Here is a possibile solution:
MasterTable <- data.frame(Concentration=rep(c(0,50,100,200,300, 350, 400),2),
Signal=c(11800,13000,12000,12000,16000,15500,15570,11600,11700,8000,8000,6000,4000,3000),
Assay=rep(1:2,each=7))
library(ggplot2)
# Reverse Signal vector of the blue series (for Assay =1)
MasterTable$Signal[MasterTable$Assay==1] <- rev(MasterTable$Signal[MasterTable$Assay==1])
ggplot(data=MasterTable, aes(x=Concentration, y=Signal, color=factor(Assay))) +
geom_line(lwd=1) + geom_point(size=3) + guides(color='none') +
scale_x_continuous('Chemical 1 (nM)', trans='reverse',
sec.axis = sec_axis(~ 400 - . , name='Chemical 2 (nM)'))
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