Endy:F2620/Data Processing/Algorithm

Background subtraction

We subtracted a media background, Amedia, from the raw absorbance data, Araw, and assumed that the resulting data, Acorrected, was directly proportional to the number of cells in the well.

 $\frac{}{}A_{corrected} = A_{raw}-A_{media}$ ...Equation 1

We subtracted a fluorescent protein-free cell background, Gcells, from the the raw fluorescent data, Graw, and assumed that the resulting data Gcorrected was proportional to the total number of GFP molecules in the well [include note here about immature GFP?].

 $\frac{}{}G_{corrected} = G_{raw}-G_{cells}$ ...Equation 2

Unit conversion

We then used standard calibration curves (see here for absorbance and here for fluorescence) to convert the background-corrected data into absolute units (CFU/well and GFP molecules per well). The calibration equations used are shown in Equations 3 & 4.

 $\frac{}{}CFU = 3.1e8 * A_{corrected} - 1.6e6$ ...Equation 3 $\frac{}{}GFP = 7.0e8 * G_{corrected} + 6.0e11$ ...Equation 4

GFP synthesis rate calculations

To calculate the mean synthesis rate of GFP per cell, Scell, we assume the total GFP synthesis rate is equal to the time differential of GFP. Scell can be calculated as the total synthesis rate divided by CFU.

 $\frac{}{}S_{total} = \frac{d[GFP]}{dt}$ ...Equation 5 $\frac{}{}S_{cell} = \frac{S_{total}}{CFU}$ ...Equation 6

Ania's c++ code

• Load the data from the excel file. Read headers of the column to know the colony number and AHL type used. Form a lookup table. Separate the medium column at this point. Count how many repeats there is for each type.
• Find the GFP background by finding the non-induced column
• GFPpre-fit by fitting all the GFP background columns
• Fit medium for OD (find mean)
• For each OD subtract this mean (media)
• For each GFP we subtract the fitted background calculated for non-induced cells of this type (e.g. for cog-AHL we subtract fitted results for non induced cog-AHL from the raw data)
• Calibrate GFP relative units to conc of GFP (from Barry's calibration run): 1.16*10e-6*GFP+9.95*10e-4
• Fit GFP
• Fit OD (don't fit media anymore)
• Plot GFP, GFP/OD, dOD/dt, gamma, (GFP/OD)/dT, total sythesis and output (this is for debugging and outputs a huge .pdf and .tex)
• to params.csv outputs all the fitting parameters and errors (the errors are not really important)
• to surfaces.tsv output points for superimposed transfer functions in 3D (so you can plot the 3D surfaces yourself)
• evaluate the fitting equations for the total synthesis at many timepoints and select the hightest value from cog-AHL and store this time value.
• output to transfer.tsv all values of total function for all series at time calculated above and low/high repeat, st dev (Mathworld definition, I think it is what you call standard error), 95% confidence
• plot using gnuplot 3D superimposed lines "ser*.pdf" files (we don't use them anymore) surfaces (those are the green ones we post on wiki) into files "sersurf*.pdf") and the transfer functions to "tranfer.pdf" with 95% confidence intervals, transferlh.pdf transfer functions with low/high errors, where * is series number

Notes: 1. Evaluation of the total synthesis function is done using arbitrary precision numbers. B/c they exceeded double range