### Welcome

This calculator is designed to help biologists culture marine phytoplankton under iron-limiting conditions. In these experiments the iron concentration in the media is held constant by the chelator EDTA, which buffers the metal concentration in a manner similar to a pH puffer. Unfortunately, phytoplankton can begin to remove un-chelated iron from the media faster that it is replenished by dissociation from the FeEDTA complex, causing the concentration of un-chelated iron to decrease. This calculator estimates the maximum cell density that a culture medium can support.

For an in depth discussion of the methods used by this calculator see the paper:
Rivers, A.R., Rose, A.L., Webb E.A. (2013) An online calculator for marine phytoplankton iron culturing experiments. Journal of Phycology. 49(5) 1017-1021.

### Instructions

The calculator is designed for marine phytoplankton in seawater or full salinity artificial seawater media at 20°C and pH 8.0-8.2. Outside of these conditions, the calculator may give erroneous results. Estimates are made based on the cellular diameter of the phytoplankton cell, see Sunda and Huntsman (1997).

• 1. Enter the diameter of your phytoplankton cell. Approximate values can be found for over 2000 strains using the table on this site.
• 2. Enter the concentration of EDTA and iron added to the media. Iron should not be chelated to other ligands like citrate, and additional Fe chelators should not be added. Adding additional ligands makes it difficult to accurately estimate the Fe concentration in your media.
• 3. Set the light intensity of the fluorescent lighting in your incubator and hours of light supplied per day. This calculator should not be used for natural sunlight because UV radiation significantly changes the photochemistry of the system.
• ### User Input

 Cell diameter, (µm) [EDTA], (M) Total [Fe], (M) Light intensity, (µE m-2 s-1) Hours of light per day

### Results

 The initial Fe' concentration is: mol L-L The maximum cell density supported before buffer failure is: Cells mL-1 The maximum biomass supported by the media is: µg L-1 If buffer failure occurs it is shown in gray on the plot.
 Fe' (pM) Fe' (pM) Cell carbon (µmol per L) Cells per mL

The online calculator is based on work by Sunda et al (2005). The $$\mathrm{Fe}^{\prime}$$ concentration in culture media is determined by the relative rates of $$\mathrm{Fe}^{\prime}$$ being supplied from dissociation of the FeEDTA complex and Fe being lost from cellular uptake and association with EDTA.

In this calculator, we model the cellular uptake of phytoplankton using a size-dependent uptake rate from Sunda (1997), which is based on Michaelis-Menten type kinetics. We compared their uptake rates from two linear approximations used in Sunda and Huntsman (1995) and Sunda et al. (2005) with the Michaelis-Menten approximation used here. The Michaelis-Menten approximation fit best over the full range of $$\mathrm{Fe}^{\prime}$$ values used in this calculator. The uptake rate is represented as:

\begin{align} \rho &= \rho_{max}\frac{\mathrm{Fe}^{\prime}}{\mathrm{Fe}^{\prime} + K_{\rho}}\\ \rho_{max} &=4 \pi r^2 V_{max} \\ \end{align}

Where $$V_{max} = 1276\,\mathrm{nmol\,m^{-2}\,d^{-1}}$$ and $$K_{\rho}= 0.51\, \mathrm{nmol \, L^{-1}}$$ (Sunda and Huntsman, 1997).

Fe is controlled by the balance between FeEDTA dissociation, association and cellular uptake. This is represented by the equation:

$\mathrm{\frac{d[Fe^\prime]}{dt}} = -N\,\rho_{max} \frac{\mathrm{Fe}^{\prime}}{\mathrm{Fe}^{\prime} + K_{\rho}} - k_{f} \mathrm{[ Fe^\prime ][ EDTA ]} +k^{\prime}_{d} \mathrm{[FeEDTA]}$

By setting $$\mathrm{\frac{d[Fe^\prime]}{dt}}$$ equal to zero and solving for $$\mathrm{Fe^{\prime}}$$ or $$N$$ we arrive at the equations relating $$\mathrm{[Fe^{\prime}]}$$ and cell concentration.

\begin{align} \mathrm{[Fe^{\prime}]} &= \frac{-\left( K_{rho} \mathrm{[EDTA]} k_{f} - \mathrm{[FeEDTA]} k^{\prime}_{d} + N \rho_{max} - \sqrt{K_{rho}^2 \mathrm{[EDTA]}^2 k_{f}^2 + 2 K_{rho} \mathrm{[EDTA]} \mathrm{[FeEDTA]} k^{\prime}_{d} k_{f} +\mathrm{[FeEDTA]}^2 k^{\prime2}_{d} + N^2 \rho_{max}^2 + 2 (K_{rho} \mathrm{[EDTA]} k_{f} - \mathrm{[FeEDTA]} k^{\prime}_{d}) N \rho_{max} } \right)} {2\mathrm{[EDTA]} k_{f}}\\ N &= \frac{-(\mathrm{[EDTA]} \mathrm{[Fe}^{\prime}]kf - \mathrm{[Fe}^{\prime}]\mathrm{[FeEDTA]}k_d^{\prime} + ( \mathrm{[EDTA]} \mathrm{[Fe}^{\prime}] -\mathrm{[FeEDTA]}k_d^{\prime})K_{\rho})}{\mathrm{[Fe}^{\prime}]\rho_{max}} \end{align}

for additional details of the methods see the publication describing this calculator:
Rivers, A.R., Rose, A.L., Webb E.A. (2013) An online calculator for marine phytoplankton iron culturing experiments. Journal of Phycology. 49(5) 1017-1021.

The blown buffer calculator requires a cell diameter to estimate the number of cells your media can support. To help accurately estimate the size of your phytoplankton we have provided size data for 2144 phytoplankton strains in a searchable table. These data provide an estimate of size, but you should consult primary literature for the most accurate values.

Size data are provided courtesy of the Provasoli-Guillard National Center for Marine Algae and Microbiota (NCMA).

NCMA Strain Number Class Genus Species Minimum length µm Maximum length µm Minimum width µm Maximum width µm Link to AlgaeBase Link to NCMA

The R source code for the models and figures in the paper and all code for the web application is in our github repsitory https://github.com/arivers/fidoplankter.

Liu, X., Millero, F.J. (2002). The solubility of iron in seawater. Marine Chemistry 77(1): 43-54.

Sunda, W.G.,Huntsman, S.A. (1995). Iron uptake and growth limitation in oceanic and coastal phytoplankton. Marine Chemistry 50(1-4): 189-206.

Sunda, W.G., Huntsman, S.A. (1997). Interrelated influence of iron, light and cell size on marine phytoplankton growth. Nature 390(6658): 389-392.

Sunda, W.G., Price, N.M., Morel, F.M.M. (2005). Trace metal ion buffers and their use in culture studies. In: Anderson R (ed). Algal Culturing Techniques. Elsevier Academic Press: Burlington, MA. pp 35-69.