Calculation of Single Cell Assimilation Rates From SIP-NanoSIMS-Derived Isotope Ratios: A Comprehensive Approach.

The nanoSIMS-based chemical microscopy has been introduced in biology over a decade ago. The spatial distribution of elements and isotopes analyzed by nanoSIMS can be used to reconstruct images of biological samples with a resolution down to tens of nanometers, and can be also interpreted quantitatively. Currently, a unified approach for calculation of single cell assimilation rates from nanoSIMS-derived changes in isotope ratios is missing. Here we present a comprehensive concept of assimilation rate calculation with a rigorous mathematical model based on quantitative evaluation of nanoSIMS-derived isotope ratios. We provide a detailed description of data acquisition and treatment, including the selection and accumulation of nanoSIMS scans, defining regions of interest and extraction of isotope ratios. Next, we present alternative methods to determine the cellular volume and the density of the element under scrutiny. Finally, to compensate for alterations of original isotopic ratios, our model considers corrections for sample preparation methods (e.g., air dry, chemical fixation, permeabilization, hybridization), and when known, for the stable isotope fractionation associated with utilization of defined growth substrates. As proof of concept we implemented this protocol to quantify the assimilation of 13C-labeled glucose by single cells of Pseudomonas putida. In addition, we provide a calculation template where all protocol-derived formulas are directly available to facilitate routine assimilation rate calculations by nanoSIMS users.

Introduction

The use of nanoSIMS as a single-cell technique in pan class="Species">environmentaln> microbiology and microbial ecology has been enhanced over the mical">pan>st years (Milucka et al., 2012; Berry et al., 2013; Koch et al., 2014; Woebken et al., 2014; McGlynn et al., 2015; Martínez-Pérez et al., 2016; Oswald et al., 2017; Raina et al., 2017). A great number of studies employ the use of stable isotope labeling and nanoSIMS to track metabolic processes of single cells, in situ, in mical">pan>n class="Species">environmental and synthetic systems (Pett-Ridge and Weber, 2012; Musat N. et al., 2016). Thus, changes in isotope composition of single cells upon biotic assimilation of the stable isotope labeled growth substrate are measured by the nanoSIMS and further used quantitatively (e.g., (Musat et al., 2008; Thompson et al., 2012; Martínez-Pérez et al., 2016). Most studies employing the nanoSIMS combination with stable isotope probing (nanoSIP) have presented the isotope ratio values (Lechene et al., 2006, 2007), isotope enrichment values as atomic % excess or in delta notation (Popa et al., 2007; Fike et al., 2008; Dekas et al., 2009; Morono et al., 2011; Tourna et al., 2011; Thompson et al., 2012; Woebken et al., 2012; Berry et al., 2013; Lee et al., 2014; McGlynn et al., 2015) and some used the nanoSIMS-derived isotope ratios to quantify single-cell assimilation (Popa et al., 2007; Musat et al., 2008; Krupke et al., 2013, 2015; Martínez-Pérez et al., 2016; Schreiber et al., 2016; Nikolic et al., 2017; Zimmermann et al., 2018). In order to acquire accurate isotope ratios with nanoSIMS, required to calculate single cell assimilation rates with a great confidence, the following steps need to be carefully considered: processing of nanoSIMS data (e.g., selection of the optimal number of scans to be accumulated), proper identification of single cells, and accurate definition and selection of regions of interest (RoIs) around single cells. Finally, the calculations should consider the cellular biovolume and elemental density (e.g., cellular density of carbon or nitrogen), corrections for isotope dilution by various treatments during sample preparation (Musat et al., 2014; Woebken et al., 2014; Pernice et al., 2015; Musat N. et al., 2016). and, when known, corrections for compound-specific stable isotope fractionation during assimilation of labeled substrates (Elsner et al., 2005; Musat F. et al., 2016).

A comprehensive protocol to obtain assimilation rates of single cells from nanoSIMS-derived isotopic ratios and consensus formulas that can be applied by the scientific community on a general base are presently n class="Chemical">missing. The available calculation approaches based on empirical expressions for assimilation and growth rate differ considerably between nanoSIMS working groups, leading to difficulties in choosing the appropriate pan class="Disease">mathemical">pan class="Disease">matical formulas to analyse particular samples with high confidence. The nanoSIP-based computation method reported for quantitation of single cell activity in chemostats (Kopf et al., 2015) implies a series of intermediate numerical calculations limiting the possibility to derive a generalized analytical expression for single cell assimilation applicable to other cell cultivation systems. Here we present a protocol where we explain step by step how one can use the isotopic ratios measured by nanoSIMS to calculate meaningful element-specific assimilation rates, what other parameters have to be considered when such calculations are applied, including how to account for the label dilution due to chemical treatments like fixation, dehydration, embedding, or hybridization steps. As a proof of concept, we further demonstrate how to use this protocol to quantify single cell assimilation rate on a set of data obtained by nanoSIMS analysis of P. putida culture incubated in the presence of 13C-glucose.

Materials and methods

Chemicals, organisms, and cultivation conditions

pan class="Chen class="Chemical">mical">13C6-glucose was purchased from Chemotrade (Düsseldorf, Germany). n class="Chemical">mical">pan class="Species">Pseudomonas putida KT2440 (DSM6125) was routinely cultivated in 250 ml flasks containing 100 ml defined salt medium with glucose as growth substrate (1 g·l−1), as previously described (Musat et al., 2014). The bottles were inoculated with 5 ml of a culture in mid-exponential growth phase. Labeling experiments were conducted in 100 ml serum bottles with 66.5 ml mineral medium, 3.5 ml inoculum, 9.5 mg 13C6-labeled and 66 mg unlabeled glucose resulting in 13.5 at% labeling of the growth substrate with 13C isotope. To prevent transfer of unlabeled substrate with the inoculum, a volume of 10 ml was collected from a culture in the mid-exponential growth phase. The cells were collected by centrifugation, washed twice with 5 ml mineral medium devoid of carbon and nitrogen sources, and finally suspended in 3.5 ml mineral medium. The bottles were incubated in the dark at 30°C with horizontal shaking (200 rpm). Samples (20 ml) were collected after 10 h of incubation during the mid-exponential growth phase, and fixed for 2 h at room temperature with 2% v/v paraformaldehyde in 1 × PBS. Fixed cells were washed twice with deionized water, and suspended in 1 ml ethanol 50% v/v in deionized water. Volumes of 10 μl of fixed cells suspension were filtered on Au-Pd coated GTTP filters (Millipore, Eschborn, Germany; 25 mm diameter, 0.22 μm pore size), air dried and stored in vacuum at room temperature until nanoSIMS analysis.

Nano-focused secondary ion mass spectrometry (NanoSIMS)

For the quantitative analysis of pan class="Chen class="Chemical">mical">carbon assimilation rates the cells of n class="Chemical">mical">pan class="Species">P. putida were analyzed with a NanoSIMS-50 L instrument (CAMECA, AMETEK) in negative extraction mode employing a DC source of primary Cs+ ions. Implantation of cesium was done via presputtering of 80 × 80 μm2 sample areas with 0.15 nA of 16 keV Cs+ beam for 5 min with the purpose to stabilize the working function for negative secondary ions. The 4 pA beam of 16 keV Cs+ ions was focused into about 80 nm spot at the sample surface during the analysis. The sample was scanned in 256 × 256 pixels raster over 40 × 40 μm2 of presputtered area with 40 ms dwell time per pixel. The secondary ions were analyzed with double-focusing magnetic sector mass spectrometers for their mass-to-charge ratio (m/z) and detected in seven available collectors set for the following ion species: 12C− (collector-1), 13C− (collector-2), 16O− (collector-3), 12C14N− (collector-4), 13C14N− (collector-5), 12C16O− (collector-6), 13C16O− (collector-7). The mass resolving power (MRP) was checked to be between 7,000 and 9,000 with the exit slit width of 100, 20 μm wide entrance slit, 200 μm aperture slit, and with the energy slit cutting 20% of secondary ions in high-energy tail of their energy distribution. The analyzed microbial cells were almost entirely sputtered within 8 scans upon the analysis conditions used and the scans 1–6 were considered for the analysis employing LANS software (Polerecky et al., 2012) allowing for the dead-time correction, accumulation of scanned planes with the lateral drift correction, definition of RoIs (Regions of Interest) for quantitative analysis of carbon isotope ratios (13C/12C, 13C14N/12C14N, and 13C16O/12C16O) explained in the description of results presented below.

Determination of carbon density for P. putida cells

To determine the cellular n class="Chemical">pan class="Chemical">carbon content of mical">pan class="Species">P. putida cells in fg·cell−1, their total carbon content measured with elemental analyzer was divided by the number of analyzed cells obtained by cell counting using a fluorescence microscope. The cellular carbon content was divided further by cell volume to get the final carbon-specific density of cell in fg·μm−3. For this calculation, the measurements of total carbon content, cell counting, and determination of cell volumes were performed as described below.

Measurement of total carbon content

pan class="Species">P. putidan> cells were cultivated in 250 ml flasks provided with 200 ml culture media. Cultures were incubated as described above. Cells were collected at four different time points that fully encommical">pan>ss the initial and exponential growth phases (0, 4, 6, and 8 h). Culture volumes of 5 ml were filtered onto pre-combusted (450°C for 5 h) GF/F filters (25 mm diameter, Whatman™,GE Healthcare) using a vacuum filtration manifold device (Millipore® model 1225). Cells were washed three times with 5 ml of deionized mical">pan>n class="Chemical">water and dried at room temperature for 10 min. The filters were decalcified by incubation in an desiccator with 20% v/v HCl overnight. Round pieces of 5 mm diameter were cut out from the GFF filters using a hollow punch-out tool and packed in tin cups (HEKAtech GmbH, Germany). The filters were analyzed for their total carbon content with an EuroEA3000 elemental analyser (HEKAtech, Germany) in which the samples were completely combusted to CO2. The flash combustion was performed with a 10 mL O2 pulse in a combustion reactor filled with wolfram oxide and silver cobalt oxide (HE46820995, HEKAtech, Germany) at 1,050°C. Conversion products were separated on a packed GC-column (HE 26070500, HEKAtech, Germany) and transferred with helium as carrier gas via a ConFlo IV open split system to a MAT 253 IRMS (Thermo Fisher, Bremen). For quantification, a multi-point calibration with known amounts of sucrose was done.

Cell counting and calculation of cellular carbon content

For cell counpan class="Chemical">ting, volumes of 1 ml were collected from the same cultures and time points as above, and fixed for 2 h with 2% n class="Chemical">mical">pan class="Chemical">paraformaldehyde in 1 × PBS at 4°C. Volumes of 100 μl of the fixed cells suspension were diluted in 5 ml of PBS, filtered onto polycarbonate filters (25 mm diameter) using a vacuum filtration manifold device (Millipore® model 1225), washed once with PBS, once with deionized water and once with each of the following ethanol concentrations: 50, 70, and 80% v/v in deionized water. Filters were air dried for 15 min, stained with 4′,6-diamidine-2′-phenylindol (DAPI) dissolved in ultrapure water (1 μg·ml−1) for 10 min, washed twice with deionized water and once with 80% v/v ethanol. DAPI-stained filters were air dried for 15 min in the dark and mounted on glass slides with Citifluor/VectaShield (4:1). For each culture time point the cells from 10 fields of view were counted under a fluorescence microscope (Axio Imager.Z2, Carl Zeiss). The cell number counted within 87 × 67 μm2 field of view (FoV) was scaled up to the area of filter piece of 5 mm diameter to get the cell number analyzed for carbon content with the elemental analyzer. The division of total carbon content by the resulted cell number yielded a carbon cellular content of 277 ± 47 fg·cell−1 for the analyzed P. putida cells.

Determination of biovolume for P. putida cells

To derive the pan class="Chen class="Chemical">mical">carbon cellular content per volume unit, the biovolume of n class="Chemical">mical">pan class="Species">P. putida cells was determined. P. putida cells were harvested in mid-exponential growth phase and fixed with 1% v/v glutaraldehyde (GA) in cacodylate buffer for 2 h at room temperature. Fixed cells were transferred on GTTP filters coated with a 30 nm layer of Au-Pd with the help of a stainless steel syringe filter holder (Sartorius, Germany), washed twice with 1 ml cacodylate buffer and post-fixed in KMnO4 (1% w/v in deionized water) at room temperature for 90 min. Filters were washed once with deionized water, followed by dehydration in an ethanol series of 30, 50, 70, 80, 90, 96, and 100% (3 min each). Subsequently, the filters were dried with a critical point dryer machine (Leica EM CPD 300a). The cells were observed and imaged with a scanning electron microscope (Merlin VP Compact, Carl Zeiss). Example of a SEM image is shown in Supplementary Material 1.1. The length (1.04 ± 0.14 μm) and width (0.57 ± 0.04 μm) of the cells measured with ImageJ on the acquired SEM images were used to calculate the biovolume of single cells with Equation (13). The obtained values of cell biovolume (0.22 ± 0.06 μm3) and the cellular carbon content derived from elemental analysis and cell counting resulted in the carbon cellular density of 1.27 ± 0.22 pg·μm−3.

Different chemical fixations of n class="Chemical">pan class="Species">P. putida cells were considered for SEM imaging and nanoSIMS analysis. Preservation of cell morphology with GA was found to be superior to n class="Chemical">mical">pan class="Chemical">PFA fixation and was therefore applied in cell preparation for SEM imaging performed to determine the cell size for biovolume and elemental density calculations. We tested comparatively the cell fixation with GA and PFA (data are not shown). The best preservation of the cell morphology was achieved upon fixation with 1% GA. Instead, when preparing cells for the nanoSIMS analysis, we used a 2% PFA fixative, similar to fixation employed for CARD-FISH and fluorescence microscopy, since quite often these techniques are applied on environmental samples prior to and in combination with the nanoSIMS analysis. In addition, by applying the 2% PFA fixative we were consistent with our previous work (Musat et al., 2014) where the same concentration of PFA was used in chemical fixation of cells for the nanoSIMS analysis.

Results and discussion

Mathematical model to calculate assimilation rates

Calculation of assimilated elemental fraction from changes in isotope ratios

The fraction K of an element (e.g., pan class="Chen class="Chemical">mical">carbon or n class="Chemical">mical">pan class="Chemical">nitrogen) assimilated by a cell during growth with isotope-labeled substrates can be evaluated from the changes in the cell's isotopic composition.

E – amount of assimilated element,

E – initial cellular amount of the same element.

In the case of isotope ratio (R) defined as heavy-to-light ratio for pan class="Chen class="Chemical">mical">carbon isotopes

the fractions of heavy and light isotopes (D and D) can be expressed as following.

The amounts of heavy and light isotopes (E = E and E = E) in cells after incubation with isotope-labeled growth substrates can be expressed as a function of isotope ratios (R), initial and assimilated amount of an element (E and E as in Equation 1). For simplicity, in this first approach the assin class="Chemical">milation of an element is considered as the mixing of two components with different isotopic composition (the cell and the culture media) as applied elsewhere (Popa et al., 2007).

R—isotope ratio of growth substrate during incubation;

R—initial cellular isotope ratio before incubation.

The isotope ratio after incubation (R) can be expressed as ratio between heavy and light isotope amounts

Taking the Equations (2) and (3) into account

Division of the nominator and denon class="Chemical">minator of (4) by E will bring

Further transforpan class="Disease">matn>ions of Equation (4') yield the expression for K.

K can be finally expressed as a function of the initial and final isotope ratios of cells and the fraction D of the heavy isotope in the growth substrate.

Equation (6) expresses the fraction K of the element incorporated by a cell during incubation with isotope-labeled growth substrates, relative to its initial cellular content.

Usually, the cellular isotope ratios measured by nanoSIMS are directly used as the initial and final cellular isotope ratios (R, R in Equation 6). In such cases, calculation of K does not account for inherent alterations of isotopic composition due to sample processing prior to the nanoSIMS analyses. However, in most studies, biological samples are subjected to various treatments following incubations with stable isotope labeled substrates. In the following section, we present a concept to restore cellular isotope ratios after sample treatments.

Restoration of isotope composition after chemical treatments

Preparation of biological samples for nanoSIMS analyses range from sample n class="Chemical">pan class="Disease">dehydration to meet the high vacuum analytical conditions of the nanoSIMS instrument, to metabolic inactivation, chemical fixation or cell wall permeabilization. Typical agents include n class="Chemical">mical">pan class="Chemical">aldehyde based compounds (e.g., formaldehyde, glutaraldehyde) or alcohols (e.g., ethanol, methanol). In addition, in many microbial ecology studies, cell phylogenetic identification is desired and chemical fixation is followed by fluorescence in situ hybridization based protocols such as FISH or CARD-FISH. This is increasing considerably the number of chemicals applied on the samples, and may significantly alter the isotopic composition. For example, we showed that chemical fixation and hybridization strongly affects the carbon and nitrogen isotope composition of microbial cells (Musat et al., 2014). Such changes of carbon isotope composition are mainly due to introduction of carbon from chemicals possessing natural isotope composition (~1.1 at% of 13C) into 13C-enriched microbial cells causing the dilution of 13C label. Such dilution effects have to be considered for the evaluation of element assimilation rates.

The original isotope ratios R of cells before chemical treatment can be restored from the isotope ratios R' derived after nanoSIMS experiment on chen class="Chemical">mically treated cells. For such a restoration, the fraction (K) of an element introduced into microbial cells upon chemical treatment and the D fraction of heavy isotope of the applied chemicals have to be considered.

The fraction K of an element introduced into microbial cells upon chen class="Chemical">mical treatments can be defined relative to (i) an initial element content (E) in cells before treatment or (ii) final element content (E) including the element amount (E) introduced into cells upon chemical treatment. The K fraction is expressed as K relative to E and as K relative to E in the following way.

The value of K has been derived from the pan class="Chen class="Chemical">mical">carbon isotope ratio R' measured for n class="Chemical">mical">pan class="Species">P. putida cells grown on medium with 100% 13C-labeled glucose as carbon source after applying different chemical treatments (Musat et al., 2014).

where: R—original cellular isotope ratios before chemical treatment;

R′—nanoSIMS measured isotope ratios after chemical treatment;

D—fraction of pan class="Chen class="Chemical">mical">13C isotope of the chemicals applied.

These K values can be cautiously applied to similar n class="Chemical">microorganisms or derived specifically for other types of microbial cells and chemical treatments in the same way (Musat et al., 2014). Other K values were determined for pan class="Species">Vibrio cholerae, mical">pan class="Species">Bacillus subtilis, E. coli and Deltaproteobacteria from microbial mats (Woebken et al., 2014; Musat N. et al., 2016). When choosing an appropriate K value for the restoration of original isotope ratios, one should consider the difference and the following relation between K and K fractions.

With the measured R′ ratios and an appropriate K or K value, the original isotope ratios R can be calculated using one of the following expressions.

The fraction of pan class="Chen class="Chemical">mical">13C isotope in chemicals (D) can be assumed to be 0.011 corresponding to the natural n class="Chemical">mical">pan class="Chemical">13C abundance (1.1 at%) or it can be measured for specific chemicals to increase the accuracy of the calculation.

The R values expressed with (8) are to be used as final or initial isotope ratios (R or R) for the calculation of the K fraction of pan class="Chen class="Chemical">mical">carbon assimilated by the cells during their incubation in n class="Chemical">mical">pan class="Chemical">13C labeled medium.

The error ΔR is calculated taking into account the uncertainties of input values (ΔR′, ΔK, ΔD contribupan class="Chen class="Chemical">mical">ting in the error proclass="Chemical">n class="Chemical">mical">pagation (Fitzsimons et al., 2000).

For the correction of pan class="Chen class="Chemical">mical">nitrogen isotope ratio with (8) the applicability of the dilution model has to be proved and the treatment-specific K values for n class="Chemical">mical">pan class="Chemical">nitrogen have to be derived or set to “0” if the reduction of 15N/14N ratio is not observed for the treatment applied. The K = 0 case implies the absence of isotope dilution and yields R = R' (8).

Consideration of stable isotope fractionation effects

Biochemical reactions usually discrin class="Chemical">minate against the heavy isotopes, i.e., preferential processing of lighter molecules of the growth substrate, leading to an accumulation of heavy isotopes in the residual substrate pool. This effect, described by the isotope fractionation factor α (10), may cause differences between the isotope ratio of assimilated substrate (R) and the respective ratio of the growth substrate (R). If the isotope fractionation factor α is known, it can be considered to refine the calculation of an element fraction assimilated from growth substrate (Equation 6).

In the expression of K (6) we will substitute the D with a fraction of heavy isotope in assimilated substrate (D):

D is expressed as a function of R and α. With the R and R denotations, the isotope fractionation factor is defined as

The expression for the isotope fraction of assimilated substrate (D) is derived in following way.

According to Equation 10:

Considering the expression of D in Equation 9 leads to:

Note that if the fractionation factor α is set to 1 (unknown for the organism or growth substrate under study), Equation 11 will revert to Equation 6.

The error ΔK is calculated taking into account the contribution of input value uncertainties (ΔR, ΔR, ΔR, Δα) in the error propan class="Chemical">gation (Fitzsimons et al., 2000).

Dynamics of KA as a function of the final fraction Df of an assimilated element

The graphs in Figure 1 show the fraction of pan class="Chen class="Chemical">mical">carbon (K, Equation 11) which a cell of an initial (natural) n class="Chemical">mical">pan class="Chemical">carbon isotope composition (D = 1 at%) has to assimilate (relatively to an initial carbon cellular content) from growth substrate with 13C fraction D to reach the final D cellular fraction of 13C. The K (D) dependence shows the nonlinear relation between the assimilation and heavy isotope fraction. An increase in heavy isotope fraction (ΔD) requires more labeled substrate to be assimilated (ΔK) at higher D A K fraction value ≥ n × 100 at% means that it was achieved by a cell in n + 1 generation (after n divisions). The K dependences show asymptotic profiles limiting the cellular 13C fraction D below the 13C fraction in growth substrate D. The value of cellular 13C fraction D > D can be achieved only with isotope fractionation factor α < 1 (see Equation 11). The comparison of K expression (Equation 11) with the expression of net assimilation reported by (Popa et al., 2007) is presented in Supplementary Material 2.

Figure 1

Dependence of assimilated carbon fraction K (11) on the final 13C fraction D simulated for the cells incubated from the inoculum with D = 1 at% in growth substrates with different D values of 13C fraction.

Dependence of assimilated n class="Chemical">pan class="Chemical">carbon fraction K (11) on the final mical">pan class="Chemical">13C fraction D simulated for the cells incubated from the inoculum with D = 1 at% in growth substrates with different D values of 13C fraction.

The K(D) dependence shows fast changes of K when D approaches the D. These fast changes of K are revealed in high absolute values of K derivatives expressed above and imply an increase in ΔK when K is calculated for D approaching the D. Uncertainty of K calculated with isotope fractionation factor neglected (α set to 1) or incorrectly set becomes also considerable with D approaching the D (see Supplementary pan class="Disease">Matn>erial 1.2 and Figure S4). It can therefore be recommended to derive the K with D below 0.6 × D. In general, higher D value reduces the uncertainty of K due to neglected or incorrect α value and provides a broader dynamic range for K. It is therefore important to have sufficiently high value of D especially for analysis of complex microbial communities when (i) isotope fractionation factor α has to be neglected (α set to 1) or set to an approximical">pan>n class="Disease">mated value and (ii) different species reveal considerably different K values (assimilation) distributed in a broad range. On the other hand, (i) increase in heavy isotope content in growth substrate (D) may affect the metabolic processes in the studied microbial systems, (ii) extreme D value yields poor counting rate for a light isotope.

Cell volume and element-specific cellular density

Besides K values describing relative assimilation, the expression of assin class="Chemical">milation rate in mass units per time for each single cell (see detailed implementation in Supplementary pan class="Disease">Material Excel Template Table) requires also (i) a value of element-specific cell density (e.g., mass of mical">pan class="Chemical">carbon or nitrogen per cell volume) for expression of the volume-specific assimilation rate for each single cell in e.g., fg·μm−3·h−1 and (ii) volume of each single cell for expression of the cell-specific assimilation rate in e.g., fg·cell−1·h−1. Dispersion of cell volumes may be considerable even for cells in pure cultures (e.g., relative to their growth state).

Calculation of RoI-confined cellular volume from NanoSIMS data

Treatment of nanoSIMS data considering single-cells implies the definition of each single cell by drawing the RoIs confining single cells in nanoSIMS-acquired ion yield maps. Cellular volume confined by RoI can be estipan class="Disease">matn>ed from the data of nanoSIMS experiment providing the area (Sp, given in pixels) of RoI defined around a single cell and the Length-to-Width Ratio of RoI (LWR). Very often RoI defined with a nanoSIMS map does not confine a single cell, but rather a cell fragment. The length (mical">pan>n class="Chemical">Lp) and width (Wp) of RoI-confined fragments of rod-shaped and coccoid cell can be expressed in pixels as following.

The raster metric dimension (length of rectangular raster, FoV [μm]) and the Raster size in pixels [number of pixels along the raster edge, Rst [pixel]] can be used to convert L and W into corresponding L and W values in metric scale.

For example, for rod-shaped cells the biovolume (V) can be calculated as the sum of a cylinder of W μm in diameter and (L–W) μm in length, capped on it's both sides with hemispheres of W μm in diameter:

and the volume of two capping hemispheres

in the following way

Note that if L = W, equation 13 will express the volume of a sphere, so it can be also used to calculate the biovolume of coccoid cells. Expression (13) can also be applied to calculate cellular volumes when L and W are derived from other analyses, e.g., Scanning Electron Microscopy (SEM) or Aton class="Chemical">mic-Force Microscopy (AFM), as well as for the calculation of volume for ROI-confined cell fragments considering the values of L and W derived from the nanoSIMS data according to expressions (12). For the measurements of cell volume a series of cautions has to be obeyed upon different treatments (e.g., fixation, pan class="Disease">dehydration, and premical">paration for Ultra-High Vacuum (UHV) sample environment of SEM, SIMS etc.) in order to avoid any distortion of cell native geometry due to cell exmical">pansion/burst, shrinkage, cell agglomeration etc.

Calculation of cellular element-specific density

An absolute value of elemental (pan class="Chen class="Chemical">mical">carbon, n class="Chemical">mical">pan class="Chemical">nitrogen etc.) content per cell volume (partial density of e.g., carbon: ρC [g/μm3]) can be expressed in terms of (i) total amount of an element per sample [e.g., MC [g] of carbon]; (ii) number of cells per sample (N); and (iii) averaged cell volume (V) in the following way.

Total absolute amount of an element per sample (MC [g]) can be derived from an Elemental Analysis Mass Spectrometry (n class="Chemical">pan class="Disease">EA-MS) experiment.

Number of cells per sample (N) can be determined by flow cytometry or, depending on the size of the target cells, by direct counn class="Chemical">pan class="Chemical">ting under a haemocytometer. Both methods are most effective if interferences from other mical">particles (e.g., detritus, sediment) are not expected, and hence amenable to relatively clean samples like pure or enriched cultures, or mical">pan class="Species">environmental water samples. Alternatively, cells can be stained with nucleic acid dyes (e.g., DAPI) and counted under a epifluorescence microscope, a method that can be applied to most types of samples.

Cell volume (V) can be calculated using the expression (13) with cell length and width values measured using ImageJ on SEM images of cells as mentioned in the section Determination of Biovolume for n class="Chemical">pan class="Species">P. putida Cells. Note that the mean value of cell volume (V) and its standard deviation derived from SEM images are used here for calculation of cellular element-specific density (e.g., ρ) only and should not be confused with the RoI-confined cellular volumes (V) derived from nanoSIMS data for each single cell analyzed to calculate the cell-specific assimilation rate (see section Cell-Specific Assimilation Rate).

If pan class="Disease">EA-MSn> or Flow Cytometry are not available, the element-specific cell density can be calculated as follows.

Estipan class="Disease">matn>e the cell dry mass (DM) from cell volume (V) within the approach developed by Loferer-Krössbacher et al. (1998)

Calculate an element-specific content for a single cell (e.g., m of pan class="Chen class="Chemical">mical">carbon) from the total dry mass of cell (DM) using Redfield elemental ratio of cell composition (Fagerbakke et al., 1996). Note that this approach may introduce uncertainties since the cellular elemental ratios may deviate from the Redfield ratio among different phylogenetic groups, or may be influenced by the type, growth conditions or availability of nutrients.

Calculate an element-specific cell density e.g., for pan class="Chen class="Chemical">mical">carbon

Considering the molar masses (μ and μ) and the Redfield ratio, e.g., for atomic composition of marine phytoplankton

the element-specific partial densities (ρ and ρ) can be linked with the following expression.

With the values from Redfield ratio sequence (17) and respective molar masses Equation 18 yields

The cellular density of major elements, particularly n class="Chemical">pan class="Chemical">carbon, has been experimentally determined for phylogenetically and morphologically diverse microorganisms (Table 1). Such values could be cautiously considered for phylogenetically and physiologically related strains if any of the required mical">parameters to calculate the density of an element for cells of interest is missing.

Table 1

Carbon density/content and cell biovolume for a selection of microorganisms from various phylogenetic clades.

Strain	Cell volume [μm3]	Carbon density [fg·μm−3]	Carbon content [fg ·cell−1]	References
Alphaproteobacteria
Ca. Pelagibacter			32.2	Zimmerman et al., 2014
Oceanicola granulosus			94.8	Zimmerman et al., 2014
Ruegeria pomeroyi			142	Zimmerman et al., 2014
Pelagibaca bermudensis			172	Zimmerman et al., 2014
Gammaproteobacteria
Cycloclasticus oligotrophus	0.26 ± 0.02		9.46 ± 3.64	Robertson et al., 1998
Vibrio campbellii	0.21*		14.51 ± 3.48	Troussellier et al., 1997
Enterobacter cloacae	0.27*		18.57 ± 2.44	Troussellier et al., 1997
Salmonella typhimurium	0.57*		24.07 ± 3.00	Troussellier et al., 1997
Escherichia coli	0.71*		24.96 ± 4.55	Troussellier et al., 1997
Alteromonas rubra	0.70*		29.96 ± 7.50	Troussellier et al., 1997
Aeromonas hydrophyla	0.64*		30.59 ± 2.84	Troussellier et al., 1997
Alteromonas nigrifaciens	0.34*		31.63 ± 4.20	Troussellier et al., 1997
Alteromonas tetraodonis	0.37*		33.26 ± 6.09	Troussellier et al., 1997
Vibrio fischeri	0.22*		33.45 ± 5.36	Troussellier et al., 1997
Pseudomonas putida KT2440	0.22 ± 0.06	1269 ± 216	277.0 ± 47.0	This study
Vibrio natriegens	3.5 ± 0.5	350 ± 40		Fagerbakke et al., 1996
Deltaproteobacteria
Desulfosarcina sp. strain BuS5	2.96	55.2	163.2	Jaekel et al., 2013
Cyanobacteria
Phormidium autumnale		93.37 ± 3.27		Mahlmann et al., 2008
Anabaena cf. thermalis		118.84 ± 4.04		Mahlmann et al., 2008
Spirulina platensis		125.77 ± 3.72		Mahlmann et al., 2008
Oscillatoria cf. rupicola		129.26 ± 5.56		Mahlmann et al., 2008
Prochlorococcus SARG	0.144 ± 0.008	237 ± 7		Heldal et al., 2003
Prochlorococcus SB	0.22 ± 0.01	147 ± 5		Heldal et al., 2003
Synechococcus WH 7803	0.62 ± 0.07		120 ± 10	Heldal et al., 2003
Synechococcus WH 8103	0.83 ± 0.06		220 ± 10	Heldal et al., 2003
Environmental species
Bacterioplankton Lake Slaen,Vermount USA	0.286 ± 0.027	210 ± 30		Bjørnsen, 1986
Bacterioplankton Lake Bryrup, Danemark	0.278 ± 0.042	340 ± 90		Bjørnsen, 1986
Bacterioplankton Roskilde Fjord, Danemark	0.101 ± 0.009	340 ± 10		Bjørnsen, 1986
Bacterioplankton Raunefjorden, Norway	1.78 ± 0.17		149 ± 8	Vrede et al., 2002

Calculated using Equation 13 (this study) with values of cell length and width from Table 1 in Troussellier et al. (.

pan class="Chen class="Chemical">mical">Carbon density/content and cell biovolume for a selection of microorganisms from various phylogenetic clades.

Calculation of assimilation rates

Rates of assimilation can be calculated for each single n class="Chemical">microbial cell by dividing the assimilated amount of an element (e.g., pan class="Chemical">carbon or mical">pan class="Chemical">nitrogen) by the incubation time. The fraction of heavy isotope in growth substrate (D must be accepted to be stable (within a precision) during the considered time-frame of incubation. An incubation period may be split into several time-frames when strong changes in the availability or isotopic composition of the growth substrate are revealed/expected. Generalized scheme of assimilation rate studies is presented in Supplementary Material 3. The calculation procedure is implemented in Supplementary Material Excel Template Table.

Relative assimilation

The value of K (Equation 11) represents the fraction of an assimilated element relative to its initial content in a cell. The relative assimilation expressed with K values can be used in comparative studies for analysis of a relative difference and heterogeneity in single cell activity revealed in relative amount of assimilated pan class="Disease">material (in K values). If K values are derived at several time points, the slope in K (t) plot shows the trend of assimilation rate in time.

Cell-specific assimilation rate

Multiplying the absolute value of an element mass per cell volume (pan class="Chen class="Chemical">mical">carbon n class="Chemical">mical">partial density ρ [g/μm3], for example) by the RoI-confined cellular volume (V [μm3], i ∈ {1 … n}) calculated for each of n analyzed cells using (12) and (13) results in the mass (m [g], i ∈ {1 … n}) of n class="Chemical">mical">pan class="Chemical">carbon of each of the analyzed cells

where n is the number of analyzed cells.

To derive the mass of pan class="Chen class="Chemical">mical">carbon (u) assimilated by each cell, the cell-specific mass of n class="Chemical">mical">pan class="Chemical">carbon (m) has to be multiplied by the fraction K (11) of carbon incorporated into each cell.

The cell-specific assimilation rate (F is calculated for each cell by dividing the u over the incubation time (t).

The error ΔF is calculated taking into account the uncertainties of input values (Δρ, ΔV, ΔK, Δt) in the following way (Fitzsimons et al., 2000).

Volume-specific assimilation rates

To eliminate the dispersion of F values due to the variation of RoI-confined cellular volume, the cell-specific assimilation rate (F of each cell can be normalized by the RoI-confined volume (V). This normalization is particularly important when isotopic ratios are derived for cell fragments confined within RoIs in isotope ratio maps acquired with nanoSIMS. The volume-specific assimilation rate (F is expressed in following way:

for each of n analyzed microbial cells or cell fragments.

The error ΔF is calculated taking into account the uncertainties of input values (Δρ, ΔK, Δt) in the following way (Fitzsimons et al., 2000).

Concept application on P. putida cells

pan class="Chen class="Chemical">mical">Carbon assimilation rates were calculated for n class="Chemical">mical">pan class="Species">P. putida cells employing the developed quantification procedure using the results of the nanoSIMS experiment. The distribution maps for the relative yield in (i) 12C−, 13C−; (ii) 12C14N−, 13C14N−; and (iii) 12C16O−, 13C16O− secondary ion pairs (Figure 2) were acquired by nanoSIMS. We aimed to derive the carbon isotope ratio (13C/12C) from both, the counts of monoatomic (C−) and molecular (CN− and CO−) ions containing different (12C and 13C) carbon isotopes in order to determine which of these would be more suitable to consider for further calculation of carbon assimilation rates for microbial cells from environmental samples.

Figure 2

Lateral distribution maps for the relative yield of monoatomic 12C− (a), 13C− (b), and molecular 12C14N− (c), 13C14N− (d), 12C16O− (e), and 13C16O− (f) secondary ions containing light 12C (a,c,e) and heavy 13C (b,d,f) carbon isotopes. Scale bar length is 4 μm.

Lateral distribution maps for the relative yield of monoatomic n class="Chemical">pan class="Chemical">12C− (a), mical">pan class="Chemical">13C− (b), and molecular 12C14N− (c), 13C14N− (d), 12C16O− (e), and 13C16O− (f) secondary ions containing light 12C (a,c,e) and heavy 13C (b,d,f) carbon isotopes. Scale bar length is 4 μm.

The lateral distribution of counts in monoatomic C− ions (Figures 2a,b) reveals a relatively even distribution of n class="Chemical">pan class="Chemical">12C− counts (Figure 2a) over the analyzed FoVs involving microbial cells and polymical">pan class="Chemical">carbonate filter substrate, whereas a clear pattern of 13C-labeled microbial cell distribution is delivered in 13C− counts (Figure 2b). The cell distribution pattern is nicely reproduced with the lateral maps acquired in counts of molecular CN− secondary ions with light and heavy carbon isotopes (Figures 2c,d). Lateral distribution maps of CO− ion counts (Figures 2e,f) as well as their ratio did not revealed any kind of cell distribution pattern and were therefore not considered for further quantitative data evaluation. The detected CO− ion counts were concluded to originate mostly from volatile organic contaminant and residual gas molecules adhered on the sample surface. This adhesion occurs even in ultra-high vacuum (UHV) where residual gas molecules and dust particles are still present. Clarification of unspecific CO− ion origin requires further studies implying detailed analysis of sample molecular composition upon different sample preparation and storage conditions.

The maps of pan class="Chen class="Chemical">mical">13C− and n class="Chemical">mical">pan class="Chemical">13C14N− ion counts (Figures 2b,d) showed a similar distribution and were used to define single cells and reference filter areas (ROIs) by confining of respective cell- or filter-related pixels in freehand drawn loops [(Polerecky et al., 2012); Figures 3a,c, white lines]. More precise and reproducible RoI definition can be done employing the function of “interactive thresholding” (Polerecky et al., 2012) on isotope/ion ratio maps. For a direct comparison of the analysis results the ROIs defined from similarly distributed 13C− and 13C14N− ion counts were used for calculation of 13C fraction in monoatomic C− and molecular CN− ions.

Figure 3

Lateral distribution of 13C fraction in at% derived from the isotope ratio of single atomic C− ions (a) and molecular CN− ions (c) measured by nanoSIMS. Frames and show the depth profiles of respective 13C fractions (gray circles) for all defined RoIs (Ranges of Interest, white line confined) involving microbial cells and filter areas. The mean value of 13C fraction with its standard deviation is shown for cells (solid rectangles) and filter areas (solid circles) in each scanned plain (b,d). Scale bar length is 4 μm.

Lateral distribution of pan class="Chen class="Chemical">mical">13C fraction in at% derived from the isotope ratio of single atomic C− ions (a) and molecular CN− ions (c) measured by nanoSIMS. Frames and show the depth profiles of respective n class="Chemical">mical">pan class="Chemical">13C fractions (gray circles) for all defined RoIs (Ranges of Interest, white line confined) involving microbial cells and filter areas. The mean value of 13C fraction with its standard deviation is shown for cells (solid rectangles) and filter areas (solid circles) in each scanned plain (b,d). Scale bar length is 4 μm.

Lateral distribution maps of pan class="Chen class="Chemical">mical">13C fraction derived from the count ratio of monoatomic C− and molecular CN− ions are shown in Figures 3a,c together with the depth profiles of n class="Chemical">mical">pan class="Chemical">13C fraction over 6 acquired plains (Figures 3b,d) for all defined ROIs.

Contrary to the similar distribution of relative intensity in n class="Chemical">pan class="Chemical">13C− and mical">pan class="Chemical">13C14N− ion count maps (Figures 2b,d), the maps of 13C isotope fraction derived from counts of monoatomic C− and molecular CN− ions (Figures 3a,c) were found to be different. The cell size appears to be smaller in 13C fraction derived from monoatomic C− ratio (Figure 3a) due to the contribution of 12C from filter at the edge of microbial cell. Such a trapping of extrinsic 12C from sample substrate (polycarbonate filter) or embedding material into an analyzed RoI area or volume causes a reduction of calculated 13C fraction due to the dilution effect. From the monoatomic C− ion ratio the 13C fraction of 8.003 ± 0.378 at% has been derived for microbial cells (Figure 3b, solid rectangles) and 1.057 ± 0.003 at% complying with the natural 13C abundance for filter areas (Figure 3b, solid circles). Considerably higher mean value of 13C fraction with reduced standard deviation (10.585 ± 0.153 at%) have been derived for microbial cells from molecular CN− ion ratios (solid rectangles in Figure 3d). Secondary CN− ions (originating from proteins or nucleic acids) are inherent products of microbial cell ionization and their carbon isotopic composition can be admitted for the whole microbial cell actively growing or grown in environment with a defined isotopic composition. The 13C fraction derived from molecular CN− ion ratios for filter areas (1.294 ± 0.045 at%; solid circles in Figure 3d) exceeds the natural 13C abundance and the residual CN− ion yield detected from the filter areas may be associated with N-containing cell components (low molecular mass compounds) escaping cells during sample preparation.

The lateral dilution effect observed for the pan class="Chen class="Chemical">mical">13C fraction in monoatomic C− ratio (Figures 3a,b) may be reduced when RoI definition is based on the C− isotope ratio map by excluding the n class="Chemical">mical">pan class="Chemical">12C-rich filter material from the RoI area. Deviation in 13C fraction derived for microbial cells from isotopic composition of C− (CN−) may occur due to the dilution of native cell-specific C− (CN−) ions not only with those originating from a sample substrate, but also with C− (CN−) from embedding material, from overlapping extracellular organics and other microbial species possessing different 13C enrichment. To check for such a spatial dilution in C− (CN−) isotopic composition, the depth profile (changes over the scanned planes) of respective (C− or CN−) isotope ratio has to be analyzed for each RoI. If a set of planes shows an isotope ratio value which is considerably different from those revealed in other planes of the same RoI, then the planes with close values of isotope ratios have to be accumulated and quantified separately as they are originating from sample compartment with different 13C enrichment. Such analysis on complex organic sample is rather complicated due to the ion beam induced intermixing of sample material, sample geometry, its heterogeneity, and surface topography.

Reconstruction of original 13C fraction in P. putida cells

Chemical fixation of n class="Chemical">pan class="Species">P. putida cells leads to a 4.4 at% dilution of n class="Chemical">mical">pan class="Chemical">13C isotope content, relative to the initial cellular carbon content (Musat et al., 2014). With the measured R' ratio and a K value of 0.044 ± 0.014, the original carbon isotope ratio R has been reconstructed for each cell using the expression (8). The 13C fraction in chemicals used for cell fixation (D) was set at 1.1 at%. The analysis has been done for 100 cells in two FoVs measured with nanoSIMS instrument in the same conditions. The 13C fraction R' has been calculated for each cell considering the ion counts accumulated in each pixel confined within a corresponding RoI over 6 analyzed planes. The restoration results are shown in Figure 4 and represented in Table 2.

Figure 4

Distribution of microbial cell by the 13C fraction derived from isotope ratio of single atomic C− ions (1) and molecular CN− ions (3) as measured with nanoSIMS (D') and the respective distributions (2 and 4) with the 13C fraction (D) corrected for the dilution of 13C label with the chemicals used during cell fixation.

Table 2

The values of 13C fractions derived for the microbial cells from the measured R' and reconstructed R isotope ratios of monoatomic C− and molecular CN− ions.

Considered secondary ions	Measured 13C fraction D' ±ΔD' [at.%]	Restored 13C fraction D ±ΔD [at.%]	Difference D- D' [at.%]
Monoatomic C−	7.99 ± 0.79	8.29 ± 0.82	0.30
Molecular CN−	10.64 ± 0.19	11.06 ± 0.19	0.42

Distribution of microbial cell by the n class="Chemical">pan class="Chemical">13C fraction derived from isotope ratio of single atomic C− ions (1) and molecular CN− ions (3) as measured with nanoSIMS (D') and the respective distributions (2 mical">pan class="Species">and 4) with the 13C fraction (D) corrected for the dilution of 13C label with the chemicals used during cell fixation.

The values of pan class="Chen class="Chemical">mical">13C fractions derived for the microbial cells from the measured R' and reconstructed R isotope ratios of monoatomic C− and molecular CN− ions.

Calculation of carbon assimilation rate

The values of pan class="Chen class="Chemical">mical">13C fraction restored from the counts of molecular CN− ions have been chosen for the calculation of n class="Chemical">mical">pan class="Chemical">carbon assimilation rate. The fraction K of carbon incorporated into the cells via biotic assimilation has been calculated for each cell according to (11) with the isotope ratio R corresponding to 1.1 at% initial 13C fraction (D) in the microbial cells, R corresponding to 13.5 at% 13C fraction (D) in growth substrate and the isotope fractionation factor α set to 1. The carbon assimilation rates calculated per cell (F) according to (22) and per μm3 of cell volume (F) according to (23) are presented in Figure 5.

Figure 5

Carbon assimilation rate calculated per volume F (solid circles, [pg·μm−3·h−1]) and per single cell F (open rectangles, [pg·cell−1·h−1]) of P. putida incubated in 13C-glucose medium (D = 13.5 at%) for 10 h. Initial 13C fraction D has been set at 1.1 at%. Assimilation rates are shown with mean value and standard deviation for all 105 single cells in the left frame. The distributions of cell-specific (F) and volume-specific (F) assimilation rates are shown in the right frame with Min-Max whiskers, box representing the 16–84 percentile range, median value (horizontal line) and mean value (solid rectangle) inside the percentile box.

pan class="Chen class="Chemical">mical">Carbon assimilation rate calculated per volume F (solid circles, [pg·μm−3·h−1]) and per single cell F (open rectangles, [pg·cell−1·h−1]) of n class="Chemical">mical">pan class="Species">P. putida incubated in 13C-glucose medium (D = 13.5 at%) for 10 h. Initial 13C fraction D has been set at 1.1 at%. Assimilation rates are shown with mean value and standard deviation for all 105 single cells in the left frame. The distributions of cell-specific (F) and volume-specific (F) assimilation rates are shown in the right frame with Min-Max whiskers, box representing the 16–84 percentile range, median value (horizontal line) and mean value (solid rectangle) inside the percentile box.

The cell volume V (13) used for the calculation of F (22) was derived from the size and geometry of RoIs that are supposed to be drawn around single microbial cells, but are often drawn around their visualized fragments of different sizes. The variation of RoI size affects the estin class="Chemical">pan class="Disease">mated cell volume and results in strong dispersion of n class="Chemical">mical">pan class="Chemical">carbon assimilation rate values delivering 0.37 ± 0.19 pg·cell−1·h−1 as calculated per microbial cell (Figure 5, open rectangles). The volume-specific carbon assimilation rate F (23) calculated per μm3 of single cell volume shows considerably lower dispersion (Figure 5, solid circles) delivering 0.52 ± 0.04 pg·μm−3·h−1.

Conclusions, applicability, and critical considerations

Here we provide a comprehensive model to derive assimilation rates of single cells from SIP-nanoSIMS experiments. n class="Chemical">Particular features of our model include careful consideration of both physiological (isotope fractionation during substrate uptake) and experimental (sample preparation applied) effects on the isotopic composition of cells. In addition we provide detailed considerations and recommendations to determine the cellular density of pan class="Chemical">carbon, which could also be applied to obtain the cellular density of other elements as well, for example N, P, or O.

Application of our concept on a model culture showed that when pan class="Disease">isotope dilutionn> due to various sample premical">pan>ration methods, or substrate-specific isotope fractionation factors are not considered, assimilation rates can be significantly underestimical">pan>n class="Disease">mated. In addition, we observed that even upon normalization of the assimilation rates by cellular volume, P. putida cells still showed a relatively high functional heterogeneity. Since the cells were grown with a soluble substrate, constant mixing, and were collected in their mid-exponential growth phase, it is unlikely that heterogeneity was caused by diffusion limitations of oxygen or growth substrate. An attractive hypothesis is that the heterogeneity could be a response of cell physiology to depletion of substrate concentration in a closed system. The heterogeneity and relative difference in cell activity can be represented with the distribution of K values showing the relative assimilation of single cells.

The calculation method presented here considers the uncertainties of all input parameters (ΔR, ΔK, ΔD, Δρ, ΔD, ΔD, Δα, Δt) pron class="Chemical">pagapan class="Chemical">ting into the error of relative assimilation (K), volume-specific (F), and cell-specific (F) assimilation rates expressed for each single cell. The error consideration is mical">particularly important for the input values used in calculations on single-cell level (i.e., fraction K of mical">pan class="Chemical">carbon introduced via chemical treatment, element-specific cellular density, e.g., ρ or ρ) but derived on a bulk level for similar phylotypes. The demand of element-specific cellular density (ρ) is an inherent shortcoming of the single-cell assimilation rate quantitation when it is applied to environmental populations, where the ρ values of individual cells are unknown and have to be approximated with an average value derived for a pure culture or for an environmental bulk population. Although the approximation of element-specific cellular density introduces an uncertainty in the calculated rates, no viable alternative is available to date. Consideration of an element-specific cellular density (e.g., ρ or ρ) estimated using the Loferer-Krossbacher approach (Equation 15) and Redfield elemental ratio (e.g., Equation 17) may also cause significant errors in the calculated volume- and cell-specific assimilation rates (F and F). If the value of element-specific cellular density (ρ) is unknown and its approximation is considered to cause an unacceptable uncertainty in the calculated assimilation rates, then assimilation can be expressed relatively with K values (Equation 11) derived without ρ consideration.

Calculation of cell-specific assimilation rate (F, Equation 22) involves the RoI-confined volume of each single cell (V) that may result in uncertainty and artificial dispersion of F values when not entire cells but rather cell fragments are confined within the defined RoIs. The calculation of volume-specific assin class="Chemical">milation rate (F, Equation 23) may be a viable solution in this case. The F values are independent from the RoI-confined cellular volume and can be considered together with biovolume and cell abundance in specific pan class="Species">environmental microbial populations for upscaling the assimilation rate from single-cell to ecosystem level. For example, one can quantify the role of certain microbial populations in specific biogeochemical processes, like mical">pan class="Chemical">nitrogen fixation in oligotrophic waters (Thompson et al., 2012; Martínez-Pérez et al., 2016). This type of quantitative data, previously inferred from bulk measurements and cell counts or sequence abundances, were often underestimating the role of key players and their significance in the environment. Nowadays, the quantitation of assimilation rate at single-cell level in complex microbial communities cannot be performed without SIP-FISH-nanoSIMS technique and the suggested calculation method has therefore an inevitable applicability in many experimental as well as environmental studies.

Author contributions

NM, HR, and HS conceived the study and the experimental design. NM and FC performed the cell incubation and sampling. FC and SK executed the elemental density analysis. FC and HS performed the nanoSIMS analysis. HS developed the pan class="Disease">matn>hemical">pan>n class="Disease">matical model development and the first draft of the manuscript. HS, NM, and FM wrote the manuscript with contribution from all authors. All authors contributed to manuscript revision, read and approved the submitted version.

Conflict of interest statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.