LARS

Look@Rates is a Matlab function for calculating substrate assimilation rates in cells from their isotopic composition determined by nanoSIMS. The function implements calculation approaches described in the manuscript

• Polerecky et al. (2021) Calculation and interpretation of substrate assimilation rates in microbial cells based on isotopic composition data obtained by nanoSIMS. Submitted to Frontiers in Microbiology.

Please contact the developer in case you encounter problems when running the function or if you find an error or a bug.

Install Look@Rates

1. You need Matlab to run Look@Rates. The core Matlab binaries should be sufficient, no need for extra toolboxes.

2. Download lookatrates.m from the matlab folder (see list of files above) and save it on your computer.

3. Create a subfolder called data in the same folder where you saved lookatrates.m. This is where the input xlsx files are expected to be and where the output will be exported.

4. A faster approach may be to click on the green Code button (at the top of this page) and download the zip-file of the entire LARS project, including the Matlab code, documentation, and the template input spreadsheet.

Input data

Look@Rates reads input data from a spreadsheet (xlsx format). The required data are organized in columns, with rows corresponding to individual cells (see an example below). Description of the required data is provided in Table 1 available in the folder manual. A template spreadsheet (called DataCells1.xlxs) is available in the data folder.

Output data

Look@Rates exports calculated rates as a new sheet (called rates) in the input spreadsheet (xlsx format). The output values are organized in columns, with rows corresponding to individual cells (see an example below). Description of the output data is provided in Table 2 available in the folder manual.

Run Look@Rates

1. In Matlab, set the working directory to the folder where you saved lookatrates.m.

2. In the Matlab command line, type lookatrates; (including the semi-colon) and press enter.

   This will execute the function with the following default values of the input paramers:

   • Input_file = 'DataCells1.xlsx' (name of the xlsx input file; the file is assumed to be in the data subfolder; see above)
   • Nsimul = 2000 (number of Monte-Carlo simulations for each cell)
   • pause_for_each_cell=1 (make a pause after calculating the rate for each cell; good for viewing the graphical results)
   • export_graphs_as_png=1 (export calculation results as a PNG image)

3. If you want to change the input parameters, run the function as

   lookatrates(Input_file, Nsimul, pause_for_each_cell, export_graphs_as_png);

   and specify the parameter values as you want. Use [] (i.e., an empty value) if you want to use a default value for a given input parameter. Examples of possible commands:

   lookatrates('DataCells2.xlsx');

   lookatrates([], 5000, 1);

   lookatrates('DataCells2.xlsx', [], [], 0);

4. Alternatively, you can change the default values of the input parameters by editing the lookatrates.m file in the Matlab editor and then proceed as explained in point 2. The default values are specified on line 28 (or thereabout).

Test runs

To check that everything works well, use DataCells1.xlsx, DataCells2.xlsx, and DataCells3.xlsx as input, and compare your output to the output in DataCells1-*.xlsx, DataCells2-*.xlsx, and DataCells3-*.xlsx, respectively. These data files are available in the data folder.

Calculation approach

Consult the manuscript above and Table 1 in the manual folder to become familiar with the meaning of the different parameters and variables used in the description below. Note that the description assumes assimilation of carbon (C), but the calculation method is applicable to any other element.

The general approach employed in Look@Rates is based on a Monte-Carlo method. It proceeds according to the following steps.

1. C content of the cell is calculated as C = ρ · V, uncertainty of the C content is calculated as ΔC = ρ · ΔV, and the average C content of the cell is calculated as ⟨C⟩ = ρ · ⟨V⟩, where V, ΔV, ⟨V⟩, and ρ are provided as input (see Table 1). See Important notes below if one or more of these parameters cannot be constrained by experimental data.

2. ¹³C atom fraction of the cell, x_j, is sampled from a normal distribution: x_j = N(mean=x, SD=Δx), where x and Δx is provided as input (see Table 1).

3. C content of the cell, C_j, is sampled from a distribution describing cells with partially synchronized cell cycles (see Eq. 17 in the manuscript). If ΔC is not too large and C is not too close to the critical value of C_max/2 or C_max (where C_max is calculated from ⟨C⟩ as described in the manuscript), this distribution is essentially a normal distribution, i.e., C_j = N(mean=C, SD=ΔC).

4. The substrate-normalized ¹³C atom fraction of the cell is calculated as

   x_S,j^E = (x_j - x_ini) / (x_S,eff - x_ini),

   where x_S,eff is the effective ¹³C atom fraction of the substrate and x_ini is the initial ¹³C atom fraction of the cell (both provided as input; see Table 1).

5. The carbon-specific carbon assimilation rate (in h^-1) is calculated as

   k_j = -(1/t) · ln(1-x_S,j^E)

   where t is the incubation time (provided as input; see Table 1).

6. The cell-specific carbon assimilation rate (in fmol C cell^-1 h^-1) is calculated according to four approaches:

   Approach A: r_j = k_j · ⟨C⟩ (later denoted as avg-cell-cycle)

   Approach B: r_j = k_j · C_j (later denoted as end-SIP)

   Approach C (accounts for cell division): r_j = Z^-1(t, C_j, C_max, x_S,j^E) (later denoted as avg-SIP-div)

   Approach NON-DIV (does not account for cell division): r_j = (x_S,j^E · C_j)/t (later denoted as avg-SIP-nondiv)

   See the manuscript above for the interpretation of the assimilation rates calculated by the different approaches.

7. Steps 2-6 are repeated for N=Nsimul randomly sampled values of x_j and C_j, yielding N=Nsimul values of predicted rates, r_j. Mean and SD are calculated based on these values, separately for each calculation approach.

8. Results for the current cell are displayed and exported in a PNG file. Example is shown here:

   
   • The top-left graph shows the predicted substrate normalized ¹³C atom fraction, x_S^E, and cell cycle stage, s, of the cell as a function of time. Because both values are random variables, they are displayed as time-dependent histograms. That is, at a give time, the black and cyan band represents the probability distribution (in a log-scale) of predicted x_S^E and s values, respectively. The cell cycle stage is calculated from the C content of the cell as s=C/(C_max/2)-1, where C_max = ⟨C⟩ · ln(2) · 2. Binary cell division occurs when the C content of the cell reaches the critical value C_max, i.e., when s reaches 1. After division, the C content of the cell is set to C_max/2, i.e., s is set to 0.
   • The top-middle graph shows a scatter plot of the sampled pairs [x_j, C_j] (see Steps 2-3 above).
   • The top-right graph shows a 2D-histogram of the sampled pairs [x_j, C_j] (see Steps 2-3 above).
   • The bottom-left graph shows histograms of the initial (s_ini) and predicted final (s_end) cell cycle stage.
   • The bottom-middle graph shows a 2D-histogram of the predicted pairs [r_j, s_ini,j], where r_j is calculated according to Approach C.
   • The bottom-right graph shows histograms of r values predicted by the four approaches listed above (Step 6).

9. Steps 1-8 are repeated for all cells in the input file.

10. Mean and SD values of the calculated rates are exported. Consult Table 2 in the manual folder for the description of the exported values.

Important notes

1. If ⟨C⟩ is known but C is unknown, only Approach A is used to calculate r. This happens when the spreadsheet-cell avgVcell contains a positive value and the spreadsheet-cell Vcell is empty.

• If C is known but ⟨C⟩ is unknown, only Approach B and NON-DIV are used to calculate r. This happens when the spreadsheet-cell Vcell contains a positive value and the spreadsheet-cell avgVcell is empty.

• If both C and ⟨C⟩ are known, r is calculated by all approaches. This happens when both spreadsheet-cells Vcell and avgVcell contain a positive value.