Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data.

Comparable measurements are a sine qua non for both science and engineering, and one 2 of the most commonly needed measurements of microbes is the number (or 3 concentration) of cells in a sample. The most common method for estimating the 4 number of cells in a liquid suspension is the use of optical density measurements (OD) 5 at an absorbance wavelength of 600nm (OD600) [1]. The dominance of OD 6 measurements is unsurprising, particularly in plate readers, as these measurements are 7 extremely fast, inexpensive, simple, relatively non-disruptive, high-throughput, and 8 readily automated. Alternative measurements of cell count-microscopy (with or 9 without hemocytometer), flow cytometry, colony forming units (CFU), and others, 10 e.g., [2][3][4][5]-lack many of these properties, though some offer other benefits, such as 11 distinguishing viability and being unaffected by cell states such as inclusion body 12 formation, protein expression, or filamentous growth [6]. 13 A key shortcoming of OD measurements is that they do not actually provide a direct 14 measure of cell count. Indeed, OD is not even linearly related to cell count except 15 within a limited range [7]. Furthermore, because the phenomenon is based on light 16 scatter rather than absorbance, it is relative to the configuration of a particular 17 instrument. Thus, in order to relate OD measurements to cell count-or even just to 18 compare measurements between instruments and experiments-it is necessary to 19 establish a calibration protocol, such as comparison to a reference material. 20 While the problems of interpreting OD values have been studied (e.g., [1,6,7]), no 21 previous study has attempted to establish a standard protocol to reliably calibrate 22 estimation of cell count from OD. To assess reliability, it is desirable to involve a large 23 diversity of instruments and laboratories, such as those participating in the 24 International Genetically Engineered Machines (iGEM) competition [8], where hundreds 25 of teams at the high school, undergraduate, and graduate levels been organized 26 previously to study reproducibility and calibration for fluorescence measurements in 27 engineered E. coli [9,10]. As iGEM teams have a high variability in training and 28 available resources, organizing an interlaboratory study with iGEM also demands that 29 protocols be simple, low cost, and highly accessible. The large scale and high variability 30 between teams also allows investigation of protocol robustness, as well as how readily 31 issues can be identified and debugged in protocol execution. 32 We thus organized a large-scale interlaboratory study within iGEM to compare three 33 candidate OD calibration protocols: a colony-forming unit (CFU) assay, the de facto 34 standard assay for determining viable cell count; comparison with colloidal silica 35 (LUDOX) and water, previously used for normalizing fluorescence measurements [9]; 36 and serial dilution of silica microspheres, a new protocol based on a recent study of 37 microbial growth [7]. Overall, this study demonstrates that serial dilution of silica 38 microspheres is by far the best of these three protocols, allowing highly precise, 39 accurate, and robust calibration that is easily assessed for quality control and can also 40 evaluate the effective linear range of an instrument. 41

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To evaluate the three candidate OD calibration protocols, we organized an 43 interlaboratory study as part of the 2018 International Genetically Engineered Machine 44 (iGEM) competition. The precision and robustness of each protocol is assessed based on 45 the variability between replicates, between reference levels, and between laboratories. 46 The overall efficacy of the protocols was then further evaluated based on the 47 reproducibility of cross-laboratory measurements of cellular fluorescence, as normalized 48 by calibrated OD measurements. 49 Experimental Data Collection 50 Each contributing team was provided with a set of calibration materials and a collection 51 of eight engineered genetic constructs for constitutive expression of GFP at a variety of 52 levels. Specifically, the constructs consisted of a negative control, a positive control, and 53 six test constructs that were identical except for promoters from the Anderson 54 library [11], selected to give a range of GFP expression (illustrated in Figure 1

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Each team transformed E. coli K-12 DH5-alpha with the provided genetic constructs, 60 culturing two biological replicates for each of the eight constructs. Teams measured 61 absorbance at 600nm (OD600) and GFP in a plate reader from 4 technical replicates 62 per biological replicate at the 0 and 6 hour time points, along with media blanks, thus 63 producing a total of 144 OD600 and 144 GFP measurements per team. Teams with 64 access to a flow cytometer were asked to also collect GFP and scatter measurements for 65 each sample, plus a sample of SpheroTech Rainbow Calibration Beads [12] for 66 fluorescence calibration.

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Measurements of GFP fluorescence were calibrated using serial dilution of fluorescein 68 with PBS in quadruplicate, using the protocol from [9], as illustrated in Figure 1  Measurements of OD via absorbance at 600nm (OD600) were calibrated using three 75 protocols and for each of these a model was devised for the purpose of fitting the data  Quadruplicate measurements are made for both LUDOX CL-X and water, with 90 conversion from arbitrary units to OD measurement in a standard 91 spectrophotometer cuvette estimated as the ratio of their difference to the OD 92 measurement for LUDOX CL-X in a reference spectrophotometer. This protocol 93 has the advantage of using extremely cheap and stable materials, but the 94 disadvantage that LUDOX CL-X provides only a single reference value, and that 95 it calibrates for instrument differences in determination of OD but cannot 96 determine the number of particles.

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• Comparison with serial dilution of silica microspheres, illustrated in Figure 1(e).

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This novel protocol, inspired by the relationship between particle size, count, and 99 Year after year, we have found that most teams are highly successful when they follow these protocols, even if alternative protocols are used within your lab. If you are having trouble transforming your test devices, please try the protocols above.  Accurate pipetting is essential. Serial dilutions will be performed across columns 1-11. COLUMN 12 MUST CONTAIN PBS BUFFER ONLY. Initially you will setup the plate with the fluorescein stock in column 1 and an equal volume of 1xPBS in columns 2 to 12. You will perform a serial dilution by consecutively transferring 100 μl from column to column with good mixing.  This procedure can be used to calibrate OD600 to colony forming unit (CFU) counts, whic concentration of the culture, i.e. viable cell counts per mL. This protocol assumes that 1 For the CFU protocol, you will need to count colonies for your two Positive Control (BBa_ Negative Control (BBa_R0040) cultures.

Step 1: Starting Sample Preparation
This protocol will result in CFU/mL for 0.1 OD600. Your overnight cultures will have a muc of the protocol, called "Starting Sample Preparation", will give you the "Starting Sample" 1. Measure the OD600 of your cell cultures, making sure to dilute to the linear de e.g. to 0.05 -0.5 OD600 range. Include blank media (LB + Cam) as well.
For an overnight culture (16-18 hours of growth), we recommend dilut in LB + Cam before measuring the OD600.    OD [7], uses quadruplicate serial dilution protocol of 0.961µm diameter 100 monodisperse silica microspheres (selected to match the approximate volume and 101 optical properties of E. coli) in water (similar to fluorescein dilution, but with 102 different materials). With a known starting concentration of particles, the number 103 of particles per OD600 unit is estimated by dividing the expected number of 104 particles in each well by the measured OD for the well. This protocol has the 105 advantages of low cost and of directly mapping between particles and OD, but the 106 disadvantage that the microspheres tend to settle and are freeze-sensitive.

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Data from each team were accepted only if they met a set of minimal data quality 108 criteria (Supplementary Note: Data Acceptance Criteria), including values being 109 non-negative, the positive control being significantly brighter than the negative control, 110 and measured values for calibrants decreasing as dilution increases. In total, 244 teams 111 provided data meeting these minimal criteria, with 17 teams also providing usable flow 112 cytometry data. Complete anonymized data sets and analysis results are available in 113 Supplementary Data 2 Complete Data.

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Robustness of calibration protocols 115 We assessed the robustness of the calibration protocols under test in two ways: replicate 116 precision and residuals. Replicate precision can be evaluated simply in terms of the 117 similarity of values for each technical replicate of a protocol. The smaller the coefficient 118 of variation (i.e., ratio of standard deviation to mean), the more precise the protocol.

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With regards to residuals, on the other hand, we considered the modeled mechanism 120 that underlies each calibration method and assess how well it fits the data. Here, the 121 residual is the distance between each measured value provided by a team and the 122 predicted value of a model fit using that same set of data (see Materials and Methods 123 for details of each mechanism model and residual calculations). The smaller the residual 124 value, the more precise the protocol. Moreover, the more similar the replicate precision 125 and residuals across teams, the more robust the protocol is to variations in execution 126 conditions. should have been (e.g., 10-fold less colonies after a 10-fold dilution). The closer the ratio 156 was to one, the more the protocol was operating in conformance with the theory 157 supporting its use for calibration, and thus the more likely that the calibration process 158 produced an accurate value.

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Here we see a critical weakness of the LUDOX/water protocol: the LUDOX and 160 water samples provide only two measurements, from which two model parameters are 161 set: the background to subtract (set by water) and the scaling between 162 background-subtracted LUDOX and the reference OD. Thus, the dimensionality of the 163 model precisely matches the dimensionality of the experimental samples, and there are 164 no residuals to assess. As such, the LUDOX/water protocol may indeed be accurate, 165 but its accuracy cannot be empirically assessed from the data it produces. If anything 166 goes wrong in the reagents, protocol execution, or instrument, such problems cannot be 167 detected unless they are so great as to render the data clearly invalid (e.g., the OD of 168 water being less than the OD of LUDOX).

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The CFU protocol and the two serial dilution protocols, however, both have multiple 170 dilution levels, overconstraining the model and allowing likely accuracy to be assessed. 171 Figure 3 shows the distribution of residuals for these three protocols, in the form of a protocol is also highly precise and may be accurate, but its execution quality cannot be 202 directly assessed due to its lack of residuals. The CFU protocol, on the other hand, 203 appears likely to be highly problematic, producing unreliable and likely inaccurate comparison, there are some differences that must be considered between the two 233 modalities. Gene expression typically has a log-normal distribution [13], meaning that 234 bulk measurements will be distorted upward compared to the geometric mean of

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Of the three OD calibration methods, the LUDOX/water measurement is 247 immediately disqualified as it calibrates only to a relative OD, and thus cannot produce 248 comparable units. Comparison of CFU and microsphere dilution to flow cytometry is 249 shown in Figure 5. The CFU-calibrated measurements are far higher than the values 250 produced by flow cytometry, a geometric mean of 28.4-fold higher, indicating that this 251 calibration method badly underestimates the number of cells. It is unclear the degree to 252 which this is due to known issues of CFU, such as cells adhering into clumps, as 253 opposed to the problems with imprecision noted above or yet other possible unidentified 254 causes. Whatever the cause, however, CFU calibration is clearly problematic for 255 obtaining anything like an accurate estimate of cell count.

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Microsphere dilution, on the other hand, produces values that are remarkably close 257 to those for flow cytometry, a geometric mean of only 1.07-fold higher, indicating that 258 this calibration method is quite accurate in estimating cell count. Moreover, we may 259 note that the only large difference between values comes with the extremely low 260 fluorescence of the J23117 construct, which is unsurprising given that flow cytometers 261 generally have a higher dynamic range than plate readers, allowing better sensitivity to 262 low signals.

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Reliably determining the number of cells in a liquid culture has remained a challenge in 265 biology for decades. For the field of synthetic biology, which seeks to engineer based on 266 standardized biological measurements, it was critical to find a solution to this challenge. 267 Here, we have compared the most common method for calibrating OD to cell number 268 (calculation of CFU) to two alternative methods of calibration: LUDOX/water and 269 microsphere serial dilution. The qualitative and quantitative benefits and drawbacks of 270 these three methods for OD calibration are summarized in Table 6  protocol has well-known issues of cell clumping and slow, labor-intensive execution, and 274 counts only live and active cells, which can be either a benefit or a limitation depending 275 on circumstances. Additionally, the CFU counts in this study exhibited a remarkably 276 high level of variability, which may call into question the use of the CFU method as the 277 a standard for determining cell counts. This observed variability is not without 278 precedent-prior work has also demonstrated E. coli CFU counting performing poorly 279 on measures of reproducibility and repeatability in an interlaboratory study [14].

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The microsphere protocol, on the other hand, has no major drawbacks and provides 281 a number of significant benefits. First, the microsphere protocol is highly robust and 282 reliable, particularly compared to CFU assays. Second, failures are much easier to 283 diagnose with the microsphere protocol, since it has many distinct levels that can be 284 compared. This is particularly significant when compared to the LUDOX/water 285 protocol, which only provides a single calibration point at low absorbance (and thus 286 susceptible to instrument range issues), and to the CFU protocol, where failures may be 287 difficult to distinguish from inherent high variability. With the microsphere protocol, on 288 the other hand, some failures such as systematic dilution error and instrument 289 saturation can not only be detected, but also modeled and corrected for. Finally, the 290 microsphere protocol also permits a unit match between plate reader and flow 291 cytometry measurements (both in cell number and in fluorescence per cell), which is 292 highly desirable, allowing previously impossible data fusion between these two 293 complementary platforms (e.g., to connect high-resolution time-series data from a plate 294 reader with high-detail data about population structure from a flow cytometer). 295 Accordingly, based on the results of this study, we recommend the adoption of silica 296 microsphere calibration for robust estimation of bacterial cell count.

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With regards to future opportunities for extension, we note that these methods seem 298 likely to be applicable to other instruments that measure absorbance (e.g., 299 spectrophotometers, automated culture flasks) by appropriately scaling volumes and 300 particle densities. Similarly it should be possible to adapt to other cell types by 301 selecting other microspheres with appropriately adjusted diameters and materials for 302 their optical properties, and a wide range of potential options are already readily 303 available from commercial suppliers. Finally, further investigation would be valuable for 304 more precisely establishing the relationship between cell count and particle count. It 305 would also be useful to quantify the degree to which the estimates are affected by 306 factors such as changing optical properties associated with cell state, distribution, shape, 307 and clustering, and to investigate means of detecting and compensating for such effects. 308

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Participating iGEM teams measured OD and fluorescence among the same set of 310 plasmid-based devices, according to standardized protocols. In brief, teams were 311 provided a test kit containing the necessary calibration reagents, a set of standardized 312 protocols, and pre-formatted Excel data sheets for data reporting. Teams provided their 313 own plate reader instruments, consumables/plasticware, competent E. coli cells, PBS, 314 water, and culture medium. First, teams were asked to complete a series of calibration 315 measurements by measuring LUDOX and water, and also making a standard curve of 316 both fluorescein and silica microspheres. Next, each team transformed the plasmid 317 devices into E. coli and selected transformants on chloramphenicol plates. They selected 318 two colonies from each plate to grow as liquid cultures overnight, then the following day 319 diluted their cultures and measured both fluorescence and OD after 0 and 6 hours of 320 growth. Some of these cultures were also used to make serial dilutions for the CFU 321 counting experiment. Teams were asked to report details of their instrumentation, E. The scaling factor S c relating CFU/ML to Abs600 is computed as follows: where µ(C i ) is the mean number of colonies for dilution level i and δ i is the dilution fold 378 for level i. For the specific protocol used, there are three effective dilution factors, 1.6e5, 379 1.6e6, and 1.6e7 (including a 2-fold conversion between 200µl and 100µl volumes).

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The overall scaling factor S c for each data set is then taken to be: i.e., the scaling factor for the valid level with the lowest coefficient of variation.

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The residuals for this fit are then S c,i /S c for all other valid levels.

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The scaling factor S l relating standard OD to Abs600 is computed as follow: where R is the measured reference OD in a standard cuvette (in this case 0.063 for 386 LUDOX CL-X), µ(L) is the mean Abs600 for LUDOX CL-X samples and µ(W ) is the 387 mean Abs600 for water samples.

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No residuals can be computed for this fit, because there are two measurements and 389 two degrees of freedom.

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Mean Conversion Factor If we ignore pipetting error, then the model for serial 397 dilution has an initial population of calibrant p 0 that is diluted n times by a factor of α 398 at each dilution, such that the expected population of calibrant for the ith dilution level 399 is: In the case of the specific protocols used here, α = 0.5. For the microsphere dilution 401 protocol used, p 0 = 3.00e8 microspheres, while for the fluorescein dilution protocol used, 402 p 0 = 6.02e14 molecules of fluorescein.

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The local conversion factor S i for the ith dilution is then: where µ(O i ) is the mean of the observed values for the ith dilution level and µ(B) is the 405 mean observed value for the blanks.

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The mean conversion factor is thus: i.e., the mean over local conversion factors for valid dilution levels.

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The residuals for this fit are then S i /S µ for all valid levels.

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Systematic Pipetting Error Model The model for systematic pipetting error 410 modifies the intended dilution factor α with the addition of an unknown bias β, such 411 that the expected biased population b i for the ith dilution level is: We then simultaneously fit β and the scaling factor S p to minimize the sum squared 413 error over all valid dilution levels: where is sum squared error of the fit and x n is the mean corrected arbitrary unit value 415 of the nth titration stage.

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The residuals for this fit are then the absolute ratio of fit-predicted to observed net 417 mean For analysis of E. coli culture measurements, a data set was only eligible to be included 425 if both its fluorescence calibration and selected OD calibration were above a certain 426 quality threshold. The particular values used for the four calibration protocols were:

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• CFU: Coefficient of variation for best dilution level is less than 0.5.

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• LUDOX/water: Coefficient of variation for both LUDOX and water are less 429 than 0.1.

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Measurements of the cellular controls were further used to exclude data sets with 435 apparent problems in their protocol: those with a mean positive control value more 436 than 3-fold different than the median mean positive control.

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Finally, individual samples without significant growth were removed, that being 438 defined as all that are either less than the 25% of the 75th percentile Abs600 439 measurement in the sample set or less than 2 media blank standard deviations above 440 the mean media blank in the sample set.

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Flow Cytometry Data Processing

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Flow cytometry data was processed using the TASBE Flow Analytics software 443 package [15]. A unit conversion model from arbitrary units to MEFL was constructed 444 per the recommended best practices of TASBE Flow Analytics for each data set using 445 the bead sample and lot information provided by each team:

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• Gating was automatically determined using a two-dimensional Gaussian fit on the 447 forward-scatter area and side-scatter area channels for the first negative control 448 (Supplementary Figure 3 Example of Flow Cytometry Gating).

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• The same negative control was used to determine autofluorescence for background 450 subtraction.

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• As only a single green fluorescent protein was used, there was no need for spectral 452 compensation or color translation.

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This color model was then applied to each sample to filter events and convert GFP 454 measurements from arbitrary units to MEFL, and geometric mean and standard 455 deviation computed for the filtered collection of events. culturing for many teams, as did the J23100 construct to a lesser degree.