PhotoGEA (version 1.4.0)

calculate_gamma_star: Calculate Gamma_star from Rubisco specificity

Description

Calculates the CO2 compensation point in the absence of non-photorespiratory CO2 release (Gamma_star) from the Rubisco specificity (on a molarity basis), the oxygen concentration (as a percentage), and the temperature-dependent solubilities of CO2 and O2 in H2O.

Usage

calculate_gamma_star(
    exdf_obj,
    alpha_pr = 0.5,
    oxygen_column_name = 'Oxygen',
    rubisco_specificity_column_name = 'rubisco_specificity_tl',
    tleaf_column_name = 'TleafCnd'
  )

Value

An exdf object based on exdf_obj that includes the following additional columns, calculated as described above: Gamma_star_tl (the value of Gamma_star at the leaf temperature), H_CO2,

H_O2, and specificity_gas_basis. There are many choices for expressing Henry's constant values; here we express them as molalities per unit of pressure: (mol solute / kg H2O) / Pa. The category for each of these new columns is calculate_gamma_star to indicate that they were created using this function.

Arguments

exdf_obj

An exdf object.

alpha_pr

The number of CO2 molecules released by the photorespiratory cycle following each RuBP oxygenation.

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.

rubisco_specificity_column_name

The name of the column in exdf_obj that contains the Rubisco specificity S_aq at the leaf temperature; the units must be M / M, where the molarity M is moles of solute per mole of solvent.

tleaf_column_name

The name of the column in exdf_obj that contains the leaf temperature in degrees C.

Details

The CO2 compensation point in the absence of non-photorespiratory CO2 release (Gamma_star) is the partial pressure of CO2 in the chloroplast at which CO2 gains from Rubisco carboxylation are exactly balanced by CO2 losses from Rubisco oxygenation; this quantity plays a key role in many photosynthesis calculations. One way to calculate its value is to use its definition, which can be found in many places, such as Equation 2.17 from von Caemmerer (2000):

Gamma_star = alpha_pr * O / S,

where O is the partial pressure (or mole fraction) of oxygen in the chloroplast, S is the Rubisco specificity on a gas basis, and alpha_pr is the number of CO2 molecules released by the photorespiratory cycle following each RuBP oxygenation (usually assumed to be 0.5).

The Rubisco specificity is often measured from an aqueous solution where the concentrations of O2 and CO2 are specified as molarities (moles of dissolved CO2 or O2 per mole of H2O). In this context, the equation above becomes

Gamma_star_aq = alpha_pr * O_aq / S_aq,

where Gamma_star_aq and O_aq are the molarities of CO2 and O2 corresponding to Gamma_star and O under the measurement conditions and S_aq is the specificity on a molarity basis.

Henry's law can be used to relate these two versions of the equation; Henry's law states that the concentration of dissolved gas is proportional to the partial pressure of that gas outside the solution. The proportionality factor H is called Henry's constant (or sometimes the solubility), and its value depends on the temperature, gas species, and other factors. Using Henry's law, we can write Gamma_star_aq = Gamma_star_aq * H_CO2 and O = O_aq * H_O2, where H_CO2 is Henry's constant for CO2 dissolved in H2O and H_O2 is Henry's constant for O2 dissolved in H2O. With these replacements, we can re-express the equation above as:

Gamma_star / H_CO2 = alpha_pr * (O / H_O2) / S_aq

Solving for Gamma_star, we see that:

Gamma_star = (alpha_pr * O / S_aq) * (H_CO2 / H_O2).

In other words, both the Rubisco specificity (as measured on a molarity basis) and the ratio of the two Henry's constants (H_CO2 / H_O2) play a role in determining Gamma_star. This equation also shows that it is possible to relate S (the specificity on a gas concentration basis) and S_aq as S = S_aq * H_O2 / H_CO2.

The values of H_O2 and H_CO2 can be calculated from the temperature using Equation 18 from Tromans (1998) and Equation 4 from Carroll et al. (1991), respectively.

In calculate_gamma_star, it is assumed that the value of specificity S_aq was was measured or otherwise determined at the leaf temperature; the leaf temperature is only used to determine the values of the two Henry's constants. Sometimes it is necessary to calculate the temperature-dependent value of the specificity using an Arrhenius equation; this can be accomplished via the calculate_temperature_response_arrhenius function from PhotoGEA.

Finally, it is important to note that Gamma_star can also be directly calculated using an Arrhenius equation, rather than using the oxygen concentration and the specificity. The best approach for determining a value of Gamma_star in any particular situation will generally depend on the available information and the measurement conditions.

References:

von Caemmerer, S. "Biochemical Models of Leaf Photosynthesis." (CSIRO Publishing, 2000) [tools:::Rd_expr_doi("10.1071/9780643103405")].

Carroll, J. J., Slupsky, J. D. and Mather, A. E. "The Solubility of Carbon Dioxide in Water at Low Pressure." Journal of Physical and Chemical Reference Data 20, 1201–1209 (1991) [tools:::Rd_expr_doi("10.1063/1.555900")].

Tromans, D. "Temperature and pressure dependent solubility of oxygen in water: a thermodynamic analysis." Hydrometallurgy 48, 327–342 (1998) [tools:::Rd_expr_doi("10.1016/S0304-386X(98)00007-3")].

Examples

# Example 1: Calculate Gamma_star for each point in a gas exchange log file
licor_data <- read_gasex_file(
  PhotoGEA_example_file_path('licor_for_gm_site11.xlsx'),
)

licor_data <- get_oxygen_from_preamble(licor_data)

licor_data <- set_variable(
    licor_data,
    'rubisco_specificity_tl',
    'M / M',
    value = 90
)

licor_data <- calculate_gamma_star(licor_data)

licor_data[, c('specificity_gas_basis', 'Oxygen', 'Gamma_star_tl'), TRUE]

# Example 2: Calculate Gamma_star at 21% and 2% oxygen for a Rubisco whose
# specificity was measured to be 100 M / M at 25 degrees C.

exdf_obj <- calculate_gamma_star(
  exdf(
    data.frame(
      Oxygen = c(2, 21),
      rubisco_specificity_tl = c(100, 100),
      TleafCnd = c(25, 25)
    ),
    data.frame(
      Oxygen = 'percent',
      rubisco_specificity_tl = 'M / M',
      TleafCnd = 'degrees C',
      stringsAsFactors = FALSE
    )
  )
)

exdf_obj[, c('specificity_gas_basis', 'Oxygen', 'Gamma_star_tl'), TRUE]

# Example 3: Here we recreate Figure 1 from Long, S. P. "Modification of the
# response of photosynthetic productivity to rising temperature by atmospheric
# CO2 concentrations: Has its importance been underestimated?" Plant, Cell and
# Environment 14, 729–739 (1991). This is a fairly complicated example where
# Arrhenius constants for Rubisco parameters are determined by fitting
# published data and then used to determine the Rubisco specificity across a
# range of temperatures.

# Specify leaf temperature and oxygen concentration
leaf_temp <- seq(0, 50, by = 0.1)

exdf_obj <- exdf(
  data.frame(
    Oxygen = rep_len(21, length(leaf_temp)),
    TleafCnd = leaf_temp
  ),
  data.frame(
    Oxygen = 'percent',
    TleafCnd = 'degrees C',
    stringsAsFactors = FALSE
  )
)

# Get Arrhenius constants for Rubisco parameters using data from Table 2 of
# Jordan, D. B. and Ogren, W. L. "The CO2/O2 specificity of ribulose
# 1,5-bisphosphate carboxylase/oxygenase" Planta 161, 308–313 (1984).
rubisco_info <- data.frame(
  temperature = c(7,    12,   15,   25,   30,   35),
  Vc          = c(0.13, 0.36, 0.63, 1.50, 1.90, 2.90),
  Kc          = c(2,    3,    4,    11,   14,   19),
  Ko          = c(550,  510,  510,  500,  600,  540),
  Vo          = c(0.24, 0.48, 0.69, 0.77, 1.1,  1.3)
)

rubisco_info$x <- 1 / (8.314e-3 * (rubisco_info$temperature + 273.15))

lm_Vc <- stats::lm(log(Vc) ~ x, data = rubisco_info)
lm_Kc <- stats::lm(log(Kc) ~ x, data = rubisco_info)
lm_Ko <- stats::lm(log(Ko) ~ x, data = rubisco_info)
lm_Vo <- stats::lm(log(Vo) ~ x, data = rubisco_info)

arrhenius_info <- list(
  Vc = list(
    c = as.numeric(lm_Vc$coefficients[1]),
    Ea = -as.numeric(lm_Vc$coefficients[2]),
    units = 'micromol / mg / min'
  ),
  Kc = list(
    c = as.numeric(lm_Kc$coefficients[1]),
    Ea = -as.numeric(lm_Kc$coefficients[2]),
    units = 'microM'
  ),
  Ko = list(
    c = as.numeric(lm_Ko$coefficients[1]),
    Ea = -as.numeric(lm_Ko$coefficients[2]),
    units = 'microM'
  ),
  Vo = list(
    c = as.numeric(lm_Vo$coefficients[1]),
    Ea = -as.numeric(lm_Vo$coefficients[2]),
    units = 'micromol / mg / min'
  )
)

# Get temperature-dependent values of Rubisco parameters using Arrhenius
# equations
exdf_obj <- calculate_temperature_response_arrhenius(
  exdf_obj,
  arrhenius_info
)

# Calculate temperature-dependent specificity values
exdf_obj <- set_variable(
  exdf_obj,
  'rubisco_specificity_tl',
  units = 'M / M',
  value = exdf_obj[, 'Vc'] * exdf_obj[, 'Ko'] /
    (exdf_obj[, 'Vo'] * exdf_obj[, 'Kc'])
)

# Calculate Gamma_star and Henry constants
exdf_obj <- calculate_gamma_star(exdf_obj)

# Make a plot similar to Figure 1 from Long (1991)
lattice::xyplot(
  rubisco_specificity_tl + H_CO2 / H_O2 ~ TleafCnd,
  data = exdf_obj$main_data,
  auto = TRUE,
  grid = TRUE,
  type = 'l',
  xlim = c(0, 50),
  ylim = c(0, 250),
  xlab = "Temperature [ degrees C ]",
  ylab = "Rubisco specificity or ratio of Henry's constants (H_CO2 / H_O2)\n[ dimensionless ]"
)

# We can also make a plot of Gamma_star across this range
lattice::xyplot(
  Gamma_star_tl ~ TleafCnd,
  data = exdf_obj$main_data,
  auto = TRUE,
  grid = TRUE,
  type = 'l',
  xlim = c(0, 50),
  ylim = c(0, 120),
  xlab = "Temperature [ degrees C ]",
  ylab = paste('Gamma_star at leaf temperature [', exdf_obj$units$Gamma_star_tl, ']')
)