Estimate the relative limiting factors to C3 photosynthesis — calculate_c3_limitations

Uses the method from Grassi & Magnani (2005) to estimate the relative limitations to C3 photosynthesis due to stomatal conductance, mesophyll conductance, and biochemistry. This function can accomodate alternative column names for the variables taken from the data file in case they change at some point in the future. This function also checks the units of each required column and will produce an error if any units are incorrect.

Usage

calculate_c3_limitations_grassi(
    exdf_obj,
    atp_use = 4.0,
    nadph_use = 8.0,
    cc_column_name = 'Cc',
    gamma_star_column_name = 'Gamma_star',
    gmc_column_name = 'gmc',
    gsc_column_name = 'gsc',
    kc_column_name = 'Kc',
    ko_column_name = 'Ko',
    oxygen_column_name = 'oxygen',
    total_pressure_column_name = 'total_pressure',
    vcmax_column_name = 'Vcmax_tl',
    j_column_name = NULL
  )

Arguments

exdf_obj: An exdf object representing gas exchange data.
atp_use: The number of ATP molecules used per C3 cycle.
nadph_use: The number of NADPH molecules used per C3 cycle.
cc_column_name: The name of the column in exdf_obj that contains the chloroplastic CO2 concentration in micromol mol^(-1). Typically these are calculated using apply_gm.
gamma_star_column_name: The name of the column in exdf_obj that contains the Gamma_star values in micromol mol^(-1). Typically these are the leaf-temperature dependent values calculated using calculate_arrhenius.
gmc_column_name: The name of the column in exdf_obj that contains the mesophyll conductance to CO2 in mol m^(-2) s^(-1) bar^(-1).
gsc_column_name: The name of the column in exdf_obj that contains the stomatal conductance to CO2 in mol m^(-2) s^(-1). Typically this column is calculated using calculate_gas_properties.
kc_column_name: The name of the column in exdf_obj that contains the Michaelis-Menten constant for rubisco carboxylation in micromol mol^(-1). Typically these are the leaf-temperature dependent values calculated using calculate_arrhenius.
ko_column_name: The name of the column in exdf_obj that contains the Michaelis-Menten constant for rubisco oxygenation in mmol mol^(-1). Typically these are the leaf-temperature dependent values calculated using calculate_arrhenius.
oxygen_column_name: The name of the column in exdf_obj that contains the concentration of O2 in the ambient air, expressed as a percentage (commonly 21% or 2%); the units must be percent.
total_pressure_column_name: The name of the column in exdf_obj that contains the total pressure in bar. Typically this is calculated using calculate_total_pressure.
vcmax_column_name: The name of the column in exdf_obj that contains values of the maximum Rubisco carboxylation rate (Vcmax) in micromol m^(-2) s^(-1). Typically these are the leaf-temperature adjusted values that are automatically calculated by fit_c3_aci.
j_column_name: The name of the column in exdf_obj that contains values of the RuBP regeneration rate (J) in micromol m^(-2) s^(-1). Typically these are the leaf-temperature adjusted values that are automatically calculated by fit_c3_aci.

Details

When analyzing or interpreting C3 gas exchange data, it is often useful to estimate the relative limitations to assimilation that are due to stomatal conductance, mesophyll conductance, and biochemistry. This can be done using a framework first introduced by Grassi & Magnani (2005). In this framework, the relative limitation due to stomatal conductance (ls) is

ls = [(g_t / g_sc) * (dAdC)] / [g_t + dAdC],

the relative limitation due to mesophyll conductance (lm) is

lm = [(g_t / g_mc) * (dAdC)] / [g_t + dAdC],

and the relative limitation due to biochemistry (lb) is

ln = [g_t] / [g_t + dAdC],

where g_sc is the stomatal conductance to CO2, g_mc is the mesophyll conductance to CO2, gt = 1 / (1 / g_mc + 1 / g_sc) is the total conductance to CO2, and dAdC is the partial derivative of the net CO2 assimilation rate (An) with respect to the chloroplast CO2 concentration (Cc). These can be found in Equation 7 from Grassi & Magnani (2005).

These equations were derived by assuming that CO2 assimilation is limited by Rubisco activity; in other words, that the net CO2 assimilation rate is given by

Ac = Vcmax * (Cc - Gamma_star) / (Cc + Km) - Rd,

where Vcmax is the maximum Rubisco carboxylation rate, Gamma_star is the CO2 compensation point in the absence of day respiration, Rd is the day respiration rate, Km is the effective Michaelis-Menten constant for Rubisco carboxylation. In turn, Km is given by Km = Kc * (1 + O / Ko), where Kc is the Michaelis-Menten constant for carboxylation, Ko is the Michaelis-Menten constant for oxygenation, and O is the oxygen concentration in the chloroplast.

Under this assumption, it is possible to analytically determine the partial derivative dAdC:

dAdC_rubisco = Vcmax * (Gamma_star + Km) / (Cc + Km)^2

In this case, the limitation due to "biochemistry" actually refers to limitation due to the value of Vcmax. Note that sometimes this derivative is estimated from the initial slope of a measured A-Ci curve rather than calculated analytically. (See, for example, Pathare et al. (2023).) However, we do not take that approach here. Also note that the value of Vcmax can be estimated using different approaches. For example, Xiong (2023) uses single-point gas exchange measurements. When possible, it would be better to use an estimate from fitting an entire A-Ci curve, as shown in the example below.

To understand the meaning of these limiting factors, note that simultaneously making small fractional increases to g_sc, g_mc, and Vcmax will generally cause an associated small fractional increase in An. The limiting factors describe the fraction of the increase in An that can be attributed to each of g_sc, g_mc, and Vcmax. For example, ls = 0.2, lm = 0.3, lb = 0.5 would mean that 20 percent of the increase in An would be due to an increase in stomatal conductance, 30 percent due to an increase in mesophyll conductance, and 50 percent due to an increase in Vcmax. Note that ls, lm, and lb always add up to 1.

Thus, when one of the factors is large, changes in the related parameter produce relatively larger changes in the assimilation rate. In that case, it can be said that that parameter is setting a large limit on the assimilation rate. On the other hand, if a factor is small, small changes in the related parameter produce relatively small changes in An, and therefore that parameter is not setting a large limit on the assimilation rate.

It is also possible to calculate dAdC when assimilation is limited by RuBP regeneration. In this case, we have

Aj = J * (Cc - Gamma_star) / (4 * Cc + 8 * Gamma_star) - Rd,

where J is the RuBP regeneration rate, and the limitation due to "biochemistry" actually refers to limitation due to the value of J (rather than Vcmax. The same equations as before can be used to calculate the limiting factors (ls, lm, lb), but the partial derivative is now given by

dAdC_j = J * Gamma_star * 12 / (4 * Cc + 8 * Gamma_star)^2.

Most users will want the limitations assuming Rubisco-limited assimilation. However, if j_column_name is not NULL, values of J will be used to calculate the limiting factors assuming RuBP-regeneration-limited assimilation. For an example of how these additional factors can be used, see Sakoda et al. (2021).

References:

Grassi, G. & Magnani, F. "Stomatal, mesophyll conductance and biochemical limitations to photosynthesis as affected by drought and leaf ontogeny in ash and oak trees." Plant, Cell & Environment 28, 834–849 (2005) [doi:10.1111/j.1365-3040.2005.01333.x ].

Pathare, V. S. et al. "Altered cell wall hydroxycinnamate composition impacts leaf- and canopy-level CO2 uptake and water use in rice." Plant Physiology kiad428 (2023) [doi:10.1093/plphys/kiad428 ].

Xiong, D. "Leaf anatomy does not explain the large variability of mesophyll conductance across C3 crop species." The Plant Journal 113, 1035–1048 (2023) [doi:10.1111/tpj.16098 ].

Sakoda, K., Yamori, W., Groszmann, M. & Evans, J. R. "Stomatal, mesophyll conductance, and biochemical limitations to photosynthesis during induction." Plant Physiology 185, 146–160 (2021) [doi:10.1093/plphys/kiaa011 ].

Value

This function returns an exdf object based on exdf_obj but with several new columns representing the partial derivatives and limiting factors discussed above: dAdC_rubisco, ls_rubisco_grassi, lm_rubisco_grassi, and lb_rubisco_grassi. If j_column_name is not NULL, the output will also include dAdC_j, ls_j_grassi, lm_j_grassi, and lb_j_grassi.

Examples

# Read an example Licor file included in the PhotoGEA package
licor_file <- read_gasex_file(
  PhotoGEA_example_file_path('c3_aci_1.xlsx')
)

# Define a new column that uniquely identifies each curve
licor_file[, 'species_plot'] <-
  paste(licor_file[, 'species'], '-', licor_file[, 'plot'] )

# Organize the data
licor_file <- organize_response_curve_data(
    licor_file,
    'species_plot',
    c(9, 10, 16),
    'CO2_r_sp'
)

# Specify mesophyll conductance
licor_file <- set_variable(
  licor_file,
  'gmc', 'mol m^(-2) s^(-1) bar^(-1)', value = 0.5
)

# Calculate the total pressure in the Licor chamber
licor_file <- calculate_total_pressure(licor_file)

# Calculate additional gas properties
licor_file <- calculate_gas_properties(licor_file)

# Calculate Cc
licor_file <- apply_gm(licor_file)

# Calculate temperature-dependent values of C3 photosynthetic parameters
licor_file <- calculate_arrhenius(licor_file, c3_arrhenius_bernacchi)

# Fit all curves in the data set. Here we use a faster optimizer than the
# default one to ensure the example runs quickly.
aci_results <- consolidate(by(
  licor_file,
  licor_file[, 'species_plot'],
  fit_c3_aci,
  Ca_atmospheric = 420,
  OPTIM_FUN = optimizer_nmkb(1e-7)
))

# Get a subset of fitting results corresponding to the first measured point
# in each curve (where CO2_r_sp = 400 ppm)
aci_fit_subset <- aci_results$fits[aci_results$fits[, 'CO2_r_sp'] == 400, , TRUE]

# Calculate limiting factors
aci_fit_subset <- calculate_c3_limitations_grassi(aci_fit_subset)

# View the limiting factors for each species / plot
col_to_keep <- c(
  'species', 'plot',                                            # identifiers
  'ls_rubisco_grassi', 'lm_rubisco_grassi', 'lb_rubisco_grassi' # limitation info
)

aci_fit_subset[ , col_to_keep, TRUE]
#>    species [UserDefCon] (NA) plot [UserDefCon] (NA)
#> 8                    soybean                     5a
#> 21                   tobacco                      1
#> 34                   tobacco                      2
#>    ls_rubisco_grassi [calculate_c3_limitations_grassi] (dimensionless)
#> 8                                                            0.5018295
#> 21                                                           0.3797255
#> 34                                                                  NA
#>    lm_rubisco_grassi [calculate_c3_limitations_grassi] (dimensionless)
#> 8                                                            0.1984663
#> 21                                                           0.2731928
#> 34                                                                  NA
#>    lb_rubisco_grassi [calculate_c3_limitations_grassi] (dimensionless)
#> 8                                                            0.2997042
#> 21                                                           0.3470817
#> 34                                                                  NA

# One of these fits has NA for all the limiting factors, which causes problems
# when making bar charts with some versions of the `lattice` package, so we
# exclude that curve for plotting
data_for_barchart <-
  aci_fit_subset$main_data[aci_fit_subset$main_data$species_plot != 'tobacco - 2', ]

# Display as a bar chart
lattice::barchart(
  ls_rubisco_grassi + lm_rubisco_grassi + lb_rubisco_grassi ~ species_plot,
  data = data_for_barchart,
  stack = TRUE,
  auto = TRUE,
  ylab = 'Factors limiting assimilation'
)