Calculate C3 variable J — calculate_c3_variable

Calculates values of mesophyll conductance and chloroplast CO2 concentration using the "variable J" equation, as originally described in Harley et al. (1992) and modified in Moualeu-Ngangue, Chen, & Stutzel (2016). This function can accomodate alternative colum names for the variables taken from Licor files 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_variable_j(
    exdf_obj,
    alpha_g,
    alpha_s,
    alpha_t,
    Gamma_star_at_25,
    RL_at_25,
    tau,
    Wj_coef_C = 4.0,
    Wj_coef_Gamma_star = 8.0,
    a_column_name = 'A',
    ci_column_name = 'Ci',
    gamma_star_norm_column_name = 'Gamma_star_norm',
    phips2_column_name = 'PhiPS2',
    qin_column_name = 'Qin',
    rl_norm_column_name = 'RL_norm',
    total_pressure_column_name = 'total_pressure',
    hard_constraints = 0,
    perform_checks = TRUE,
    return_exdf = TRUE
  )

Arguments

exdf_obj: An exdf object.
alpha_g: A dimensionless parameter where 0 <= alpha_g <= 1, representing the proportion of glycolate carbon taken out of the photorespiratory pathway as glycine. alpha_g is often assumed to be 0. If alpha_g is not a number, then there must be a column in exdf_obj called alpha_g with appropriate units. A numeric value supplied here will overwrite the values in the alpha_g column of exdf_obj if it exists.
alpha_s: A dimensionless parameter where 0 <= alpha_s <= 0.75 * (1 - alpha_g) representing the proportion of glycolate carbon taken out of the photorespiratory pathway as serine. alpha_s is often assumed to be 0. If alpha_s is not a number, then there must be a column in exdf_obj called alpha_s with appropriate units. A numeric value supplied here will overwrite the values in the alpha_s column of exdf_obj if it exists.
alpha_t: A dimensionless parameter where 0 <= alpha_t <= 1 representing the proportion of glycolate carbon taken out of the photorespiratory pathway as CH2-THF. alpha_t is often assumed to be 0. If alpha_t is not a number, then there must be a column in exdf_obj called alpha_t with appropriate units. A numeric value supplied here will overwrite the values in the alpha_t column of exdf_obj if it exists.
Gamma_star_at_25: The chloroplastic CO2 concentration at which CO2 gains from Rubisco carboxylation are exactly balanced by CO2 losses from Rubisco oxygenation, at 25 degrees C, expressed in micromol mol^(-1). If Gamma_star_at_25 is not a number, then there must be a column in exdf_obj called Gamma_star_at_25 with appropriate units. A numeric value supplied here will overwrite the values in the Gamma_star_at_25 column of exdf_obj if it exists.
RL_at_25: The respiration rate at 25 degrees C, expressed in micromol m^(-2) s^(-1). If RL_at_25 is not a number, then there must be a column in exdf_obj called RL_at_25 with appropriate units. A numeric value supplied here will overwrite the values in the RL_at_25 column of exdf_obj if it exists.
tau: The proportionality factor used to calculate the RuBP regeneration rate from chlorophyll fluorescence measurements (dimensionless). If tau is not a number, then there must be a column in exdf_obj called tau with appropriate units. A numeric value supplied here will overwrite the values in the tau column of exdf_obj if it exists.
Wj_coef_C: A coefficient in the equation for RuBP-regeneration-limited carboxylation, whose value depends on assumptions about the NADPH and ATP requirements of RuBP regeneration; see calculate_c3_assimilation for more information.
Wj_coef_Gamma_star: A coefficient in the equation for RuBP-regeneration-limited carboxylation, whose value depends on assumptions about the NADPH and ATP requirements of RuBP regeneration; see calculate_c3_assimilation for more information.
a_column_name: The name of the column in exdf_obj that contains the net assimilation in micromol m^(-2) s^(-1).
ci_column_name: The name of the column in exdf_obj that contains the intercellular CO2 concentration in micromol mol^(-1).
gamma_star_norm_column_name: The name of the column in exdf_obj that contains the normalized Gamma_star values (with units of normalized to Gamma_star at 25 degrees C).
phips2_column_name: The name of the column in exdf_obj that contains values of the operating efficiency of photosystem II (dimensionless).
qin_column_name: The name of the column in exdf_obj that contains values of the incident photosynthetically active flux density in micromol m^(-2) s^(-1).
rl_norm_column_name: The name of the column in exdf_obj that contains the normalized RL values (with units of normalized to RL at 25 degrees C).
total_pressure_column_name: The name of the column in exdf_obj that contains the total pressure in bar.
hard_constraints: An integer numerical value indicating which types of hard constraints to place on the values of input parameters; see below for more details.
perform_checks: A logical value indicating whether to check units for the required columns. This should almost always be TRUE. The option to disable these checks is only intended to be used when fit_c3_variable_j calls this function, since performing these checks many times repeatedly slows down the fitting procedure.
return_exdf: A logical value indicating whether to return an exdf object. This should almost always be TRUE. The option to return a vector is mainly intended to be used when fit_c3_variable_j calls this function, since creating an exdf object to return will slow down the fitting procedure.

Details

The "Variable J" method is a way to estimate the chloroplast CO2 concentration Cc and the mesophyll conductance to CO2 gmc from combined gas exchange and chlorophyll fluorescence measurements, and was originally described in Harley et al. (1992). The main idea is that along with Cc, the net CO2 assimilation rate (An), day respiration rate (RL), and CO2 compensation point in the absence of day respiration (Gamma_star) determine the actual RuBP regeneration rate (J_actual) required to support the Calvin-Benson cycle:

J_actual = (A + RL) * (4 * Cc + 8 * Gamma_star) / (Cc - Gamma_star)

This is Equation 6 in Harley et al. (1992). (Note: this equation can be derived by solving the equation for Aj from the FvCB model for J. However, this relationship holds true even when CO2 assimilation is not limited by RuBP regeneration. Hence, we distinguish between the actual regeneration rate J_actual and the maximum regeneration rate for a given incident light level J.)

This equation can be rewritten by using a 1D diffusion equation to replace Cc with Cc = Ci - An / gmc and then solving for the mesophyll conductance. The result is Equation 7 in Harley et al. (1992), which we do not reproduce here. The importance of Equation 7 is that it calculates gmc from several quantities that can be measured using gas exchange (Ci, An, and RL), a quantity whose values can be known beforehand (Gamma_star), and J_actual (which can be estimated from chlorophyll fluorescence measurements). Here we update Equation 7 to include alpha_g and alpha_s following Busch et al. (2018) (also see calculate_c3_assimilation.)

The actual RuBP regeneration rate is related to the incident photosynthetically active flux density Qin and the operating efficiency of photosystem II PhiPSII according to:

J_actual = alpha_g * beta * Qin * PhiPSII,

where alpha_g is the leaf absorptance and beta is the fraction of absorbed light energy directed to photosystem II. Qin is set by the measurement conditions, while PhiPSII can be estimated from chlorophyll fluorescence. However, the values of alpha_g and beta are generally unknown; beta in particular is difficult or impossible to measure and is often assumed to be 0.5. Thus, while Equation 7 from Harley et al. (1992) can be used to estimate gmc, there is a practical uncertainty associated with determining a value of J_actual to be used in Equation 7.

Moualeu-Ngangue, Chen, & Stutzel (2016) developed a way to address this issue. The method from that paper replaces the product of alpha_g and beta by a single new parameter tau, and uses it to estimate the actual RuBP regeneration from fluoresence (J_F):

J_F = tau * Qin * PhiPSII.

This new parameter tau is assumed to be constant across an A-Ci curve, and is treated as an unknown whose value will be determined during a fitting procedure.

In this function, the supplied values of Qin, PhiPSII, and tau are used to calculate values of J_F. Then, the values of J_F are used along with Equation 7 from Harley et al. (1992) to calculate gmc. Finally, a 1D diffusion equation is used to calculate Cc.

Hard constraints:

Most input parameters to the Variable J equations have hard constraints on their values which are set by their biochemical or physical interpretation; for example, RL cannot be negative and tau must lie between 0 and 1. Yet, because of measurement noise, sometimes it is necessary to use values outside these ranges when fitting an A-Ci curve with fit_c3_variable_j. To accomodate different potential use cases, it is possible to selectively apply these hard constraints by specifying different values of the hard_constraints input argument:

hard_constraints = 0: Constraints are only placed on inputs that are user-supplied and cannot be fit, such as Qin.
hard_constraints = 1: Includes the same constraints as when hard_constraints is 0, with the additional constraint that all Ci values must be non-negative.
hard_constraints = 2: Includes the same constraints as when hard_constraints is 1, which additional constraints on the parameters that can be fitted. For example, RL_at_25 must be non-negative and tau must lie between 0 and 1.

If any input values violate any of the specified constraints, an error message will be thrown.

References:

Harley, P. C., Loreto, F., Di Marco, G. & Sharkey, T. D. "Theoretical Considerations when Estimating the Mesophyll Conductance to CO2 Flux by Analysis of the Response of Photosynthesis to CO2" Plant Physiology 98, 1429–1436 (1992) [doi:10.1104/pp.98.4.1429 ].
Moualeu-Ngangue, D. P., Chen, T.-W. & Stutzel, H. "A new method to estimate photosynthetic parameters through net assimilation rate-intercellular space CO2 concentration (A-Ci) curve and chlorophyll fluorescence measurements" New Phytologist 213, 1543–1554 (2017) [doi:10.1111/nph.14260 ].
Busch, Sage, & Farquhar, G. D. "Plants increase CO2 uptake by assimilating nitrogen via the photorespiratory pathway." Nature Plants 4, 46–54 (2018) [doi:10.1038/s41477-017-0065-x ].

Value

The return value depends on the value of return_exdf:

If return_exdf is TRUE, the return value is an exdf object with the following columns, calculated as described above: J_F, gmc, Cc, tau, and RL_tl. The category for each of these new columns is calculate_c3_variable_j to indicate that they were created using this function.
If return_exdf is FALSE, the return value is a list with the following named elements: gmc, Cc, and J_F. Each element is a numeric vector.

Examples

# Read an example Licor file included in the PhotoGEA package. This file
# includes gas exchange and chlorophyll fluorescence data.
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'])

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

# Calculate temperature-dependent values of C3 photosynthetic parameters
licor_file <- calculate_temperature_response(licor_file, c3_temperature_param_bernacchi)

# Calculate values of J_F, gmc, and Cc assuming alpha_g = alpha_s = alpha_t = 0,
# RL_at_25 = 1.5, and tau = 0.55.
vj_res <- calculate_c3_variable_j(licor_file, 0, 0, 0, '', 1.5, 0.55)

# Plot mesophyll conductance against Cc. Note: this information is not very
# meaningful since the values of Gamma_star, tau and RL used above are
# arbitrary.
lattice::xyplot(
  gmc ~ Cc | licor_file[, 'species_plot'],
  data = vj_res$main_data,
  type = 'b',
  pch = 16,
  auto = TRUE,
  xlab = paste0('Chloroplast CO2 concentration (', vj_res$units$Cc, ')'),
  ylab = paste0('Mesophyll conductance to CO2 (', vj_res$units$gmc, ')')
)