomass for each culture. Biomass is calculated as the total cell number times the median cell volume (also plotted for each culture). (b) The image used for this analysis is shown along with the ellipses used for signal extraction.

Figure 3

Spot intensities of culture images are used for kinetic analysis of proliferation. An overnight culture was serially diluted, by 2-fold, across a 96- well plate. (a) Raw image intensities are plotted versus time for a representative culture at each dilution. (b) The images of spot cultures for each data point in panel (a) are shown. (c) After fitting the data to the logistic equation, TMR, which is the time at which the overall population growth rate is maximal, was calculated for each curve and is plotted versus time. The difference between values of TMR for each curve reflects the doubling time, since cultures were created by serial two-fold dilution. (d) The spot intensities were normalized by spot area, and curves were shifted on the time axis by the difference between TMR of the culture and TMR of the 256x-diluted culture.

Figure 4

Normalizing spot intensity by spot area increases precision of growth curve analysis. An overnight culture was diluted 1:2000 and distributed into a 96 well plate. Agar arrays were printed using 2 uL and 4 uL drops. A time series of images was collected for 72 hrs. The data used to generate this figure are in Additional file 2. (a) From the final time point, spot intensity is plotted against spot area (scale to left), and normalized spot area is also plotted (scale to right). (b) Averaged data from all 96 cultures (4 μL drop array) are plotted for normalized and non-normalized spot intensities. Standard deviation bars show the effect of spot area normalization on measurement variation across time. (c) To further see the effect of normalization, arrays made with 2 μL and 4 μL spots from the same starting culture were analyzed. The averaged data from each set of 96 cultures, normalized and non-normalized, were plotted vs. time. (d) To observe the effect of spot area normalization on the MSR and AUGC, non-normalized and normalized values for each CPP were plotted vs. spot area.

Figure 5

Spot intensity time series data are accurately modeled by the logistic growth equation. Spot intensity data from a typical spot culture, on the edge of a cell array, were used to illustrate three different growth models. (a) Raw spot intensity is plotted versus time. Also plotted are the growth rate and specific growth rate, as calculated directly from the raw data. (b) A spline was used to fit the raw data from panel A. The raw data are plotted vs. time, along with the fitted growth curve, growth rate, and specific growth rate. (c) The logistic growth equation was used to fit the raw data and to calculate growth rate and specific growth rate. Refer to Tables 1 and 2 for comparison of cell proliferation phenotype values obtained by each model.

Figure 6

Data filtering is used to reduce the variable effect of spot area increases on growth curve modeling. (a) The increase in spot culture area, between 39 and 72 hours, is plotted for 96 replicate cultures (an 8 × 12 cell array). Internal and edge cultures are labeled differently to highlight the increases in spot area of edge cultures. (b) The spot intensity, spot area, growth rate (derived from a spline fit), and logistic-fitted growth curve are plotted vs. time to illustrate that the initial carrying capacity is reached about the time that the spot area begins to increase (after ~40 hrs in this example). Hence, late data are filtered to avoid the effect of this artifact on growth modeling with the logistic equation (see Materials and Methods).

Figure 7

Dense initial population cultures can be used to measure lag time. Lag time is defined as the delay that a culture demonstrates from the time it is freshly inoculated to the time that it achieves its minimal doubling time. The spline model was used to measure lag for a representative culture printed at (a) lower dilution (1:4) and (b) higher dilution (1:2000). In panel (a), lag time can be directly observed, because the spot is detectable (average pixel intensity > 1) at time = 0. In contrast, in panel (b) cultures have passed through lag phase and exhibit MSR by the time spot intensities reach the threshold of detection.

Figure 8

The logistic growth equation model is relatively robust against sparse data. Using the data represented in Tables 1 and 2, time points were randomly removed [see Additional file 5], and MSR was recalculated using each growth model. Average MSR (with standard error bars; n = 96) is plotted against the number of data points removed. The logistic model exhibits lower variation between replicates and is more precise as data is removed.