Scatchard_Analysis.R

library(tidyr)
library(dplyr)
library(ggplot2)

data <- data.frame(
  total_ligand_cpm = c(0, 12500, 25000, 50000, 100000, 175000, 250000, 400000, 900000),
  bound_cpm_total = c(0, 480, 850, 1550, 2850, 4750, 5760, 7190, 9980),
  bound_cpm_nonspecific = c(0, 50, 100, 200, 350, 650, 1200, 1900, 3600)
)

data <- data %>%
  mutate(bound_cpm_specific = bound_cpm_total - bound_cpm_nonspecific)

data <- data %>%
  mutate(free_cpm = total_ligand_cpm - bound_cpm_specific)

# Need a conversion from CPM --> umole
counter_efficiency = 0.55
conversion_factor = 2.2e12
specific_activity = 1.45 #Ci/µmole
volume_factor = 1000/1

cpm_to_umole_factor <- 1 / (specific_activity * conversion_factor * counter_efficiency) # µmoles per CPM

data <- data %>%
  mutate(
    total_ligand_uM = total_ligand_cpm * cpm_to_umole_factor * volume_factor, # Convert to µM
    bound_specific_uM = bound_cpm_specific * cpm_to_umole_factor * volume_factor,
    free_ligand_uM = free_cpm * cpm_to_umole_factor * volume_factor
  ) %>%
  mutate(bound_over_free_uM = bound_specific_uM / free_ligand_uM)

  
  
# Remove the first row (0 values) 
data_scatchard <- data[-1, ]


scatchard_plot <- ggplot(data_scatchard, 
                         aes(x = bound_specific_uM, 
                             y = bound_over_free_uM)) +
  geom_point() +
  geom_smooth(method = "lm", formula = y ~ x, se = FALSE, color = "blue") +
  labs(
    title = "Scatchard Plot",
    x = "Bound (µM)",
    y = "Bound/Free",
    caption = "Data in µM"
  ) +
  theme_minimal()


scatchard_model <- lm(bound_over_free_uM ~ bound_specific_uM, data = data_scatchard)

slope <- coef(scatchard_model)[2]
intercept <- coef(scatchard_model)[1]
Kd_uM <- -1/slope
Bmax_uM <- intercept/(-slope) # This is how the algebra shakes out for y=mx+b when y=0, solving for x