#Abstract: Comparing Monoprotic Titration Curve vs. Binding Curve

#Titration Data

Data <- read.csv("Titration Lab Data 1.csv")

Data
##       pH Volume.Of.NaOH..mL.  X X.1
## 1   3.60                 0.0 NA    
## 2   3.61                 1.0 NA    
## 3   3.70                 2.0 NA    
## 4   3.75                 3.0 NA    
## 5   3.81                 4.0 NA    
## 6   3.85                 5.0 NA    
## 7   4.00                 6.0 NA    
## 8   4.10                 7.0 NA    
## 9   4.25                 8.0 NA    
## 10  4.35                 9.0 NA    
## 11  4.40                10.0 NA 0,1
## 12  4.50                11.0 NA    
## 13  4.67                12.0 NA    
## 14  4.90                13.0 NA    
## 15  5.10                14.0 NA    
## 16  5.23                16.0 NA    
## 17  5.29                17.0 NA    
## 18  5.32                18.0 NA    
## 19  5.38                19.0 NA    
## 20  5.40                20.0 NA    
## 21  5.50                21.0 NA    
## 22  5.58                22.0 NA    
## 23  5.74                23.0 NA    
## 24  6.22                24.0 NA    
## 25  7.40                25.0 NA    
## 26 11.35                26.0 NA    
## 27 11.59                27.0 NA    
## 28 11.80                28.0 NA    
## 29 11.91                29.5 NA
Volume <- Data$Volume.Of.NaOH..mL.

Volume
##  [1]  0.0  1.0  2.0  3.0  4.0  5.0  6.0  7.0  8.0  9.0 10.0 11.0 12.0 13.0 14.0
## [16] 16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.5
pH <-Data$pH

pH
##  [1]  3.60  3.61  3.70  3.75  3.81  3.85  4.00  4.10  4.25  4.35  4.40  4.50
## [13]  4.67  4.90  5.10  5.23  5.29  5.32  5.38  5.40  5.50  5.58  5.74  6.22
## [25]  7.40 11.35 11.59 11.80 11.91

#Binding Curve Information

H <- 10^-(pH)

H
##  [1] 2.511886e-04 2.454709e-04 1.995262e-04 1.778279e-04 1.548817e-04
##  [6] 1.412538e-04 1.000000e-04 7.943282e-05 5.623413e-05 4.466836e-05
## [11] 3.981072e-05 3.162278e-05 2.137962e-05 1.258925e-05 7.943282e-06
## [16] 5.888437e-06 5.128614e-06 4.786301e-06 4.168694e-06 3.981072e-06
## [21] 3.162278e-06 2.630268e-06 1.819701e-06 6.025596e-07 3.981072e-08
## [26] 4.466836e-12 2.570396e-12 1.584893e-12 1.230269e-12
plot(Volume,pH,main = "Volume of NaOH vs. pH",xlab = "Volume of NaOH (mL)",ylab = "pH")

Vinital<- 25.00

Vadd <- Volume

Vend <- 25.5

CB <- 0.10

FB <-  1 -(CB * Vadd + H * (Vinital + Vadd)) / (CB *  Vend) 
FB
##  [1]  0.99753737  0.95828147  0.91945600  0.88040032  0.84137586  0.80225976
##  [7]  0.76349020  0.72449339  0.68554677  0.64646325  0.60729672  0.56818101
## [13]  0.52910155  0.49000847  0.45085891  0.37245434  0.33324886  0.29403694
## [19]  0.25483003  0.21561602  0.17641354  0.13720642  0.09800496  0.05881195
## [25]  0.01960706 -0.01960784 -0.05882353 -0.09803922 -0.15686275
plot(pH,FB,main="Fraction Bound vs. pH",xlim = c(3,8), ylim = c(0,1), ylab="Fraction Bound")

library(nls2)
## Loading required package: proto
fit <- nls2(FB ~ H/(KD+H), start=c(KD=0.001))

summary(fit)
## 
## Formula: FB ~ H/(KD + H)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## KD 1.695e-05  1.655e-06   10.24 5.68e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.07523 on 28 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 2.534e-06
lines(pH,predict(fit),col="red")