Mangan NM, Brenner MP. 2014. Systems analysis of the CO2 concentrating mechanism in cyanobacteria. eLife 3:e02043. doi: 10.7554/eLife.02043
Published 29 April 2014
We would like to issue the following corrections to our research article entitled, ‘Systems analysis of the CO2 concentrating mechanism in cyanobacteria.’ The code used to generate the plots in the paper, mistakenly used 6.022 × 1022 instead of 6.022 × 1023 for Avogadro's number. This correction changes the quantitative numbers in the original paper but none of the conclusions are affected. Here are the corrected tables, figures, and text that changed. We thank Avi Flamholz for catching this error.
We recalculated the enzymatic rates for carbonic anhydrase and RuBisCO. The values for Vmax and K1/2 listed in the previous version of Table 2 used the incorrect 6.022 × 1022 value for Avogadro's number. All plots in the original paper were for those values. All new plots are for the values listed in the updated table, using Avogadro's number 6.022 × 1023. The Vmax values are all about an order of magnitude lower than previously calculated.
|Enzyme reaction||active sites||kcat||Vmax in ‘cell’||Vmax in carboxysome||K1/2|
|carbonic anhydrase hydration||80||8 × 104||8.8 × 103||1.5 × 107||3.2 × 103|
|carbonic anhydrase dehydration||80||4.6 × 104||1.5 × 104||8.8 × 106||9.3 × 103|
|RuBisCO carboxylation||2160||26||178||1.8 × 105||270|
The main effect of correcting Avagadro's number is that the peak defining optimal carboxysome permeability is lower and broader. The optimal carboxhysome permeability for a target carboxysomal CO2 concentration is found by looking at the leftmost value on a line of constant concentration on the permeability vs transport plot. This point represents the carboxysome permeability where the least amount of transport is needed to achieve a given carboxysomal CO2 concentration. For 99% carboxylation (cyan curve below) this value is now around kc = 10−3 cm/s (previously kc = 6 × 10−3 cm/s). Carbonic anhydrase also saturates at a lower transport value.
We plot Figure 3 assuming the new optimal carboxysome permeability of kc = 10−3 cm/s (previously kc = 6 × 10−3 cm/s). There is very little change from the previous Figure 3, with the updated carboxysome permeability. Had we plotted at the same kc = 6 × 10−3 cm/s, the CO2 would have been lower, because the system would not be at the optimal permeability.
The correction did not at all effect the conclusion that the organization of carbonic anhydrase within the carboxysome has no effect on the resulting concentrations. Consistent with updated Figure 2—figure supplement 1, the effect of decreasing the diffusion in carboxysome is much less prominent than in the original manuscript.
The correction does not effect the conclusion that an optimal carboxysome permeability exists, or what causes it, but it changes its absolute value. The correction has two main effects: (1) it decreases the optimal carboxysome permeability (seen as a shift in the peak) by a factor of 6, and (2) for carboxysome permeabilities higher than optimal (kc > 0.1 cm/s) the CO2 concentration is an order of magnitude lower. Therefore the optimal carboxysome permeability peak is at a lower kc value and more prominent.
We updated the flux to the value at which cytosolic is 30 mM and carboxysome permeability is optimal. Previously they were jc = 0.7 cm/s and kc = 6 × 10−3 cm/s.
The discussion of the number of transporters needed for this magnitude of influx increases by an order of magnitude from to . While the change in uptake is less than a factor of two different, the conversion from picomoles/s to molecules/s for a cell used the incorrect value of Avogadro's number. So this is now about an order of magnitude larger than the number of ATP synthase complexes on the thylakoid membrane of spinach.
The numbers for net flux of change slightly. For jc = 0.6 cm/s the net flux is compared to the previous value of and for jc = 0.06 cm/s the net flux is compared with the previous value of . So the conclusion that measured net fluxes of compares best with the lower flux still holds.
Since Avagadro's number effects the rate of carboxylation and oxygenation, the recalculated values for 2-phosphoglycolate and 3-phosphoglycerate production are lower. This exacerbates the large amount of energy that appears to go into CO2 concentration compared to the actual fixation. Now around 0.03% of concentrated inorganic carbon is fixed into 3-phosphoglycerate. Over 99.9% is lost to leakage either in the form of CO2 or (previously these values were calculated to be 99%). The higher flux assumption (Table 3) predicts that only 217 2-phosphoglycolate are produced a second, and the lower flux assumption (Table 4) predicts that 1.4 × 103 2-phosphoglycolate are produced a second. So the higher flux allows the production of many fewer 2-phosphoglycolate than previously estimated. Recalculating the time to fix the necessary carbon to replicate a cell results in 7–21 hr for the higher flux rate (Table 3) and 11–35 hr for the lower flux rate (Table 4). Both are consistant with the division times of cyanobacteria, but the higher flux rate is a better match.
In conclusion, the correction further highlights the puzzle of how much energy cyanobacteria must use to achieve a level of CO2 which creates adequate fixation rates. Either cyanobacteria use a much larger amount of energy to achieve this internal concentration than to fix each CO2, the permeability of the cell must be much lower for than assumed here, or there is another mechanism not covered in this model.
The correction decreases the effect of CO2 scavenging at high permeabilities (kc = 1 cm/s and 10−2 cm/s). It now appears to be negligible compared to uptake and CO2 uptake for all permeabilities. Only when CO2 concentration is a very small percentage of the external carbon, does the scavenging contribute more than the CO2 uptake, and both are far less than uptake.
Throughout the text the default flux has been changed from to and optimal carboxysome permeability from to .
In the discussion of fluxes and concentrations we previously had written:
‘Our simulated cell has a flux of 2 × 107 molecules/s. Assuming the rate of transport per transporter of and our cell’s surface area this requires about . This is actually not that far off from the number of ATP synthase complexes on the thylakoid membrane in spinach, (Miller and Staehelin, 1979), although it is still quite high.’
This is now: ‘Our simulated cell has a flux of 2 × 108molecules/s. Assuming the rate of transport per transporter of and our cell’s surface area this requires about . This is about an order of magnitude higher than the number of ATP synthase complexes on the thylakoid membrane in spinach, (Miller and Staehelin, 1979).’
In the discussion of fluxes and concentrations we previously had written:
‘At the higher flux rate (Table 3) this means that a cell could replicate every 1–2 hr, so faster than cyanobacteria replicate. The lower flux rate (Table 4) would produce fix enough CO2 for the cell to replicate every 8 to 21 hr, which is similar to the division times of cyanobacteria.’
This is now: ‘At the higher flux rate (Table 3) this means that a cell could replicate every 7–21 hr and the lower flux rate (Table 4) allows replication every 11 to 35 hr. Both are consistent with the division times of cyanobacteria.’
In the caption of Figure 5 we had written:
‘When the carboxysome permeability is larger than optimal, kc = 1 cm/s, scavenging can contribute more than facilitated uptake at low external CO2 concentrations. However, when the carboxysome permeability at or below our geometric bound, kc <= 0.02 cm/s, scavenging is negligibly small.’
This is now: ‘Scavenging is negligibly small for all values of kc shown.’
In the text of the Benefit of CO2 to conversion: facilitated uptake or scavenging of CO2 we had written: ‘Scavenging only contributes significantly to total incoming when the carboxysome permeability is higher than optimal, Figure 5, and does not contribute significantly below our calculated upper bound of . In these ranges for carboxysome permeability, there is very little CO2 leaking out of the carboxysome into the cytosol, so there is very little CO2 to scavenge, Figure 5.’
This is now: ‘Scavenging is negligibly small for all values of kc shown. There is very little CO2 in the cytosol, so there is very little CO2 to scavenge, Figure 5.’
There were also a few typos we have now corrected:
In the Reaction diffusion model section we had: ‘RuBisCO also requires ribulose-1,5-bisphosphate, the substrate which CO2 reacts with to produce 3-phosphoglycolate.’ This has been corrected to ‘… CO2 reacts with to produce 3-phosphoglycerate.’
in Table 1: ‘ permeability of cell membrane to CO2’ has been corrected to: ‘ permeability of cell membrane to ’.
Table 2 header said kcut which has been corrected to kcat.
In the Varying transport saturates enzyme section we had:
The chemical equilibrium is , for pH around 7 (DeVoe and Kistiakowsky, 1961), so that > CO2 in the carboxysome.
The equation is now: .
In Figure 3—figure supplement 1 the units for Dc on both the plot and caption are cm/s, they should be cm2/s.