Photorespiration
Photorespiration is a side pathway of photosynthesis that occurs when the enzyme Rubisco binds
O2 instead of CO2. This “oxygenation” reaction reduces the efficiency of
carbon fixation because it ultimately leads to CO2 release and extra energy costs.
It is most important in C3 plants, especially under high temperature, low CO2,
or water-stress conditions that limit internal CO2.
Rubisco has two competing reactions
Rubisco can act as:
- Carboxylase: adds CO2 to RuBP (productive for sugar formation).
- Oxygenase: adds O2 to RuBP (starts photorespiration).
A simple way to build intuition is to compare how “available” O2 is relative to CO2 at the leaf:
higher O2 relative to CO2 tends to increase oxygenation.
Why this calculator uses partial pressures
Gas availability can be expressed as partial pressure. If the total atmospheric pressure is
Patm, then:
CO2 from ppm to partial pressure
\[
\begin{aligned}
x_{\mathrm{CO_2}} &= \frac{\mathrm{CO_2\ (ppm)}}{10^{6}} \\
p_{\mathrm{CO_2}} &= x_{\mathrm{CO_2}} \cdot P_{\mathrm{atm}}
\end{aligned}
\]
O2 from percent to partial pressure
\[
\begin{aligned}
x_{\mathrm{O_2}} &= \frac{\mathrm{O_2\ (\%)}}{100} \\
p_{\mathrm{O_2}} &= x_{\mathrm{O_2}} \cdot P_{\mathrm{atm}}
\end{aligned}
\]
The calculator also allows entering pCO2 and pO2 directly (in kPa).
A simplified “oxygenation vs carboxylation” ratio
A basic tendency measure is the ratio of O2 to CO2:
\[
\begin{aligned}
\text{ratio} = \frac{p_{\mathrm{O_2}}}{p_{\mathrm{CO_2}}}
\end{aligned}
\]
Larger values mean O2 is high relative to CO2, which generally increases the probability that
Rubisco performs oxygenation.
Baseline comparison and temperature factor
To make results easy to interpret, the calculator compares the ratio to a baseline reference condition
(approximately 420 ppm CO2, ambient 20.95% O2, and 25 °C).
Then it applies a temperature factor.
Relative index (dimensionless)
\[
\begin{aligned}
I &= \left(\frac{\text{ratio}}{\text{ratio}_{\text{base}}}\right)\cdot f_T \cdot f_{\text{plant}}
\end{aligned}
\]
Here:
-
fT is a simplified temperature factor using a Q10-style relationship
(a common biological approximation for temperature sensitivity).
-
fplant reduces the tendency for C4 and CAM plants because these
pathways concentrate CO2 near Rubisco (so oxygenation is usually less important than in C3).
Temperature factor used in the calculator
\[
\begin{aligned}
f_T = 2^{\frac{T-25}{10}}
\end{aligned}
\]
This is not a universal law. It is an educational approximation to show the trend that higher temperatures often
increase photorespiration risk in C3 leaves.
From index to “carboxylation vs oxygenation” shares
To produce an intuitive bar chart, the calculator converts the index to normalized shares (they sum to 1):
\[
\begin{aligned}
s_{\mathrm{oxy}} &= \frac{I}{1+I} \\
s_{\mathrm{carb}} &= 1 - s_{\mathrm{oxy}}
\end{aligned}
\]
These shares are not literal enzyme reaction probabilities. They are a visualization tool: higher I shifts the
balance toward oxygenation.
Estimating a net photosynthesis “penalty”
Photorespiration reduces net carbon gain, but the exact quantitative loss depends on internal CO2,
light intensity, stomatal conductance, and many biochemical constraints.
For a simple estimator, the calculator maps the index to a bounded percentage:
Penalty mapping (0–100%)
\[
\begin{aligned}
\text{penalty (\%)} = 100\cdot\frac{I}{I+K}
\end{aligned}
\]
The constant K is chosen to keep the penalty moderate near baseline and to increase smoothly as I grows.
This makes the meter easy to interpret as “low / medium / high” zones.
Optional net photosynthesis adjustment
If a baseline gross photosynthesis rate is provided (any consistent unit), the calculator estimates an adjusted net:
\[
\begin{aligned}
\text{net (adjusted)} = \text{gross}\cdot\left(1-\frac{\text{penalty}}{100}\right)
\end{aligned}
\]
The “adjusted net” output is a simple educational transformation, not a validated physiological model.
How to read the heatmap
The CO2–temperature heatmap shows where the penalty is expected to be larger under the selected
O2 level and plant type:
- Low CO2 + high temperature → higher estimated penalty (especially in C3).
- High CO2 → lower estimated penalty across temperatures.
- C4/CAM → reduced penalty pattern compared with C3.
Limitations (important)
-
This tool uses external CO2/O2 and a simplified temperature factor; it does not model
internal leaf CO2, stomatal closure, humidity, or light intensity.
-
The penalty is a heuristic mapping intended for intuition and classroom exploration.
-
Real photorespiration rates vary by species, acclimation, and environmental history.
