Calculate C3 variable J
calculate_c3_variable_j.Rd
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,
Gamma_star,
RL_at_25,
tau,
atp_use = 4.0,
nadph_use = 8.0,
a_column_name = 'A',
ci_column_name = 'Ci',
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. Ifalpha_g
is not a number, then there must be a column inexdf_obj
calledalpha_g
with appropriate units. A numeric value supplied here will overwrite the values in thealpha_g
column ofexdf_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. Ifalpha_s
is not a number, then there must be a column inexdf_obj
calledalpha_s
with appropriate units. A numeric value supplied here will overwrite the values in thealpha_s
column ofexdf_obj
if it exists.- Gamma_star
The CO2 compensation point in the absence of day respiration, expressed in
micromol mol^(-1)
. IfGamma_star
is not a number, then there must be a column inexdf_obj
calledGamma_star
with appropriate units. A numeric value supplied here will overwrite the values in theGamma_star
column ofexdf_obj
if it exists.- RL_at_25
The respiration rate at 25 degrees C, expressed in
micromol m^(-2) s^(-1)
. IfRL_at_25
is not a number, then there must be a column inexdf_obj
calledRL_at_25
with appropriate units. A numeric value supplied here will overwrite the values in theRL_at_25
column ofexdf_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 inexdf_obj
calledtau
with appropriate units. A numeric value supplied here will overwrite the values in thetau
column ofexdf_obj
if it exists.- atp_use
The number of ATP molecules used per C3 cycle.
- nadph_use
The number of NADPH molecules used per C3 cycle.
- a_column_name
The name of the column in
exdf_obj
that contains the net assimilation inmicromol m^(-2) s^(-1)
.- ci_column_name
The name of the column in
exdf_obj
that contains the intercellular CO2 concentration inmicromol mol^(-1)
.- 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 inmicromol m^(-2) s^(-1)
.- rl_norm_column_name
The name of the column in
exdf_obj
that contains the normalizedRL
values (with units ofnormalized to RL at 25 degrees C
).- total_pressure_column_name
The name of the column in
exdf_obj
that contains the total pressure inbar
.- 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 whenfit_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 beTRUE
. The option to return a vector is mainly intended to be used whenfit_c3_variable_j
calls this function, since creating anexdf
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 asQin
.hard_constraints = 1
: Includes the same constraints as whenhard_constraints
is 0, with the additional constraint that allCi
values must be non-negative.hard_constraints = 2
: Includes the same constraints as whenhard_constraints
is 1, which additional constraints on the parameters that can be fitted. For example,RL_at_25
must be non-negative andtau
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
isTRUE
, the return value is anexdf
object with the following columns, calculated as described above:J_F
,gmc
,Cc
,tau
, andRL_tl
. The category for each of these new columns iscalculate_c3_variable_j
to indicate that they were created using this function.If
return_exdf
isFALSE
, the return value is a list with the following named elements:gmc
andCc
. 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_arrhenius(licor_file, c3_arrhenius_bernacchi)
# Calculate values of J_F, gmc, and Cc assuming alpha_g = alpha_s = 0,
# tau = 0.2, and RL = 0.5
vj_res <- calculate_c3_variable_j(licor_file, 0, 0, '', 1.5, 0.55)
# Combine with original data
licor_file <- cbind(licor_file, vj_res)
# Plot mesophyll conductance against Cc. Note: this information is not very
# meaningful since the values of tau and RL used above are arbitrary.
lattice::xyplot(
gmc ~ Cc | species_plot,
data = licor_file$main_data,
type = 'b',
pch = 16,
auto = TRUE
)