Abstract
R package rbcmodel is a package to calculate Rubisco
carbon fixation rates at a particular CO2 concentration,
O2 concentration, and temperature, using a combination of
Michaelis-Menten kinetics and the temperature dependences of the basic
Rubisco kinetic parameters (kcat,c, Ko,
Kc, and SC/O). In addition to the actual
carboxylation rate, the effect of Rubisco’s oxygenation reaction is also
modeled, which effectively reduces the rate of CO2 fixation
due to the subsequent need for phosphoglycolate salvage. As there are
several different phosphoglycolate salvage pathways, each with a
different CO2 cost per O2 fixed, Rubisco carbon
fixation rates are simulated with appropriate phosphoglycolate salvage
stoichiometries. This package also includes a searchable data library of
collected Rubisco kinetics and temperature dependences.
1. Introduction
The enzyme Rubisco, ribulose-1,5-bisphosphate carboxylase/oxygenase,
is one of the most common enzymes on the planet [1]. In the
Calvin-Benson-Bassham cycle (the most common carbon fixation pathway,
found in plants, algae, cyanobacteria, and chemolithoautotrophic
bacteria), Rubisco catalyzes the rate-limiting step, in which
CO2 is added to a five-carbon organic sugar to form two
3-phosphoglycerate molecules. Thus, Rubisco is directly responsible for
the conversion of inorganic carbon to organic carbon.
In addition to this reaction, Rubisco can also catalyze the addition
of O2 to the same five-carbon organic sugar. This reaction
produces 2-phosphoglycolate, a toxic molecule whose removal via a
phosphoglycolate salvage (PGS) pathway results in the loss of recently
fixed carbon. In plants, up to 49% of gross primary production can be
lost via PGS (also called photorespiration) [2].
There is a tremendous amount of sequence and quaternary structure
diversity in the Rubisco enzymes found across the tree of life, which
also translates to differences in the kinetics of both of its reactions.
The most commonly measured kinetic parameters are the carboxylation
speed (kcat,C), the half-saturation constants for
CO2 (Kc) and O2 (Ko), and
the specificity for CO2 vs. O2 (SC/O).
These parameters are used to qualitatively compare the carboxylation
rates of Rubisco, with the Ko used to determine competitive
inhibiton of the carboxylation reaction. The oxygenation reaction is
often left out of the picture, yet its importance in the diversion of
primary production can be significant. In order to quantitatively
compare true carbon fixation rates by Rubisco, both of its reactions
must be calculated.
The carboxylation reaction rate of a Rubisco enzyme (RC)
can be modeled for each active site under different CO2 and
O2 concentrations using a competitive-inhibitor
Michaelis-Menten equation [3] (equation 1): \[R_{C}=k_{cat,C}*\frac{[CO_{2}]}{[CO_{2}]+K_C+K_C*\frac{O_2}{K_O}}\]
where RC is the gross carboxylation rate of Rubisco, and
[CO2] and [O2] are the concentrations of
CO2 and O2, respectively. The oxygenation reaction
rate (RO) is modeled the same way, but as the value for
kcat,O is not measured, we utilize a different
commonly measured kinetic parameter: the specificity factor
(SC/O), which is the ratio of the carboxylase/oxygenase
reaction: \[S_{C/O}=\frac{k_{cat,C}}{K_O}*\frac{K_C}{k_{cat,O}}\]
The relationship between SC/O and RC/RO
can be described by the following equation, which can be rearranged to
calculate RO: \[\frac{R_C}{R_O}=S_{C/O}*\frac{[CO_2]}{[O_2]}\]
To determine the net carboxylation rate, RO must then be
converted to carbon molecules lost per second using the appropriate
stoichiometry of the PGS pathway utilized by that Rubisco’s
organism:
| 2 RO : 1 CO2 lost |
C2 cycle, glycerate pathway |
[4] |
| 1 RO : 2 CO2 lost |
malate cycle, oxalyl-CoA decarboxylation, export from cell |
[4] |
| 1 RO : 1 CO2 lost |
diatom photorespiration* |
[5] |
*Under most conditions, 2-PG in diatoms is routed through an
incomplete C2 cycle to amino acid metabolism and thus is more
appropriately modeled using the C2 cycle stoichiometry. This
stoichiometry is more appropriate for severe photorespiratory
conditions, when 2-PG is routed through a different peroxisomal
cycle.
Enzyme kinetics also change with temperature. The temperature
dependence of the four commonly measured kinetic parameters have been
measured for a range of Rubisco enzymes, and can therefore be used to
scale these parameters with temperature using an Arrhenius curve [6]:
\[x(T)=e^{c-\frac{\Delta H}{RT}}\]
This package automates these calculations, determining a quantitative
net carboxylation rate per active site across a range of temperatures
and CO2 and O2 concentrations. With a quantitative
rate, it is possible to compare any Rubisco enzyme to any other,
regardless of the distance between them on the tree of life.
The rest of the vignette is an introduction to the capabilities of
this R package, and follows the basic expected workflow of a user of the
package. We will discuss how to search the included database for
appropriate kinetics to create an enzyme object, how to use that enzyme
object and a temperature dependence scale to calculate rates of
carboxylation for that enzyme, how to plot carboxylation rates to
visualize a range of conditions, and how to compare enzyme objects to
each other. Finally, we end with a discussion of the database included
in the package and how to cite the data contained within it. For more
advanced topics, see the additional vignettes included in this
package.
2. Creating an enzyme
The first step of the basic rbcmodel workflow is to
create an enzyme object, which can be done from the
database included in the package, from custom data, or a combination of
the two. The easiest option is to create it entirely from the database.
For most users, that will mean finding an appropriate entry in the
abridged table. For more information about the database
provided in the package, see section 6.
2.1 search_enzyme(): Searching Rubisco Kinetics
In this package, we have included a database of close to 1000 studies
that have determined at least one Rubisco kinetic parameter, so that
users can more easily find data for their enzyme of interest (see
Section 6 for more information about the database). This would be a lot
of entries to look through manually, so the function
search_enzyme() will search the database for entries that
match a keyword. By default, search_enzyme() will search in
the abridged table first, which contains only entries with
all four Rubisco kinetic parameters, and check your search term against
the alias table, which contains a list of known aliases for
species who have a common name or whose names have changed in the
literature over time. After that, it will attempt to match the keyword
against genus names, species names, taxonomies, and Rubisco forms.
Search terms are matched case-insensitively.
You’ll note the existence of the PGS column in the
tables; this field is to tell you which phosphoglycolate salvage pathway
to use. If it is NA, the literature is unclear about which
PGS pathway is used in this organism, and we typically recommend using
the default, "canon", in this case, as is the best studied
PGS pathway.
Here are some examples of common ways to search through the
database:
From a species name:
search_enzyme("aestivum")[1:5,]
#> Matched species in abridged table
#> identifier genus species subspecies kcat_val kcat_T
#> 1 aestivum_Carmo-Silva_2010 Triticum aestivum <NA> 3.000 NA
#> 2 aestivum_Hermida-Carrera_2016 Triticum aestivum Cajeme 2.200 NA
#> 3 aestivum_Iñiguez_2021 Triticum aestivum <NA> 2.700 NA
#> 4 aestivum_Makino_1988 Triticum aestivum <NA> 2.964 NA
#> 5 aestivum_Orr_2016 Triticum aestivum <NA> 4.900 NA
#> Kc_val Kc_T Ko_val Ko_T S_val S_T temp form PGS taxonomy group
#> 1 10.9 NA 341 NA 100.0 NA 25 1B canon C3 plants Plants
#> 2 11.3 NA 620 NA 100.0 NA 25 1B canon C3 plants Plants
#> 3 11.9 NA 429 NA 96.3 NA 25 1B canon C3 plants Plants
#> 4 11.2 NA 383 NA 119.9 NA 25 1B canon C3 plants Plants
#> 5 20.1 NA 658 NA 100.0 NA 25 1B canon C3 plants Plants
#> note
#> 1 <NA>
#> 2 Ko is reported in Iniguez databases (Iniguez et al. 2019, Iniguez et al. 2021, etc.) although only kcat_o/Ko is reported in original paper
#> 3 methodology-corrected average from Iñiguez et al. 2021 across multiple cultivars
#> 4 S calculated from Vo given
#> 5 Points to Prins JExpB 2016 for methods. Extracted pH and pKa from there. S measured at pH 8.2, rest measured at 8.0. Not sure why.
#> short_ref
#> 1 Carmo-Silva 2010
#> 2 Hermida-Carrera 2016
#> 3 Iñiguez 2021
#> 4 Makino 1988
#> 5 Orr 2016
From a genus name:
#entries chosen to show breadth of genus entries
search_enzyme("Triticum")[c(1,3,7,15,17),]
#> Matched genus in abridged table
#> identifier genus species subspecies
#> 1 aestivum_Carmo-Silva_2010 Triticum aestivum <NA>
#> 3 aestivum_Iñiguez_2021 Triticum aestivum <NA>
#> 7 aestivum_SATYN_II_9410_Prins_2016 Triticum aestivum SATYN_II_9410
#> 15 dicoccon_ENT_2126_Prins_2016 Triticum dicoccon CI12214 (ENT:2126)
#> 17 timonovum_Prins_2016 Triticum timonovum <NA>
#> kcat_val kcat_T Kc_val Kc_T Ko_val Ko_T S_val S_T temp form PGS taxonomy
#> 1 3.00 NA 10.9 NA 341 NA 100.0 NA 25 1B canon C3 plants
#> 3 2.70 NA 11.9 NA 429 NA 96.3 NA 25 1B canon C3 plants
#> 7 3.26 NA 17.6 NA 469 NA 93.8 NA 25 1B canon C3 plants
#> 15 3.55 NA 18.6 NA 485 NA 93.8 NA 25 1B canon C3 plants
#> 17 3.48 NA 16.8 NA 495 NA 101.0 NA 25 1B canon C3 plants
#> group
#> 1 Plants
#> 3 Plants
#> 7 Plants
#> 15 Plants
#> 17 Plants
#> note
#> 1 <NA>
#> 3 methodology-corrected average from Iñiguez et al. 2021 across multiple cultivars
#> 7 all wheat variants
#> 15 all wheat variants
#> 17 all wheat variants
#> short_ref
#> 1 Carmo-Silva 2010
#> 3 Iñiguez 2021
#> 7 Prins 2016
#> 15 Prins 2016
#> 17 Prins 2016
From a common name:
search_enzyme("wheat")[1:5,]
#> Matched aliases: Wheat
#> Data found in abridged table
#> identifier genus species subspecies kcat_val kcat_T
#> 1 aestivum_Carmo-Silva_2010 Triticum aestivum <NA> 3.000 NA
#> 2 aestivum_Hermida-Carrera_2016 Triticum aestivum Cajeme 2.200 NA
#> 3 aestivum_Iñiguez_2021 Triticum aestivum <NA> 2.700 NA
#> 4 aestivum_Makino_1988 Triticum aestivum <NA> 2.964 NA
#> 5 aestivum_Orr_2016 Triticum aestivum <NA> 4.900 NA
#> Kc_val Kc_T Ko_val Ko_T S_val S_T temp form PGS taxonomy group
#> 1 10.9 NA 341 NA 100.0 NA 25 1B canon C3 plants Plants
#> 2 11.3 NA 620 NA 100.0 NA 25 1B canon C3 plants Plants
#> 3 11.9 NA 429 NA 96.3 NA 25 1B canon C3 plants Plants
#> 4 11.2 NA 383 NA 119.9 NA 25 1B canon C3 plants Plants
#> 5 20.1 NA 658 NA 100.0 NA 25 1B canon C3 plants Plants
#> note
#> 1 <NA>
#> 2 Ko is reported in Iniguez databases (Iniguez et al. 2019, Iniguez et al. 2021, etc.) although only kcat_o/Ko is reported in original paper
#> 3 methodology-corrected average from Iñiguez et al. 2021 across multiple cultivars
#> 4 S calculated from Vo given
#> 5 Points to Prins JExpB 2016 for methods. Extracted pH and pKa from there. S measured at pH 8.2, rest measured at 8.0. Not sure why.
#> short_ref
#> 1 Carmo-Silva 2010
#> 2 Hermida-Carrera 2016
#> 3 Iñiguez 2021
#> 4 Makino 1988
#> 5 Orr 2016
From a taxonomy:
search_enzyme("Cyanobacteria")[1:5,]
#> Matched taxonomy in abridged table
#> identifier genus species subspecies kcat_val
#> 1 variabilis_Badger_1980 Anabaena variabilis <NA> 2.6931
#> 2 marinus_Shih_2016 Prochlorococcus marinus MIT9313 6.5800
#> 3 elongatus_Mueller-Cajar_2008 Synechococcus elongatus 6301 11.8000
#> 4 elongatus_Read_1992b Synechococcus elongatus 6301 2.5700
#> 5 elongatus_Read_1994 Synechococcus elongatus 6301 3.7100
#> kcat_T Kc_val Kc_T Ko_val Ko_T S_val S_T temp form PGS taxonomy
#> 1 NA 293 NA 1080 NA 33.3 NA 25 1Bc canon Cyanobacteria
#> 2 NA 309 NA 1400 NA 59.9 NA 25 1Ac canon Cyanobacteria
#> 3 NA 200 NA 199 NA 41.5 NA 25 1Bc canon Cyanobacteria
#> 4 NA 142 NA 664 NA 41.0 NA 25 1Bc canon Cyanobacteria
#> 5 NA 167 NA 529 NA 41.0 NA 25 1Bc canon Cyanobacteria
#> group
#> 1 Bacteria
#> 2 Bacteria
#> 3 Bacteria
#> 4 Bacteria
#> 5 Bacteria
#> note
#> 1 Reported kcat_C&_O as specific activity; S reported in Tcherkez+ 2006 as 43 due to adjustment to pKa of 6.25 from 6.36
#> 2 pKa from Iniguez et al. 2021
#> 3 Used Kane method for S so no pKa correction needed; no pKa listed for Kc, but cites Whitney & Sharwood 2007; Whitney & Sharwood 2007 does not report pKa, but Iniguez et al. 2021 cites a pKa of 6.25 for that study
#> 4 kcat value is suspect here. unclear how they quantitated protein. it's OK since we have other measurements of this rubisco
#> 5 kcat value is suspect here. unclear how they quantitated protein. it's OK since we have other measurements of this rubisco
#> short_ref
#> 1 Badger 1980
#> 2 Shih 2016
#> 3 Mueller-Cajar 2008
#> 4 Read 1992b
#> 5 Read 1994
For all studies, including incomplete ones, or more information:
#truncated for readability
search_enzyme("Triticum",data="comprehensive")[1:5,]
#> Matched genus in comprehensive table
#> identifier genus species subspecies mutant
#> 1 aestivum_Carmo-Silva_2010 Triticum aestivum <NA> FALSE
#> 2 aestivum_Galmés_2014b Triticum aestivum Alexandria FALSE
#> 3 aestivum_Hermida-Carrera_2016 Triticum aestivum Cajeme FALSE
#> 4 aestivum_hermida-carrera_2020 Triticum aestivum cv. Cajeme FALSE
#> 5 aestivum_Iñiguez_2021 Triticum aestivum <NA> FALSE
#> mutant_details primary heterologous_expression kcat_val kcat_T kcat_pH Kc_val
#> 1 <NA> TRUE FALSE 3.0 NA NA 10.9
#> 2 <NA> TRUE FALSE 4.0 NA NA 10.3
#> 3 <NA> TRUE FALSE 2.2 NA 8 11.3
#> 4 <NA> TRUE FALSE 1.9 NA NA 10.3
#> 5 <NA> FALSE FALSE 2.7 NA NA 11.9
#> Kc_T Kc_pH Ko_val Ko_T Ko_pH S_val S_T S_pH temp pH pKa_used form PGS
#> 1 NA NA 341 NA NA 100.0 NA NA 25 8.2 6.11 1B canon
#> 2 NA NA 414 NA NA NA NA NA 25 8.0 6.12 1B canon
#> 3 NA 8 620 NA NA 100.0 NA NA 25 8.2 6.11 1B canon
#> 4 NA NA NA NA NA NA NA NA 25 8.0 6.23 1B canon
#> 5 NA NA 429 NA NA 96.3 NA NA 25 NA NA 1B canon
#> taxonomy group
#> 1 C3 plants Plants
#> 2 C3 plants Plants
#> 3 C3 plants Plants
#> 4 C3 plants Plants
#> 5 C3 plants Plants
#> note
#> 1 <NA>
#> 2 C3 plants from low stress environments; no pKa reported but cite Bird 1982 which cites McNeil 1981 which uses 6.12
#> 3 Ko is reported in Iniguez databases (Iniguez et al. 2019, Iniguez et al. 2021, etc.) although only kcat_o/Ko is reported in original paper
#> 4 <NA>
#> 5 methodology-corrected average from Iñiguez et al. 2021 across multiple cultivars
#> short_ref year
#> 1 Carmo-Silva 2010 2010
#> 2 Galmés 2014b 2014
#> 3 Hermida-Carrera 2016 2016
#> 4 Hermida-Carrera 2020 2020
#> 5 Iñiguez 2021 2021
From a partial name:
search_enzyme("Trit",match="partial")
#> Matched aliases: Triticum timpopheevii subsp. timopheevii
#> Data found in abridged table
#> identifier genus species subspecies kcat_val kcat_T Kc_val
#> 1 timonovum_Prins_2016 Triticum timonovum <NA> 3.48 NA 16.8
#> Kc_T Ko_val Ko_T S_val S_T temp form PGS taxonomy group
#> 1 NA 495 NA 101 NA 25 1B canon C3 plants Plants
#> note short_ref
#> 1 all wheat variants Prins 2016
Note in the partial match example that the search found a match in
the alias table, and thus did not show other partial
matches from the abridged or comprehensive
tables. If you want to see all possible partial matches, consider using
the level="genus" or level="species"
options.
search_enzyme("Trit",match="partial",level="genus")[1:5,]
#> Matched genus in abridged table
#> identifier genus species subspecies kcat_val kcat_T
#> 1 Cando_Prins_2016 Triticale Cando <NA> 3.62 NA
#> 2 Rotego_Prins_2016 Triticale Rotego <NA> 3.46 NA
#> 3 Talentro_Prins_2016 Triticale Talentro <NA> 3.36 NA
#> 4 aestivum_Carmo-Silva_2010 Triticum aestivum <NA> 3.00 NA
#> 5 aestivum_Hermida-Carrera_2016 Triticum aestivum Cajeme 2.20 NA
#> Kc_val Kc_T Ko_val Ko_T S_val S_T temp form PGS taxonomy group
#> 1 16.1 NA 384 NA 99.7 NA 25 1B canon C3 plants Plants
#> 2 15.1 NA 369 NA 96.8 NA 25 1B canon C3 plants Plants
#> 3 15.8 NA 436 NA 95.2 NA 25 1B canon C3 plants Plants
#> 4 10.9 NA 341 NA 100.0 NA 25 1B canon C3 plants Plants
#> 5 11.3 NA 620 NA 100.0 NA 25 1B canon C3 plants Plants
#> note
#> 1 all wheat variants
#> 2 all wheat variants
#> 3 all wheat variants
#> 4 <NA>
#> 5 Ko is reported in Iniguez databases (Iniguez et al. 2019, Iniguez et al. 2021, etc.) although only kcat_o/Ko is reported in original paper
#> short_ref
#> 1 Prins 2016
#> 2 Prins 2016
#> 3 Prins 2016
#> 4 Carmo-Silva 2010
#> 5 Hermida-Carrera 2016
2.2 Creating an enzyme from the database: Enzyme() and
check_enzyme()
Now that you have the kinetics and the PGS pathway to use, you can
make the enzyme. Using only database entries automates most of the
creation.
Using the identifier for a particular enzyme, in this case the
Iñiguez methodology-corrected wheat enzyme, we can create the
enzyme object with the function Enzyme():
Rbc_wheat <- Enzyme("aestivum_Iñiguez_2021",enzyme_name="wheat")
If your enzyme is created from an identifier in the
comprehensive table, it may have missing values, so it is
good practice to double-check that your enzyme has been created
successfully with check_enzyme().
check_enzyme() will warn you if you have used an
unacceptable PGS string, or failed to provide a numeric value for any of
the kinetics parameters.
check_enzyme(Rbc_wheat)
#> Enzyme "wheat":
#> kcat = 2.7 s⁻¹ @ T_kcat = 25°C
#> K_c = 11.9 μM @ T_c = 25°C
#> K_o = 429 μM @ T_o = 25°C
#> S = 96.3 @ T_S = 25°C
#> Upper thermal limit = 55°C
#> PGS = "canon"
For instructions on modifying parameters or creating an enzyme from
scratch, see the Designing a Custom Enzyme vignette.
3. Calculating Rates
Now that the enzyme object has been created, it can be
combined with a temperature dependence scale and the PGS stoichiometry
to model carbon fixation rates.
3.1 Creating a temperature dependence scale:
search_DHScale(),DHScale(), and
modify_DHScale()
We have provided many temperature dependence measurements from the
literature within the package, along with averages modified from Galmés
et al. 2016 [6]. These scales can be searched and used to create a
DHScale object as with the kinetics, using
search_DHScale() and DHScale() instead of
search_enzyme() and Enzyme(). Given the much
smaller number of temperate dependence studies, we often recommend
searching based on form or taxonomy instead of genus or species.
search_DHScale("Triticum")
#> Matched genus in abridged table
#> identifier genus species subspecies kcat_dH Kc_dH Ko_dH
#> 1 aestivum_galmés_2015_dH Triticum aestivum <NA> 58.1 NA NA
#> 2 aestivum1_galmés_2016_dH Triticum aestivum <NA> NA NA NA
#> 3 aestivum2_galmés_2016_dH Triticum aestivum <NA> NA 41.3 NA
#> 4 aestivum_orr_2016_dH Triticum aestivum <NA> 64.0 42.7 -38.7
#> 5 boeoticum_orr_2016_dH Triticum boeoticum <NA> 92.5 55.0 -15.0
#> S_dH form taxonomy group note short_ref
#> 1 NA 1B C3 plants Plants From Makino et al. 1988 Galmés 2015
#> 2 -20.5 1B C3 plants Plants From Haslam et al. 2005 Galmés 2016
#> 3 -19.7 1B C3 plants Plants From Hermida-Carrera et al. 2016 Galmés 2016
#> 4 -16.6 1B C3 plants Plants <NA> Orr 2016
#> 5 -19.5 1B C3 plants Plants <NA> Orr 2016
search_DHScale("Cyanobacteria")
#> Matched taxonomy in abridged table
#> identifier genus species subspecies
#> 1 variabilis_galmés_2015_dH Anabaena variabilis <NA>
#> 2 lividus_galmés_2015_dH Parathermosynechococcus lividus <NA>
#> 3 synechococcus_galmés_2015_dH Synechococcus strain a-1 <NA>
#> 4 t_elongatus_galmés_2016_dH Thermosynechococcus elongatus BP-1
#> 5 s_elongatus_galmés_2016_dH Synechococcus elongatus 6301
#> 6 variabilis_galmés_2016_dH Anabaena variabilis M3
#> kcat_dH Kc_dH Ko_dH S_dH form taxonomy group
#> 1 57.3 NA NA NA 1Bc Cyanobacteria Bacteria
#> 2 35.2 NA NA NA 1Bc Cyanobacteria Bacteria
#> 3 27.8 NA NA NA 1Bc Cyanobacteria Bacteria
#> 4 NA NA NA -43.0 1Bc Cyanobacteria Bacteria
#> 5 NA NA NA -11.7 1Bc Cyanobacteria Bacteria
#> 6 NA 38.8 NA NA 1Bc Cyanobacteria Bacteria
#> note short_ref
#> 1 From Badger 1980 Galmés 2015
#> 2 From Sheridan & Ulik 1976 Galmés 2015
#> 3 From Yaguchi et al. 1992; probably related to Thermosynechococcus Galmés 2015
#> 4 From Gubernator et al. 2008 Galmés 2016
#> 5 From Zhu et al. 1998 Galmés 2016
#> 6 From Badger 1980 Galmés 2016
search_DHScale("1A")
#> Matched species in averaged table
#> identifier genus species subspecies kcat_dH Kc_dH
#> 1 average_1A_Proteobacteria_dH Average 1A Proteobacteria 47.2 40.5
#> Ko_dH S_dH form taxonomy group
#> 1 26.7 -17.6 1A <NA> Bacteria
#> note
#> 1 Ko from in vivo estimates, kcat from mean of T. tepidum, A. vinosum, and T. endosymbiont values, Kc median of all values, S median of all form 1 values
#> short_ref
#> 1 this package
As seen in our example above, only a few of the entries in the
species-specific table are complete, and entries must generally be
modified to include all parameters using the function
modify_DHScale(). We recommend filling in missing values
with the average for the enzyme’s taxonomic group. Averages are found in
their own table, which can be searched using the
data="average" option. For more information, see section 3
of the Designing a Custom Enzyme vignette.
In this case, we’ll use the wheat temperature dependence data from
Orr et al. 2016, and adjust the Ko to 26.7, the value we
suggest using for all ΔH Ko values:
#look for wheat-specific data
search_DHScale("Triticum")
#> Matched genus in abridged table
#> identifier genus species subspecies kcat_dH Kc_dH Ko_dH
#> 1 aestivum_galmés_2015_dH Triticum aestivum <NA> 58.1 NA NA
#> 2 aestivum1_galmés_2016_dH Triticum aestivum <NA> NA NA NA
#> 3 aestivum2_galmés_2016_dH Triticum aestivum <NA> NA 41.3 NA
#> 4 aestivum_orr_2016_dH Triticum aestivum <NA> 64.0 42.7 -38.7
#> 5 boeoticum_orr_2016_dH Triticum boeoticum <NA> 92.5 55.0 -15.0
#> S_dH form taxonomy group note short_ref
#> 1 NA 1B C3 plants Plants From Makino et al. 1988 Galmés 2015
#> 2 -20.5 1B C3 plants Plants From Haslam et al. 2005 Galmés 2016
#> 3 -19.7 1B C3 plants Plants From Hermida-Carrera et al. 2016 Galmés 2016
#> 4 -16.6 1B C3 plants Plants <NA> Orr 2016
#> 5 -19.5 1B C3 plants Plants <NA> Orr 2016
#create the wheat one from its known data
wheat_DH<-DHScale("aestivum_orr_2016_dH",data="abridged")
#modify scale to replace Ko value
wheat_DH<-modify_DHScale(wheat_DH,Ko_dH=26.7)
check_DHScale(wheat_DH)
#> ΔH scaling "aestivum_orr_2016_dH":
#> ΔH_kcat = 64 kJ/mol
#> ΔH_Kc = 42.7 kJ/mol
#> ΔH_Ko = 26.7 kJ/mol
#> ΔH_S = -16.6 kJ/mol
3.2 CO2_dependence(): Calculating rates of net
carboxylation
Combining the enzyme, the temperature dependence, and a PGS
stoichiometry using the function CO2_dependence() creates a
function that calculates the rate of carbon fixation given
CO2, O2, and temperature. If the enzyme has been
created from a database entry with a PGS value or the PGS value was
added manually, the only two inputs CO2_dependence() needs
are the enzyme object and the DHScale
object.
wheat_carbon<-CO2_dependence(Rbc_wheat,wheat_DH)
When given a value for CO2 (μmol), O2 (μmol),
and temperature (°C), a CO2_dependence object will output a
carbon fixation rate in carbon per second (C/s):
wheat_carbon(15,200,25)
#> [1] 1.161751
4 Plotting rates
4.2 slice_4D_grid(): Slicing the grid for
visualization
Plotting a 4D object in R can be quite difficult, so the plotting
functions provided rely on slicing the 4D object to create a 3D grid.
slice_4D_grid() needs three things: a 4D grid to slice
(grid), which independent variable you wish to slice
(dim), and the value at which to slice (val).
dim will be 1 if you wish to use a constant CO2
value, 2 if you want a constant O2 value, and 3 if you want a
constant temperature value.
For example, if I wish to view the carbon fixation rate at 25°C as a
function of CO2 and O2, I would make a 3D slice in
my temperature variable (dim=3):
#create the temperature slice at 25C from the grid
s1<-slice_4D_grid(wheat_grid,dim=3,25)
A note about val: if you want to slice at a particular
value, it is wise to include it in the vector of values you supplied to
make_4D_grid! By default, slice_4D_grid() will
only match val with values in the vector that are within
.001. If you wish to increase or decrease that tolerance, you can do so
with the option tol.
4.3 plot_slice_3D(): Plotting a 3D slice
Now that we have a slice, we can use plot_slice_3D() to
see how the carbon fixation rate varies over two of our independent
variables. plot_slice_3D() has a few useful utilities,
including the ability to place contours over your graph for easier
evaluation of the changing colors.
The most basic input to plot_slice_3D() is just a slice.
With no other inputs, it will plot the slice with an automatic color
scale: blue for negative values, white at 0, and red for positive
values. Larger absolute values are shown with increasing saturation. It
sizes the legend to match the range of the plot, as seen in the plot of
our slice from section 4.2:
In this default configuration, it does not add contours or labels,
and NA values (when O2 is 0 in either the
"canon", diatom, or "alt" PGS
schemes), will be colored grey. Contours and labels can be provided
using the contours, xlabel, and
ylabel arguments:
#plot the slice with some contours
plot_slice_3D(s1,contours=c(1.5,2,2.5),xlabel="CO2",ylabel="O2")
Further configuration options are detailed in the description of
plot_slice_3D() and illustrated in the Creating Custom
Plots vignette.
4.4 transpose_3D_slice(): Swapping the x- &
y-axes
A slice at constant temperature will always have CO2 on
the x-axis and O2 on the y-axis, just as a slice at constant
O2 will always have CO2 on the x-axis and
temperature on the y-axis, and so on. If you want to invert this you can
use transpose_3D_slice:
#transpose the temperature slice we made
s2<-transpose_3D_slice(s1)
#plot the new slice
plot_slice_3D(s2,contours=c(1.5,2,2.5),xlabel="O2",ylabel="CO2")
5. Comparing enzymes
Until this point, we have only been working with a single enzyme.
This package is also able to compare two Rubisco enzymes, calculating
the difference between the two enzymes’ rates rather than the rate
itself.
We will compare wheat with spinach, another model enzyme. Both
enzymes need to have a CO2_dependence object, so we need to
construct the one for spinach:
Rbc_spinach<-Enzyme("oleracea_Iñiguez_2021",enzyme_name="spinach")
spinach_dH<-new_DHScale(46.2,50.2,26.7,-18.15,name="spinach")
spinach_carbon<-CO2_dependence(Rbc_spinach,spinach_dH)
…and then compare the two with the function
CO2_comparison(), that takes both enzyme
objects as inputs and outputs an enzyme object that
represents the difference between the two enzymes. Since wheat is listed
first, positive values will mean wheat fixes more carbon under those
conditions, while negative values mean spinach fixes more carbon.
#create the comparison
wh_v_sp<-CO2_comparison(wheat_carbon,spinach_carbon)
#the original carbon fixation rates of both enzymes
wheat_carbon(15,200,25)
#> [1] 1.161751
spinach_carbon(15,200,25)
#> [1] 0.8259237
#using the comparison to calculate the difference between the enzymes
wh_v_sp(15,200,25)
#> [1] 0.3358278
A plot of the comparison is accomplished through the same method as a
single enzyme alone:
#create the grid
wh_v_sp_grid<-make_4D_grid(wh_v_sp,CO2_seq,O2_seq,temp_seq,var_names=c("CO2","O2","T","wheat/spinach comp"))
#slice at 25C
s3<-slice_4D_grid(wh_v_sp_grid,dim=3,25)
#plot the slice
plot_slice_3D(s3,xlabel="CO2",ylabel="O2")
According to our results, wheat Rubisco fixes more carbon at all
shown concentrations of CO2 and O2 at 25°C. This
is not the case at 0°C, where spinach Rubisco is faster across the whole
parameter space (albeit at very small magnitudes).
#slice at 0C
s4<-slice_4D_grid(wh_v_sp_grid,dim=3,0)
#plot 0C slice
plot_slice_3D(s4,contours=NULL,xlabel="CO2",ylabel="O2")
And in between, at 13°C, whether wheat or spinach Rubisco is faster
depends on the CO2 and O2 concentration.
#slice at 13C
s5<-slice_4D_grid(wh_v_sp_grid,dim=3,13)
#plot slice
plot_slice_3D(s5,contours=seq(-0.03,.03,length.out=7),xlabel="CO2",ylabel="O2")
The temperature switch in which enzyme has a higher carbon fixation
rate can more easily be visualized by slicing O2 instead and
allowing CO2 and temperature to change:
#slice O2 at 500uM
s6<-slice_4D_grid(wh_v_sp_grid,dim=2,500)
#plot slice
plot_slice_3D(s6,contours=c(-1,0,1,2,3,4),dims=c(1,3,4),xlabel="CO2",ylabel="T")
6. The included database
To allow users to access published data more easily, this package
includes a compilation of published Rubisco kinetics, including
temperature dependences. They can be accessed through the
search_enzyme() and search_DHScale()
functions.
To assist with citing this data, use the function
cite_Rbc(). An input of a list of identifiers will return a
list of citations for that data, or if using the
type="short" argument, a list of pmid numbers or doi
numbers.
cite_Rbc(c("aestivum_orr_2016_dH","oleracea_Iñiguez_2021"))
#> [1] "Orr, D. J. et al. Surveying Rubisco Diversity and Temperature Response to Improve Crop Photosynthetic Efficiency. Plant Physiol 172, 707–717 (2016)."
#> [2] "Iñiguez, C., Niinemets, Ü., Mark, K. & Galmés, J. Analyzing the causes of method-to-method variability among Rubisco kinetic traits: from the first to the current measurements. J Exp Bot 72, 7846–7862 (2021)."
6.1 Abridged table: the curated kinetics data
The abridged table (~290 entries) is the first table to be searched
by search_enzyme(), unless otherwise specified. It only
includes complete records, i.e. entries where all of the standard
kinetic parameters (kcat,c, Ko,
Kc, and SC/O) for a particular enzyme are
included. Most of the 260 entries are studies that published all four
parameters. For many model species, methodology-corrected averages are
also available from Iñiguez et al. 2021 [7]. Where there are gaps in the
reported enzyme kinetics from Iñiguez et al., composites have been
constructed using averages from multiple other studies. Finally, there
are average versions of each of the forms of Rubisco, with separate
options for taxonomy (i.e., there is a plant/algae average form IB, but
there are also separate average form IB enzymes for green algae and C3
plants). All the average entries can be found by searching for
“Average”. An entry in the abridged table looks like:
search_enzyme("Average")[1,]
#> Matched genus in abridged table
#> identifier genus species subspecies kcat_val kcat_T
#> 1 average_1Ac_cyanobacteria Average 1Ac Cyanobacteria 9.4 NA
#> Kc_val Kc_T Ko_val Ko_T S_val S_T temp form PGS taxonomy group
#> 1 169 NA 1310 NA 53.5 NA 25 1Ac canon Cyanobacteria Bacteria
#> note short_ref
#> 1 values medians of collected cyanobacterial measurements at 25C this package
6.2 Comprehensive table
The comprehensive table (~1500 entries) contains all of the entries
from the abridged table but also includes data from many more enzymes
for which not all kinetics parameters have been determined. Mutant
enzymes are also present in this table, unlike in the abridged table. In
addition, this table includes more data about the studies, including the
pKa used for the calculations of Kc, Ko, and
Sc/o, the pH at which the data was collected, and the host
species for heterologously-expressed proteins. An entry in the
comprehensive table looks like:
search_enzyme("Triticum",data="comprehensive")[1,]
#> Matched genus in comprehensive table
#> identifier genus species subspecies mutant mutant_details
#> 1 aestivum_Carmo-Silva_2010 Triticum aestivum <NA> FALSE <NA>
#> primary heterologous_expression kcat_val kcat_T kcat_pH Kc_val Kc_T Kc_pH
#> 1 TRUE FALSE 3 NA NA 10.9 NA NA
#> Ko_val Ko_T Ko_pH S_val S_T S_pH temp pH pKa_used form PGS taxonomy
#> 1 341 NA NA 100 NA NA 25 8.2 6.11 1B canon C3 plants
#> group note short_ref year
#> 1 Plants <NA> Carmo-Silva 2010 2010
If you choose to use an enzyme available in this table, it is more
likely that you will need to combine kinetics from multiple sources or
use one of the average enzymes from the abridged table as a starting
point (see the Designing a Custom Enzyme vignette for more details on
constructing an enzyme).
6.3 Temperature dependence tables
Like with the kinetics, there are two different temperature
dependence tables. One table, abridged, includes ΔH values
for particular enzymes, while the other table, average,
includes only average ΔH values for taxonomic groups or forms of
Rubisco.
#an entry in the abridged DHScale table
search_DHScale("Triticum",data="abridged")[1,]
#> Matched genus in abridged table
#> identifier genus species subspecies kcat_dH Kc_dH Ko_dH S_dH
#> 1 aestivum_galmés_2015_dH Triticum aestivum <NA> 58.1 NA NA NA
#> form taxonomy group note short_ref
#> 1 1B C3 plants Plants From Makino et al. 1988 Galmés 2015
#an entry in the averages DHScale table
search_DHScale("1B",data="averaged")[1,]
#> Matched species in averaged table
#> identifier genus species subspecies kcat_dH Kc_dH Ko_dH S_dH
#> 1 average_1B_Plants_dH Average 1B Plants 58.1 41.1 26.7 -21.5
#> form taxonomy group
#> 1 1B <NA> Plants
#> note
#> 1 Ko from in vivo estimates, all others average Streptophyta from Galmés 2016
#> short_ref
#> 1 this package
All Ko ΔH values in the averages table are the same, as
published ΔH values vary sometimes even in sign, likely a result of the
indirect measurements of Ko values. Our value here comes from
the average of the three in vivo measurements reported in
Galmés et al. 2016 [6], excepting A. thaliana as its
correlation coefficient was much smaller than the other three. Where
individual studies report Ko ΔH values, we have included them
in the abridged table, but in general we recommend using the average
Ko ΔH values provided.