Single-Cell Growth Rates in Photoautotrophic Populations Measured by Stable Isotope Probing and Resonance Raman Microspectrometry

A new method to measure growth rates of individual photoautotrophic cells by combining stable isotope probing (SIP) and single-cell resonance Raman microspectrometry is introduced. This report explores optimal experimental design and the theoretical underpinnings for quantitative responses of Raman spectra to cellular isotopic composition. Resonance Raman spectra of isogenic cultures of the cyanobacterium, Synechococcus sp., grown in 13C-bicarbonate revealed linear covariance between wavenumber (cm−1) shifts in dominant carotenoid Raman peaks and a broad range of cellular 13C fractional isotopic abundance. Single-cell growth rates were calculated from spectra-derived isotopic content and empirical relationships. Growth rates among any 25 cells in a sample varied considerably; mean coefficient of variation, CV, was 29 ± 3% (σ/x¯), of which only ~2% was propagated analytical error. Instantaneous population growth rates measured independently by in vivo fluorescence also varied daily (CV ≈ 53%) and were statistically indistinguishable from single-cell growth rates at all but the lowest levels of cell labeling. SCRR censuses of mixtures prepared from Synechococcus sp. and T. pseudonana (a diatom) populations with varying 13C-content and growth rates closely approximated predicted spectral responses and fractional labeling of cells added to the sample. This approach enables direct microspectrometric interrogation of isotopically- and phylogenetically-labeled cells and detects as little as 3% changes in cellular fractional labeling. This is the first description of a non-destructive technique to measure single-cell photoautotrophic growth rates based on Raman spectroscopy and well-constrained assumptions, while requiring few ancillary measurements.


SM1: Evaluation of 13 C-enriched media preparation methods
The first critical steps in performing quantitative SIP experiments with cultures is to establish whether DIC replacement or augmentation is preferable, to determine how much 13 C-bicarbonate tracer can be added without significantly altering seawater chemistry, and then to accurately determine the fractional contribution (f media = 13 C media / ( 13 C media + 12 C media )) of the heavy isotope to the total inorganic carbon pool (C T = CO 2 + H 2 CO 3 + HCO 3 -+ CO 3 2-).
Three DIC replacement methods were evaluated for how effectively DI 12 C was removed prior to media preparation and 13 C-bicarbonate amendment. The first method was boiling filtered seawater (FSW) for 1 min in a microwave oven according to Li et al. (2012). The second was to actively sparge FSW with N 2 for 10 min. The third approach was to acidify FSW to pH 3.5 with 1N HCl, then seal in a gas-tight vessel and autoclave. Once cool, pH was returned to 8.0 with 0.1N NaOH. Standard f/2 nutrients and sodium bicarbonate were aseptically transferred to 200ml septum bottles to yield a final C T of ~2 mM in nominal f media ratios of 0.011 (natural abundance), 0.25, 0.50, 0.75, and 1.00. However, media prepared in this way usually became viscous and turbid due to mineral precipitation and Synechococcus sp. cultures did not grow well under these conditions. DI 13 C augmentation to the culture media was evaluated for pH and growth effects. At the extreme, 2.3 mM DI 13 C additions (final C T ~4.1 mM or 130% enrichment) only depressed pH by 0.23 units (Table S1). At C T enrichments of <50%, pH excursions were < 0.13, suggesting that amendments at these levels will not significantly affect photoautotrophic growth.
Total dissolved inorganic carbon (C T ) concentrations were determined using a flow injection analysis (FIA) system (Hall and Aller, 1992). This instrument permits transfer of CO 2 from an acidified (SCO 2 ) reagent stream across a gas-permeable membrane into a receiving carrier stream which flows over a conductivity detector. C T levels of unknown samples were compared to conductivity measurements of known standards. pH measurements were made on a Thermo Scientific® Orion 2-Star™ Benchtop pH meter, which was calibrated immediately prior to all measurements.
In principle, for accurate DI 13 C replacement, all or a known amount of the C T pool must be removed before replacing with sufficient 13 C-bicarbonate to return media to the original C T pool size. Microwave heating as employed by Li et al. (2012) or N 2 sparging only removed 30 or 60% of the original C T pool, respectively, while acidification effectively removed 96% of the C T pool as determined by FIA-conductivity measurements of SCO 2 (Table S2). Microwave heating had the additional effect of raising the pH above 9.0. Adding 1.8 mmol L -1 bicarbonate to previously acidified and neutralized FSW returned DIC to the original pool size and an acceptable pH. Doing the same to the microwaved or sparged samples in the present case would have increased C T by 71 and 40% and without independent verification, the actual f media would be poorly constrained. Therefore, pH manipulation is clearly the most reliable approach for DIC replacement.
Partial or complete DIC replacement may be a suitable approach for media preparation and culture experiments, but clearly is inappropriate for field experiments with natural assemblages. DIC augmentation requires far less manipulation and therefore introduces fewer potential artifacts. Alteration of pH is foremost among potential artifacts for DIC augmentation and was therefore evaluated. We note that pH of the aged seawater (Table S1) was higher than that of average seawater (pH = 7.5-8.4), which we attribute to prolonged photoautotrophic growth within the storage vessel. Increasing C T by 11% to as much as 130% depressed the pH of FSW from 8.79 to 8.56 (Table S1). Consequently, our experimental data were derived from media augmented with a constant amount of total DIC, but varying 13 C-bicarbonate content, and then returned to a pH of 8.0. Reported f media are based on IRMS and FIA-conductivity results, which were within ~6% of nominal ratios (gravimetrically formulated from C T concentration in FSW) (Table S2). f -C T = CO 2 + CO 3 -2 + HCO 3 and determined as SCO 2 by flow injection and conductivity analysis of acidified sample (Hall and Aller, 1992)

SM2: Expected relationships between mean SIP-SCRR wavenumbers ( ) and fractional isotopic abundance (f cell )
Slight differences in vibrational frequencies upon substituting 13 C for 12 C in a carbon-carbon bond are manifested as unique peaks in the Raman spectrum. Since these isotopologue peaks tend to overlap, their relative areas are imprecise predictors of the fractional isotopic abundance of 13 C (f 13 ). However, a strong relationship exists between the mean Raman wavenumber of overlapping isotopologue peaks and fractional isotopic abundance, which can be derived as follows.
First, we assume that all isotopologue bonds have symmetric Raman peaks with characteristic central wavenumbers (∆ṽ i , where the subscript i = 0, 1, 2 is the number of 13 C atoms in 12 C 12 C, 12 C 13 C, or 13 C 13 C bonds, respectively). Therefore, the mean wavenumber ( Δ ) for overlapping isotopologue bond peaks is the average of their characteristic wavenumbers weighted by their peak areas (A i ).
The areas are obtained by integrating each peak over all values of ∆ṽ. We assume that the peak heights are equal to the products of their Raman efficiencies (εi(∆ṽ), the effective wavenumberdependent cross-section with units of intensity · effective cell area · bond i −1 ) and the number of isotopologue bonds of interest in the optical path. The latter is equal to the product of the average cell thickness (l), concentration of the molecule of interest in the cell ([m]), stoichiometric number of bonds in that molecule expressing the desired resonance (e.g., b = 9 conjugated double bonds in the chain per β-carotene), and expected proportions of isotopologues among those bonds (⟨f i ⟩). These terms are constants on the timescale of acquiring a Raman spectrum can be factored out of the peak integral. Therefore, the peak area (intensity · cm −1 ) is the product of these constants and a bulk efficiency ( 4 5 , with units of intensity · effective cell area · bond i −1 · cm −1 ) that is equal to the integral of ε i (∆ṽ) over all values of ∆ṽ (Eq. S2).
The expected proportions of 12 C 12 C, 12 C 13 C, and 13 C 13 C bonds can be estimated by assuming a stochastic distribution of 13 C atoms throughout the principle resonance structure of the molecule (i.e., assuming negligible isotopic clumping). Hence, the proportions (probability = P(k|n,f 13 )) of each set of isotopomers with k 13 C atoms in a molecule containing n carbon atoms will be given by the individual terms of the binomial distribution (Eq. S3), where the bulk binomial coefficient ("n over k" term) represents the number of possible unique isotopomers in that set. = Thus, expressions for the number of possible 12 C 12 C, 12 C 13 C, and 13 C 13 C bonds in each set of isotopomers defined by k can be obtained by factoring combinations out of the bulk binomial coefficient that are consistent with the physical limitations of isotopic substitution (Eq. S6). Specifically, n is decreased by the number of atoms in a bond (i.e., 2) and k is decreased by i 13 C atoms because, for example, there cannot be any 13 C 13 C bonds in a molecule with just k = 0 or 1 13 C atoms, nor can there be any 12 C 12 C bonds in a molecule with at least n -1 13 C atoms. Accordingly, each combination is only meaningful for values of k that range from i to n -2 + i. The additional binomial coefficient ("2 over i") accounts for two possible sites of 13 C substitution in a 12 C 13 C bond ( 12 C 13 C vs. 13 C 12 C), while the coefficient b scales the result to account for all possible bonds of interest in the set.
Therefore, the proportions (f i,k ) of the numbers of possible 12 C 12 C, 12 C 13 C, and 13 C 13 C bonds in each set of isotopologues defined by k are found by dividing Eq. S6 by Eq. S5.
The expected proportions of 12 C 12 C, 12 C 13 C, and 13 C 13 C bonds in the entire suite of 2 n isotopic species are equal to the averages of their proportions in each set defined by k.
Substituting Eq. S3 and S7 into S8 gives an expression for the expected proportions of 12 C 12 C, 12 C 13 C, and 13 C 13 C bonds as a function of f 13 , n, and k.
These expected proportions can be greatly simplified by first implementing a change of variables and factoring (let 5 = − 2, and 5 = − ).
The summation in Eq. S10 represents a complete binomial distribution and is therefore equal to one. Thus, the expected stochastic proportions of 12 C 12 C, 12 C 13 C, and 13 C 13 C bonds are independent of the number of atoms or bonds of interest in a molecule (where n ≥ 2). Instead, they are equivalent to the proportions expected for a diatomic molecule via binomial expansion. Finally, substituting Eq. S2 and S11 into Eq. S1 and simplifying yields the expected general relationship between mean SCRR shift and fractional 13 C abundance.

SM3: Expected relationship between fractional isotopic abundance (f cell ), generation number (n), and mean SIP-SCRR wavenumbers ( )
The relationship between f cell and the number of generations (j, where 0 ≤ j ≤ n) can be estimated assuming that (1)  Substituting Eq. S15 into Eq. S17 reduces the summation to N n -N o and the ensuing N o /N n terms to e -n ln(2) , producing a general isotopic mass balance expression for f cell after n generations.
(S18) WXYY,D = DX] + WXYY,U − DX] EDYD * When constructing a calibration curve ( Δ vs. f cell ) it is easier to directly measure the fractional isotopic abundances of growth media (f media ) than of discrete cellular constituents. Therefore, the definitions for fractionation factors (a biomass-media = R biomass /R media ), isotope ratios (R = 13 C/ 12 C), and fractional isotopic abundances (f 13 = 13 C/( 12 C+ 13 C)) can be used to predict the isotopic composition of cellular biomass from the isotopic composition of growth media.

SM4: Calculating the number of generations (n) from SCRR ⟨∆ṽ⟩ measurements, associated uncertainties, and experimental design
The general equation for calculating the number of generations (n) from f media , f o , a, b 0 , and b 1 is obtained by rearranging Eq. S22.
Ignoring the (1+(a−1)f o ) term in the denominator of the logarithm will introduce a constant but negligible offset of +0.0004 generations for a = 0.976 and f o = 0.011. Therefore, n can be calculated more simply via Eq. S24.
The anticipated uncertainty on n and the experimental conditions needed to minimize this uncertainty, can be evaluated by propagating the uncertainties (single standard deviations, s i ) on all terms in Eq. S24.
Finally, the relative uncertainty of SIP-SCRR generation times (g = t/n) and specific growth rates (µ sc = ln(2) n/t) can be estimated through propagation of uncertainties and the reasonable assumption that s t /t ≪ s n /n.
The values of most parameters in Eq. S24 and S25 are beyond the analyst's control (a, b 1 , b 0 , Δ , f o ). However, an experiment can be optimized by careful selection of the 13 C-enriched growth medium (f media ) and the duration of an incubation (i.e., t or n). First, the most precise measurements of n and the growth rate must happen after shifts in f cell become detectable (n >0) but before f cell reaches its asymptote (i.e., f cell = a f media /(1+(a -1)f media ), as per Eq. S20) (Figs. S2 and S3). This optimum condition was readily found for the ν(C-C) stretch by numerically locating the minimum value of the relative uncertainty (± s n /n) as a function of Δ for various values of f media (ranging from 0 to 1, ±0.002). This required assuming reasonable values and uncertainties for a (0.976 ± 0.003), f o (0.0110 ± 0.0002), and Δ (ranging from 1120 to 1160 cm -1 , with σ⟨ ∆ṽ ⟩ = ± 0.34) based on known measurements. The two remaining quantities, b 1 (-30.34 ± 0.18 cm -1 ) and b 0 (1157.04 ± 0.05 cm -1 ), were obtained from a least squares linear regression of 961 individual measurements (r 2 = 0.97; Fig. S2).
This analysis suggests that the most precise determinations of n will be obtained by measuring Δ after ~1.5 cell divisions. More importantly, the minimum relative uncertainties (±1s n /n) can be significantly reduced from 0.356 (f media = 0.10) to a theoretically lowest achievable value of 0.033 (i.e., in the limit of f media = 1.0) by using more isotopically-enriched growth media (Fig.  S2). In addition, cells grown in highly enriched media exhibit both broader and flatter relative uncertainty minima (Fig. S2), making the highest precision measurements much less sensitive to the number of generations or the precise timing of measurements. As a practical compromise between measurement performance, incubation artifacts, and costs, we advocate amending routine samples to f media values between 0.3 and 0.5, where the optimum value of n has a minimum theoretical relative uncertainty between 0.11 and 0.066, respectively (Fig. S3).
Further analysis of Eq. S25 suggests that the greatest contribution of uncertainty (i.e., the individual "(∂n/∂x) 2 σ x 2 " terms under the radical, where x = , f o , f media , b 0 , b 1 , or ⟨∆ṽ⟩) to SCRR determinations of n comes from measurements of ⟨∆ṽ⟩ (Fig S4). Under optimal measurement conditions, the uncertainty contributions from measurements of and f o are at least 3 to 5 orders of magnitude smaller than that of ⟨∆ṽ⟩, respectively, and therefore can be ignored. The remaining measurements (f media , b 0 , and b 1 ) make approximately equal contributions to the total uncertainty and suggest avenues for future improvements in performance. Therefore, the accuracy and precision of SIP-SCRR growth rate determinations are presently limited by individual ⟨∆ṽ⟩ measurements and the calibration curve (b 0 and b 1 ), rather than uncertainty or variations in the isotopic composition of original growth medium (f o ) or fractionation factors for carotenoid biosynthesis (a).