Quantitative analysis of the effects of morphological changes on extracellular electron transfer rates in cyanobacteria

Background Understanding the extracellular electron transport pathways in cyanobacteria is a major factor towards developing biophotovoltaics. Stressing cyanobacteria cells environmentally and then probing changes in physiology or metabolism following a significant change in electron transfer rates is a common approach for investigating the electron path from cell to electrode. However, such studies have not explored how the cells’ concurrent morphological adaptations to the applied stresses affect electron transfer rates. In this paper, we establish a ratio to quantify this effect in mediated systems and apply it to Synechococcus elongatus sp. PCC7942 cells grown under different nutritional regimes. Results The results provide evidence that wider and longer cells with larger surface areas have faster mediated electron transfer rates. For rod-shaped cells, increase in cell area as a result of cell elongation more than compensates for the associated decline in mass transfer coefficients, resulting in faster electron transfer. In addition, the results demonstrate that the extent to which morphological adaptations account for the changes in electron transfer rates changes over the bacterial growth cycle, such that investigations probing physiological and metabolic changes are meaningful only at certain time periods. Conclusion A simple ratio for quantitatively evaluating the effects of cell morphology adaptations on electron transfer rates has been defined. Furthermore, the study points to engineering cell shape, either via environmental conditioning or genetic engineering, as a potential strategy for improving the performance of biophotovoltaic devices.

. Due to the change in light regime from 24h continuous light to a 12:12 light-dark cycle on day 3, the Gompertz model was fit twice. Since the Gompertz model requires at least 4 points to fit, it was fit first from day 3 to the end of the experiment to obtain µ max,2 and A. The fitted value of A was then fixed and the Gompertz model fit a second time from day 0 to day 3 to obtain and µ max,1 . Each parameter is quoted with ±95% confidence interval. (b) For the continuously diluted cultures that were maintained in exponential growth, average growth rate (µ) was estimated from the gradients of the solid lines. Y-axis error bars for ln(N/N 0 ) data points show ±1 Standard Error of the Mean (SEM). Where no error bars are visible, they are smaller than the markers. The size of the incubator restricted the volume of flasks that could be used for culturing the cells in 3 replicates for each growth regime. In turn, this limited the volume of culture, since the depth of the culture had be shallow enough to allow sufficient light penetration. Due to the significant withdrawal of culture volume for measurements, a trade-off was made between frequency of readings, and length of the experiment. In order to have the experiment run for at least 20 days, it was decided to conduct ferricyanide assays every 4 days, and to measure the other metrics (cell concentration, pH and chlorophyll a) every 48 hours. In addition, significant withdrawal of the culture volume would have altered the natural growth curve, particularly for the control cultures, as it changes the light penetration appreciably.  Cell size histograms  To assess significance of the pairwise difference in rates, a one-tailed Student's t-test at 5% significance level was conducted, with alternative hypothesis that reduction rates are higher for the continuously diluted cultures. Significant p-values are asterisked (above bars).
Chlorophyll a profile

Simplified model for iron concentration profiles
The bioavailable iron in BG11 is from ammonium ferric citrate [2]. The evolution of the bioavailable iron concentration in the media can be estimated using a mass balance equation and a model for the growth kinetics of the culture. The rate of change of iron in the BG11 media is equivalent to the negative rate of consumption of iron by the cells, eq. S.1, where [F e] bio is the concentration of bioavailable iron in the BG11 media in mol dm 3 , r is the iron uptake rate by cyanobacteria in mol dm 3 day 1 , and t is time in days. The rate of of consumption of dissolved inorganic iron or iron-siderephore complexes by cyanobacteria can be calculated from the uptake rate constant, k in (eq. S.2) as defined in [3].
where k in has the units of dm 3 cell 1 day 1 . The uptake rate constant is linearly correlated to the area of the cyanobacteria [3]. The cyanobacteria Synechococcus elongatus sp. PCC7942, is a siderophore producer. In order to simplify calculations, it is assumed that the cells uptake iron primarily through siderophore secretion, and negligible amounts through a reductive mechanism. The value of k in in units of dm 3 cell 1 hr 1 for iron-siderophore complexes can then be calculated using eq. S.3, which is a linear fit of empirical data [3]: where A is the surface area of the cyanobacterium in µm 2 . Thus, by combining eq. S.1, S.2 and S.3, the rate of change of iron in the BG11 media per day can be written as: where N is the cell number in cells dm 3 . In the continuously diluted cultures, it was shown in Fig. 3 in the main text that A remains constant during the exponential phase of growth. In order to simplify calculations for the control culture, it is assumed that the value of A also remains constant at its average value over the duration of the experiment.
The growth kinetics for the continuously diluted cultures are modelled using the standard exponential growth equation, eq. S.5. It was assumed that the equation also applies in the lag phase since there are no equations describing the rate of change of cells during this period. This simplification over estimates the cell number during the first 24 hours of growth, and as a consequence, the value of d[F e] bio /dt. However, because there is evidence that the majority of iron uptake occurs in the lag phase, it is reasonable to have a higher uptake rate during this time [4,5]: where µ is the average growth rate over the 21 day experiment as shown in Fig. S Thus, the rate of change of y = ln(N/N 0 ) is given by eq. S.7: where µ max , and A are as previously defined and fitted in Fig. S.1a. Equations S.4 and S.5 or S.7 for the continuously diluted or control cultures respectively were solved simultaneously using MATLAB's ode23s solver.
For the control culture, the initial cell number, N 0 , was the cell number at inoculation, (⇡ 3.39·10 4 cells dm 3 ), and the initial concentration of bioavailable iron in the media, [F e] bio,0 , was the concentration of iron in fresh BG11 media (⇡1.3 mg dm 3 or 2.29·10 5 mol dm 3 ).

Initial conditions for the continuously diluted cultures
Since the continuously diluted cultures were diluted every 48 hours to OD 750 = 2, starting two days after entering the exponential phase of growth (day 3), equations S.4 and S.5 above were solved for the first 72 hours, and then for every 48 hour period that follows a dilution. For the first 72 hours, [F e] bio,0 was the concentration of iron in fresh BG11 media. At the start of dilutions, [F e] t bio,0 was corrected using a mass balance (Accumulation = Initial Output + Input) to take into account the dilution step. During dilution, half of the culture (by volume) was removed and replaced with an equal volume of fresh BG11 media. Therefore, the amount of iron in the media immediately after a dilution event is given by the following mass balance: where V is the culture volume in dm 3 , [F e] t 1 bio,0 is the bioavailable iron concentration at the end of the previous 48 hour period and [F e] BG11 is the bioavailable iron concentration in fresh BG11 media. Equation S.8 can be simplified to eq. S.9 by dividing both sides by V : [ The initial cell number, N 0 , was the cell number at inoculation of the culture for the first 72 hour period, (⇡ 3.39·10 4 cells dm 3 ). For the subsequent 48 hour periods, N 0 was the cell number immediately after dilution to OD 750 = 0.2 (⇡ 6.78·10 4 cells dm 3 ).

Estimated iron concentration profiles
Figure S.10 shows the calculated iron concentration profiles. In the continuously diluted cultures, the iron concentration immediately after a dilution reaches its terminal value by day 13 and does not change further for the remainder of the experiment. The iron concentration remains constricted within a narrow window, declining from ⇡ 1.71·10 5 mol dm 3 immediately after dilution to ⇡ 1.21·10 5 after 48 hours. Interestingly, the maximum ferricyanide reduction rate was also reached on day 13, suggesting a link between iron assimilation and extracellular electron transfer[6].
The iron concentration in the control cultures decreases and reaches zero by day 13. At the beginning of the decline phase (day 11), the iron concentration relative to the iron concentration in fresh BG11 media is 0.02. This value is the same as that measured by Watanabe et. al after culturing Synechococcus elongatus sp. PCC7942 for 7 days, at which time the culture was in stationary phase [5]. In their study, the culture was grown in continuous light, under 2% CO 2 , and a light intensity of 40 µmol m 2 s 1 , resulting in µ max of 1.2 day 1 (estimated from the growth curve reported) or 2.5 times faster than in this work.
Comparison to particle sizer measurements Figure S.11: Mean cell volume of Synechococcus sp. PCC7942 cells in the control culture on days 5 and 9 obtained using a coulter counter (blue bars) and evaluated using the rod-shaped model (red bars). Combined error in the volume value evaluated using the rod-shaped model ( V ) was calculated using error propagation: ( V /V ) 2 = 2 · ( D/D) 2 + ( L/L) 2 + 3 · ( D/D) 2 . Volumes on both days agreed within experimental uncertainty, justifying the use of the model to calculate stereological properties of the cells from projected cell dimensions obtained using confocal microscopy. Figure S.12: Culture pH profiles. Evolution of culture pH was also measured as an indicator of the changing external environment of the cells. Cyanobacteria are alkaliphilic and increase the pH of their environment by assimilating carbonate ions and compounds during photosynthesis [7,8].The pH of both cultures increased from 7.4 to approximately 9.3 over a period of 11 days. After this, control cultures experienced a slight increase in pH to approximately 9.7, which may be due to increased number of cells consuming more carbonate ions and compounds. Error bars show ±1 SEM. Where error bars are not visible, they are smaller than the marker size.