CHEMTAX

#Chemtax analysis for HPLC photosynthetic pigment data

CHEMTAX ANALYSES

MSM80 2018-19

script: Allanah Paul, 2019

load packages required

library(limSolve)

define pigment ratios manually using DiTullio 2005 L&O

The input ratio matrix Ratio contains the pigment compositions (columns) for each algal group (rows);

the compositions are scaled relative to Chla (last column).

Chla = matrix( c(1,1,1,1,1,1,1,1,1,0), nrow=10, ncol=1) DVChla = matrix( c(0,0,0,0,0,0,0,0,0,1), nrow=10, ncol=1)

Chlb = matrix( c(0,0,0,0,0,0,1.05,0.2,0,0.14), nrow=10, ncol=1)

ChlC1.2 = matrix( c(0.32,0.32,0.19,0.2,0.22,0.17,0,0,0,0), nrow=10, ncol=1)

ChlC3 = matrix( c(0,0,0,0.33,0.24,0.49,0,0,0,0), nrow=10, ncol=1)

Perid = matrix( c(0, 0.6,0,0,0,0,0,0,0,0), nrow = 10, ncol = 1)

But19 = matrix( c(0, 0, 0, 1.12, 0.01, 0.02, 0, 0, 0, 0), nrow = 10, ncol = 1)

Fucox = matrix( c(0.6,0,0,0.1,0.35,0.29,0,0,0,0), nrow = 10, ncol = 1)

Neox = matrix( c(0,0,0,0,0,0,0.1,0.01,0,0), nrow = 10, ncol = 1)

Prasin = matrix( c(0,0,0,0,0,0,0.24,0,0,0), nrow = 10, ncol = 1)

Viol = matrix( c(0,0,0,0,0,0,0.10,0.11,0,0), nrow = 10, ncol = 1)

Hex19 = matrix( c(0,0,0,0.1,1.34,0.36,0,0,0,0), nrow = 10, ncol = 1)

DD_DT = matrix( c(0.09,0.2,0,0.96,0.19,0.06,0,0,0,0), nrow = 10, ncol = 1)

Allox = matrix( c(0,0,0.29,0,0,0,0,0,0,0), nrow = 10, ncol = 1)

Zeax = matrix( c(0,0,0,0,0,0,0.03,0.07,0.4,0.05), nrow = 10, ncol = 1)

Lutein = matrix( c(0,0,0,0,0,0,0.01,0.71,0,0), nrow = 10, ncol = 1)

create matrix as combination of all columns

ratios <- cbind(Chla, DVChla, Chlb, ChlC1.2, ChlC3, Perid, But19, Fucox, Neox, Prasin, Viol, Hex19, DD_DT, Allox, Zeax, Lutein) colnames(ratios) <- c('Chla', 'DVChla', 'Chlb', 'ChlC1.2', 'ChlC3', 'Perid', '19But', 'Fucox', 'Neo', 'Pras', 'Viol', '19Hex', 'DD_DT', 'Allox', 'Zeax', 'Lutein') rownames(ratios) <- c('Diatoms', 'Dinoflagellates', 'Crytophytes', 'Pelagophytes', 'T3 haptophytes', 'T4 haptophytes', 'Prasinophytes', 'Chlorophytes', 'Synechococcus', 'Prochlorophytes') str(ratios) subset(ratios[,1:16])

IMPORTANT TO CHECK

Do the ratios and the pigments and the phytoplankton group names in the Ratios fit to the samples?

Example taken from R documentation:

https://www.rdocumentation.org/packages/limSolve/versions/1.5.5.3/topics/Chemtax

1. Graphical representation of chemtax example input data

palette(rainbow(12, s = 0.6, v = 0.75))

mp <- apply(Chemtax$Ratio, MARGIN = 2, max) # Named num [1:12] pstars <- rbind(t(t(Chemtax$Ratio)/mp) , # num [1:9, 1:12] sample = Chemtax$Field/max(Chemtax$Field)) stars(pstars, len = 0.9, key.loc = c(7.2, 1.7),scale=FALSE,ncol=4, main = "CHEMTAX pigment composition", draw.segments = TRUE, flip.labels=FALSE)

2. Estimating the algal composition of the field sample

Nx <-nrow(Chemtax$Ratio) # int 8

equations that have to be met exactly Ex=f:

sum of all fraction must be equal to 1.

EE <- rep(1, Nx) # num [1:8] FF <- 1 # num 1

inequalities, Gx>=h:

all fractions must be positive numbers

GG <- diag(nrow = Nx) # num [1:8, 1:8] HH <- rep(0, Nx) # num [1:8]

equations that must be reproduced as close as possible, Ax ~ b

= the field data; the input ratio matrix and field data are rescaled

AA <- Chemtax$Ratio/rowSums(Chemtax$Ratio) # num [1:8, 1:12] --> matrix BB <- Chemtax$Field/sum(Chemtax$Field) # num [1:12]

1. Solve with lsei method

X <- lsei(t(AA), BB, EE, FF, GG, HH)$X (Sample <- data.frame(Algae = rownames(Chemtax$Ratio), fraction = X))

plot results

barplot(X, names = rownames(Chemtax$Ratio), col = heat.colors(8), cex.names = 0.8, main = "Chemtax example solved with lsei")

Hello Joaquin, Silvia and Joaquin, Here is the script that Allanah wrote to analyze HPLC data. You cna use it as a basis to develop your own script to analyze the HPLC data from Gran Canaria 2018 (Joaquin) and MSM80 2019 (Silvia). Each of you can create your own project to work on it and invite Allanah and me as collaborators so that we can help you with tracking the changes. The aim at the end is to have a general Chemtax script that anyone can use to analyze HPLC data.

CHEMTAX analyses with MSM80 data

setwd("V:/PhD/Experimental/MSM80 - CUSCO-Humboldt tipping/Data/HPLC") # change as necessary

Generic for individual samples

load data as 'Field' for the samples and 'Ratio' for pigment ratios

Field <- read.table(file = "Field.txt", # needs to be converted or extracted as a vector header = TRUE) Ratio <- read.table(file = "Ratio.txt", # needs to be a matrix header = TRUE) # be careful here that the group names are not in the matrix themselves...

these two lines make the 1st column into row names as otherwise this causes issues in the script

Ratio.n <- Ratio[,-1] # removes the first column of names rownames(Ratio.n) <- Ratio[,1] # selects the 1st column of old matrix as new row names Ratio <- as.matrix(Ratio.n) # ensure this remains as a matrix! This is important for further lines of script below.

do the same for sample no. in the Field

Field.n <- Field[,-1] Field <- Field.n[1,] # select the first sample Field.v <- as.vector(unlist(Field)) # extracts data for 1st sample as vector called Field.v

now create list of Ratio and Field data for sample 1. This is called CHEMTAX.

CHEMTAX <- list(Ratio = Ratio, Field = Field.v)

back to CHEMTAX script according to R Documentation

https://www.rdocumentation.org/packages/limSolve/versions/1.5.5.3/topics/Chemtax

1. Graphical representation of chemtax example input data

mp <- apply(CHEMTAX$Ratio, MARGIN = 2, max) pstars <- rbind(t(t(CHEMTAX$Ratio)/mp), sample = CHEMTAX$Field/max(CHEMTAX$Field))

this plot seems to distract a little but kept it here for good measure (graphical representation)

stars(pstars, len = 0.9, key.loc = c(7.2, 1.7),scale=FALSE,ncol=4, main = "CHEMTAX pigment composition", draw.segments = TRUE, flip.labels=FALSE)

2. Estimating the algal composition of the field sample

Nx <- nrow(CHEMTAX$Ratio) # int 10

equations that have to be met exactly Ex=f:

sum of all fraction must be equal to 1.

EE <- rep(1, Nx) ## must equal 1 as full fraction # num [1:10] FF <- 1 # num 1

inequalities, Gx>=h:

all fractions must be positive numbers

GG <- diag(nrow = Nx) # num [1:10, 1:10] HH <- rep(0, Nx) # num [1:10]

equations that must be reproduced as close as possible, Ax ~ b

= the field data; the input ratio matrix and field data are rescaled

AA <- CHEMTAX$Ratio/rowSums(CHEMTAX$Ratio) # num [1:10, 1:16]
BB <- CHEMTAX$Field/sum(CHEMTAX$Field) # Named num [1:12] --> should be 10! or 16?

now for limSolve! linear regression? This is the calculation step

1. Solve with lsei method

X <- lsei(t(AA), BB, EE, FF, GG, HH)$X # t is for transposition of matrix AA (Sample <- data.frame(Algae = rownames(CHEMTAX$Ratio), fraction = X))

plot results

barplot(X, names = rownames(CHEMTAX$Ratio), col = heat.colors(8), cex.names = 0.8, main = "CHEMTAX analysis",las=2, ylab = 'Contribution to Chla')

For multiple samples --> how to loop it using functions etc

load data as 'Field' for the samples and 'Ratio' for pigment ratios

Field <- read.table(file = "Field.txt", # needs to be converted or extracted as a vector header = TRUE) Ratio <- read.table(file = "Ratio.txt", # needs to be a matrix header = TRUE) # be careful here that the group names are not in the matrix themselves...

these two lines make the 1st column into row names as otherwise this causes issues in the script

Ratio.n <- Ratio[,-1] # removes the first column of names rownames(Ratio.n) <- Ratio[,1] # selects the 1st column of old matrix as new row names Ratio <- as.matrix(Ratio.n) # ensure this remains as a matrix! This is important for further lines of script below.

do the same for sample no. in the Field

Field.n <- Field[,-1] # removes first column as sample number

this function is designed to extract pigment concs from each sample as vectors

extract.field.dat <- function(i) { Field <- Field.n[i,] # select the first sample Field.v <- as.vector(unlist(Field)) # extracts data for 1st sample as vector called Field.v }

this line produces a list 'CHEMTAX.Field.dat' of samples and corresponding pigment concs

CHEMTAX.Field.dat <- lapply(seq_along(Field[,1]), extract.field.dat) # apply function along sample list

now create list of Ratio and Field data for each sample within list CHEMTAX.l.

#This is called CHEMTAX.l where l = list.

CHEMTAX.l <- list() # create list

create function 'list.CHEMTAX'

list.CHEMTAX <- function(i) { Field.temp = CHEMTAX.Field.dat[[i]] CHEMTAX.l[[i]] <- list(ratios = Ratio, field = Field.temp)

names(CHEMTAX.l[[i]]) <- Field[[,i]]

}

apply function 'list.CHEMTAX' along sample list to create a list of all samples with two components

1) ratios as a matrix and 2) pigment concs as a vector

CHEMTAX.list <- lapply(seq_along(CHEMTAX.Field.dat), list.CHEMTAX)

renames the list items with the sample number for easy identification

names(CHEMTAX.list) <- Field[,1]

now the data is ready, time for running the CHEMTAX analysis part!

create new function called 'CHEMTAX.analysis'

note: Ratio --> ratios and Field --> field to distinguish between individual analysis and looping

CHEMTAX.output <- list() # creates list for output CHEMTAX.analysis <- function(i){ mp <- apply(CHEMTAX.list[[i]]$ratios, MARGIN = 2, max) pstars <- rbind(t(t(CHEMTAX.list[[i]]$ratios)/mp), sample = CHEMTAX.list[[i]]$field/max(CHEMTAX.list[[i