Schell: Data from Schell et al 2018
In troelsring/ABCharge: ABCharge
Description
Usage
Format
Details
Source
Examples
Description
Data from Schell et al J Cem End Data 2018; 63: 2151-2161
Usage
1
data("Schell")
Format
A data frame with 0 observations on the following 2 variables.
Na,K,Cl,Ca,Mg,Lacta numeric vector of strong ions
Alb,PCO2a numeric vector of Albumin and PCO2, 0 if absent
WAlist of buffers and pKas
TOTALMatrix of buffer concentrations
S1Results from Schell et al
A,bConstants from Davies' equation
Details
A series of 30 mixtures of citric acid with dihydrogen sodium phosphate
Source
Schell et al. J Cem End Data 2018; 63: 2151-2161
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data(Schell)
pHRES <- c();KpH <- c(); Charge <- IonStr <- iterations <- CCCH <-
UNCOR_pH <- c()
FF1 <- array(rep(NA,3*30),c(30,3))
SPECS <- array(rep(NA,8*30),c(30,8))
for (j in 1:30) {
UNCOR_pH[j] <- pH_general(Na=Na[j],K=0,Cl=0,Lact=0,Ca=0,Mg=0,PCO2=0,Alb=0,
WA=WA,TOT=TOTAL[j,],A=0.5108,b=0.1)$UNCOR_pH
pHRES[j] <- pH_general(Na=Na[j],K=0,Cl=0,Lact=0,Ca=0,Mg=0,PCO2=0,Alb=0,
WA=WA,TOT=TOTAL[j,],A=0.5108,b=0.1)$pH
SPECS[j,] <- pH_general(Na=Na[j],K=0,Cl=0,Lact=0,Ca=0,Mg=0,PCO2=0,Alb=0,
WA=WA,TOT=TOTAL[j,],A=0.5108,b=0.1)$SPECS
FF1[j,] <- pH_general(Na=Na[j],K=0,Cl=0,Lact=0,Ca=0,Mg=0,PCO2=0,Alb=0,
WA=WA,TOT=TOTAL[j,],A=0.5108,b=0.1)$FF1
Charge[j]<- pH_general(Na=Na[j],K=0,Cl=0,Lact=0,Ca=0,Mg=0,PCO2=0,Alb=0,
WA=WA,TOT=TOTAL[j,],A=0.5108,b=0.1)$Charge
}
###**Point 1**
#### Analysis in ideal state
pHOBS <- S1[,5]
DFF <- data.frame(pHOBS,UNCOR_pH)
PP <- with(DFF,cor.test(pHOBS,UNCOR_pH)) #0.9999631
PP
gg <- ggplot2::ggplot()+ggplot2::geom_point(data=DFF,ggplot2::aes(
x=pHOBS,y=UNCOR_pH),
size=3) + ggplot2::geom_abline(intercept=0,slope=1,col="red")+
ggplot2::scale_x_continuous(limits=c(2,9))+ggplot2::scale_y_continuous(
limits=c(2,9))+ggplot2::xlab("pH reported by Schell")+
ggplot2::ylab("pH calculated from charge-balance")+
ggplot2::annotate("text",x=4,y=7,label="Correlation = 0.9999631",size=7.5)
gg + ggplot2::ggtitle("pH from Schell, S1 column 5 on abscissa.Activity
coefficients forced = 1")+
ggplot2::theme(plot.title = ggplot2::element_text(size = 15, face = "bold"))
#options(digits=10)
ss <-pHOBS-UNCOR_pH ;
ss <- summary(ss)
###**Point 2**
#### Analysis with correction for ionic strength
pHOBS = S1[,7]
cor.test(pHOBS,pHRES) #0.999959
DFF <- data.frame(pHOBS,pHRES)
gg <- ggplot2::ggplot()+ggplot2::geom_point(data=DFF,ggplot2::aes(
x=pHOBS,y=pHRES),size=3) + ggplot2::geom_abline(intercept=0,slope=1,col="red")+
ggplot2::scale_x_continuous(limits=c(2,8))+ggplot2::scale_y_continuous(
limits=c(2,8))+ggplot2::xlab("pH reported by Schell")+
ggplot2::ylab("pH calculated from charge-balance")
gg + ggplot2::annotate("text",5,7,label="Correlation = 0.99996",size=7.5)+
ggplot2::ggtitle("pH from charge-balance and
as reported (S1, column 7) by Schell")+
ggplot2::theme(plot.title = ggplot2::element_text(size = 15, face = "bold"))
###**Point 3**
####Analysis of pKs from Schell et al^1^
IS_stated <- S1[,13]
A <- 0.5108
f1 <- 10^(-A*1^2*(sqrt(IS_stated)/(1+sqrt(IS_stated))-IS_stated*0.1))
f2 <- 10^(-A*2^2*(sqrt(IS_stated)/(1+sqrt(IS_stated))-IS_stated*0.1))
f3 <- 10^(-A*3^2*(sqrt(IS_stated)/(1+sqrt(IS_stated))-IS_stated*0.1))
IND <- Citrate[,6]>0 & Citrate[,3]>0; A1 <- sum(IND)
CitpK1 <- (S1[,8]-log10(Citrate[,6]*f1/Citrate[,3]))[IND]
IS1 <- IS_stated[IND]
summary(CitpK1)
IND <- Citrate[,6]>0 & Citrate[,9]>0;A2 <- sum(IND)
CitpK2 <- (S1[,8]-log10(Citrate[,9]*f2/(Citrate[,6]))*f1)[IND]
IS2 <- IS_stated[IND]
summary(CitpK2)
IND <- Citrate[,12]>0 & Citrate[,9]>0;A3 <- sum(IND)
CitpK3 <- (S1[,8]-log10(Citrate[,12]*f3/(Citrate[,9]))*f2)[IND]
IS3 <- IS_stated[IND]
summary(CitpK3)
CIT <- c(CitpK1,CitpK2,CitpK3)
ISS <- c(IS1,IS2,IS3)
PK <- factor(c(rep(1,A1),rep(2,A2),rep(3,A3)),labels=c("pK1","pK2","pK3"))
PKT <- c(rep(3.13,A1),rep(4.76,A2),rep(6.4,A3))
DDD <- data.frame(CIT,PK,ISS,PKT)
ff <- ggplot2::ggplot(DDD,ggplot2::aes(PK,CIT))+ggplot2::geom_boxplot() +
ggplot2::geom_dotplot(binaxis="y",stackdir="center",binwidth=.1)+
ggplot2::xlab("")+
ggplot2::ylab("Citrate pKa1-3")
ff + ggplot2::geom_segment(x=0.75,xend=1.25,y=3.13,yend=3.13,col="red",size=2)+
ggplot2::geom_segment(x=1.75,xend=2.25,y=4.76,yend=4.76,col="red",size=2)+
ggplot2::geom_segment(x=2.75,xend=3.25,y=6.40,yend=6.40,col="red",size=2)+
ggplot2::ggtitle("The 3 observed Citrate pK values based on\n
measured H activity \n and printed species distribution.
3.13, 4.76, and 6.40 indicated by red bars")
#ggplot2::ggsave("Citrate-pKs.pdf",width = 8.3, height = 8.3, units = c("cm"))
dd <- ggplot2::ggplot()
dd <- dd + ggplot2::geom_point(data=DDD,ggplot2::aes(x=ISS,y=PKT-CIT,col=PK),
size=2)+ggplot2::xlab("Ionic strength")+ggplot2::ylab("True- calculated pK")
dd
####Phosphate
IND <- Phosphate[,6]>0 & Phosphate[,3]>0; B1 <- sum(IND)
PhospK1 <- (S1[,8]-log10(Phosphate[,6]*f1/Phosphate[,3]))[IND]
summary(PhospK1)
# Min. 1st Qu. Median Mean 3rd Qu. Max.
# 2.020 2.142 2.158 2.162 2.169 2.409
#
IS1 <- IS_stated[IND]
IND <- Phosphate[,6]>0 & Phosphate[,9]>0; B2 <- sum(IND)
PhospK2 <- (S1[,8]-log10(Phosphate[,9]*f2/(Phosphate[,6]))*f1)[IND]
summary(PhospK2)
# Min. 1st Qu. Median Mean 3rd Qu. Max.
# 6.313 6.610 6.913 6.942 7.232 7.613
IS2 <- IS_stated[IND]
IND <- Phosphate[,12]>0 & Phosphate[,9]>0; B3 <- sum(IND)
PhospK3 <- (S1[,8]-log10(Phosphate[,12]*f3/(Phosphate[,9]))*f2)[IND]
summary(PhospK3)
# Min. 1st Qu. Median Mean 3rd Qu. Max.
# 8.848 8.848 8.848 8.848 8.848 8.848
IS3 <- IS_stated[IND]
PHO <- c(PhospK1,PhospK2,PhospK3)
PK <- factor(c(rep(1,B1),rep(2,B2),rep(3,B3)),labels=c("pK1","pK2","pK3"))
PKT <- c(rep(2.16,B1),rep(7.21,B2),rep(12.32,B3))
ISS <- c(IS1,IS2,IS3)
DDD <- data.frame(PHO,PK,PKT,ISS)
ff <- ggplot2::ggplot(DDD,ggplot2::aes(PK,PHO))+ggplot2::geom_boxplot() +
ggplot2::ylim(c(1,13))
ff + ggplot2::geom_segment(x=0.75,xend=1.25,y=2.16,yend=2.16,
col="blue",size=2)+
ggplot2::geom_segment(x=1.75,xend=2.25,y=7.21,yend=7.21,col="blue",size=2)+
ggplot2::geom_segment(x=2.75,xend=3.25,y=12.32,yend=12.32,col="blue",size=2)+
ggplot2::geom_dotplot(binaxis="y",stackdir="center",binwidth=.2)+
ggplot2::xlab("")+ggplot2::ylab("Phosphate pKa1-3")+
ggplot2::ggtitle("The 3 observed Phosphate pK values based on measured
H activity and printed species distribution. 2.16, 7.21, and 12.32
indicated by blue bars")
####Charge balance
Charge <- S1[,3]*2-Citrate[,6]*1e-3-Citrate[,9]*2*1e-3-Citrate[,12]*3*
1e-3-Phosphate[,6]*1e-3-Phosphate[,9]*2*1e-3-Phosphate[,12]*3*1e-3 + 10^-S1[,7]-
kw/10^-S1[,7]
(ss <- summary(Charge))
# Min. 1st Qu. Median Mean 3rd Qu. Max.
# -0.0009095 -0.0002690 0.0001403 0.0002145 0.0008153 0.0011996
GRP <- factor(rep(1,length(Charge)))
DFF <- data.frame(Charge,GRP)
ff <- ggplot2::ggplot(DFF,ggplot2::aes(GRP,Charge))+ggplot2::geom_boxplot() +
ggplot2::geom_dotplot(binaxis="y",stackdir="center",binwidth=.00005)+
ggplot2::xlab("")+ggplot2::ylab("Charge Eql/l")
ff
##Our charge balance
ZZ <- c(0,-1,-2,-3,0,-1,-2,-3)
CH <- c()
for (i in 1:30) CH[i] <- sum(SPECS[i,] * ZZ) + Na[i] + 10^-pHRES[i] - kw/(10^-pHRES[i]*FF1[i,1]^2)
(ss <- summary(CH))
## Revocery of pks
# Is total phosphate conserved
PHOSTOT <- c()
for (i in 1:30) PHOSTOT[i] <- sum(SPECS[i,1:4])
all.equal(PHOSTOT,S1[,3]) #TRUE
# Is total citrate conserved
CITTOT <- c()
for (i in 1:30) CITTOT[i] <- sum(SPECS[i,5:8])
all.equal(CITTOT,S1[,2]) #TRUE
RPK1 <- (-log10(SPECS[,2]*FF1[,1]^2*10^-pHRES/SPECS[,1]))
RPK2 <- (-log10(SPECS[,3]*FF1[,2]*10^-pHRES/SPECS[,2]))
RPK3 <- (-log10(SPECS[,4]*FF1[,1]*FF1[,3]*10^-pHRES/(SPECS[,3]*FF1[,2])))
RCK1 <- (-log10(SPECS[,6]*FF1[,1]^2*10^-pHRES/SPECS[,5]))
RCK2 <- (-log10(SPECS[,7]*FF1[,2]*10^-pHRES/SPECS[,6]))
RCK3 <- (-log10(SPECS[,8]*FF1[,1]*FF1[,3]*10^-pHRES/(SPECS[,7]*FF1[,2])))
summary(RPK1)
summary(RPK2)
summary(RPK3)
summary(RCK1)
summary(RCK2)
summary(RCK3)
troelsring/ABCharge documentation built on May 21, 2019, 11:11 a.m.
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Description Usage Format Details Source Examples
Description
Data from Schell et al J Cem End Data 2018; 63: 2151-2161
Usage
1 | data("Schell")
|
Format
A data frame with 0 observations on the following 2 variables.
Na,K,Cl,Ca,Mg,Lacta numeric vector of strong ions
Alb,PCO2a numeric vector of Albumin and PCO2, 0 if absent
WAlist of buffers and pKas
TOTALMatrix of buffer concentrations
S1Results from Schell et al
A,bConstants from Davies' equation
Details
A series of 30 mixtures of citric acid with dihydrogen sodium phosphate
Source
Schell et al. J Cem End Data 2018; 63: 2151-2161
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 | data(Schell)
pHRES <- c();KpH <- c(); Charge <- IonStr <- iterations <- CCCH <-
UNCOR_pH <- c()
FF1 <- array(rep(NA,3*30),c(30,3))
SPECS <- array(rep(NA,8*30),c(30,8))
for (j in 1:30) {
UNCOR_pH[j] <- pH_general(Na=Na[j],K=0,Cl=0,Lact=0,Ca=0,Mg=0,PCO2=0,Alb=0,
WA=WA,TOT=TOTAL[j,],A=0.5108,b=0.1)$UNCOR_pH
pHRES[j] <- pH_general(Na=Na[j],K=0,Cl=0,Lact=0,Ca=0,Mg=0,PCO2=0,Alb=0,
WA=WA,TOT=TOTAL[j,],A=0.5108,b=0.1)$pH
SPECS[j,] <- pH_general(Na=Na[j],K=0,Cl=0,Lact=0,Ca=0,Mg=0,PCO2=0,Alb=0,
WA=WA,TOT=TOTAL[j,],A=0.5108,b=0.1)$SPECS
FF1[j,] <- pH_general(Na=Na[j],K=0,Cl=0,Lact=0,Ca=0,Mg=0,PCO2=0,Alb=0,
WA=WA,TOT=TOTAL[j,],A=0.5108,b=0.1)$FF1
Charge[j]<- pH_general(Na=Na[j],K=0,Cl=0,Lact=0,Ca=0,Mg=0,PCO2=0,Alb=0,
WA=WA,TOT=TOTAL[j,],A=0.5108,b=0.1)$Charge
}
###**Point 1**
#### Analysis in ideal state
pHOBS <- S1[,5]
DFF <- data.frame(pHOBS,UNCOR_pH)
PP <- with(DFF,cor.test(pHOBS,UNCOR_pH)) #0.9999631
PP
gg <- ggplot2::ggplot()+ggplot2::geom_point(data=DFF,ggplot2::aes(
x=pHOBS,y=UNCOR_pH),
size=3) + ggplot2::geom_abline(intercept=0,slope=1,col="red")+
ggplot2::scale_x_continuous(limits=c(2,9))+ggplot2::scale_y_continuous(
limits=c(2,9))+ggplot2::xlab("pH reported by Schell")+
ggplot2::ylab("pH calculated from charge-balance")+
ggplot2::annotate("text",x=4,y=7,label="Correlation = 0.9999631",size=7.5)
gg + ggplot2::ggtitle("pH from Schell, S1 column 5 on abscissa.Activity
coefficients forced = 1")+
ggplot2::theme(plot.title = ggplot2::element_text(size = 15, face = "bold"))
#options(digits=10)
ss <-pHOBS-UNCOR_pH ;
ss <- summary(ss)
###**Point 2**
#### Analysis with correction for ionic strength
pHOBS = S1[,7]
cor.test(pHOBS,pHRES) #0.999959
DFF <- data.frame(pHOBS,pHRES)
gg <- ggplot2::ggplot()+ggplot2::geom_point(data=DFF,ggplot2::aes(
x=pHOBS,y=pHRES),size=3) + ggplot2::geom_abline(intercept=0,slope=1,col="red")+
ggplot2::scale_x_continuous(limits=c(2,8))+ggplot2::scale_y_continuous(
limits=c(2,8))+ggplot2::xlab("pH reported by Schell")+
ggplot2::ylab("pH calculated from charge-balance")
gg + ggplot2::annotate("text",5,7,label="Correlation = 0.99996",size=7.5)+
ggplot2::ggtitle("pH from charge-balance and
as reported (S1, column 7) by Schell")+
ggplot2::theme(plot.title = ggplot2::element_text(size = 15, face = "bold"))
###**Point 3**
####Analysis of pKs from Schell et al^1^
IS_stated <- S1[,13]
A <- 0.5108
f1 <- 10^(-A*1^2*(sqrt(IS_stated)/(1+sqrt(IS_stated))-IS_stated*0.1))
f2 <- 10^(-A*2^2*(sqrt(IS_stated)/(1+sqrt(IS_stated))-IS_stated*0.1))
f3 <- 10^(-A*3^2*(sqrt(IS_stated)/(1+sqrt(IS_stated))-IS_stated*0.1))
IND <- Citrate[,6]>0 & Citrate[,3]>0; A1 <- sum(IND)
CitpK1 <- (S1[,8]-log10(Citrate[,6]*f1/Citrate[,3]))[IND]
IS1 <- IS_stated[IND]
summary(CitpK1)
IND <- Citrate[,6]>0 & Citrate[,9]>0;A2 <- sum(IND)
CitpK2 <- (S1[,8]-log10(Citrate[,9]*f2/(Citrate[,6]))*f1)[IND]
IS2 <- IS_stated[IND]
summary(CitpK2)
IND <- Citrate[,12]>0 & Citrate[,9]>0;A3 <- sum(IND)
CitpK3 <- (S1[,8]-log10(Citrate[,12]*f3/(Citrate[,9]))*f2)[IND]
IS3 <- IS_stated[IND]
summary(CitpK3)
CIT <- c(CitpK1,CitpK2,CitpK3)
ISS <- c(IS1,IS2,IS3)
PK <- factor(c(rep(1,A1),rep(2,A2),rep(3,A3)),labels=c("pK1","pK2","pK3"))
PKT <- c(rep(3.13,A1),rep(4.76,A2),rep(6.4,A3))
DDD <- data.frame(CIT,PK,ISS,PKT)
ff <- ggplot2::ggplot(DDD,ggplot2::aes(PK,CIT))+ggplot2::geom_boxplot() +
ggplot2::geom_dotplot(binaxis="y",stackdir="center",binwidth=.1)+
ggplot2::xlab("")+
ggplot2::ylab("Citrate pKa1-3")
ff + ggplot2::geom_segment(x=0.75,xend=1.25,y=3.13,yend=3.13,col="red",size=2)+
ggplot2::geom_segment(x=1.75,xend=2.25,y=4.76,yend=4.76,col="red",size=2)+
ggplot2::geom_segment(x=2.75,xend=3.25,y=6.40,yend=6.40,col="red",size=2)+
ggplot2::ggtitle("The 3 observed Citrate pK values based on\n
measured H activity \n and printed species distribution.
3.13, 4.76, and 6.40 indicated by red bars")
#ggplot2::ggsave("Citrate-pKs.pdf",width = 8.3, height = 8.3, units = c("cm"))
dd <- ggplot2::ggplot()
dd <- dd + ggplot2::geom_point(data=DDD,ggplot2::aes(x=ISS,y=PKT-CIT,col=PK),
size=2)+ggplot2::xlab("Ionic strength")+ggplot2::ylab("True- calculated pK")
dd
####Phosphate
IND <- Phosphate[,6]>0 & Phosphate[,3]>0; B1 <- sum(IND)
PhospK1 <- (S1[,8]-log10(Phosphate[,6]*f1/Phosphate[,3]))[IND]
summary(PhospK1)
# Min. 1st Qu. Median Mean 3rd Qu. Max.
# 2.020 2.142 2.158 2.162 2.169 2.409
#
IS1 <- IS_stated[IND]
IND <- Phosphate[,6]>0 & Phosphate[,9]>0; B2 <- sum(IND)
PhospK2 <- (S1[,8]-log10(Phosphate[,9]*f2/(Phosphate[,6]))*f1)[IND]
summary(PhospK2)
# Min. 1st Qu. Median Mean 3rd Qu. Max.
# 6.313 6.610 6.913 6.942 7.232 7.613
IS2 <- IS_stated[IND]
IND <- Phosphate[,12]>0 & Phosphate[,9]>0; B3 <- sum(IND)
PhospK3 <- (S1[,8]-log10(Phosphate[,12]*f3/(Phosphate[,9]))*f2)[IND]
summary(PhospK3)
# Min. 1st Qu. Median Mean 3rd Qu. Max.
# 8.848 8.848 8.848 8.848 8.848 8.848
IS3 <- IS_stated[IND]
PHO <- c(PhospK1,PhospK2,PhospK3)
PK <- factor(c(rep(1,B1),rep(2,B2),rep(3,B3)),labels=c("pK1","pK2","pK3"))
PKT <- c(rep(2.16,B1),rep(7.21,B2),rep(12.32,B3))
ISS <- c(IS1,IS2,IS3)
DDD <- data.frame(PHO,PK,PKT,ISS)
ff <- ggplot2::ggplot(DDD,ggplot2::aes(PK,PHO))+ggplot2::geom_boxplot() +
ggplot2::ylim(c(1,13))
ff + ggplot2::geom_segment(x=0.75,xend=1.25,y=2.16,yend=2.16,
col="blue",size=2)+
ggplot2::geom_segment(x=1.75,xend=2.25,y=7.21,yend=7.21,col="blue",size=2)+
ggplot2::geom_segment(x=2.75,xend=3.25,y=12.32,yend=12.32,col="blue",size=2)+
ggplot2::geom_dotplot(binaxis="y",stackdir="center",binwidth=.2)+
ggplot2::xlab("")+ggplot2::ylab("Phosphate pKa1-3")+
ggplot2::ggtitle("The 3 observed Phosphate pK values based on measured
H activity and printed species distribution. 2.16, 7.21, and 12.32
indicated by blue bars")
####Charge balance
Charge <- S1[,3]*2-Citrate[,6]*1e-3-Citrate[,9]*2*1e-3-Citrate[,12]*3*
1e-3-Phosphate[,6]*1e-3-Phosphate[,9]*2*1e-3-Phosphate[,12]*3*1e-3 + 10^-S1[,7]-
kw/10^-S1[,7]
(ss <- summary(Charge))
# Min. 1st Qu. Median Mean 3rd Qu. Max.
# -0.0009095 -0.0002690 0.0001403 0.0002145 0.0008153 0.0011996
GRP <- factor(rep(1,length(Charge)))
DFF <- data.frame(Charge,GRP)
ff <- ggplot2::ggplot(DFF,ggplot2::aes(GRP,Charge))+ggplot2::geom_boxplot() +
ggplot2::geom_dotplot(binaxis="y",stackdir="center",binwidth=.00005)+
ggplot2::xlab("")+ggplot2::ylab("Charge Eql/l")
ff
##Our charge balance
ZZ <- c(0,-1,-2,-3,0,-1,-2,-3)
CH <- c()
for (i in 1:30) CH[i] <- sum(SPECS[i,] * ZZ) + Na[i] + 10^-pHRES[i] - kw/(10^-pHRES[i]*FF1[i,1]^2)
(ss <- summary(CH))
## Revocery of pks
# Is total phosphate conserved
PHOSTOT <- c()
for (i in 1:30) PHOSTOT[i] <- sum(SPECS[i,1:4])
all.equal(PHOSTOT,S1[,3]) #TRUE
# Is total citrate conserved
CITTOT <- c()
for (i in 1:30) CITTOT[i] <- sum(SPECS[i,5:8])
all.equal(CITTOT,S1[,2]) #TRUE
RPK1 <- (-log10(SPECS[,2]*FF1[,1]^2*10^-pHRES/SPECS[,1]))
RPK2 <- (-log10(SPECS[,3]*FF1[,2]*10^-pHRES/SPECS[,2]))
RPK3 <- (-log10(SPECS[,4]*FF1[,1]*FF1[,3]*10^-pHRES/(SPECS[,3]*FF1[,2])))
RCK1 <- (-log10(SPECS[,6]*FF1[,1]^2*10^-pHRES/SPECS[,5]))
RCK2 <- (-log10(SPECS[,7]*FF1[,2]*10^-pHRES/SPECS[,6]))
RCK3 <- (-log10(SPECS[,8]*FF1[,1]*FF1[,3]*10^-pHRES/(SPECS[,7]*FF1[,2])))
summary(RPK1)
summary(RPK2)
summary(RPK3)
summary(RCK1)
summary(RCK2)
summary(RCK3)
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