Figures and data in Systems analysis of the CO2 concentrating mechanism in cyanobacteria

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Tables
Additional files

6 figures, 4 tables and 1 additional file

Figures

Figure 1

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Schematic of the CCM in cyanobacteria.

Outer and cell membranes (in black), as well as, thylakoid membranes where the light reactions take place (in green) are treated together. Carboxysomes are shown as four hexagons evenly spaced along the centerline of the cell. The model treats a spherically symmetric cell, with one carboxysome at the center. Active ${HCO}_{3}^{-}$ transport into the cell is indicated (in light blue), as well as active conversion from CO₂ to ${HCO}_{3}^{-}$ , sometimes called ‘facilitated uptake’ or ‘scavenging’, at membranes (in orange). Both CO₂ and ${HCO}_{3}^{-}$ can leak in and out of the cell, with CO₂ leaking out much more readily. Both species passively diffuse across the carboxysome shell. Carbonic anhydrase (red) and RuBisCO (blue) are contained in the carboxysomes and facilitate reactions as shown.

https://doi.org/10.7554/eLife.02043.003

Figure 2 with 2 supplements

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Phase space for ${HCO}_{3}^{-}$ transport, j_c, and carboxysome permeability k_c.

Plotted are the parameter values at which the CO₂ concentration reaches some critical value. The left most line (dark blue) indicates for what values of j_c and k_c the CO₂ concentration in the carboxysome would half-saturate RuBisCO (K_m). The middle line (light blue) indicates the parameter values which would result in a CO₂ concentration where 99% of all RuBisCO reactions are carboxylation reactions and only 1% are oxygenation reactions when O₂ concentration is 260 μM. The right most (red) line indicates the parameter values which result in carbonic anyhdrase saturating. Here α = 0, so there is no CO₂ scavenging or facilitated uptake. The dotted line (grey) shows the k_c and j_c values, where the ${HCO}_{3}^{-}$ concentration in the cytosol is 30 mM. The ${HCO}_{3}^{-}$ concentration in the cytosol does not vary appreciably with k_c in this parameter regime, and reaches 30 mM at $j_{c} \approx 0.6 \frac{c m}{s}$ . All other parameters, such as reaction rates are held fixed and the value can be found in the Table 1 and Table 2.

https://doi.org/10.7554/eLife.02043.007

Figure 2—figure supplement 1

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Phase space for ${HCO}_{3}^{-}$ transport and carboxysome permeability.

Solid lines show lines of constant CO₂ concentration in the carboxysome for $D_{c} = 1 e - 5 \frac{c m^{2}}{s}$ , or the diffusion constant of small molecule in water. Dashed lines show the same lines of constant CO₂ concentration, bur for $D_{c} = 1 e - 7 \frac{c m^{2}}{s}$ , or the diffusion constant of a small molecule in a 60% sucrose solution.

https://doi.org/10.7554/eLife.02043.008

Figure 2—figure supplement 2

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Phase space for ${HCO}_{3}^{-}$ transport, j_c, and carboxysome permeability, k_c.

Plotted are the parameter values at which CO₂ concentration reaches some critical value. The left most line (dark blue) indicates for what values of j_c and k_c the CO₂ concentration in the carboxysome would saturate RuBisCO. The middle line (light blue) indicates the parameter values which would result in a CO₂ concentration where 99% of all RuBisCO reactions are carboxylation reactions and only 1% are oxygenation reactions when O₂ concentration is 260 µM. The right most (red) line indicates the parameter values which result in carbonic anyhdrase saturating. Here $α = 0 \frac{c m}{s}$ (solid lines) and $α = 0 \frac{c m}{s}$ (dashed line), showing the effect of CO₂ scavenging or facilitated uptake on the phase space. All other parameters, such as reaction rates are held fixed and the value can be found Table 1.

https://doi.org/10.7554/eLife.02043.009

Figure 3 with 1 supplement

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Numerical solution (diamonds and circles) and analytic solutions (carbonic anhydrase unsaturated, solid lines, and saturated, dashed lines) correspond well.

${HCO}_{3}^{-}$ transport is varied, and all other system parameters are held constant. The CO₂ concentration above which RuBisCO is saturated is K_m (grey dashed line). The CO₂ concentration where the oxygen reaction error rate will be 1% is C_99% (grey dash-dotted line). The transition between carbonic anyhdrase being unsatruated and saturated happens where the two analytic solutions meet (where the dashed and solid red lines meet). Below a critical value of transport, $j_{c} \approx 10^{- 3} \frac{c m}{s}$ the level of transport is lower than the ${HCO}_{3}^{-}$ leaking through the cell membrane. A value of $k_{c} = 10^{- 3} cm / s$ for the carboxysome permeability was used for these calculations.

https://doi.org/10.7554/eLife.02043.010

Figure 3—figure supplement 1

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No effect of localizing carbonic anhydrase to the shell of the carboxysome.

We assume the same amount of carbonic anhydrase and RuBisCO activity for each simulation and compare the case with the enzymes evenly distributed throughout the carboxysome to the case where the carbonic anhydrase is localized to the inner carboxysome shell. The (-.-) lines are for no organization and (x) for localization with $D_{c} = 10^{- 5} \frac{c m^{2}}{s}$ . The (…) lines are for no organization and (o) are for localization with $D_{c} = 10^{- 7} \frac{c m^{2}}{s}$ .

https://doi.org/10.7554/eLife.02043.011

Figure 4

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Concentration of CO₂ in the carboxysome with varying carboxysome permeability (A).

Numerical solution (diamonds and circles) and analytic solutions (carbonic anhydrase unsaturated, solid lines, and saturated, dashed lines) correspond well. On all plots CO₂ (red circle) < ${HCO}_{3}^{-}$ (blue diamond). Concentration in the cell along the radius, r, with carboxysome permeability $k_{c} = 10^{- 5} \frac{c m}{s}$ (B), $k_{c} = 10^{- 3} \frac{c m}{s}$ (C), $k_{c} = 1 \frac{c m}{s}$ (D). Grey dotted lines in (B), (C), (D) indicate location of the carboxysome shell boundary. The transition from low CO₂ at high permeability (D) to maximum CO₂ concentration at optimal permeability (C) occurs at $k_{c}^{*} = \frac{D}{R_{c}} = 2 \frac{c m}{s}$ . At low carboxysome permeability (B) ${HCO}_{3}^{-}$ diffusion into the carboxysome is slower than consumption. For all subplots $α = 0 \frac{c m}{s}$ and $j_{c} = 0.6 \frac{c m}{s}$ . Qualitative results remain the same with varying j_c, increasing α will increase the gradient of CO₂ across the cell as CO₂ is converted to ${HCO}_{3}^{-}$ at the cell membrane.

https://doi.org/10.7554/eLife.02043.012

Figure 5

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Size of the ${HCO}_{3}^{-}$ flux in one cell from varying sources, as the proportion of ${CO}_{2}$ to ${HCO}_{3}^{-}$ outside the cell changes changes.

We show results for three carboxysome permeabilities, $k_{c}$ , and only the scavenging is effected. Total external inorganic carbon is $15 μ M$ , $j_{c} = 1 \frac{c m}{s}$ and $\frac{α}{K_{α}} = 1 \frac{c m}{s}$ . Scavenging is negligibly small for all values of $k_{c}$ shown. Unless there is very little ${HCO}_{3}^{-}$ in the environment, ${HCO}_{3}^{-}$ transport seems to be more efficient than ${CO}_{2}$ facilitated uptake.

https://doi.org/10.7554/eLife.02043.015

Figure 6

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Concentration of CO₂ achieved through various cellular organizations of enzymes, where we have selected the ${HCO}_{3}^{-}$ transport level such that the ${HCO}_{3}^{-}$ concentration in the cytosol is 30 mM.

O₂ concentration is 260 μM. The oxygenation error rates, as a percent of total RuBisCO reactions are indicated on the concentration bars. The cellular organizations investigated are RuBisCO and carbonic anhydrase distributed throughout the entire cytosol, co-localizing RuBisCO and carbonic anhydrase on a scaffold at the center of the cell without a carboxysome shell, RuBisCO and carbonic anhydrase encapsulated in a carboxysome with high permeability at the center of the cell, and RuBisCO and carbonic anhydrase encapsulated in a carboxysome with optimal permeability at the center of the cell.

https://doi.org/10.7554/eLife.02043.004

Tables

Table 1

Parameter values chosen for main set of simulations, unless otherwise indicated

https://doi.org/10.7554/eLife.02043.005

Parameter	Definition	Value	Reference
H_out	concentration of bicarbonate outside the cell	14 μM*	(Price et al., 2008)
C_out	concentration of carbon dioxide outside of cell	0.14 μM*	(Price et al., 2008)
D	diffusion constant of small molecules, CO₂ and ${HCO}_{3}^{-}$	10⁻⁵ $\frac{c m^{2}}{s}$	(Fridlyand et al., 1996)
$k_{m}^{c}$	permeability of cell membrane to CO₂	0.3 $\frac{c m}{s}$	(Missner et al., 2008; Gutknecht et al., 1977)
$k_{m}^{H}$	permeability of cell membrane to ${HCO}_{3}^{-}$	$3 \times 10^{- 4} \frac{c m}{s}$	(Missner et al., 2008; Gutknecht et al., 1977)
R_c	radius of carboxysome	5×10⁻⁶ cm	(Cheng et al., 2008; Schmid et al., 2006)
R_b	radius of bacteria	5 × 10⁻⁵ cm	(Savage et al., 2010)
j_c	${HCO}_{3}^{-}$ transport rate resulting in 30mM cytosolic ${HCO}_{3}^{-}$ pool	0.6 $\frac{c m}{s}$ *	calculated here
$k_{c}$	optimal carboxysome permeability	10⁻³ $\frac{c m}{s}$ *	calculated here
$V_{c e l l}$	cell volume	$5.2 \times 10^{- 10} μ L$	calculated
$S A_{c e l l}$	cell surface area	$3 \times 10^{- 8} c m^{2}$	calculated

*

these parameters are varied in the text, but these values are use unless noted otherwise.

Table 2

Table comparing enzymatic rates (Woodger et al., 2005; Sultemeyer et al., 1995; Heinhorst et al., 2006)

https://doi.org/10.7554/eLife.02043.006

Enzyme reaction	active sites	$k_{c a t}$ $[\frac{1}{s}]$	$V_{\max}$ in ‘cell’ $[\frac{μ M}{s}]$	$V_{\max}$ in carboxysome $[\frac{μ M}{s}]$	$K_{1 / 2}$ $[μ M]$
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

$V_{\max}$ in cell and carboxysome refer to the volumetric reaction rate assuming the enzymes are distributed throughout the entire cell or only carboxysome. V_ba (V_max for carbonic anhydrase dehydration) is estimated by assuming K_eq = 5 and using parameters found in (Heinhorst et al., 2006). V_ca is V_max for carbonic anhydrase hydration. Similarly, K_ba, and K_ca are $K_{1 / 2}$ for dehydration and hydration respectively.

Table 3

Fate of carbon brought into the cell for j_c = 0.6cm/s and k_c = 10^–3cm/s

https://doi.org/10.7554/eLife.02043.013

	formula	$[\frac{p i c o m o l e s}{(c e l l s)}]$	% of flux
${HCO}_{3}^{-}$ transport	j_cH_out	3.26 × 10⁻⁴
${HCO}_{3}^{-}$ leakage	$k_{m}^{H} (H_{o u t} - H_{c y t o s o l} (R_{b}))$	3.2 × 10⁻⁴	98.6%
CO₂ leakage	$k_{m}^{C} (C_{o u t} - C_{c y t o s o l} (R_{b}))$	4.5 × 10⁻⁴	1.4 %
carboxylation	$\frac{V_{\max} C}{C + K_{m} (1 + \frac{O}{K_{O}})}$	8.2 × 10⁻⁸	0.03 %
oxygenation	$\frac{V_{\max}^{O} C}{C + K_{m}^{O} (1 + \frac{C}{K_{C}})}$	6.7 × 10⁻¹⁰	2 × 10⁻⁴ %

Table 4

Fate of carbon brought into the cell for j_c = 0.06 cm/s and k_c = 10^–3cm/s

https://doi.org/10.7554/eLife.02043.014

	formula	$[\frac{p i c o m o l e s}{(c e l l s)}]$	% of flux
${HCO}_{3}^{-}$ transport	j_cH_out	2.8 × 10⁻⁵
${HCO}_{3}^{-}$ leakage	$k_{m}^{H} (H_{o u t} - H_{c y t o s o l} (R_{b}))$	2.7 × 10⁻⁵	96.6 %
CO₂ leakage	$k_{m}^{C} (C_{o u t} - C_{c y t o s o l} (R_{b}))$	8.8 × 10⁻⁷	3.2 %
carboxylation	$\frac{V_{\max} C}{C + K_{m} (1 + \frac{O}{K_{O}})}$	5.4 × 10⁻⁸	0.2 %
oxygenation	$\frac{V_{\max}^{O} C}{C + K_{m}^{O} (1 + \frac{C}{K_{C}})}$	2.3 × 10⁻⁹	8 × 10⁻³ %

Additional files

Supplementary file 1 Mathematical derivation appendix. Mathematical derivations of analytic solutions for a spherical cell with reactions organized in a variety of ways. We present analytic solutions for the concentration of CO₂ and HCO₃⁻ a carboxysome located at the center of the cell. We derive analytic solutions assuming a number of different cases for the enzymatic rates in the carboxysome: RuBisCO reaction rate negligible with carbonic anhydrase saturated and unsaturated, RuBisCO reaction rate non-negligible with carbonic anhydrase unsaturated. Additionally we derive analytic solutions for the enzymatic reactions throughout the cell and localized to a scaffold without a carboxysome shell.: https://doi.org/10.7554/eLife.02043.016
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Niall M Mangan
Michael P Brenner

(2014)

Systems analysis of the CO₂ concentrating mechanism in cyanobacteria

eLife 3:e02043.

https://doi.org/10.7554/eLife.02043

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Schematic of the CCM in cyanobacteria.

Phase space for HCO3− transport, jc, and carboxysome permeability kc.

Phase space for HCO3− transport and carboxysome permeability.

Phase space for HCO3− transport, jc, and carboxysome permeability, kc.

Numerical solution (diamonds and circles) and analytic solutions (carbonic anhydrase unsaturated, solid lines, and saturated, dashed lines) correspond well.

No effect of localizing carbonic anhydrase to the shell of the carboxysome.

Concentration of CO2 in the carboxysome with varying carboxysome permeability (A).

Size of the HCO3− flux in one cell from varying sources, as the proportion of CO2 to HCO3− outside the cell changes changes.

Concentration of CO2 achieved through various cellular organizations of enzymes, where we have selected the HCO3− transport level such that the HCO3− concentration in the cytosol is 30 mM.

Supplementary file 1

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Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)

Phase space for ${HCO}_{3}^{-}$ transport, j_c, and carboxysome permeability k_c.

Phase space for ${HCO}_{3}^{-}$ transport and carboxysome permeability.

Phase space for ${HCO}_{3}^{-}$ transport, j_c, and carboxysome permeability, k_c.

Concentration of CO₂ in the carboxysome with varying carboxysome permeability (A).

Size of the ${HCO}_{3}^{-}$ flux in one cell from varying sources, as the proportion of ${CO}_{2}$ to ${HCO}_{3}^{-}$ outside the cell changes changes.

Concentration of CO₂ achieved through various cellular organizations of enzymes, where we have selected the ${HCO}_{3}^{-}$ transport level such that the ${HCO}_{3}^{-}$ concentration in the cytosol is 30 mM.