An Easy-To-Use Simulation Program Demonstrates Variations in Bacterial Cell Cycle Parameters Depending on Medium and Temperature

Many studies are performed on chromosome replication and segregation in Escherichia coli and other bacteria capable of complex replication with C phases spanning several generations. For such investigations an understanding of the replication patterns, including copy numbers of origins and replication forks, is crucial for correct interpretation of the results. Flow cytometry is an important tool for generation of experimental DNA distributions of cell populations. Here, a Visual Basic based simulation program was written for the computation of theoretical DNA distributions for different choices of cell cycle parameters (C and D phase durations, doubling time etc). These cell cycle parameters can be iterated until the best fit between the experimental and theoretical DNA histograms is obtained. The Excel file containing the simulation software is attached as supporting information. Cultures of Escherichia coli were grown at twelve different media and temperature conditions, with following measurements by flow cytometry and simulation of the DNA distributions. A good fit was found for each growth condition by use of our simulation program. The resulting cell cycle parameters displayed clear inter-media differences in replication patterns, but indicated a high degree of temperature independence for each medium. The exception was the poorest medium (acetate), where the cells grew with overlapping replication cycles at 42°C, but without at the lower temperatures. We have developed an easy-to-use tool for determination of bacteria's cell cycle parameters, and consequently the cells' chromosome configurations. The procedure only requires DNA distribution measurements by flow cytometry. Use of this simulation program for E. coli cultures shows that even cells growing quite slowly can have overlapping replication cycles. It is therefore always important not only to assume cells' replication patterns, but to actually determine the cell cycle parameters when changing growth conditions.

growing without overlapping replication rounds, the internal standard and the FITC staining are not necessary for the cell cycle analyses. Treating cells which have only one round of ongoing replication with rifampicin and cephalexin to determine the initiation age should be avoided, since rifampicin resistant initiations can occur for slowly growing populations (Flatten et al., 2009). Instead, the initiation age should be fitted directly by iteration until the theoretical and experimental histograms fit.
Cell growth and flow cytometry Grow cells in desired medium. Perform flow cytometry analyses (see methods section).

Simulation program input
Note that an example experimental histogram is provided in the Excel file (green curve) for testing. See guide for cells with overlapping replication cycles for more information. a) Open the Excel file "Simulation program" (supporting file 1), and activate macros.  d) The initiation generation is the current (type C in cell H4). e) Mb/channel (cell H3) can be found by dividing the DNA content of a peak by the peak's DNA channel. F. ex for E.coli, which has a chromosome size of 4.64 Mb, a sample with the one chromosome peak in channel 40 will have: 4,64Mb / 40channels = 0,116 Mb/channel. f) By varying the C period (cell B3) and the initiation age (E2) you can now find the best fit to your experimental sample. The standard deviation of the theoretical histogram (the width of the peaks) can be varied in cell H2. Press Ctrl+d to run the VBA macro after adjusting parameters. Compare the shape of the experimental (green) and theoretical (red) histogram to determine the fit. The quantitative deviation between the two histograms is also calculated (cell E5).
Simulation program output

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The termination age and generation are given in cells K6 and K7 respectively.
• The D period duration in B4.

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The percentage of cells in B-, C-, and D-phase are given in cells K2-4.
• In addition to the first graph, a second graph can also be found underneath. The theoretical histogram without a normal distribution is plotted in blue, so the effect of varying the standard deviation can be seen.

Step by step guide for cells with overlapping replication cycles
Cell growth and flow cytometry • Grow cells in desired medium. Treat cells with rifampicin and cephalexin. See methods section.
• Grow standard cells. Use a minimal medium to ensure a population containing only cells with one or two chromosomes. (See Tip 2 below.) • Perform flow cytometry analyses as described. The samples are now stained by FITC, and the internal standard is not (Tip 3). One "sample" should be FITC positive standard (added FITC negative standard as the other samples). Make sure to keep the peaks of the FITC-negative standard at fixed channels by tuning the PMT voltage (Torheim et al., 2000). (See Tip 4 for exclusion of standard.)

Simulation program input
Note that an example experimental histogram (green curve) is provided in the Excel file for testing. This histogram is the same as shown for cells grown in glucose medium at 37°C in the article ( Figure 2E). By inserting the parameters found for these cells (Table 1)  o If the rif/cpx sample contains one and two chromosome equivalents, then the initiation occurs in the current generation (type C in cell H4). See guide for cells without overlapping replication rounds.
o If the rif/cpx sample contains two and four chromosome equivalents, then the initiation occurs in the mother (type M in cell H4).
o If the rif/cpx sample contains four and eight chromosome equivalents, then the initiation occurs in the grandmother (type G in cell H4).
o If the rif/cpx sample contains eight and sixteen chromosome equivalents, then the initiation occurs in the great grandmother (type GG in cell H4). e) To find Mb/channel (cell H3), use the histogram of the rif/cpx treated sample. Divide the DNA content of a peak by the channel number. F. ex for E.coli, which has a chromosome size of 4.64 Mb, a sample containing two and four chromosomes in channel 60 and 120 will have: 2*4,64Mb / 60channels = 0,155 Mb/channel.
(If you experience some non-linearity in the fluorescence signal, the rif/cpx peaks nearest the bulk of the experimental histogram should be used.) f) Calculation of the initiation age can be performed in the Excel sheet. Insert the percentage of the population in the first peak in the histogram of the rif/cpx treated sample in cell N2. Make sure the correct initiation generation is already inserted in cell H4. The initiation timepoint is then given in cell N3, and can be inserted in cell E2. g) By varying the C period (cell B3) you can now find the best fit to your experimental sample. The standard deviation of the theoretical histogram can be varied in cell H2. Press Ctrl+d to run the VBA macro after adjusting parameters. Compare the shape and DNA axis placement of the experimental (green) and theoretical (red) histogram to determine the fit. The quantitative deviation between the two histograms is also calculated (cell E5). The initiation age can also be adjusted by a few minutes.
(Simulations can also be performed without the use of a rif/cpx sample, see Tip 5 below.) Simulation program output

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The termination age and generation are given in cells K6 and K7 respectively.

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The D period duration in B4.
• In addition to the first graph, a second graph can also be found underneath. The theoretical histogram without a normal distribution is plotted in blue, so the effect of varying the standard deviation can be seen.
• Not all parameter sets are valid for the software. If the box "Microsoft Visual Basic, Overflow" appears, press End, and vary the C-period by a minute. o Select all (CtrlA) and copy (Ctrl C) o Insert the numbers in the simulation program, cells C10-C265 • Tip 2: You should ideally use a standard with DNA content in about the same range as your sample cells. So if you find that your sample cells' average DNA value is high, you may consider making a new standard containing cells with two and four or four and eight chromosomes by treating more rapidly growing cells with rifampicin and cephalexin.
• Tip 3: If estimation of the cell size by FITC staining is not of interest, the internal standard can be stained by FITC instead of the samples to save time.
• Tip 4: If you are positive that your flow cytometer is stable you can exclude the standard. Run every other exponential and rif/cpx sample and make sure the positions of the rif/cpx peaks do not shift.
• Tip 5: If you do not want to or are unable to treat your cells with rif/cpx you can iterate the initiation timepoint as well as the C period and standard deviation (g). The initiation generation will also have to be estimated (d). For the Mb/channel parameter (e), use the histogram of the FITC positive standard instead.